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Spatial reuse scheduling and localization for underwater acoustic communication networks Roee, Diamant 2013

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Spatial Reuse Scheduling andLocalization for UnderwaterAcoustic CommunicationNetworksbyRoee DiamantB.Sc., The Technion, Israel Institute of Technology, 2002M.Sc., The Technion, Israel Institute of Technology, 2007A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)The University Of British Columbia(Vancouver)August 2013c? Roee Diamant 2013AbstractOcean exploration, through the development of ocean-observation systems, is a keystep towards a fuller understanding of life on Earth. Underwater acoustic commu-nication networks (UWANs) will help to fulfill the needs of these ocean-observationsystems, whose applications include gathering of scientific data, early warning sys-tems, ecosystem monitoring and military surveillance. The data derived from UWANsis typically interpreted with reference to the location of a data collecting node, e.g.when reporting an event occurrence, or the location of an object itself is of interest,e.g. when tracking a moving underwater vehicle or diver. In this dissertation, wedevelop methods for localization and efficient data exchange in UWANs.In the first part of this work, we focus on underwater localization (UWL). Sinceglobal positioning system signals do not propagate through water, UWL is oftenbased on fusing information from acceleration-based sensors and ranging informationto anchor nodes with known locations. We consider practical challenges of UWL. Thepropagation speed varies with depth and location, anchor and unlocalized nodes arenot time-synchronized, nodes are moving due to ocean currents, propagation delaymeasurements for ranging of non-line-of-sight communication links are mistakenlyidentified as line-of-sight, and unpredictable changes in the ocean current makesit hard to determine motion models for tracking. Taking these features of UWLinto account, we propose localization and tracking schemes that exploit the spatiallycorrelated ocean current, nodes? constant motion, and the periodicity of ocean waves.In the second part of this thesis, we use location information to develop mediumaccess control scheduling algorithms and channel coding schemes. We focus on adap-tive scheduling in which each node transmits based on timely network information.Specifically, our scheduling algorithms utilize the long propagation delay in the chan-nel and the sparsity of the network topology to improve throughput, reliability androbustness to topology changes. To evaluate performance, we have developed a simu-lator combining existing numerical models of ocean current and of power attenuationin the ocean. We have also verified simulation results in four sea experiments ofdifferent channel bathymetry structures, using both industry and self-developed un-derwater acoustic modems.iiPrefaceHereby, I declare that I am the first author of this thesis. The following publicationshave resulted from the thesis research.Journal Papers1. Roee Diamant, Ghasem Naddafzadeh Shirazi, and Lutz Lampe, ?Robust Spa-tial Reuse Scheduling in Underwater Acoustic Communication Networks,? IEEEJournal of Oceanic Engineering, Dec. 2012 (Included in Part II, Chapter 7).2. Roee Diamant, Hwee-Pink Tan, and Lutz Lampe, ?LOS and NLOS Classifi-cation for Underwater Acoustic Localization,? IEEE Transactions of MobileComputing, Nov. 2012 (Included in Part I, Chapter 4).3. Roee Diamant, Wenbo Shi, Wee-Seng Soh, and Lutz Lampe, ?Time and Spa-tial Reuse Handshake Protocol for Underwater Acoustic Communication Net-works,? IEEE Journal of Oceanic Engineering, Oct. 2012 (Included in Part II,Chapter 6).4. Roee Diamant and Lutz Lampe, ?Underwater Localization with Time Synchro-nization and Propagation Speed Uncertainties,? IEEE Transactions on MobileComputing, Oct. 2012 (Included in Part I, Chapter 2).5. Hwee-Pink Tan, Roee Diamant, Marc Waldmeyer, and Winston K.G. Seah, ?ASurvey of Techniques and Challenges in Underwater Localization,? ACM Jour-nal of Ocean Engineering,, vol. 38, no. 14, pp. 1663-1676, Oct. 2011 (Includedin Chapter 1).6. Roee Diamant and Lutz Lampe, ?Spatial Reuse TDMA for Broadcast Ad-HocUnderwater Acoustic Communication Networks,? IEEE Journal of Oceanic En-gineering,, vol. 36, no. 2, pp. 172-185, Apr. 2011 (Included in Part II, Chap-ter 7).7. Roee Diamant and Yunye Jin, ?AMachine Learning Approach for Dead Reckon-ing Navigation at Sea Using a Single Accelerometer,? IEEE Journal of OceanicEngineering, Apr. 2013 (Included in Part I, Chapter 5).iiiPreface8. Roee Diamant and Lutz Lampe, ?Adaptive Error-Correction Coding Schemefor Underwater Acoustic Communication Networks,? submitted (Included inPart II, Chapter 8).9. Roee Diamant, Lars Michael Wolff, and Lutz Lampe, ?Tracking for UnderwaterNavigation,? submitted (Included in Part I, Chapter 3).Conference Papers1. Roee Diamant, Lars Michael Wolff, and Lutz Lampe, ?Utilizing Ocean CurrentSpatial Correlation for Velocity Estimation of Underwater Drifting Nodes,? inProc. of IEEE Workshop on Advances in Network Localization and Navigation(ANLN), in ICC, Budapest, Hungary, Jun. 2013 (Included in Part I, Chap-ter 3).2. Lars Michael Wolff, Roee Diamant, and Lutz Lampe, ?Spatial and TemporalDependencies of Velocities of Underwater Drifting Nodes,? (extended abstract)in Proc. of ACM Conference on Underwater Networks and System (WUWNet),Los Angeles, USA, Nov. 2012 (Included in Part I, Chapter 3).3. Roee Diamant, Wenbo Shi, Wee-Seng Soh, and Lutz Lampe, ?Joint Time andSpatial Reuse Handshake Protocol for Underwater Acoustic CommunicationNetworks,? in Proc. of IEEE OCEANS Conference, Kona, Hawaii, Sep. 2011(Included in Part II, Chapter 6).4. Roee Diamant, Ghasem Naddafzadeh Shirazi, and Lutz Lampe, ?Robust Spa-tial Reuse Scheduling in Underwater Acoustic Communication Networks,? inProc. of IEEE Vehicular Technology Conference (VTC), San Francisco, USA,Sep. 2011, (Included in Part II, Chapter 7).5. Roee Diamant and Lutz Lampe, ?Underwater Localization with Time Synchro-nization and Propagation Speed Uncertainties,? in Proc. of IEEE Workshopon Positioning, Navigation and Communication (WPNC), Dresden, Germany,Apr. 2011 (Included in Part I, Chapter 2).6. Roee Diamant, Hwee-Pink Tan, and Lutz Lampe, ?NLOS Identification Using aHybrid ToA-Signal Strength Algorithm for Underwater Acoustic Localization,?in Proc. of IEEE OCEANS Conference, Seattle, USA, Sep. 2010 (Included inPart I, Chapter 4).7. Roee Diamant and Lutz Lampe, ?A Hybrid Spatial Reuse MAC Protocol forAd-Hoc Underwater Acoustic Communication Networks,? invited paper in Proc.of IEEE Workshop on Acoustic Underwater Networks, in ICC, Cape Town,South Africa, May. 2010 (Included in Part II, Chapter 7).ivPrefaceUnless stated differently, for all publications, I conducted the survey on related topics,identified the challenges, formalized the suggested solution, performed the analysis,and carried out all of the simulations and sea experiments. I also wrote all paperdrafts. My supervisor, Prof. Lutz Lampe, guided my research, validated analysisand methodology, and edited the manuscripts for papers co-authored by him. Partsof the thesis are a result of research collaboration with additional contributors. Theco-authors? contribution is listed below.1. Journal paper 1 and Conference paper 4: Ghasem Naddafzadeh Shirazi wroteroughly 10% of the simulation code and helped with editing the manuscript.2. Journal paper 2 and Conference paper 7: Hwee-Pink Tan organized the Singa-pore sea trial, and helped with editing the manuscript.3. Journal paper 3 and Conference paper 3: Wenbo Shi wrote the simulation codefor the slotted-FAMA benchmark method (roughly 5% of the code); Wee-SengSoh helped with editing the manuscript.4. Journal paper 5: For this survey publication I was a co-author. Hwee-Pink Tanwrote the paper drafts, and conducted half of the survey. Marc Waldmeyer andWinston K.G. Seah helped with editing the manuscript. I conducted and wrotehalf of the survey and identified the research challenges. The material includedin the thesis comprises only my contribution from this work.5. Journal paper 7: Yunye Jin organized the sea trial, and helped with editing themanuscript.6. Journal paper 9 and Conference papers 1 and 2: Lars Michael Wolff was co-supervised by me during this work. He wrote roughly 40% of the simulationcode, and formalized roughly 20% of the suggested solution.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Abbreviations and Symbols . . . . . . . . . . . . . . . . . . . . . xvAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Underwater Localization and Tracking . . . . . . . . . . . . . . . . . 31.1.1 Underwater Localization . . . . . . . . . . . . . . . . . . . . . 41.1.2 Tracking the Location of Nodes . . . . . . . . . . . . . . . . . 91.1.3 Considerations of Measurement Errors . . . . . . . . . . . . . 111.2 Spatial Reuse Scheduling in UWANs . . . . . . . . . . . . . . . . . . 131.2.1 Scheduling Algorithms for UWANs . . . . . . . . . . . . . . . 131.2.2 Adaptive Transmissions . . . . . . . . . . . . . . . . . . . . . 171.3 Open Problems Addressed in this Thesis . . . . . . . . . . . . . . . . 171.3.1 Challenges for Underwater Localization . . . . . . . . . . . . 171.3.2 Challenges for Scheduling of UWANs . . . . . . . . . . . . . . 191.4 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19I Underwater Localization and Tracking . . . . . . . . . . . 212 UWL with Time-Synchronization and Propagation Speed Uncer-tainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.1 Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 System Setup and Assumptions . . . . . . . . . . . . . . . . . . . . . 23viTable of Contents2.3 The STSL Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3.1 Step 1: Time-Synchronization . . . . . . . . . . . . . . . . . . 262.3.2 Step 2: Localization . . . . . . . . . . . . . . . . . . . . . . . 282.3.3 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.3.4 Scalability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3.5 Pseudo-Code for STSL . . . . . . . . . . . . . . . . . . . . . 322.4 Crame?r-Rao Lower Bound . . . . . . . . . . . . . . . . . . . . . . . . 322.4.1 General Crame?r-Rao Lower Bound . . . . . . . . . . . . . . . 322.4.2 Application to STSL . . . . . . . . . . . . . . . . . . . . . . . 342.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.6 Sea Trial Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.6.1 Channel and System Characteristics . . . . . . . . . . . . . . 402.6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Spatially Dependent Underwater Navigation . . . . . . . . . . . . . 453.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.2 The SSM and Measurement Model . . . . . . . . . . . . . . . . . . . 473.2.1 State Space Model (SSM) . . . . . . . . . . . . . . . . . . . . 483.2.2 Measurement Model . . . . . . . . . . . . . . . . . . . . . . . 483.2.3 Crame?r Rao Lower Bound (CRLB) . . . . . . . . . . . . . . . 513.3 The DD-UT Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.3.1 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.3.2 Drift Velocity Estimation . . . . . . . . . . . . . . . . . . . . 533.3.3 Confidence Index (CI) . . . . . . . . . . . . . . . . . . . . . . 553.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.4.2 Sea Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664 LOS and NLOS Classification for UWL . . . . . . . . . . . . . . . . 674.1 System Setup and Assumptions . . . . . . . . . . . . . . . . . . . . . 684.1.1 RSS-Based Range Measurements . . . . . . . . . . . . . . . . 694.1.2 PDF for PD Measurements . . . . . . . . . . . . . . . . . . . 704.1.3 Remark on Algorithm Structure . . . . . . . . . . . . . . . . 714.2 Step One: Identifying ONLOS Links . . . . . . . . . . . . . . . . . . 714.2.1 Classification of non-ONLOS Links . . . . . . . . . . . . . . . 724.2.2 Classification of ONLOS Links . . . . . . . . . . . . . . . . . 734.3 Step 2: Classifying LOS and SNLOS Links . . . . . . . . . . . . . . 734.3.1 Basic Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3.2 Equivalence Constraints . . . . . . . . . . . . . . . . . . . . . 744.3.3 Formalizing the Log-Likelihood Function . . . . . . . . . . . . 74viiTable of Contents4.3.4 Estimating the Distribution Parameters ?1 and ?2 . . . . . . 754.3.5 Forming Initial Estimation ?0 . . . . . . . . . . . . . . . . . . 764.3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.3.7 Summarizing the Operation of the Classifier . . . . . . . . . . 764.3.8 Deriving the HCRLB . . . . . . . . . . . . . . . . . . . . . . 784.4 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 794.4.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4.2 Sea Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875 A Machine Learning Approach for Underwater DR . . . . . . . . 895.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.2 The DR-A Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.2.1 Forming A?h: Estimation of the Heading Angle . . . . . . . . 935.2.2 Forming A?h,p: Estimating the Time-varying Pitch Angle . . . 945.2.3 Distance Estimation . . . . . . . . . . . . . . . . . . . . . . . 1005.2.4 Summarizing the Operation of the DR-A Method . . . . . . . 1005.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.3 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 1035.3.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 1035.3.2 Sea-Trial Results . . . . . . . . . . . . . . . . . . . . . . . . . 1075.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110II Spatial Reuse MAC techniques for UWANs . . . . . . 1126 Time and Spatial Reuse Handshake Protocol for UWANs . . . . 1136.1 System Model and Objectives . . . . . . . . . . . . . . . . . . . . . . 1136.1.1 MAC Throughput . . . . . . . . . . . . . . . . . . . . . . . . 1156.1.2 Fairness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166.1.3 Scheduling Delay . . . . . . . . . . . . . . . . . . . . . . . . . 1166.2 Maximizing Channel Utilization in Handshake Protocols . . . . . . . 1166.2.1 Types of Primary Conflicts . . . . . . . . . . . . . . . . . . . 1186.2.2 Formalizing Constraints . . . . . . . . . . . . . . . . . . . . . 1186.2.3 Channel Utilization Maximization Problem . . . . . . . . . . 1226.3 The TSR Protocol - A Sub-Optimal Approach . . . . . . . . . . . . 1236.3.1 Priority of Control Packets . . . . . . . . . . . . . . . . . . . 1266.3.2 Scheduling Control Packets . . . . . . . . . . . . . . . . . . . 1276.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.4.1 Simulation Setting . . . . . . . . . . . . . . . . . . . . . . . . 1336.4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 1346.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138viiiTable of Contents7 Robust Spatial Reuse Scheduling in UWANs . . . . . . . . . . . . . 1397.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1407.1.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . 1407.1.2 Objectives of Resource Allocation . . . . . . . . . . . . . . . 1417.2 Formalizing the BSP . . . . . . . . . . . . . . . . . . . . . . . . . . . 1437.2.1 Basic Approach . . . . . . . . . . . . . . . . . . . . . . . . . 1437.2.2 Formalizing the T-BSP . . . . . . . . . . . . . . . . . . . . . 1447.2.3 Formalizing the R-BSP . . . . . . . . . . . . . . . . . . . . . 1467.3 Obtaining the Topology Matrix . . . . . . . . . . . . . . . . . . . . . 1547.3.1 Obtaining the Topology Matrix . . . . . . . . . . . . . . . . . 1547.3.2 Constructing the Conflict Graph . . . . . . . . . . . . . . . . 1567.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1577.4.1 Model-Based Topology . . . . . . . . . . . . . . . . . . . . . 1587.4.2 Sea-Trial-Based Topology . . . . . . . . . . . . . . . . . . . . 1627.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1658 Adaptive Error-Correction Coding Scheme for UWANs . . . . . . 1678.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1688.2 The Adaptive Coding Scheme . . . . . . . . . . . . . . . . . . . . . . 1688.2.1 Gain of Adaptive Coding . . . . . . . . . . . . . . . . . . . . 1698.2.2 Optimization of Nactualt,i . . . . . . . . . . . . . . . . . . . . . 1728.2.3 Extension to IR-HARQ . . . . . . . . . . . . . . . . . . . . . 1738.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1748.4 Performance Results and Discussion . . . . . . . . . . . . . . . . . . 1778.4.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1778.4.2 Sea Trial Results . . . . . . . . . . . . . . . . . . . . . . . . . 1848.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185III Summary of Thesis and Further Research . . . . . . . 187Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A Alternating Optimization Approach for Solving (4.21) . . . . . . . 206B Expressions for the HCRB . . . . . . . . . . . . . . . . . . . . . . . . 208ixList of Tables3.1 Drift velocity estimation results from the Israel and Singapore sea trials. 644.1 Israel sea trial: distribution of estimated values of ?Plastm , m = 1, 2. . . 844.2 Singapore sea trial: cx??E(di)E(di) . . . . . . . . . . . . . . . . . . . . . . . . 86xList of Figures1.1 Communications architecture for UWSNs [1]. . . . . . . . . . . . . . . 21.2 Mapping between the challenges and desirable properties of underwa-ter localization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Illustration of AUV-aided localization. . . . . . . . . . . . . . . . . . 71.4 Illustration of various types of communication links: LOS, SNLOS andONLOS links. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.5 Illustration of the vessel?s wave-induced motion. . . . . . . . . . . . . 131.6 Structure of thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.1 ?err from (2.31) as a function of 1/?2. Sound speed is known andall nodes are time-synchronized. Vertical bars show 95% confidenceintervals of the simulation results for STSL. . . . . . . . . . . . . . . 352.2 ?err from (2.31) as a function of esync. Sound speed is known and 1?2 =46 dB. Vertical bars show 95% confidence intervals of the simulationresults for STSL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.3 ?err from (2.31) as a function of |c? c?|. All nodes are time-synchronizedand 1?2 = 46 dB. Vertical bars show 95% confidence intervals of thesimulation results for STSL. . . . . . . . . . . . . . . . . . . . . . . . 372.4 ?err from (2.31) for the STSL algorithm as a function of number ofiteration steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.5 Empirical PDF of cest for c = 1500 m/sec. . . . . . . . . . . . . . . . 392.6 ?err from (2.31) for time-synchronization and sound speed uncertainties. 402.7 Time-varying location of nodes in the sea trial. . . . . . . . . . . . . . 412.8 T? pddiff for all communication links as a function of time slots. . . . . . . 422.9 ??err from (2.32) as a function of |c? c?| for W = 30 time slots. R-STSLmethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.10 Probability that ??err ? x for STSL and MR-STSL. . . . . . . . . . . . 443.1 Simulated scenario: (a) simulated velocity field at depth 20 m, (b)simulated speeds of the anchor nodes and TN. . . . . . . . . . . . . . 583.2 (a) Mean of ev(k) from (3.32) as a function of number of anchor nodes,(b) PD vs. PF for different ?2anc and The values. . . . . . . . . . . . . 593.3 Simulated scenario: (a) speed of the TN, (b) tracking error edk from(3.40) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61xiList of Figures3.4 Tracking performance (simulations): (a) empirical C-CDF for MSNR=50dB,(b) edk as a function of MSNR (thick line shows results for the CRLB). 623.5 Node locations in Cartesian coordinates: (a) Singapore sea trial, (b)Israel sea trial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.6 edk from (3.40) vs. time: (a) Singapore sea trial, (b) Israel sea trial. . 654.1 Classification results: (a) Prd,non?ONLOS and Prd,ONLOS vs. ?UB, (b)Empirical detection probabilities of LOS and SNLOS. . . . . . . . . . 804.2 Empirical C-CDF of ?err from (4.27). . . . . . . . . . . . . . . . . . . 814.3 Estimation error of LOS and SNLOS distribution parameters vs. EMiteration number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.4 Israel harbor experiment: (a) location (picture taken from Googlemaps on Sep. 09), (b) results for ONLOS link classification. . . . . . 834.5 Empirical C-CDF of ?err from (4.28), T?c = 10Ts. . . . . . . . . . . . . 854.6 Histogram of ?erri from (4.29). Bin width 0.3 m, E(di) = 324.1 m. . . 864.7 Localization error, ?e, as a function of the number of received packets,W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.1 Flow chart for the DR-A algorithm. . . . . . . . . . . . . . . . . . . . 905.2 Graph representation for positive and negative constraints. . . . . . . 965.3 Example of a modeled wave in the x? y plane. t = 10 seconds. . . . 1045.4 C-CDF results of ?angle. . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.5 Average results of ?err as a function of (a) M? (for T?c = Tc), (b) T?c (forM? = 10). Tc = 6 seconds. . . . . . . . . . . . . . . . . . . . . . . . . 1065.6 Results of ?err as a function of 1? . M? = 10, T?c = Tc. . . . . . . . . . . 1075.7 C-CDF results of ?err. 1? = 20 dB, M? = 10, T?c = Tc. . . . . . . . . . . 1075.8 Sea trial: nodes location in Cartesian coordinates. (a) x-axis. (b) y-axis.1085.9 Sea trial: measured and projected acceleration along the x axis relativeto g for M? = 5 and T?c = 40 seconds. Boat 1. . . . . . . . . . . . . . . 1095.10 Sea trial: (a) C-CDF results of ?angle for the two boats, (b) ?angle vs.the accumulated change of the boat?s heading angle within the timeslot, Tslot = 300 seconds. . . . . . . . . . . . . . . . . . . . . . . . . . 1095.11 Sea trial: C-CDF results of ?err for the two boats. Tslot = 200 sec . . . 1106.1 Illustration of channel reservation process (note that the first datapacket of node j is smaller than the rest). . . . . . . . . . . . . . . . 1176.2 Illustration of different types of primary conflicts. . . . . . . . . . . . 1196.3 Illustration of packet exchange mechanism. . . . . . . . . . . . . . . . 1256.4 Structure of RTS, CTS, NT, and data packets. . . . . . . . . . . . . . 1316.5 Scheduling of RTS and CTS and determining of CS parameters in theTSR protocol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132xiiList of Figures6.6 Average of ?through from (6.2) and ?delayTmsgj,j?from (6.4) as a function ofRmsg =Tmsgj?,jTmsgj,j?for TSR with and without DSSS. . . . . . . . . . . . . . 1346.7 Empirical C-CDF of ?fair,through in (6.3) for the TSR, TDMA, Slotted-FAMA, BiC-MAC, and APCAP protocols. |N | = 6 . . . . . . . . . . 1356.8 Empirical CDF of ?delay in (6.4) for the TSR, Slotted-FAMA and BiC-MAC protocols. |N | = 15. . . . . . . . . . . . . . . . . . . . . . . . . 1366.9 Empirical C-CDF of ?through from (6.2) for the TSR, TDMA, Slotted-FAMA, APCAP, and BiC-MAC protocols. |N | = 6. (a) without DSSSsignaling, (b) with DSSS signaling. . . . . . . . . . . . . . . . . . . . 1376.10 ?change(|N | = 6, 10, 15) from (6.37). . . . . . . . . . . . . . . . . . . . 1387.1 Example: (a) sample topology for a UWAN. (b) constructing matrixIskel using Algorithms 4 and 5 for the sample network. (c) maskingmatrix used in (7.14). . . . . . . . . . . . . . . . . . . . . . . . . . . . 1497.2 Flow chart to obtain the R-BSP scheduling matrix M . . . . . . . . . 1527.3 Probability (7.23) for k = u?1 and empirical probability of ? ? u?1when generating a Bernoulli random graph with N nodes and edgeprobability p. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1547.4 Convergence parameters b1 and b2 vs. transmission range . . . . . . . 1567.5 C-CDF of ?through from (7.2) for matched and mismatched OTT andstatic model-based topology. . . . . . . . . . . . . . . . . . . . . . . . 1597.6 C-CDF of ?through from (7.2), for static model-based topologies anddifferent MPR scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . 1607.7 C-CDF of ?through from (7.2) for model-based topologies. (a) static (nooutdated topology). (b) dynamic (slowly propagating topology) . . . 1617.8 CDF of ?delay from (7.3) for static model-based topologies. . . . . . . 1627.9 Structure of Sea Trial: (a) satellite picture of the sea trial location(picture taken from Google maps on September 29, 2009). (b) recordednetwork topologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.10 Results of ?through from (7.2) for topologies recorded in the sea trial andT = 10 time-slots. Each vertical line represents the time a topologychange starts affecting results. . . . . . . . . . . . . . . . . . . . . . . 1647.11 ?delay from (7.3), for static and dynamic sea-trial-based topologies. . . 1658.1 Gain gcoding from (8.5) as a function of ?t,i from (8.2). . . . . . . . . 1698.2 Gain genergy from (8.7) as a function of Th and ?t,i from (8.2). Non-erasure channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1718.3 Illustration of the procedure of updating channel conditions for multi-ple packet transmission. . . . . . . . . . . . . . . . . . . . . . . . . . 1748.4 Illustration of adaptive coding implementation for single packet trans-mission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175xiiiList of Figures8.5 Transmission loss vs. range. Output from the Bellhop simulator [2]. . 1788.6 PER as a function of channel erasure rate. . . . . . . . . . . . . . . . 1798.7 Channel utilization as a function of channel erasure probability (for?t,i ? 650 m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1808.8 Channel utilization as a function of ?t,i (for erasure probability ofroughly 0.21). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1818.9 Error ?p(m) as a function of packet number m. (Note that values inthe y-axis are reversed). . . . . . . . . . . . . . . . . . . . . . . . . . 1828.10 Histogram of network latency in terms of number of packets neededtill decoding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1838.11 CDF of the number of symbols transmitted till successful decoding,Nfinal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1838.12 CDF of network goodput. . . . . . . . . . . . . . . . . . . . . . . . . 1848.13 Satellite picture of the experiment location (picture taken from GoogleEarth on July 23, 2012.) The three locations of the nodes are marked. 1858.14 Packet success rate for the three links from the sea trial. . . . . . . . 186xivList of Abbreviations and SymbolsAcronymsARQ automatic repeat requestAUV autonomous underwater vehicleBSP broadcast scheduling problemCA collision avoidenceC-CDF complementary cumulative density functionCI confidence indexCL connectivity listCRLB Cramer-Rao lower boundCS communication sessionCSI channel state informationCTS clear-to-sendCUMP channel-utilization-maximization problemDR-A DR navigation using a single accelerometerDR dead-reckoningDSSS direct sequence spread spectrumDVL Doppler-velocity-loggerEKF extended Kalman filterEM expectation-maximizationHCRLB hybrid Cramer-Rao lower boundHST-TDMA hybrid spatial-reuse time-division multiple accessINR interference-to-noise ratioINS inertial systemIR-HARQ incremental redundancy hybrid automatic repeat requestLDPC low-density parity checkLOS line-of-sightMAC medium access controlMIS maximal independent setMPR multiple packet receptionNLOS non-line-of-sightNT noticationONLOS object-related NLOSOTT orthogonal topology-transparentxvList of Abbreviations and SymbolsPCA principal component analysisPD propagation delayPDF probability density functionPER packet error rateR-BSP robust BSPRS Reed-SolomonRTS request-to-sendSD-UT spatially dependent underwater trackingSINR signal-to-interference-plus-noise ratioSNLOS sea-related NLOSSNR signal-to-noise ratioSSP sound speed profileSSM space state modelSSV state space vectorSTSL sequential time-synchronization and localizationT-BSP topology-dependent BSPTDMA time-division-multiple-accessTN tracked nodeToF time-of-flightTSR joint time and spatial reuseUAC underwater acoustic channelUKF unscented Kalman filterUL unlocalizedUT underwater trackingUWAC underwater acoustic communicationUWAN underwater acoustic communication networksUWL underwater localizationNotations and OperatorsBold upper case and lower case letters denote matrices and vectors, respectively.Accents x? and x? represents estimation and approximation of x, respectively. Theremaining notation and operators used in this thesis are listed below.L Number of anchor nodes directly connected to the UL nodeji 2-D UTM coordinates of the UL nodepi 2-D UTM coordinates of the lth anchor nodec Sound speed in water [m/sec]W Duration of the localization windowN Number of packets transmitted during the localization windowSl Clock skew of the UL node relative to the lth anchor nodexviList of Abbreviations and SymbolsOl Clock offset of the UL node relative to the lth anchor node [sec]T pdi Propagation delay of the ith packet [sec]Ti Transmission local time of the ith packet [sec]Ri Reception local time of the ith packet [sec]d?i,i? Self estimation of distance between locations ji and ji???i,i? Self estimation of angle between locations ji and ji? [rad]? Threshold for location quantization [m]?2 variance of ToA measurement noise [sec2]?li Ratio between Tpdi and the actual propagation delayak state space vectoryk measurement vectorhk measurement model vectorrk 3-D coordinates of the TNranck 3-D coordinates of the anchor nodedk distance vector rk ? ranckvk velocity of the TNv?drift drift velocity estimate of the TNvanc,driftk estimated drift speed and heading direction of the anchor nodec?k average sound speed between the anchor and TN? INS time interval between consecutive INS measurements? range time interval between consecutive range measurementsmINSk INS measurement vectormToFk ranging measurementmDopplerk Doppler shift measurementxi PD measurementsxLOS, dLOS delay and distance in the LOS link, respectivelyX vector of PD measurements xi of the same communication linkdRSS,LB lower bound of RSS-based range measurement? propagation loss factor? absorption loss factorM assumed number of classes in PD modelkm weight of the mth distribution in the mixture distribution model?m vector of parameters of the mth distribution? vector of parameters of the distribution of XTLIR upper bound on the length of the channel impulse responsec propagation speed in the channeldONLOS distance of the ONLOS linkRL reflection loss in ONLOS link?l group of xi measurements with the same distribution ?m?l classifier for group ?l%i classifier for xixviiList of Abbreviations and Symbolsdi,j distance traveled by the vessel at time period [ti, tj]N number of acceleration measurementsTc coherence time of acceleration along the horizontal plane?n the vessel orientation with respect to the reference system?n the vessel heading angle with respect to ?n?n the vessel pitch angle in time tnan the vessel 3-D acceleration in the horizontal plane coordinate systema?n acceleration measurementA? vector of acceleration measurementsA?h Matrix A? projected to match the vessel headingA?h,p Matrix A? projected into the horizontal plane along the vessel headingM? pre-defined number of pitch-states?l group of same pitch-stateL number of groups ?l?l classifier for group ?l??p the distribution parameters of A? at the pth EM iteration?m,x mean of the mth class for the x axis?m,x standard deviation of the mth class for the x axiskm prior probability of the mth classxviiiAcknowledgmentsFirst and foremost, I would like to express my utmost gratitude to my supervisor, Pro-fessor Lutz Lampe, for his assistance, support, and guidance throughout the course ofthis work. Your fine sense of constructive criticism was invaluable to me throughoutthe work.I would also like to thank Dr. Hwee-Pink Tan and Dr. Mandar Chitre for theirvaluable comments and assistance.I would like to thank my parents for believing in me and encouraging me through-out my life. I am indebted to my father and my mother for their endless love, care,and support.Last but not least, I would like to thank my lovely wife, Hadas, for raising ourfamily, my greatest accomplishment, joy, and pride. Without your support none ofthis could have happened.xixTo Hadas, Ronya, Gili, and Itamar?speak to the earth, and it shall teach thee?xxChapter 1IntroductionThe oceans with their diverse biology systems, vast energy resources, and climate andhistory records of our planet, have always attracted researchers and industries. In thelast decade, ocean exploration has considerably increased through the use of ocean-observation systems, autonomous underwater vehicles (AUVs), and fixed or mobilesensor networks. These submerged devices need to report the collective data backto base stations or to share information in the setting of a wireless communicationnetwork. Wireless communication underwater is usually established using acoustictransducers since radio frequency communication is only possible for very short dis-tances underwater. Underwater acoustic communication (UWAC) can fulfil the needsof a multitude of underwater applications, including: oceanographic data collection,warning systems for natural disasters (e.g., seismic and tsunami monitoring), ecolog-ical applications (e.g., pollution, water quality and biological monitoring), militaryunderwater surveillance, assisted navigation, industrial applications (offshore explo-ration), to name just a few [3]. For example, in offshore engineering applications,underwater sensors can measure and report parameters such as foundation strengthand mooring tensions to monitor the structural health of deepwater mooring sys-tems. In addition, underwater acoustic communication networks (UWANs) comprisecommunication between surface stations and AUVs. Two common communicationsarchitectures for UWANs are shown in Figure 1.1.Most of the UWAC research in the past has concentrated on the development ofmodels for the underwater acoustic channel (UAC) and the design of secure pointto point links. Only recently, networking aspects of UWAC consisting of a fixed butad-hoc infrastructure (alike base stations in a cellular network) and mobile AUVs(alike mobile phones) have started to attract significant interest in the research com-munity to enable fast, reliable, and cost effective UWAN [4]. One of the majorchallenges of UWANs is resource assignment which has become the bottleneck forUWAN applications. Scheduling for UWANs is governed by several factors such aslow sound speed (approximately 1500 m/sec [5]), half-duplex communication (due todesign constraints of the acoustic transducers [6]), large power attenuation, long delayspread, time varying propagation channel, and a very limited signal bandwidth dueto absorption loss (which increases with frequency) and noise level (which decreaseswith frequency) [7], as well as transducer constraints. These factors lead to generallypoor availability and reliability performance of UWAN systems and pose engineeringchallenges that are very different from those experienced in radio frequency wirelessnetworks [8, 9]. In particular, even though UWAC systems have been implemented1Chapter 1. Introduction(a) (b)Figure 1.1: Communications architecture for UWSNs [1].for many years, many design and implementation problems remain to be solved to-wards developing advanced communication network systems enabling applicationswith high quality of service requirements.The long propagation delay in the channel, as well as the often sparse nature ofUWANs, make location-dependent medium access control (MAC) protocols highlyattractive to improve latency and throughput performance of UWANs via spatial-reuse techniques. In this context, underwater localization (UWL) of unlocalized (UL)UWAN nodes (infrastructure elements and mobile devices) is a key element towardsefficient communication networks enabling, e.g., an ocean-observation system. (Wenote that the network has to provide its own localization, since global positioningsystem (GPS) systems do not work underwater.) Moreover, sensed data can only beinterpreted meaningfully when referenced to the location of the sensor. The followingare desirable properties of UWL:? AccuracyThe location of the sensor for which sensed data is derived should be accu-rate and unambiguous for meaningful interpretation of data. Localization al-gorithms usually minimize the distance between the estimated and the truelocation.? SpeedSince nodes constantly move, the localization and its tracking procedure shouldbe fast so that it reports the actual location when data is sensed.? Wide Coverage2Chapter 1. IntroductionThe localization scheme should ensure that most of the nodes in the networkcan be localized.? Low Communication CostsAccurate localization requires ranging estimation to anchor nodes whose loca-tion is known, usually via UWAC. Since the nodes are battery-powered and maybe deployed for long durations, communication overhead should be minimized.In addition to the above quantifiable properties, practical considerations such as easeand cost of deploying reference nodes and other required infrastructure should betaken into account too.The remainder of this chapter is organized as follows. In Section 1.1, we presenta survey of UWL and tracking schemes, and identify important challenges that needto be addressed. In Section 1.2, we describe the state-of-the-art in UWAN MACprotocols with a focus on spatial reuse scheduling that utilize location information.In Section 1.3, we list the open problems in UWL and UWAN MAC design addressedin this thesis. Finally, in Section 1.4 we present the structure of this thesis.1.1 Underwater Localization and TrackingAlthough localization has been widely studied for terrestrial wireless sensor networks,existing techniques cannot be directly applied to UWANs because of the followingunique characteristics:Deployment of Anchor Nodes Assuming depth sensors are used, to localize un-derwater nodes deployed in the 3D sea environment, reference locations of at leastthree anchor nodes are required. However, since due to restrictions on energy con-sumption for long deployment period and sparse network topology, localization cov-erage is limited, and a node may not always be in the communication range of atleast three anchor nodes.Node Mobility Underwater nodes will inevitably drift due to the water current,winds, shipping activity etc. [10]. While anchor nodes attached to surface buoyscan be precisely located through GPS updates, it is difficult to maintain submergedunderwater nodes at precise locations. This may affect localization accuracy, as somedistance measurements may have become obsolete by the time the node position isestimated. Furthermore, due to the unpredictable nature of the ocean current it ishard to track the location of drifting nodes using a predefined motion model.Inter-Node Time Synchronization Since GPS signals are severely attenuatedunderwater, it cannot be used to time-synchronize nodes deployed underwater to3Chapter 1. Introductioncompensate for clock drifts due to both offset and skew. Consequently, the accuracyof time-of-flight (ToF)-based range measurement may be affected. Furthermore, thespeed of sound underwater is five orders of magnitude lower than RF propagationover the air. Hence, both clock skew and offset should be compensated for.Signal Reflection In near-shore or harbor environments, where obstacles may existbetween nodes, non-line-of-sight (NLOS) signals reflected from object (e.g., vessels,harbor wall), or multipath (indirect) signals from the sea surface or bottom can bemistaken for line-of-sight (LOS) signals, and may significantly impact the accuracyof range measurement.Sound speed variation Unlike the speed of light which is constant, the speedof sound underwater varies with water temperature, pressure and salinity, givingrise to refraction. Without measuring the sound speed, the accuracy of distancemeasurements based on time-of-arrival approaches may be degraded.Asymmetric Power Consumption Unlike RF modems, acoustic modems typi-cally consume much more power (order of tens of Watts) in transmit mode comparedto receive mode (order of milliWatts). This asymmetry in transmission mode makesit preferable for ordinary nodes to be localized through passive / silent listening.Low bit rate Compared to RF communications, the bit rates achievable withacoustic communications is significantly lower. As a result, localization packets hold-ing anchors? location information are long and have high impact on network through-put.Figure 1.2 maps the above challenges to each desirable localization performancemetric.In the following, we start with a survey of the state-of-the-art in UWL. Next,we present current works on tracking the time-varying location of underwater nodes,and discuss approaches to mitigate localization measurement errors.1.1.1 Underwater LocalizationWe review both range-free and range-based UWL techniques. In range-free schemes,UL nodes may infer their proximity to anchor nodes (e.g., in terms of number of hops)so as to achieve coarse localization, e.g., in an area instead of a specific location.Range-based approaches rely on time and/or bearing information to evaluate thedistance to anchor nodes, usually using acoustic communications. The UL node thenutilizes multilateration/angulation to estimate its own location.4Chapter 1. IntroductionFigure 1.2: Mapping between the challenges and desirable properties of underwaterlocalization.Range-free LocalizationRange-free UWL schemes are designed for cases where range measurements sufferfrom large errors due to node mobility or strong attenuation. In [11], a UWL schemebased on an assumed attenuation model is proposed. When an anchor node i trans-mits at power Pi, the UL node can receive the transmission as long as it falls withinthe anchor node?s transmission range, which depends on the transmission power.Hence, by deploying several reference nodes that transmit beacons at multiple powerlevels, the plane is divided into many small sub-regions defined by intersecting circles.By receiving reports from each UL node of the minimum transmit power at which itreceived the respective anchor node beacon, a central sink can estimate the locationof the UL nodes. However, it is a centralized scheme where mobility is not consid-ered. A range-free UWL scheme for moving anchors is presented in [12]. Here, anAUV traverses a preprogrammed route and performs directional (vertical) beaconingperiodically. Assuming that the AUV moves with constant and known speed andknows its position underwater accurately, relying on the AUV periodic broadcasts,the UL node can estimate its position within a circle formed by the intersection ofthe transmitted beams with the horizontal plane.A different variant of range-free UWL schemes based on finger-printing have beenproposed in [13]. Such schemes involve an offline (or training) stage prior to theonline (or prediction) stage. The setup comprises an acoustic signal source capable oftransmitting at M different frequencies. During the offline stage, a receiver is placedat a reference location (with known position), and collects N samples of receivedpower at each frequency to constitute anM?N acoustic-signal map. This is repeatedat each reference locations. In the online stage, the receiver measures received powersamples from M different frequencies and compare these to the ones samples in the5Chapter 1. Introductionoffline stage using a likelihood function and a ?probabilistic-weighted? summation ofdifferent reference locations.Range-based LocalizationRange-based localization typically comprises the following steps:1. Range measurement: Each UL node estimates its distance from each anchornode within its communication range using either received signal strength indi-cator (RSSI), time difference of arrival (TDoA) or time of arrival (ToA). Sincethe path loss in UAC is usually time varying and multipath effect can result insignificant energy fading, the RSSI method is not the primary choice for under-water localization. Hence, most proposed range-based localization schemes useeither TDoA or ToA for ranging. The TDoA method involves computing thetime difference of arrival between beacons from different anchor nodes trans-mitted using acoustic signalling, and the ToA method performs ranging basedon the relationship among transmission time, speed and distance.2. Location estimation: Each UL node then estimates its position, typically,according to the intersection of various circles centered at each reference nodewith radii corresponding to the range measurements. In general, to localize anode in d-dimensional space, the number of independent range measurementsrequired should be at least d + 1.3. Tracking: The location estimate is refined e.g., using measurements from on-board sensors, measurement error models, mobility models, etc.Range-based UWL method can be classified into 1) single-stage schemes whichrely solely on message exchanges with the anchor nodes, and 2) multi-stage schemesin which newly localized nodes can serve as anchor nodes. The key innovation of thefirst type of UWL schemes lie in how they address localization inaccuracy due to time-synchronization and measurement errors and availability of anchor nodes. While itis usually assumed that clock offset is the main cause of time-synchronization errors,also clock skew cannot be neglected for UWL due to the long propagation delay in theUAC [14]. Furthermore, since anchor nodes are usually submerged we cannot assumethese nodes to be time synchronized. Regarding this problem, [14] suggested toestimate both skew and offset based on packet exchange with an already synchronizednode. Alternatively, the problem of time-synchronization can be avoided by usingTDoA techniques. In [15] ?silent positioning? is provided, i.e., UL nodes do nottransmit any beacon signal and just listen to the broadcasts of reference nodes toself-position, reducing the communication costs. The scheme relies on TDoA overmultiple beacon intervals, and thus does not require time synchronization amongstnodes. However, this kind of ?reactive beaconing? makes it susceptible to failure dueto transmission losses that are prevalent in harsh UACs. An improvement has been6Chapter 1. Introductionsuggested in [16], where a dynamic mechanism for leader reference node identificationand a time-out mechanism to trigger beaconing in the event of transmission loss ispresented. However, the scheme does not manage motion of nodes.AUV (t0)AUV (t2)AUV (t1)2-way message exchangeAUV routeFigure 1.3: Illustration of AUV-aided localization.Allowing node mobility is important for UWL, where the deployment of fixed ref-erence nodes such as surface buoys is time consuming, limits the localization coverageand may be infeasible or undesirable. Several algorithms have been suggested to com-pensate for node movements, either by regarding these movements as ToA noise [17]or by applying mobility prediction [10]. A few UWL schemes rely on a moving anchornode, where, as illustrated in Figure 1.3, a single node can localize the network. Inthe AUV-aided scheme proposed in [18], the AUV obtains position updates by risingto the surface to use GPS, and then dives to a predefined depth and periodicallyperforms a two-way message exchange with UL nodes. A 2D localization is achievedonce successful two-way message exchanges take place in at least three non-collinearAUV locations. However, UL nodes should remain static. Instead of AUVs, the?Dive?N?Rise? localization scheme [19] uses a weight/bladder mechanism to controlthe diving/rising of each mobile beacon. These beacons update their positions atthe surface, and broadcast them when they dive to a certain depth. However, theseapproaches consider node movements as an undesired phenomenon and do not utilizethe possibility of additional ToA measurements when coupled with self-localization.7Chapter 1. IntroductionWhile, ideally, three range measurements should be enough to localize a nodein a 2D plane through triangularization, ranging errors require the use of multi-ple range measurements through multilateration. Instead of the commonly-adoptedcircle-based least-squares multilateration, [20] suggested a hyperbola-based approach.The premise is that when range measurement errors due to imperfect time synchro-nization, or varying speed in acoustic transmission exist, two hyperbolas always in-tersect with each other with one cross point, or partial solution, while two circleswill likely intersect with either two or zero cross point(s). Several works suggestedmethods to compensate for location ambiguities such as flips and rotations that arisedue to NLOS-related range estimation errors. In [21], a three-phase algorithm issuggested, where first an ambiguity-free sub-tree of nodes is determined. Then, mul-tilateration is performed where the node is first assumed to be located in the center ofa rectangular area. Finally, a refinement phase is performed using a Kalman filter tomitigate remaining noise. A robust algorithm for mitigating localization ambiguitiesis suggested in [22] by rejecting measurements leading to ambiguities, e.g., when thereare insufficient anchor nodes or when the location of anchor nodes is almost collinear.In [23], an NLOS factor (i.e., the difference between the arrival times of the NLOSand LOS-based signals) is estimated using a maximum likelihood estimator basedon an attenuation model, and NLOS-based measurements are incorporated after afactor correction instead of being rejected. The problem of localization when all mea-surements are obtained from NLOS links is considered in [24], where the relationshipbetween anchor node distances and the NLOS factor is used to improve localization.Another significant challenge of UWL is the variability of the sound speed in wateras it depends on water temperature, depth and salinity [5]. Considering this problem,[25] suggested to first estimate the sound speed using packet exchange between float-ing buoys on the seabed and the sea surface. Alternatively, several works suggestedsound speed estimation based on measuring the channel characteristics and a soundspeed model, e.g., [26], [27]. Differently, [28] suggested to jointly estimate the nodelocation and the propagation speed in the channel by considering the propagationspeed as an additional variable. However, they made the assumptions that all nodesin the network are static, at least four anchor nodes are available and that all nodesare time synchronized, which do not hold true in most UWL applications. Whilechanges in the sound speed profile (SSP) with depth have been considered for UWL(e.g., [29]), for shallow water and short to medium range applications, a good approx-imation for the depth-related sound speed in water is a single parameter, c?, whichchanges as a function of the mean depth of the transmitter and receiver and can beconsidered as an average sound speed. In [28], c? is treated as a system parameterand is separately estimated during the initial localization process. However, due tochanges in the depth of the tracked node (TN), the evaluated parameter c? may shiftand its value should be tracked over time.The key innovations of proposed schemes within the category of multi-stage UWLlie in the trade-off between minimizing error propagation and delay while maximizing8Chapter 1. Introductioncoverage and energy efficiency. In [30], a two-phase algorithm is proposed where arelative coordinate system is built using the first three discovered UL nodes, followedby a selection of new nodes to localize based on their proximity from the new lo-calized nodes. However, the first-stage discovery algorithm requires high volume ofmessage exchange, node mobility is not considered, and only the relative coordinatesfrom the primary seed node is acquired. To combat nodes? mobility, the authors in[31] proposed a joint localization and synchronization scheme. The 3D network ispartitioned into cells, and localization is performed at the cell level. The authorsdetermined the required sensor node density, as well as cell partitioning in order tolocalize all nodes.Since multi-stage localization might lead to error-propagation in the network, self-evaluation of the localization accuracy is required to determine if the localized nodeis elidible to serve as a new anchor node. Several works suggested methods for suchself-evaluation, relying either on a node?s expected location in the network [30] orby assigning each node with a confidence index. In [32], a hard-decision confidenceindex is used based on detecting localization based on outdated range information.Alternatively, in [33], soft decision confidence value is obtained by normalizing theexpected position error with the sum of the Euclidean distance to anchor nodes. How-ever, in doing so these methods reuse the information used already for localization,which might cause biased self-evaluation of the localization accuracy.1.1.2 Tracking the Location of NodesAfter obtaining initial location information via UWL, in case of a moving node, atracking procedure begins where the time-varying location of the node is recursivelyestimated. This process is referred to as underwater tracking (UT). Since GPS isnot available underwater, UT has similarities to indoor navigation. However, due tothe difficulty of modeling motion at sea, UT includes additional challenges. First,the unpredictable water current with fast changes in speed and direction, and theexistence of water turbulences, cause irregularities in the motion of the TN [34].Second, the speed of acoustic signals changes with depth. Last, compared to RADARapplications, where directivity is applied and the emitter is fixed or slowly movingand the propagation speed in known, uncertainties in the sound speed as well as thecontinuous motion of nodes also make it more challenging to incorporate Dopplershift measurements in the UT scheme.The scenario adopted by most UT algorithms consists of several anchor nodesand a moving TN, usually an AUV, with an initial location estimate [34]. A varietyof on-board sensors are used. The most common are inertial sensors, providing ac-celeration measurements. Since acceleration is affected by the vessel pitch and roll,an inertial system (INS) also includes a gyrocompass, vibrating angular rate sensors,or Pendulum tilt sensors [34, 35]. During the UT process, occasionally, external in-formation through packet exchange with anchor node is also available. This includes9Chapter 1. Introductionranging information as well as Doppler shift measurements. The latter are commonlyused in RADAR and Doppler velocity log (DVL) systems, where angle-to-target ismeasured and propagation speed is assumed known, and it provides information ofthe relative velocity of a tracked object. In [36], Doppler shift is also used for UWL,assuming a fixed scenario with known sound speed. However, since in underwateracoustic communication omnidirectional transducers are used, the TN and the an-chor nodes constantly move, and the sound speed is unknown and may change overtime, incorporating Doppler shift measurements into UT is challenging.External and internal measurements for UT are often incorporated using an statespace model (SSM) to update a state space vector (SSV), and a key point is howto reliably determine the SSM. In [37], this problem is handled through a bank ofKalman filters (KFs), each of which uses a different motion model, and the outputof each branch is combined according to the accumulated filter errors. To combatmodel inaccuracies, [38] considered both regular and random motion, and the twocomponents are combined as inner-states of two Markov-like random states. Whilesuch an approach offers flexibility in determining the SSM, it is difficult to fit atracking filter to such a model. Indeed, a common SSM is of fixed speed with a randomGaussian acceleration [34]. To set the model parameters under motion irregularities,the velocity of the TN can directly be measured using a DVL [34]. Unfortunately,DVLs consume non-negligible energy and work well only close to the ocean bottomor surface. Alternatively, the velocity can be estimated by calculating the motor-induced thrust force [39]. However, such velocity measurement is only relative to thewater medium, and thus may not be accurate in the presence of high ocean current.Updating the SSM in time requires the implementation of a tracking filter. In[39], an extended Kalman filter (EKF)-based method is presented to fuse measure-ments from on-board sensors with occasional range measurements to anchor nodes.An interesting combination of the KF and the EKF is presented in [40], where theformer accounts for motion in the surge direction and the latter for angular motion.The scheme includes outlier mitigation using a probabilistic data association filterat the input to the KF. In [41], fusion of sensor information and ranging is formu-lated as a maximum likelihood optimization problem and the solution is found by anon-linear weighted least-squares optimization. Alternatively, [42] suggested incor-porating maximum likelihood data association in an EKF scheme. By using rangingand bearing measurements to several anchor nodes, compass sensor data, and DVL-related speed measurements, good tracking performance is obtained. In [43], it wassuggested to include previous locations of the TN in the SSV to combat delays in therange information due to the slow sound speed in the channel, and instead of an EKF,an extended information filter is used to reduce complexity in case the informationmatrix is sparse. A similar approach is presented in [35], where a post-processingcentralized EKF is used to incorporate both anchor and TN sensor information. Theused SSV is highly detailed and includes the TN pose, its depth, and its linear andangular velocities.10Chapter 1. Introduction1.1.3 Considerations of Measurement ErrorsLocalization and tracking accuracy is highly affected by measurement errors, wherethe dominant factors are ranging and acceleration measurement errors [34]. Theformer is affected by the long delay spread in the channel and strong multipath, andthe latter is caused by ambiguities of the node orientation, mostly due to ocean waves.In this section, we review current approaches to mitigate such errors.Propagation Delay ErrorsRanging information, required for both UWL and tracking, is obtained from esti-mating the ToF of a received signal, using either ToA or TDoA techniques. ToFmeasurements for range estimation can be obtained (i) from multiple impulse-typesignals transmitted in a short period of time, or (ii) from the symbols of a receiveddata packet. The former is a standard in many ultra short baseline systems for rang-ing underwater (e.g., [44]) and involves inspecting the output of an energy detector[45]. The latter involves inspecting the estimated channel impulse response by per-forming a matched filter operation at the receiver [46], or by performing a phase-onlycorrelation and using the kurtosis metric to mitigate channel enhanced noise [47].The ToF is then estimated by setting a detection threshold to identify the arrival ofthe first path. In [48], a fixed threshold is set based on the channel noise level anda target false alarm probability. In [49], an adaptive threshold is used based on theenergy level of the strongest path. A good overview of practical ToF estimators isgiven in [45].When estimating the ToF, one has to lock on to a certain arrival path, believed tobe the LOS path between sender and receiver. Existing UWL schemes, e.g., [15, 33],implicitly assume that PD measurements correspond to the LOS link between thetransmitter and receiver. However, signals can arrive from NLOS communicationlinks in several ways, as illustrated in Figure 1.4. For the node pairs (u, a2) and(u, a3), sea surface and bottom reflections links (referred to as sea-related NLOS(SNLOS )) exist, respectively, in addition to an LOS link. For (u, a1), the signalarrives from the reflection off a rock (referred to as object-related NLOS (ONLOS )).Lastly, between nodes u and a2, there is also an ONLOS link due to a ship. Whileit is expected that power attenuation in the LOS link is smaller than in NLOS links,it is common that the LOS signal is not the strongest. This is because, as shown inmultipath models [50, 2] as well as measurements [46], the UAC consists of groups ofNLOS links with small path delay, but significant phase differences, often resultingin negative superposition with the LOS link (if delay differences between the LOSand NLOS links are smaller than the system resolution for path separation) as wellas positive superposition between NLOS links. If PD measurements of NLOS linksare mistakenly treated as corresponding to delay in the LOS link, e.g., in node pairs(u, a2) and (u, a3), ranging accuracy will significantly be degraded. Clearly, rangingaccuracy affects localization performance. For example, using basic trilateration, the11Chapter 1. Introductiona1a2Unlocalized node, uAnchor nodea3Sea surfaceSea bottomONLOSSNLOSLOSd21dLOSd22ShiprocksuFigure 1.4: Illustration of various types of communication links: LOS, SNLOS andONLOS links.localization error grows quadratically with ranging offset, and a zero-mean Gaussiandistributed offset with a standard deviation of only 2 msec (which is quite commonin UWL [50, 2, 46]) would cause an average error of 6 m error.Acceleration ErrorsTracking the location of a node usually involves the use of acceleration measurementsproduced by an INS. By integrating INS measurements the distance traveled bythe TN can be estimated. This process is referred to as dead-reckoning (DR). Themain challenge in DR navigation is the possible drift and measurement noise ofinertial sensors, which may lead to errors in the order of 10% of the traveled distance,depending on the technology employed [51, 34]. For pedestrian applications, usingthe fact that velocity and orientation can be set to zero when the foot is on ground,it is customary to mount inertial sensors on foot or hip and estimate distance andorientation separately for each step, e.g., [52]. However, while at sea we can identifytime instances where the vessel pitch angle is zero, i.e., at the top or bottom ofthe ocean wave (see Figure 1.5), velocity of the vessel cannot be assumed zero atthese points. Instead, reference measurements are used, e.g., DVL, and measurementdrifts are controlled through fusion of large number of inertial sensors [53]. Forships, DR navigation involves dynamic positioning, heading autopilots, and thruster-assisted position mooring [54]. However, for small AUV-type TNs with strict energy-constraints, these options are not available.Another challenge in DR navigation is to determine the orientation of the inertial12Chapter 1. Introductionxz?zx?y?y?nz? x?z?x? z?x?x?z??nFigure 1.5: Illustration of the vessel?s wave-induced motion.sensor with respect to a reference coordinate system, usually using a gyrocompass [55].Only then the distance traveled by the tracked object can be estimated. However,when the vessel is located close to or on the sea surface such that its motion isaffected by the ocean waves, the vessel pitch angle is fast time-varying and orientationmeasurement may be too noisy to use directly [54]. For this reason, traditionally, DRnavigation at sea involves integrating a large number of inertial sensors and applyingBayesian filtering methods, e.g., EKF or particle filters (cf. [51, 56]), to mitigateoscillatory wave-dependent components and reduce measurement drifts [53].1.2 Spatial Reuse Scheduling in UWANsApart from navigation purposes, location information can greatly improve through-put in the setting of a wireless sensor network like a UWAN. For example, location-aware MAC protocols, for which scheduling of nodes? transmissions are set accordingto their geographical or relative location in the network (e.g., [57]), can greatly im-prove throughput and/or latency by utilizing network resources more efficiently whilemaintaining scheduling limitations. Another example are adaptive coding techniques,where due to the usually low reliability of communication in UWANs, the transmis-sion scheme changes adaptively as a function of the transmitter-receiver distance.In this section, we review current scheduling algorithms and adaptive transmissionstechniques for UWANs.1.2.1 Scheduling Algorithms for UWANsScheduling transmissions in UWANs is required for applications with wide range ofrequirements, e.g., latency, size of information packets, traffic rates, and reliability.Since UWANs are relatively small (usually in the order of tens of nodes), centralizedscheduling approaches are considered and both contention-based and contention-freescheduling algorithms are in use [58]. The need to develop reliable communicationlinks and the high cost of retransmissions due to the long transmission delay and large13Chapter 1. Introductionenergy consumption for transmission [59] make the handshake-based multiple accesswith collision avoidance (MACA) protocol the method of choice for contention-basedscheduling of long unicast transmissions in UWANs [60, 8]. MACA was inspired bythe carrier sense multiple access/collision avoidance (CSMA/CA) technique, stan-dardized in IEEE 802.11a, where a communication session (CS) is established byexchanging request-to-send (RTS) and clear-to-send (CTS) packets. Differently, dueto the narrow bandwidth available for UWAC, contention-free scheduling of UWANsrelies on time-division multiple-access (TDMA) algorithms, where each node is as-signed a unique time slot and each time slot includes guard interval to compensatefor the (long) propagation delay and (short) time-synchronization offset [61]. Suchscheduling is used for broadcast communication or short unicast transmissions inheavy load networks. By scheduling transmissions to avoid packet collisions, bothhandshake- or TDMA-based scheduling benefit from location information. In fact,in [62] it was shown that by carefully scheduling transmissions, unlike for terrestrialradio-frequency networks where network throughput decreases with the number ofnodes, the optimal network throughput achieved for UWANs is 12 .Handshake-based SchedulingDue to the long propagation delay in the UAC the exposure time to packet collisionsis long [60], and a modification to the basic handshake protocol is required. Con-sidering this problem, [60] suggested a slotted handshake protocol in which globallyestablished time slots, the size of which is comparable to the propagation delay, areused, and transmissions are restricted to the beginning of these time slots. The au-thors of [63] suggested improving channel utilization by employing separate time slotsfor control and data packets, and in [64] MAC throughput was further improved byallowing the receiver to warn the transmitter of expected interferences.In handshake-based scheduling, channel resources are allocated to the transmitterwhose RTS packet was the first to arrive at the receiver, whereas other nodes need totry again to gain channel access after waiting for a certain backoff period. This mightlead to an increased delay in packet transmission as the probability of successfullyreserving the channel is inversely proportional to the transmission distance [65]. In[60], this problem was resolved by using a fixed backoff-window size instead of anadaptive one as standardized in IEEE 802.11a. However, determining the size of thefixed backoff-window is difficult as it has opposite effects on throughput and transmis-sion delay [66]. For this reason, [66] suggested an algorithm to bring randomness tochannel reservation by allocating transmitters with time-varying random ranks andgiving priority to the transmitter with the currently highest rank. Unfortunately,they assumed control packets arriving almost simultaneously to the receiver, whichdoes not hold true in UWANs.In addition to the problem of increased delay, traditional handshake-based MACprotocols require nodes in the proximity of a CS to remain silent, which limits channel14Chapter 1. Introductionutilization. This effect is even more noticeable in UWANs, where longer silenceperiods are imposed by the long propagation delay [60]. This also leads to the exposedterminal problem1, which further decreases channel utilization. In [67], the longpropagation delay in the channel is utilized to allow simultaneous transmissions inexposed terminal links. Upon detecting a packet from node p directed to node p?, anode j schedules its transmissions such that its packets arrive at p before the responseof node p?. One way to increase channel utilization is to use timing-advance techniques,often called time reuse [67], such that more nodes can transmit. In UWAC, time reuseis related to the utilization of the long propagation delay in the UAC. In terrestrialradio-frequency networks, performance is inversely proportional to the network size.However, by utilizing the long propagation delay, in UWAC performance is potentiallyfixed for different network sizes [62]. In [68], time reuse is applied by allowing nodesto initiate another CS while waiting for a CTS response. [69] suggested a distance-aware protocol where channel utilization is improved by allowing both nodes involvedin a handshake CS to transmit simultaneously. Alternatively, in [70], time reuse wasapplied by allowing nodes to opportunistically transmit data packets to a node j,such that the packets arrive at j upon completion of its own transmissions. However,both in [68] and [69], nodes located within the interference range of a transmitteror receiver should remain silent, and in [70] simultaneous transmission in different(connected) CSs is not allowed, and thus the above mentioned limitation of traditionalhandshake-based protocols remains.Since network nodes at different locations experience different channel-access lim-itations, applying spatial reuse on top of time reuse can further improve channelutilization. Spatial reuse refers to simultaneous CSs in different parts of the network,and it is specifically applicable to UWANs, since low-power half-duplex transceivers,range and frequency dependent absorption loss [5], and acoustic NLOS scenarios leadto sparse network topologies. The spatial-reuse handshake protocol suggested in [71]identifies exposed terminal links when a node overhears RTS packets which are notfollowed by CTS responses. This node can then transmit simultaneously. [72] sug-gested using control gaps in each exposed terminal link, allowing nodes to scheduletheir transmissions via RTS/CTS packet exchange during those gaps. Alternatively,in [73] exposed terminal links are identified by building a conflict map using a trialand error procedure without the need to exchange RTS/CTS control packets.TDMA-based SchedulingWhen broadcast communication is required, or when transmitted messages are shortcompared to the propagation delay in the channel, the overhead of RTS/CTS pack-ets becomes significant due to the collision probability being comparable to that for1The exposed terminal problem occurs when a node, upon detecting other transmissions, decidesnot to transmit, even though these transmissions may not interfere with its own transmission, andvice versa [60].15Chapter 1. Introductionpayload packets. Furthermore, since nodes detecting an RTS or CTS packet shouldbe kept silent, channel utilization decreases. As shown in [74], the number of silencednodes grows quadratically with the communication range and the CSMA/CA algo-rithm becomes more and more conservative. Therefore, CSMA/CA is not suitable tomeet high network traffic demands for broadcast communication or for short unicastinformation packets [74]. Moreover, channel reservation cost using MACA is high inUWANs, where the long propagation delay necessitates longer silence periods [60].In fact, when considering high traffic networks, the conventional TDMA algorithmseems to outperform most of the existing random-access algorithms [74].In TDMA, besides packet duration, time slots include the expected propagationdelay at the maximal transmission range as well as a guard interval to compensate forpossible clock drifts between periodic time synchronization. To quantify the latter,consider a clock skew S, and guard-interval of ? sec. Then, time-synchronizationis required every k?S sec, where the value of k depends on the time it takes to re-synchronize. Since in UWAC propagation delay is long and message rate is low(transmission rates on the order of a few kbit/s are common [8]), the latter is notexpected to affect performance much. However, due to the long time-slots, end-to-end transmission delay in TDMA scheduling might be too large in practice even forsmall number of network nodes [75]. A different approach is to apply spatial-reusetechniques where significant improvement in channel utilization is possible. Spatialreuse allows several nodes to share network resources such as frequency bands (inmulticarrier systems, e.g. [76]) or time slots (in TDMA systems, e.g. [77]), increasingchannel utilization [78]. Spatial-reuse TDMA is an appealing technique in UWANswhere low power transceivers, range and frequency dependent absorption loss [5],and acoustic NLOS scenarios lead to sparse network graphs. The concept of spatialreuse in UWANs was first introduced in [75], where a scheduling algorithm that im-proves channel utilization by clustering the network was suggested. Assuming shortintra-cluster distances, the communication within clusters is based on TDMA, whileeach cluster is assigned a unique pseudo-random spreading sequence used for sig-nal modulation to reduce interferences between adjacent clusters. In [79] the longpropagation delay in the channel was utilized to allow staggered packet transmis-sion. Unfortunately, the scheduling algorithm is based on the propagation delayof specific node-to-node links, which cannot be exploited in node-to-multiple-nodestransmission. Assignment of network resources (i.e., time slots) to maximize chan-nel utilization is known as the broadcast scheduling problem (BSP) [80], [81]. TheBSP can be formulated as a graph-coloring problem, and various heuristics to solve(variants of) the BSP have been proposed in e.g., [77, 82, 80]. However, these BSPformulations do not consider transmission of broadcast packets, which requires packetflow control via routing.16Chapter 1. Introduction1.2.2 Adaptive TransmissionsSeveral approaches have been suggested to utilize location or propagation delay infor-mation by opportunistically transmitting more data in the channel (e.g., [83, 68, 70]).Another method to utilize location information is through transmitter-side adjust-ment of the transmission scheme or by receiver-initiated request of additional trans-missions, i.e., automatic repeat request (ARQ), to ensure successful data deliv-ery. Considering the benefit of channel-dependent adjustments of the transmissionscheme, an adaptive modulation scheme was implemented in [84] to optimize trans-mission rate for time-varying channel conditions. With regards to reliability of trans-missions, incremental redundancy hybrid ARQ (IR-HARQ) is particularly efficientas it does not suffer from a coding loss due to repetition of the same parity symbols[85]. Despite the coding efficiency of IR-HARQ, it suffers from high latency dueto retransmission requests and retransmissions. Due to the long propagation delayof sound transmission and the low link reliability, this disadvantage is particularlypronounced in UWANs. In part addressing this problem, several adaptive transmis-sion applications tailored to UWANs have been suggested. In [86], an HARQ usingrateless codes has been suggested for transferring large files underwater. A ratelesscoding scheme is also used in [87] and [88] to optimize throughput of UWANs forbroadcast communications. Recently, [89] offered to optimize the code rate for thecurrent channel conditions by forming transmitter and receiver collaboration.1.3 Open Problems Addressed in this ThesisIn the previous section, we have reviewed current approaches for UWL and UWANscheduling. While for the former, challenges associated with deployment of anchornode, time-synchronization, and mobility have been addressed to some extent in thereviewed schemes, and for the latter collision avoidance scheduling algorithms thatcombat the long propagation delay in the channel have been suggested, in our view,the following challenges should be, but have not been, fully addressed.1.3.1 Challenges for Underwater LocalizationSound Speed Variation While most range-based localization techniques assume aknown speed of sound underwater, the dependency of the speed of sound with depth,temperature, and salinity, makes it challenging to pre-estimate. In this thesis we willshow that a mismatch of roughly 10 m/sec in the assumed sound speed considerablyaffects localization accuracy. While some works suggested measuring the parametersaffecting the sound speed, it is not an easy task for small and relatively simplevehicles, and a model-based approach may induce localization errors. We thereforebelieve that the sound speed should be estimated and tracked over time.17Chapter 1. IntroductionInter-node Time Synchronization Localization schemes that rely on silent posi-tioning to minimize communication overhead assume that nodes are time-synchronized.However, unlike surface nodes that can be time-synchronized via GPS updates, theclocks of submerged nodes are subject to skew as well as offset. Although timesynchronization algorithms have been proposed for UWANs, to reduce latency andcommunication overhead they should be incorporated into localization schemes.Node mobility model Node mobility due to ocean current, which presents one ofthe greatest challenges for UWL, has only been accounted for up to various degrees.Although some schemes assumes a simple mobility model, either the anchor nodesor the UL nodes are always assumed fixed during the localization process. Further-more, node mobility exhibits different characteristics and irregularities which makesit hard to determine the motion model. By using inertial systems, often availablefor navigation, and the (possible) spatial correlation of the ocean current, we believethat more information can be available to account for such motion irregularities.Impact of MAC Delays Another important challenge that has not been fullyaddressed for UWL is MAC to resolve contention. MAC schemes inevitably introducedelays in transmission, and affect the accuracy of localization schemes that rely onimmediate or scheduled responses (e.g., two-way messaging). Due to this delay andthe constant motion of nodes in the channel, it is not possible to assume fixed nodesfor UWL.Impact of Channel Structure Since range is measured based on the ToF of thedirect path or its received power, it is essential to lock on the location of the directpath of the received signal. Existing algorithms assume that the direct path is thestrongest path and thus it?s location is easy to estimate. However, multipath fadingcan lead to destructive interference and as a result the energy of the direct path isnot always the strongest. Moreover, the presence of structures and obstacles in theUAC may result in the loss of the direct signal. Hence, designated mechanisms toclassify ToF measurements into LOS and NLOS are needed.Effect of Ocean Waves Last, current UWL schemes assume capability to es-timate or track the orientation angle of the vehicle, and thus project accelerationmeasurements to the horizontal plain. However, near the ocean surface the vehiclemay experience time-varying pitch and roll angles, which may be too irregular totrack and too rapid to directly measure. Therefore, a tailored solution to this specificcase is required.18Chapter 1. Introduction1.3.2 Challenges for Scheduling of UWANsLocation-Dependent Handshake-based Scheduling The problem of low chan-nel utilization when small-to-moderate information unicast packets are sent in handshake-based scheduling can be overcome by utilizing the long propagation delay in thechannel through location information. While some of the reviewed methods exploitexposed terminal links, this is mostly done opportunistically and performance are farfrom the optimal throughput for UWANs.Time-Varying Topology Changes While spatial-reuse TDMA scheduling algo-rithms can improve network throughput, the problem of time-varying network topol-ogy together with the slow propagation of topology information in the UWAN, cangreatly decrease performance of such scheduling algorithms. On the other hand, dueto the long duration of the time-slots in TDMA UWAN scheduling, the low through-put of topology-transparent scheduling algorithms (like pure TDMA) may not besufficient for network requirements. Considering the benefit of high throughput oftopology-dependent scheduling and reliability of topology-transparent scheduling al-gorithms, a scheme combining both approaches is the natural next step.Utilizing Location Information for Adaptive Scheduling The long propaga-tion delay in the channel together with transmitter-receiver distance information offergreat opportunities for improving performance by means of adaptive transmissions.Intuitively, by setting the transmission parameters according to the expected delayin the channel, throughput can be optimized. While some works consider adaptivecoding for UWANs, a pure distance-dependent adaptive channel coding scheme hasnot been suggested.1.4 Thesis StructureIn this thesis, we present UWL and spatial-reuse scheduling algorithms for UWANsthat address the open problems identified in Section 1.3. As illustrated in Figure 1.6,the former serves as a building tool for the latter. We divide the thesis into two parts:I) UWL, and II) spatial-reuse scheduling for UWANs. In Chapter 2, we present ascheme for joint time-synchronization and localization, which considers sound speeduncertainties and utilizes motion in the channel to allow localization even when onlya single anchor node is available. Using this location information, in Chapter 3 wepropose a location tracking scheme that combats the effect of motion irregularities,tracks the sound speed, and incorporates Doppler shift measurements. Next, weconsider the problem of ranging and INS measurement errors, which affect localizationand tracking accuracy. The former problem is considered in Chapter 4, where wepresent a classification approach of ToF information into classes of NLOS and LOS.The latter challenge is the focus of Chapter 5, where, for the case of a TN whose19Chapter 1. IntroductionFigure 1.6: Structure of thesis.motion is affected by ocean waves, we suggest a machine-learning approach to projectacceleration measurements into the horizontal plane and perform DR without usingorientation measurements. The connections between the above chapters is illustratedin Figure 1.6.In Part II, we present spatial-reuse MAC techniques that rely on either locationor topology information available through the UWL capability developed in Part I.In Chapter 6, we show how location information can be used in a handshake-basedscheduling algorithm to utilize all available network resources even in fully connectednetworks. For broadcast UWAC, in Chapter 7 we present an optimal spatial-reuseTDMA scheduling scheme to trade off robustness to topology changes and networkthroughput. Based on such TDMA scheme, in Chapter 8 we propose an adaptivechannel coding technique that utilizes location information to greatly increase net-work throughput. Finally, in Part III we summarize our contributions and suggesttopics for further research.20Part IUnderwater Localization andTracking21Chapter 2UWL with Time-Synchronizationand Propagation SpeedUncertaintiesConsidering the challenges identified in Section 1.3.1, in this chapter we propose anew algorithm for UWL. In particular, our algorithm takes into account anchor andUL node mobility as well as propagation speed uncertainties, can function with onlyone anchor node, and includes time-synchronization of nodes. These abilities areimportant to enable localization under varying conditions, such as static or mobilenodes, in shallow or deep water, and when nodes are submerged for short or longperiods of time. Our setting includes several anchor nodes at known locations andone or more UL node, whose location is estimated. We assume that UL nodes areequipped with means to self-evaluate their speed and direction such as accelerometerand compass. Since such inertial systems are relatively light weight and inexpensive,there is a large variety of applications that satisfy this assumption for UL nodes.These include AUV, remotely operated underwater vehicles (ROV), manned vehi-cles, and divers [34]. Operating in tandem with self-localization systems, our algo-rithm makes use of the permanent movements of underwater nodes. It also performsa self-evaluation of localization accuracy, by estimating the propagation speed andchecking its validity, relying on known model boundaries for it. According to thestructure of the proposed algorithm we refer to it as sequential time-synchronizationand localization (STSL) algorithm. We demonstrate the advantages of the STSL al-gorithm by simulation comparisons with two benchmark localization methods, whichreveal significant localization errors for the latter if nodes are not time-synchronizedor the propagation speed is not accurately estimated. Furthermore, we formalize theCrame?r-Rao lower bound for UWL and show that it is well approached by the STSLalgorithm. Considering the problem of accurately modeling the UAC in a simula-tion environment, we also conducted a sea trial in August 2010 in Haifa, Israel, andpresent results that confirm the performance of the proposed algorithm under realconditions.The remainder of this chapter is organized as follows. In Section 2.1, we brieflysummarize the general structure of our algorithm and the intuition behind it. InSection 2.2, we introduce the system model, followed by a detailed description anddiscussion of our STSL algorithm in Section 2.3. Crame?r-Rao lower bounds perti-22Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertaintiesnent to our problem are derived in Section 2.4. Simulation and sea trial results arepresented and discussed in Sections 2.5 and 2.6, respectively. Finally, conclusions aredrawn in Section IntuitionThe intuition behind our approach is the use of relative speed and direction infor-mation available at the mobile UL node to compensate for node mobility. In doingso, three or more range measurements obtained at different times and locations canbe combined for 2-D localization. This approach allows us to readily include thelocalization procedure as part of the operation of a communication network. Morespecifically, instead of using designated localization packet exchange (which is nec-essary if node mobility is not compensated), we rely on periodic packet exchangebetween the network nodes. This characteristic renders our approach more flexibleand easy to integrate into a UWAC system and also reduces communication overhead.The STSL algorithm uses a two-step approach, in which first nodes are time-synchronized and then location is estimated. In both steps, the measured time offlight of packets exchanged between anchor and UL nodes and self-localization dataobtained at UL nodes are linked to the unknown location, synchronization (clock skewand offset), and propagation speed parameters through linearized matrix equations.Our algorithm is modular in the sense that both time-synchronization and localizationsteps can be readily replaced with alternative solutions (as we do in this chapter tobenchmark the STSL performance).Before describing the STSL algorithm in detail, we next present the system modeland assumptions used in this work.2.2 System Setup and AssumptionsOur setting includes one or more UL nodes directly connected to L ? 1 anchor nodes,which have means to accurately measure their time-varying 2-D location and transmitit to the UL node. Both UL and anchor nodes operate in a time-slotted UWACnetwork, where nodes transmit at the beginning of globally established time slots asin, for example TDMA, slotted handshake [60] or slotted Aloha [90] transmission2.Since usually UL nodes perform localization independently of each other, we considerlocalization of one UL node in the following.We are interested in estimating the 2-D location of the UL node in terms of theuniversal transverse mercator (UTM) coordinates jN = [jxN , jyN ]T (the subscript Nbecomes clear below) after a pre-defined localization window of duration W time-slots, which without loss of generality starts at the UL node local time tUL = 0. We2We note that a relaxation of this assumption is possible by having anchor nodes time-stamptheir packets, thereby informing the UL node of the transmission time.23Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertaintiesassume that nodes are not time-synchronized. Suppose that the local time at the ULnode tUL corresponds to the time tl according to the local clock of anchor node l,and let Sl and Ol denote the clock skew and offset of the UL node relative to node l,l = 1, . . . , L, which are constant within the localization window. Then,tUL = tl ? Sl +Ol . (2.1)We assume that the time-synchronization error is small relative to the globally es-tablished time-slot duration, such that a node can match a received packet with thetime slot it was transmitted in. Thus, local transmission times of received packetsare known and time stamps of packets are not required. We note that long time slotsare common in UWAC [8] due to the low propagation speed underwater, which ismodeled between 1420 m/sec and 1560 m/sec [5].For localization we rely on a two-way packet exchange between the anchor nodesand the UL node. Let N be the total number of packets exchanged between the ULnode and the L anchor nodes during the localization window W . For convenience,we define the sets N a and N b for enumerating the packets to and from the UL node,respectively, such that N a ? N b = N = {1, . . . , N}. Denote li the index of theanchor node that transmits (i ? N a) or receives (i ? N b) the ith packet, and Ti andRi the transmission and reception local times of this packet. Also denote T pdi thepropagation delay for packet i according to local clock of anchor node li. (Note thatthe propagation delay according to the clock of the UL node is T pdi ? Sli). Considerpacket i ? N a transmitted at local time Ti and detected by the UL node at anchornode li local time Ti + T pdi + ?i, where ?i is a propagation-delay-measurement-noisesample. Also, consider packet i ? N b received by anchor node li at local time Ri + ?iand transmitted at anchor node li local time Ri + ?i ? T pdi . Then, following therelation in (2.1), the above time variables are related byRi = Sli(Ti + Tpdi + ?i) +Oli , i ? N a (2.2a)Ti = Sli(Ri + ?i ? Tpdi ) +Oli , i ? N b . (2.2b)Since for i ? N a the UL node measures Ri and is aware of Ti via packet association(recall we assume transmissions in globally established time slots), and since fori ? N b the UL node records Ti and is informed of Ri through communication withanchor node li, the UL node is able to construct equations (2.2a) and (2.2b). Formathematical tractability and formulating a practical algorithm, we assume that thenoise ?i is a zero-mean i.i.d. Gaussian random variable with variance ?2. Since morecomplicated models, such as mixture models with one component having non-zeromean, would likely be a more faithful noise representations, we study the effect ofmodel mismatch in Section 2.5.Considering a dynamic scenario in which all nodes permanently move either byown means or by ocean current, we assume that the UL node uses an inertial systemto self-estimate its speed and direction. During the localization window, the inertial24Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertaintiessystem provides N position estimations j?i = [j?xi , j?yi ]T for the true locations ji of theUL node at the time of transmission (i ? N b) or reception (i ? N a) of the ith packet.These locations are translated into a series of motion vectors, ?i,i? = [d?i,i? , ??i,i? ]T ,where d?i,i? and ??i,i? are the distance and angle between two self-estimated locationsj?i and j?i? , respectively. More specifically, assuming depth differences to be small(extensions are straightforward but not included here for brevity), the elements of asingle motion vector ?i,i? ared?i,i? = ?j?i ? j?i??2 , tan(??i,i?) =j?yi ? j?yi?j?xi ? j?xi?. (2.3)While we do not directly use the self-estimated locations j?i, whose errors accumulatewith time, we rely on the accuracy of the motion vectors for all packet pairs i, i?transmitted or received by the UL node during the localization window. That is, weassume that for i, i? ? N the estimated distance d?i,i? equals the true distance di,i? andthat ??i,i? equals the true angle ?i,i? . We note that this assumption sets limits on thevalue of W , which is determined by the specifications of the inertial system in use.We are now ready to present the STSL algorithm for UWL.2.3 The STSL AlgorithmWe are interested in accurately estimating the position jN of the UL node at theend of the localization window. In this section we first formalize the optimizationproblem for estimating jN , using ToA measurements obtained from received packetsand taking into account inertial system information. Then, we derive a sub-optimalsolution, namely the STSL algorithm, in which first nodes are time-synchronized andthen localization is performed.According to the system description in the previous section, the location pi ofanchor node li when transmitting (i ? N a) or receiving(i ? N b)the ith packet, thetransmission and reception local times Ti and Ri, respectively, and the motion vector?i,i? between locations ji and ji? are available at the UL node. Hence, denoting thepropagation speed c, the UWL problem can be formulated asj?N = arg minjN?i?N(?liTpdi ?1c?ji ? pi?2)2(2.4a)s.t. 1420m/sec ? c ? 1560m/sec (2.4b)Ri = Sli(Ti + Tpdi ) +Oli , i ? N a (2.4c)Ti = Sli(Ri ? Tpdi ) +Oli , i ? N b (2.4d)di,i? = ?ji ? ji??2 , i, i? ? N (2.4e)tan(?i,i?) =jyi ? jyi?jxi ? jxi?, i, i? ? N , (2.4f)25Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertaintieswhere the factor ?li in (2.4a) accounts for the difference between Tpdi (according toanchor node li local clock) and the actual propagation delay of packet i. Note thatproblem (2.4) is different from conventional localization problems due to the time-synchronization constraints (2.4c) and (2.4d), and due to the unknown sound speedc. Since (2.4) is a non-convex problem, we device our STSL algorithm as a pragmaticsolution to the localization problem at hand, and we will compare its performance tothe Crame?r-Rao lower bound (CRLB) associated with estimating the desired locationjN as well as the unknown parameters Sl and Ol, l = 1, . . . , L, and c.In the following we describe the details of our STSL algorithm starting from thetime-synchronization step and followed by the localization step.2.3.1 Step 1: Time-SynchronizationThe objective of the time-synchronization step is to provide estimates of the prop-agation delays T pdi , ?i ? N . This is accomplished by two-way packet exchange,obtaining equations of type (2.4c) and (2.4d). However, due to the permanent mo-tion of nodes in the channel, propagation delays T pdi , i ? N a, and Tpdj , j ? N b,might not be equal, and thus (2.4c) and (2.4d) cannot be readily compared. Com-mon time-synchronization approaches for UWAC deal with this problem by lettingthe receiving node respond immediately to limit any possible movements (e.g., [14]).However, such a requirement limits the scheduling protocol. We choose a differentapproach and apply a quantization mechanism to allow for differences in the propa-gation delay of separate packets and to enable time-synchronization per anchor nodemaking use of the ongoing network communications.Quantized Representation of Node MovementsIn the quantization step, the locations of the UL node and the anchor nodesare quantized so that multiple ToA measurements from two-way communication areassociated with the same pair of quantized locations. More specifically, consider thetwo packets n,m, n ? N a, m ? N b. If the two sets of UL node locations jn, jmand anchor node locations pn, pm with ln = lm = l are associated with the samequantized location k? and ul,? of the UL node and anchor node l, respectively, weassume that T pdn = T pdm and (2.2a) and (2.2b) can be combined as we show furtherbelow. The variables ? and ? are used to enumerate quantized locations.To quantize the locations of anchor nodes, we introduce subsets Ul,? ? N includingall packets associated with the same anchor node l such that for each pair of packetsn,m ? Ul,? , ?pn ? pm?2 < ?, where ? is a fixed threshold. Next, we associatelocation pi, i ? Ul,? , with the quantized location ul,? . Similarly, to quantize locationsof the UL node we form subsets of packets K? ? N such that for each pair of packets26Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertaintiesn,m ? K?, dn,m < ?, and associate location j?i, i ? K?, with the quantized locationk?. We note that a single packet can be associated with multiple subsets Ul,? and K?.There is a tradeoff for choosing ?. If ? is too large, the assumption of identicalpropagation delay is notably flawed and thus the accuracy of the time-synchronizationprocess is low. If ? is too small, there might not be enough two-way ToA measure-ments associated with each pair of quantized locations ul,? and k?, and again accuracyof the time-synchronization process is degraded, as we further discuss below.Estimating the Clock Skews and OffsetsWe now use the quantized locations to estimate clock skews Sl and offsets Ol,l = 1, . . . , L. Let us define subsets N al ? N a and N bl ? N b, with cardinality Nal andN bl , respectively, including all packets associated with anchor node l. Consider thepair of packets n,m, n ? N al , m ? N bl , for which locations pn and pm are mappedonto the same quantized location ul,? , and locations j?n and j?m are mapped onto thesame quantized location k?. We assume that for each anchor node l, this mappingresults into Ml pairs of equations (2.2a) and (2.2b). Clearly, Ml increases with thequantization threshold, ?. As stated above, we neglect the differences between thepropagation delays T pdn and T pdm in (2.2a) and (2.2b) and thus obtain Ml equationsof the formRn + TmSl? 2OlSl= Tn +Rm + ?n + ?m, n ? N al , m ? N bl . (2.5)Note that equations of type (2.5) are introduced separately for each anchor node l.This is because the estimated clock skew and offset are different for each l.Introducing the variable vector ?l = [?l(1),?l(2)]T = [ 1Sl ,OlSl]T , we express (2.5)as the linear matrix equationBl?l = bl + l (2.6)for each anchor node l, where Bl is an [Ml ? 2] matrix with rows [Rn + Tm,?2],and bl and l are column vectors of appropriate length with elements Tn + Rm and?n + ?m, respectively, with n ? N al , m ? N bl . Next, we apply the LS estimator??l =(BTl Bl)?1BTl bl (2.7)for each anchor node l. By (2.7), the covariance matrix of ??l is [91]Q? = ?2(BTl Bl)?1 , (2.8)whose main diagonal elements are proportional to 1Ml and1M2l, respectively. Hence,for largeMl the estimates ??l(1) and ??l(2) are expected to have much smaller variancethan ?2.27Chapter 2. UWL with Time-Synchronization and Propagation Speed UncertaintiesEstimating Propagation DelaysAfter estimating ?l(1) and ?l(2), the quantized locations are no longer in use andwe return to our initial objective, which is to estimate the propagation delay. Thus,localization accuracy of the STSL algorithm is not limited to ?. Considering (2.2),for packets n ? N al and m ? N bl , the UL node estimates the propagation delay asT? pdn = Rn??l(1)? ??l(2)? Tn, n ? N alT? pdm = ??l(2)? Tm??l(1) +Rm, m ? N bl . (2.9)We observe from (2.9) that the propagation delay estimation error is a functionof both ToA measurement error, ?i, and clock skew and offset estimation errors.However, since during the localization window Rn and Tn are bounded by W , thevariances of Rn??l(1)? ??l(2), n ? N al , and ??l(2)? Tm??l(1), m ? N bl , are expected tobe much smaller than ?2. Thus, we use the approximation T? pdi = Tpdi + ?i in thefollowing.2.3.2 Step 2: LocalizationWe now introduce the localization step of the STSL algorithm. This step is performedimmediately after time-synchronization, using propagation delay estimations (2.9).The objective of the localization step of the STSL algorithm is to estimate the ULnode UTM coordinates jxN and jyN at the end of the localization window W . For thispurpose, we adopt the common approach to linearize the estimation problem [92],and first estimate the transformed variable vector ?N =[(jxN)2 + (jyN)2 , jxN , jyN]T.Define?i,i? =d?i,i??1 + tan(??i,i?)2?i,i? = ?i,i? tan(??i,i?) , (2.10)and assume d?i,i? and ??i,i? in (2.3) to be equal to di,i? and ?i,i? from (2.4), respectively(recall that we rely on the accuracy of the motion vectors during the localizationwindow). Thus,jxi? = jxi ? ?i,i? , jyi? = jyi ? ?i,i? , i, i? ? N . (2.11)Furthermore, we have from (2.4) thatT? pdi =1?lic?ji ? pi?2 + ?i , i ? N . (2.12)Since c is unknown, and assuming small differences between ?l such that ?l?l??= 1, l, l? =1, . . . , L (a relaxation of this assumption is given further below), we reduce the set ofN equations (2.12) to N ? 1 equations, which together with (2.11) can be written as?N,i ? ?N = aN,i + N,i, i = . . . , N ? 1 (2.13)28Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertaintieswith vector ?N,i = [?N,i(1), ?N,i(2), ?N,i(3)], whereaN,i =(T? pdi)2 ((pxN)2 + (pyN)2)?(T? pdN)2((pxi + ?N,i)2 + (pyi + ?N,i)2),?N,i(1) =(T? pdN)2?(T? pdi)2,?N,i(2) = 2(T? pdi)2pxN ? 2(T? pdN)2(pxi + ?N,i) ,?N,i(3) = 2(T? pdi)2pyN ? 2(T? pdN)2(pyi + ?N,i) , (2.14)and N,i is the noise component originating from the noisy estimations (2.9). For thelocalization window W , we construct an [(N ? 1)? 3] matrix A with rows ?N,i andvectors a and  with elements aN,i and N,i, respectively. Then, the (N?1) equations(2.13) are arranged inA?N = a+  . (2.15)The elements of the error vector  depend on the elements of ?N . Thus, directestimation of ?N from (2.15) will result in low accuracy. Hence, we follow [92] andoffer a two-step heuristic approach in which first we get a coarse estimate of ?N , andthen we perform a refinement step. The coarse estimate is given by??LSN =(ATA)?1Aa . (2.16)We note that N,i from (2.13) can be formalized as ?ifN,i, where fN,i is a function ofthe elements of ?N , not given here for brevity. Thus, N,i are i.i.d random variablesand the covariance matrix ?2QN of  is a diagonal matrix whose ith diagonal elementequals ?2f 2N,i. Using ??LSN from (2.16) to estimate the elements of fN,i, i = 1, . . . , N?1,we estimate QN as Q?N . The refined estimate of ?N follows as??WLSN =(AT Q??1N A)?1AQ??1N a , (2.17)with the error covariance matrix [91]Q??N =(AT Q??1N A)?1. (2.18)Finally, we use the inner connection of the elements of ?N to estimate the locationvector jN . Defining GN =????WLSN (2) ??WLSN (3)1 00 1??, where ??WLSN (i) is the ith element of??WLSN , we obtainGNjN = ??WLSN + N , (2.19)29Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertaintieswhere N is a [3? 1] estimation noise vector of ??WLSN . Using (2.19), Q??N from (2.18)and ??WLSN from (2.17), the WLS estimator of jN isj?N =(GTNQ???1N GN)?1GNQ???1N ??WLSN , (2.20)whose elements j?N(1) = j?xN and j?N(2) = j?yN are the desired location coordinates.We would like to mention that if assumption ?l?l??= 1 used to obtain (2.13) does nothold, the localization process can be performed on a per-anchor-node basis. To thisend, packet index i in (2.13) is limited to packets transmitted or received by the sameanchor node, and the number of equations (2.13) is reduced to N?1L (assuming equalnumber of transmissions pre anchor node in the network). Since L is expected to besmall (we use L = 2 in our simulations and sea trial described below), the accuracyof the localization process is not expected to deteriorate much. Then, the UL nodelocation at the end of the localization window can be estimated by combining per-anchor-node based estimations j?N from (2.20) using data fusion techniques, cf., [93].Since per-anchor-node based estimations j?N are independent of ?l, such combinationis not affected by mismatch of ?l between anchor nodes.2.3.3 ExtensionsIn this section we introduce two extensions for the above location estimation. Thefirst is a refinement step in which we iteratively improve the location estimation(2.20). The second is a self-evaluation process to test the accuracy of the localizationprocess.Iterative RefinementThe accuracy of estimation (2.20) depends on the quality of the coarse estimate??LS from (2.16), used to construct the error covariance matrix, Q?N . We now follow[94] and propose an iterative refinement procedure in which the accuracy of Q?N isimproved.In the kth step of our iteration, vector j?N,k is estimated using (2.20) from whichthe vector ??N,k is constructed. Next, in the (k + 1)th step ??N,k replaces ??LSN in theconstruction of Q?N . As a stopping criterion, we use the covariance matrix of the kthestimation (2.20),Q???N,k =(GTNQ???1N GN)?1. (2.21)Since the determinant, |Q???N,k|, is directly proportional to the estimation accuracy [91],the iteration stops when the absolute value of |Q???N,k| ? |Q???N,k?1| is below some em-pirically chosen threshold, ?iter, or if the number of iterations exceeds its maximum,Niter. While we could not prove the convergence of this process, we demonstrate itby means of numerical simulations in Section 2.5.30Chapter 2. UWL with Time-Synchronization and Propagation Speed UncertaintiesSelf-Evaluation of Localization PerformanceIn this section, we describe a binary test for self-evaluating localization accuracy.It can be used to adjust STSL parameters, such as the localization window W , forrefining the localization procedure, such as data fusion of per-anchor-node basedlocalization (see discussion after (2.20)), or to decide whether an UL node can be usedas a new reference node. For the latter application localization should be extended totracking though, to make sure that location estimates remain accurate when nodesmove. Our self-evaluation test relies on a widely used model that bounds propagationspeed underwater between 1420 m/sec and 1560 m/sec [5]. In particular, given anestimate of the propagation speed, cest, the binary test output ? is computed as? ={1, if 1420 ? cest ? 15600, otherwise}, (2.22)and ? = 1 and ? = 0 indicate accurate and non-accurate localization, respectively.Using (2.12) and since ?l are expected to be close to 1, we obtain the propagation-speed estimate ascest =1NN?i=1?j?i ? pi?2T? pdi, (2.23)where j?i, i = 1, . . . , N ? 1, follow from j?N in (2.20) using relation (2.11). Differentfrom traditional self-evaluation techniques involving the broadcast of a confidenceindex obtained from comparing the measured propagation delay to the estimatedone (e.g. [95, 30]), the advantage of the our method lies in the comparison of cestto a given model of propagation speed, which is independent of the estimation. Ournumerical results (see Section 2.5) show that when localization error is accurate (i.e.,below 10 m), we obtain ? = 1 in more than 99% of the cases, and when localizationerror is non-accurate (i.e., above 10 m), ? = 0 results in 90% of the cases. If morereliable evaluation performance is needed, the proposed test could be combined withother self-evaluation tests.2.3.4 ScalabilityWhen more network nodes are added, often fewer packets are transmitted per node.Hence, performances of both time-synchronization and localization degrade with in-creasing number of UL nodes, NUL. Furthermore, since time-synchronization is per-formed per-anchor node, its performance degrades with increasing number of anchornodes, L. However, since the number of propagation delay measurements, avail-able for localization, increases with L, performance of the localization step by itselfimproves with L. However, since localization depends on the output of the syn-chronization step, the overall performance may improve or degrade with increasingnumber of anchor nodes. In summary, scalability of the STSL algorithm is closelyrelated to the scalability of the underlying communications protocol.31Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties2.3.5 Pseudo-Code for STSLThe operation of the STSL algorithm is summarized in the pseudo-code in Algo-rithm 1. For simplicity, the quantization mechanism introduced in Section 2.3.1 isnot included, and we start when positions are already quantized into locations ul,? andk?. First, equations (2.5) are formed, and an LS estimator is used to estimate clockskew and offset for each anchor node l (lines 2-9). Then, the time-synchronizationstep is concluded by estimating propagation delays for each transmitted or receivedpacket (line 12). The localization step begins with forming equations (2.13) (line 13),followed by an initial LS estimator (line 15). Then, an iterative procedure beginswhere in each step the covariance matrix Q?N and location j?N,k are estimated (lines18-19). The latter is then used to refine the initial estimation by iteratively formingmatrix Q?N till convergence is reached (lines 19-23). The algorithm performs a seriesof LS and WLS estimations with complexity of O (N3 +N) and is executed only onceat the end of the localization window. A software implementation of the algorithmcan be downloaded from [96].2.4 Crame?r-Rao Lower BoundFor the purpose of gauging the performance of the STSL algorithm, in this sectionwe develop analytical expressions to lower bound the performance of any unbiasedUWL estimator, assuming nodes not to be time-synchronized and propagation speedunknown. We start with general expressions for the CRLB, and then apply it to ourspecific localization problem.2.4.1 General Crame?r-Rao Lower BoundConsider a measurement vector y = h(pi,?) + n, where n is a noise vector, andh(pi,?) is some function of a vector of wanted variables, pi, and a vector of nuisancevariables, ?. For an unbiased estimator, the variance of the nth element of pi, pin,can be bounded by the CRLB [97]E[(p?in ? pin)2]? CRB(pin) , (2.24)where CRB(pin) =(I?1)n,n and I is the Fischer information matrix (FIM), whose(n,m)th element isIn,m = ?Ey[?2 lnP (y|pi)?pin?pim], (2.25)and P (y|pi) is the probability density function of y given pi. To calculate P (y|pi) oneneeds to average the nuisance variables, ?, i.e., P (y|pi) = E? [P (y,?|pi)], which makesit hard to calculate (2.25), since often P (y,?|pi) cannot be expressed. Therefore,32Chapter 2. UWL with Time-Synchronization and Propagation Speed UncertaintiesAlgorithm 1 Estimate jN1: {Step 1: Time-synchronization}2: for (l = 1, . . . , L) do3: for (n ? N al , m ? N bl ) do4: if (pn,pm ? Ul,?) ? (j?n, j?m ? K?) then5: Form equations (2.5) using Tn, Rn, Tm and Rm6: end if7: end for8: Estimate Ol and Sl using (2.7)9: end for10: {Step 2: Localization}11: for (i = 1, . . . , N) do12: set T? pdi using (2.9)13: Form equations (2.13)14: end for15: Estimate ??N,1 using (2.16)16: for (k = 1 to Niter) do17: Estimate Q?N using ??N,k18: Estimate j?N,k using (2.20)19: Construct matrix Q???N,k using (2.21)20: if (|Q???N,k| ? |Q???N,k?1| ? ?iter) then21: Return22: end if23: Construct ??N,k+1 using j?N,k24: end forinstead of CRB(pin), the modified Crame?r-Rao bound MCRB(pin) =(I??1)n,nisoften used [98], whereI?n,m = ?Ey,?[?2 lnP (y|pi,?)?pin?pim]. (2.26)In [98] it was shown thatCRB(pin) ? MCRB(pin) . (2.27)Hence, MCRB(pin) may be too loose to compare with.A different approach would be to consider the nuisance variables ? as part of theestimation problem. That is, we consider a new variable vector ? = [piT ,?T ]T andformalize CRB(?n) forIn,m = ?Ey[?2 lnP (y|?)??n??m]. (2.28)33Chapter 2. UWL with Time-Synchronization and Propagation Speed UncertaintiesWe note that CRB(?n) does not bound E[(p?in ? pin)2]but E[(??n ? ?n)2]. Thus,it can only serve as a lower bound for estimators which estimate both pi and ?.2.4.2 Application to STSLSince the STSL algorithm includes a sequence of LS and WLS estimators, it is anunbiased estimator. Thus, we next apply the MCRB(pin) and CRB(?n) bounds forour STSL algorithm. We consider the measurement vector in (2.2) for which y = Ri,pi = [jxN , jyN ], ? = [S1, . . . , SL, O1, . . . , OL, c], and n is as ?i in (2.2). Then, we haveE[(j?xN ? jxN)2+(j?yN ? jyN)2]? CRB(pi1) + CRB(pi2) . (2.29)We note that the variance of y depends on the clock skew, Sli . Thus, although ?i isassumed Gaussian, the often used simplification for the CRB in the Gaussian case(cf. [97]) cannot be used to solve (2.26) and (2.28).Following our discussion in Section 2.4.1, we consider the alternative CRLB for-mulationsCRB = CRB(?1) + CRB(?2) , MCRB = MCRB(pi1) + MCRB(pi2) , (2.30)and compare?MCRB and?CRB to?err =?E[(j?xN ? jxN)2+(j?yN ? jyN)2]. (2.31)2.5 Simulation ResultsIn this section, we present and discuss simulation and sea trial results demonstratingthe performance of the STSL algorithm in different environments. We conducted10, 000 Monte-Carlo simulations of a scenario with two anchor nodes and one ULnode, communicating in a simple TDMA fashion. The three nodes were placeduniformly in a square area of 1 ? 1 km2 and moved between two adjacent packettransmission times at uniformly distributed speed and angle between [?5, 5] knotsand [0, 360] degrees, respectively. We added a zero mean i.i.d. Gaussian noise withvariance ?2 to each of the ToA estimations [see (2.2)]. Furthermore, considering theresults in [99] we added a zero mean i.i.d. Gaussian noise with variance 1 m2 toeach of the distance elements of the motion vectors [see (2.3)] while regarding theirangle components to be accurate. To simulate time-synchronization errors the clockof each of the three nodes had a Gaussian distributed random skew and offset relativeto a common clock with mean values 1 and 0 sec and variances 0.001 and 0.5 sec2,respectively.34Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties30 35 40 45 5010?210?11001/?2 [dB]? err[m]  STSLSTSL?mixMultilaterationJLSCRBMCRBFigure 2.1: ?err from (2.31) as a function of 1/?2. Sound speed is known and all nodesare time-synchronized. Vertical bars show 95% confidence intervals of the simulationresults for STSL.We used a quantization threshold ? = 38 meters and a localization window ofW = 20 time-slots. The time-slot duration was selected Tslot = 5 seconds, consideringthe long propagation delay in the UAC (e.g., 4 sec for a range of 6 km). We comparethe performance of the STSL algorithm with those of the multilateration method [27]and the method proposed in [92], which we refer to as the joint localization and syn-chronization (JLS) algorithm. Both benchmark methods use an assumed propagationspeed c?. Furthermore, while the JLS algorithm performs joint time-synchronizationand localization (assuming anchor nodes are time-synchronized but the UL node isnot), the multilateration method assumes all nodes to be time-synchronized. Sinceboth benchmark methods assume static nodes, we used a different simulation envi-ronment for them such that a fair comparison with the STSL algorithm is possible.The simulation environment for the benchmark methods considers fixed nodes andadds virtual anchor nodes according to node movements in the original simulationscenario (i.e., the one used to test the performance of the STSL algorithm). Consider,for example, an anchor node l moving between locations pl1 and pl2 while commu-nicating with a static UL node. To test the benchmark methods, such a scenariowould change into a scenario where two static anchor nodes, l1 and l2, are locatedat pl1 and pl2 , respectively. Allowing a fair comparison between the three testedlocalization methods, the virtual anchor nodes, l1 and l2, have the same local clockas that of the real anchor node l. The implementation code of the STSL algorithmcan be downloaded from [96].First, we consider a scenario where c = c? = 1500 m/sec and all nodes are time-synchronized. Figure 2.1 shows ?err from (2.31) as a function of 1?2 for the three35Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties0 0.1 0.2 0.3 0.4 0.5 0.6 0.710?310?210?1100101102esync [%]? err[m]  STSLMultilaterationJLSFigure 2.2: ?err from (2.31) as a function of esync. Sound speed is known and 1?2 =46 dB. Vertical bars show 95% confidence intervals of the simulation results for STSL.methods and the CRB and MCRB from (2.30). For clarity, here and in the followingwe show 95% confidence intervals in error bars only for the STSL algorithm. Theresults show that both benchmark methods achieve better performances than theSTSL algorithm. This is mainly because STSL redundantly estimates c as well asclock offsets and skews, which introduces errors. This is also why the multilaterationmethod achieves slightly better performance than the JLS protocol method. We notethat the MCRB is slightly lower than the CRB and both bounds are quite close tothe STSL error, which implies that although STSL is a heuristic estimator it achievesgood localization results. To show the effect of possible mismatch of our model forthe measurement noise ?i (see (2.2)), Figure 2.1 also includes results for STSL-mix,in which ?i is modeled as a mixture of two distributions. The first distribution (withweight 0.9) is a zero mean Gaussian with variance ?2 and the second (with weight0.1) is a Rayleigh(?) distribution, which accounts for multipath propagation [86].From Figure 2.1, we observe that the performance of STSL-mix decreases comparedto that in the Gaussian-noise case, which is mainly due to the non-zero mean of noise.However, this degradation is fairly moderate demonstrating some robustness of STSLto model mismatch.In Figure 2.2 we compare ?err for the three methods when c = c? = 1500 m/sec, butnodes are not time-synchronized and 1?2 = 46 dB, as a function of esync =S?W+O??WW ,where S? and O? is the average of Sl and Ol, l = 1, . . . , L, respectively. While theperformance of the STSL algorithm is hardly affected by the synchronization error(compared to the results in Figure 2.1), the JLS protocol method, designed for time-synchronized anchor nodes, and the multilateration method suffer from significantestimation errors even for small synchronization errors.36Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties0 10 20 30 40 50 60 70 8010?310?210?1100101102|c - c?| [m/sec]? err[m]  STSLMultilaterationJLSFigure 2.3: ?err from (2.31) as a function of |c? c?|. All nodes are time-synchronizedand 1?2 = 46 dB. Vertical bars show 95% confidence intervals of the simulation resultsfor STSL.We now compare performance when c is chosen with uniform distribution betweenthe model boundaries, 1420 m/sec and 1560 m/sec, and the two benchmark methodswere still given the nominal value c? = 1500 m/sec. To understand the effect ofmismatched propagation-speed information on localization accuracy, we compare ?errfrom (2.31) when all nodes are time-synchronized. The results are shown in Figure 2.3as a function of |c ? c?|, again for 1?2 = 46 dB. We observe that for both benchmarkmethods, ?err dramatically increases even for a small difference of |c? c?| = 10 m/sec,which motivates the need to accurately estimate c in UWL. Furthermore, comparedto the results of Figure 2.1 the STSL is almost unaffected by the variations of c.Next, we consider the practical case where all nodes are not time-synchronized(same scenario as for Figure 2.2) and c is unknown (same scenario as for Figure 2.3).We study two of the properties of the STSL algorithm, namely the convergence ofthe refinement iterative process discussed in Section 2.3.3 and the self-evaluationprocess discussed in Section 2.3.3. In Figure 2.4, we demonstrate the convergence ofthe refinement iterative process by showing ?err from (2.31), averaged over all clockoffsets and skews and c instances, as a function of the number of iteration steps andseveral values of 1?2 . The results indicate that a significant performance improvementis achieved after only a few iteration steps. In Figure 2.5 we show the empiricalprobability density function (PDF) of the estimated propagation speed, cest, from(2.23) when c = 1500 m/sec. The results are shown for two cases: 1) when ?err ? 10 mand 2) when ?err ? 10 m. The results show that for small values of ?err, in more than99% of the cases, cest is inside the model boundaries (i.e., 1420 ? cest ? 1560), witha standard deviation of less than 10 m/sec. For large values of ?err, cest seems to be37Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties1 2 3 4 5 6 7 8 9 1010?210?1100101102? err[m]Number of iterations  1/?2 = 30 dB1/?2 = 40 dB1/?2 = 50 dBFigure 2.4: ?err from (2.31) for the STSL algorithm as a function of number ofiteration steps.almost uniformly distributed, with only 10% of the estimations being inside the modelboundaries. However, for some applications (e.g., localization in sparse networks) thismissed-detection probability may be too large. Thus, we conclude that cest can serveas a good indicator to confirm accurate localization, but may be used to complementother self-evaluation techniques to identify non-accurate localization.Finally, in Figure 2.6 we consider the same scenario as for Figure 2.4 and show ?errfrom (2.31) as a function of 1?2 . For clarity, since results for STSL are similar to thoseshown in Figure 2.1, error bars are omitted. We observe that while both benchmarkmethods suffer from a significant error floor, the error for the STSL algorithm de-creases with 1?2 and is the same as in Figure 2.1. Hence, the algorithm compensates forboth synchronization and propagation speed uncertainties. To demonstrate the rela-tion between the number of anchor nodes, L, and the number of UL nodes, NUL (seediscussion in Section 2.3.4), in Figure 2.6 we also include results for L = 3, NUL = 1(STSL, L = 3) and L = 2, NUL = 2 (STSL, 2UL), which had similar standard de-viation to the case of L = 2, NUL = 1. We note that since multilateration doesnot include time-synchronization, and since JLS performs joint time-synchronizationand localization, clearly their performance improves with L and degrades with NUL.Results show that, as expected, also performance of the STSL algorithm slightlyimproves with L and decreases with NUL.38Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties1100 1200 1300 1400 1500 1600 1700 180000.  ?err< 10m?err>10mFigure 2.5: Empirical PDF of cest for c = 1500 m/sec.2.6 Sea Trial ResultsIn this work we assumed 1) node?s clock skew and offset are time-invariant withinthe localization window, 2) propagation speed is time and space invariant for smalldepth differences, 3) propagation delay measurements are affected by a zero-meanGaussian noise, and 4) node movements are relatively slow such that quantization ofnode locations is possible. While the first assumption depends on the system clock,the second and the third depend on the channel. To verify our assumptions andconfirm our results we tested the STSL algorithm in a sea trial along the shores ofHaifa, Israel in August 2010.The sea trial included three drifting vessels, representing three mobile nodes, andlasted for Texp = 300 minutes. In Figure 2.7, we show the UTM coordinates of thenodes during the sea trial. We note that node 3 needed to turn on its engines aroundtime slot 150, which explains the sudden change in its direction and speed. Eachnode was equipped with a transceiver, deployed at 10 meters depth, allowing UWACat 100 bps with a transmission range of 5 km. The nodes communicated in a TDMAnetwork with a time-slot of Tslot = 60 seconds, allowing significant node motionbetween transmission of each packet. Time-slot management was performed at eachnode using an internal clock. These internal clocks were manually time-synchronizedat the beginning of the experiment with an expected clock offset of up to one second.We also note that pre-testing of these clocks showed a clock skew of one second perday.We used GPS receivers as reference for the location of each node as well as itsinertial system to obtain motion samples [see (2.3)]. The localization error of theGPS-based reference locations was reported to be uniformly distributed between 039Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties30 35 40 45 5010?210?11001011021/?2? err[m]  STSLSTSL,L=3STSL,2ULMultilaterationJLSCRBMCRBFigure 2.6: ?err from (2.31) for time-synchronization and sound speed uncertainties.and 10 m. To test the effect of this uncertainty in the anchor-node location weconducted simulations similar to the scenario considered in Figure 2.1 with error-freeToA measurement but with anchor-node location uncertainties similar to those ofthe GPS receivers in use. The results showed that using our STSL algorithm suchuncertainty results in an average estimation error of 15 m. Thus, in the sea trial anylocation error below 15 m is considered accurate.2.6.1 Channel and System CharacteristicsAt the beginning and end of the sea trial we measured the propagation speed in waterusing a measuring probe. Both measurements showed that the propagation speed cwas bounded in between 1552 m/sec (for depth of 40 m) and 1548 m/sec (for depthof 1 m) and was on average 1550 m/sec. The small variance of the measurementsof c confirms our assumption that the propagation speed can be considered fixedthroughout the localization window. In the following, for performance evaluation weconsider c = 1550 m/sec, which is within the boundaries of our model (see Section 2.2)but is different from the commonly used value of 1500 m/sec.In Figure 2.8 for each pair of nodes we show T? pddiff , which is the time differencebetween propagation delay estimations at both sides of the communication link in asingle set of receiver-transmitter quantized locations, measured directly from (2.2a)and (2.2b) neglecting the clock skew and offset. For example, for a two-way packettransmission between the quantized locations k? and ul,? with propagation delayestimations T? pd1 and T?pd2 , T?pddiff = |T?pd1 ? T?pd2 |. We note that if nodes are time-synchronized, we would expect T? pddiff to be on the same order of the length of theimpulse response, which was measured as 20 msec on average and did not exceed40Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties20004000600010002000300040000100200300 UTM X (offset by 681000)UTM Y (offset by 3641000) MinutesNode 1Node 2Node 3Figure 2.7: Time-varying location of nodes in the sea trial.30 msec. However, the results show that T? pddiff increases with time and is much greaterthan 30 msec. This implies that nodes suffered from considerable clock skew andoffset. Furthermore, since the values of T? pddiff are different for each pair of nodes,the nodes skew and offset are different, which confirms with our system model (seeSection 2.2).2.6.2 ResultsIn the following, we compare the performance of the STSL algorithm in the sea trialwith that of a method aimed to solve a relaxed sequential time-synchronization andlocalization (R-STSL) problem, in which an a-priori propagation speed c? is given. Inthe R-STSL, time-synchronization is performed similar to the process described inSection 2.3.1, but the localization process is modified as c is known. The results areshown for all three nodes, where each time a different node was considered as the ULnode and the other two nodes were the anchor nodes. We measure the performancein terms of the Euclidean distance between the estimated location and the referenceGPS location, averaged over a sliding localization window of W time-slots, i.e.,??err =1TexpTslot?W + 1TexpTslot?n=W?j?n ? jn?2 , (2.32)where for each UL node location estimation j?n we used ToA and inertial systemmeasurements from time-slot n?W + 1 till n.In Figure 2.9, we demonstrate the effect of mismatched propagation speed, i.e.,c? 6= c, by showing ??err from (2.32) for W = 30 time-slots as a function of |c ? c?|,where c = 1550 m/sec. We note that although such choice of W seems large due41Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties0 50 100 150 200 250 30000.511.522.53Time slotTpd diff [sec]  Link (1,2)Link (1,3)Link (2,3)Average increase: 1.2msec / time?slotAverage increase: 13.5msec / time?slotAverage increase: 14.3msec / time?slotFigure 2.8: T? pddiff for all communication links as a function of time the long time slot duration, the number of transmissions for each node was only10, which is in the same order as considered in our simulations. The results showthat ??err significantly increases with |c ? c?| even for a relatively small difference of10 m/sec.This result, as well as the results in Figure 2.3, validate the need to consider thepropagation speed as an additional variable in UWL. In the following we consider amatched version of R-STSL (MR-STSL), i.e., when c? = c, which in the absence ofbenchmark localization methods that take into account time-synchronization uncer-tainties and availability of inertial system to track short-term node movements, canserve as a lower bound for the STSL.Finally, in Figure 2.10 we show the empirical cumulative density function CDF of??err, averaged over the three nodes, for STSL and MR-STSL andW = 10, 20, 30 time-slots, i.e., in a single localization window an average number of packet transmissionsof 3.3, 6.6, 10 for each node, respectively. We observe that both mean and varianceof ??err improve with W , however, at a cost of delay. We observe that since STSLestimates an additional variable, its performance is worse than that of MR-STSL.However, the difference is not significant. We note that the average ??err for STSLand W = 30 time-slots is 21.5 m, which is close to the expected localization accuracydue to the GPS location uncertainties. Therefore, STSL fully compensates the largeclock skew and offset shown in Figure 2.8, node movements and propagation speeduncertainty.42Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties0 20 40 60 80 100050100150200250300350|c - c?| [m/sec]?? err[m]  Node 1Node 2Node 3Figure 2.9: ??err from (2.32) as a function of |c ? c?| for W = 30 time slots. R-STSLmethod.2.7 SummaryIn this chapter, we considered UWL in the practical scenario where nodes are nottime-synchronized and permanently moving, and where the propagation speed isunknown. We introduced a localization algorithm which uses existing self-estimationsof motion vectors of nodes, assumed to be accurate for short periods of time. Thealgorithm utilizes the constant movements of nodes in the channel and relies onpacket exchange to acquire multiple ToA measurements at different locations. We alsopresented a method to self-evaluate the localization accuracy of the node. In addition,we used the applicable Crame?r-Rao lower bounds as references for the performanceof STSL. Considering the problem of establishing a faithful simulation environmentfor the UAC, alongside simulations we tested our algorithm in a designated sea trial.Both simulations and sea trial results demonstrated that our algorithm can cope withtime-synchronization and propagation speed uncertainties in a dynamic environment,and achieves a reasonable localization accuracy using no more than two anchor nodes.43Chapter 2. UWL with Time-Synchronization and Propagation Speed Uncertainties15 20 25 30 35 40 45 50 55 600. [m]P(?? err?x)  W=10 (STSL)W=20 (STSL)W=30 (STSL)W=30 (MR?STSL)Figure 2.10: Probability that ??err ? x for STSL and MR-STSL.44Chapter 3Spatially Dependent UnderwaterNavigationSince nodes constantly move in the UAC, UWL is only the first step towards under-water navigation. At the presence of motion, underwater navigation must include atracking scheme that uses UWL as an initial estimation and recursively updates thelocation of a TN. A key challenge in UT is motion irregularities, which makes it hardto determine the SSM. In this context, since the ocean current is usually spatiallycorrelated [100], it is reasonable to assume spatial dependencies between the drift mo-tions of network nodes in close proximity. In [101], it was argued that birds in a flockor school of fish obey simple rules for distance and speed relative to others in closeproximity. With this idea in mind, [102] assumes temporal and spatial dependenciesbetween the motion of nodes in an indoor environment and achieves good trackingperformance. For UWL, [103] exploited spatial dependencies for the collaborativelocalization of fleets of vertically sinking drifters assuming equal speed. For track-ing, an acoustic Doppler current profiler is used in [104] to measure ocean currentsat different depths and update the SSM accordingly. Ocean current is treated as aseparate state parameter in [105], and both the self-propelled and drift speed of theAUV are estimated using an EKF. However, while spatial dependencies between thedrifts of the anchor nodes is observed from sea trial results in [105], to the best ofour knowledge it has not been incorporated in a UT scheme yet.In this chapter, we propose a UT scheme that accounts for the effect of oceancurrent, considers sound speed uncertainties, and incorporates Doppler shift mea-surements. To the best of our knowledge, neither of these three components hasbeen considered before for UT. We exploit that the ocean current is spatially corre-lated, and causing correlated drift velocities of nodes participating in the tracking.In particular, by letting anchor nodes report their drift velocities through acousticcommunication, we estimate the drift velocity of the TN as a combination of theformer. We therefore refer to our proposed tracking solution as the drift dependentUT (DD-UT) schemeWe offer two SSM-based tracking solutions, which are based on the EKF andthe unscented Kalman filter (UKF), respectively. The EKF is a modification tothe Kalman filter which linearizes the state-space and measurement model using thecurrent predicted state. While the EKFs are extensively used in both GPS andunderwater navigation [34, 106], they require knowledge of the probability densityfunction of both the model and measurement noise and thus are sensitive to model45Chapter 3. Spatially Dependent Underwater Navigationmismatch [107, 108]. Instead, the UKF approximates the probability density functionby a deterministic sampling of points. If a large amount of data is available, the UKFtends to be more robust than the EKF in its estimation of error and has been provensuperior to the EKF for complex cases such as time series modeling and neuralnetwork training [107]. However, no such comparison has been made for the case ofUT.Our tracking scheme starts from initial estimates of the sound speed, the locationof the TN and its speed. Then, our SSM fuses INS measurements, drift-velocityinformation from anchor nodes, and ranging and Doppler shift estimates to anchornodes, to provide timely estimates of the 2-D location of the TN. Considering thepossibility of weak correlations between drift velocities (for example in the presence ofturbulence), we present two types of confidence indices (CIs). The first one is based onthe distance between TN and anchor node and the corresponding measured Dopplershift, and the second CI is based on the normalized variance of the anchors? velocities.Since these CIs do not depend on the estimated location of the TN, we argue thatthey are unbiased. To evaluate the performance of our DD-UT scheme, we developa hybrid simulator combining the shallow water hydrodynamic finite element model(SHYFEM) for ocean current [109] and the Bellhop ray-tracing numerical model forpower attenuation of sound in water [2]. For a set of bathymetry maps, our simulationprovides time-varying trajectories of drifting nodes along with power attenuation forall communication links. We compare the performance of our DD-UT scheme tobenchmark solutions, as well as to the recursive Crame?r-Rao lower bound applicablefor tracking. To further verify our simulations, we also report results from two seatrials for different bathymetric channel structures, conducted in the MediterraneanSea and in the Indian Ocean.The remainder of this chapter is organized as follows. In Section 3.1, we introduceour system model, which is followed by the discussion of the state-space and measure-ment model in Section 3.2. Our DD-UT scheme is introduced in Section 3.3. Next,results from both simulations and sea trials are presented in Section 3.4. Finally,conclusions are drawn in Section System ModelOur system includes several anchor nodes at known locations and a TN, equippedwith a depth sensor, an INS, and an acoustic modem. The TN is assumed movingwith random acceleration in both the surge and angular direction. For simplicity, weneglect the pitch and roll Euler angles and assume that the vehicle is aligned withthe horizontal plane or its measurements from on-board sensors can be projected tothis plane. Furthermore, instead of the depth-dependent sound speed, c, for eachcommunication link between the anchor node and the TN, we use the average soundspeed c? (see Section 1.1.1). We assume the anchor nodes remain at the same depth,46Chapter 3. Spatially Dependent Underwater Navigationbut the TN can rise or dive in water. Hence, at time instance tk, where k is thesampled time index of the INS system, c?k is time-varying but similar for all anchornodes. To estimate c?k we adopt the widely used model for sound speed [5],ck = 1449+4.6Tk?0.055T 2k +0.0003T 3k +(1.39?0.012Tk)(Sk?35)+0.017zk , (3.1)where Tk is the temperature in degree Celsius, Sk is the salinity in parts-per-thousand,and zk is the depth in meters, and assume that c?k is the mean of ck from (3.1) overthe water column from the transmitting anchor to the TN. We assume a prior UWLprocess (e.g., [110, 14]) that time-synchronizes the TN relative to the anchor nodes,and gives an initial estimation for c?0 and for the TN location and heading.We focus on 2-D location tracking. This is accomplished by the on-board INSgiving timely estimates of the speed of the TN in both the surge and angular direction[34], and by packets transmitted by anchor nodes providing anchor-location and drift-velocity, ToF and Doppler shift information. The INS data rate (usually around100 Hz) is assumed to be much faster than that of the packet exchange. Hence, wedefine intervals ? INS and ? range, representing the time elapsed between two consecutiveacceleration and ranging measurements, respectively, and for simplicity assume ? range? INSis an integer.We define a reference grid system [x, y, z], where x and y are UTM coordinates,and z is the depth in meters. The communication packets carry the 3-D coordinatesof the anchor nodes in the reference grid system, ranck = [xanck , yanck , zanck ]T , and theanchor?s estimated drift vector,vanc,driftk =[vx,anc,driftk , vy,anc,driftk , v?,anc,driftk , ?anck]T,whose elements are the speed in the x, y, and angular directions, and the anchor?sheading direction, respectively. We assume a slowly changing ocean current velocityfield [100], such that vanc,driftk and the drift vector of the TN are correlated. Vec-tor vanc,driftk is measured at the anchor nodes by subtracting the self-propelled mo-tion, vthrustk , from the calculated location-based one. Following [39] (and referencestherein), the thrust velocity can be obtained by measuring the thrust force F force,and solving the differential equationmv?thrustk = F force ? 0.5Cdrag?A(vthrustk )2 , (3.2)where m is the vehicle mass, Cdrag is the vehicle drag coefficient, ? is the density ofthe water, and A is the vehicle cross-section area. Then, vanc,driftk can be estimatedusing a simple IIR filter, whose output is ?vanc,driftk + (1? ?)vanc,driftk?1 with parameter? tuned to the expected rate of change of the drift velocity.3.2 The SSM and Measurement ModelIn this section, we describe our SSM and measurement model. We consider motionat fixed speed and allow for acceleration noise. Model mismatches are considered by47Chapter 3. Spatially Dependent Underwater Navigationincluding drift velocity estimates of anchor nodes.3.2.1 State Space Model (SSM)Let rk = [xk, yk, zk]T and ?k be the 3-D coordinates of the TN in the reference gridsystem and its heading angle, respectively. Furthermore, let vxk , vyk and v?k be thevelocity of the TN in the reference-grid x and y axes and in the angular direction,respectively. Since the TN is assumed to be moving with random acceleration in boththe surge and angular direction, and since the average sound speed, c?k, is assumedtime-varying, we choose the SSV asak =[xk, vxk , yk, vyk , ?k, v?k , c?k]T. (3.3)To set up the SSM we assume a Gaussian distributed acceleration and mismatchfor model (3.1), respectively. Recall that the sound speed in (3.1) depends on watersalinity, temperature, and depth. For small depth changes of a few hundreds ofmeters, we can neglect changes in salinity. Furthermore, up to a water depth of 100 m,Tk ? 3100zk [5]. Thus, neglecting the second and third order terms of the temperaturedependence in (3.1), we can linearly update the average sound speed, c?k, based onthe depth change ?zk = (zk ? zk?1) + (zanck ? zanck?1) at a rate of 0.017 + 4.6 ? 3100 . Theassumed SSM is thereforeak = Bak?1 + u?zk +Nnak , (3.4)where u = [0, 0, 0, 0, 0, 0, 0.155]T , nk =[nxk, nyk, n?k , nc?k]Tis a zero-mean Gaussianvector with covariance matrix Rmodel, and the advance and noise matrices areB =??????????1 ? INS1 0 0 0 0 00 1 0 0 0 0 00 0 1 ? INS1 0 0 00 0 0 1 0 0 00 0 0 0 1 ? INS1 00 0 0 0 0 1 00 0 0 0 0 0 1??????????, N =?????????????(? INS1 )22 0 0 0? INS1 0 0 00 (?INS1 )22 0 00 ? INS1 0 00 0 (?INS1 )22 00 0 ? INS1 00 0 0 1?????????????,respectively.3.2.2 Measurement ModelWhile AUVs can be equipped with a large number of on-board sensors, for longterm missions, strict energy constraints may not permit the use of energy consumingsensors such as DVLs (e.g., [34]). We therefore consider UT using only an INSand occasional packet exchanges with anchor nodes. In the following, we state ourmeasurement model.48Chapter 3. Spatially Dependent Underwater NavigationINSThe on-board INS includes a 3-D accelerometer and angular sensors to measure theTN speed in the surge and angular direction [34],mINSk =??vx?kvy?kv?k??+ nINSk , (3.5)where vx?k and vy?k are the speed of the TN in the x and y directions of the TN localcoordinate system, such that vxk = vx?k cos?k, and vyk = vy?k sin?k. Vector nINSk in (3.5)is a 3-D measurement error vector with zero-mean Gaussian elements and covariancematrix RINS.ToFAt a certain time sample k, the TN receives a packet from an anchor node in itscommunication range and estimates the ToF to the transmitting anchor. We assumethat both the TN and the anchor move slowly relative to the propagation delay inthe channel. Thus, the ToF is modeled bymToFk =?dk?c?k+ nToFk , (3.6)where dk = rk ? ranck and nToFk is the ToF estimation error. While noise nToFk can bebiased due to NLOS false identification, we rely on our method from Chapter 4 toclassify NLOS and LOS ToF measurements, and assume nToFk is a zero-mean Gaussianwith variance ?2ToF.Doppler ShiftAlong with estimating the ToF from received packets, communication signals can beused to evaluate the Doppler shift using, e.g., [111]. The Doppler shift is determinedby the velocity difference of the anchor and the TN. Let vanck = [vx,anck , vy,anck ]T bethe velocity3 of the anchor node in the reference-grid x- and y-axis whose packet isreceived at time instance tk. Velocity vanck can be either reported by the anchor, or,assuming slow changes relative to ? range, be calculated by the TN using the anchor?sprevious reported location. For slow motion, the Doppler shift can be approximatedin terms of the frequency offset?fk =fcc?k?vrelk ? cos ?k , (3.7)3Note that the elements of vanck may be equal to the first two elements of vanc,driftk only if theanchor is not self-propelled.49Chapter 3. Spatially Dependent Underwater Navigationwhere fc is the carrier frequency, vrelk = [vxk , vyk ]T ? vanck , and ?k is the angle betweenvectors vrelk and dk (see (3.6)), such thatcos ?k =dTk ? vrelk?vrelk ??dk?. (3.8)By (3.7) and (3.8),?fkfc= (vxk ? vx,anck ) (xk ? xanck ) + (vyk ? vy,anck ) (yk ? yanck )?dk?c?k. (3.9)We model the Doppler shift measurement bymDopplerk =?fkfc+ nDopplerk , (3.10)where nDopplerk is assumed zero-mean Gaussian noise with variance ?2Doppler.VelocityThe spatial dependencies between the drift motions of the TN and the anchor nodesallow us to estimate the drift velocity of the TN by superimposing the drift velocitiesof the anchor nodes. In particular, by letting anchor nodes report their drift velocitiesand heading directions, vanc,driftk , we obtain an estimate for the TN drift velocity andheading directionv?driftk =?????v?x,driftkv?y,driftkv??,driftk??driftk?????. (3.11)This process will be discussed in detail in Section 3.3.We treat v?driftk as a measurement, modelled asv?driftk = ?dk????vxkvykv?k?k????+ ndriftk , (3.12)where ndriftk is an error vector whose elements are zero-mean Gaussian with covariancematrix Rdrift, and ?dk is a CI whose purpose is to limit the use of anchor velocitieswhen spatial dependencies between the motions of the TN and the anchor nodes aredeemed to be weak (a method to determine ?dk will be presented in Section 3.3). Wealso assume that the TN is drifting or that, if self-propelled, it can compensate forits self-propelled motion using (3.2).50Chapter 3. Spatially Dependent Underwater NavigationMeasurement VectorUsing measurements mINSk from (3.5), mToFk from (3.6), mDopplerk from (3.10), andv?driftk from (3.12), we form the measurement vectoryk =????mINSk?pkmToFk?pkmDopplerk?pk v?driftk????= h(ak) + nmeasurek , (3.13)where ?pk = 1 if a packet is received at time instance tk and 0 otherwise, h(ak) is themeasurement model vector, and nmeasurek is a zero-mean Gaussian measurement noisewith covariance matrix Rmeasure. For the SSV ak in (3.3), the SSM (3.4), and themeasurement vector yk from (3.13), we next derive the CRLB for UT.3.2.3 Crame?r Rao Lower Bound (CRLB)Let A?k = {a?1, . . . , a?k} and Y?k = {y1, . . . ,yk} be the set of SSV estimates (3.3)and measurement vectors (3.13) obtained till time instance tk, respectively. For anyunbiased estimator, the CRLB gives the lower bound on the varianceE[(A?k ?Ak)(A?k ?Ak)T]? J?1(k) , (3.14)whereJ(k) = E[? ?2?2AklogP (Ak,Yk)](3.15)is the inverse of the Fisher information matrix with elements Ji,j(k), P (?) denotesthe probability density function, and E[?] denotes expectation. In [112], it was shownthat if only estimation of ak is of interest, (3.15) can be formulated recursively suchthatJ(k) = J1,k ? JT2,k(J(k ? 1) + J3,k)?1J2,k , (3.16)whereJ1,k = ?E[?2?2aklogP (ak|ak?1)]? E[?2?2aklogP (yk|ak)](3.17a)J2,k = ?E[?2?ak?1?aklogP (ak|ak?1)](3.17b)J3,k = ?E[?2?2ak?1logP (ak|ak?1)]. (3.17c)Since both nak from (3.4) and nmeasurek from (3.13) are modeled to be zero-meanGaussians with corresponding covariance matrices Rmodel and Rmeasure, respectively,51Chapter 3. Spatially Dependent Underwater Navigationand since ?ak?ak?1 = B and introducing Hk =?h(ak)?ak, (3.17) becomesJ1,k =(NRmodelNT)?1 + E[HTk (Rmeasure)?1Hk](3.18a)J2,k = BT(NRmodelNT)?1 (3.18b)J3,k = BT(NRmodelNT)?1B . (3.18c)3.3 The DD-UT SchemeIn this section, we describe our DD-UT scheme. We start with the tracking algorithmand then proceed with the process of estimating the drift velocity of the TN.3.3.1 TrackingOur tracking scheme is based on the SSM (3.4) with measurement vector yk andmeasurement model (3.13). For the purpose of tracking, we consider the use of theKF which is an optimal solution for Gaussian model and measurement noise. Sinceour measurement model is not linear, we adopt the EKF and the UKF. The EKF isformalized byak|k?1 = Bak?1|k?1 + u?zk?1 (3.19a)P k|k?1 = BP k?1|k?1BT +NRmodelNT (3.19b)Kk = P k|k?1HTk(HkP k|k?1HTk +Rmeasure)?1 (3.19c)en = yk ? h(ak|k?1) (3.19d)ak|k = ak|k?1 +Kkek (3.19e)P k|k = (I ?KkHk)P k|k?1 , (3.19f)where I is the identity matrix, P 0|0 is taken as Rmodel, and a0|0 is obtained from aprior UWL process (see Chapter 2). The UKF requires more regression steps, andfor brevity we refer the reader to [108].We initiate Rmodel and Rmeasure as diagonal matrices. For the former, sinceslow acceleration is expected and assuming no bathymetric layer exists (i.e., model(3.1) holds), we use small variance elements relative to the initial SSV (3.3) givenby the UWL process. Similarly, since both ToF and Doppler shift measurementsare expected to be fairly accurate, small values are used for ?2ToF from (3.6) and?2Doppler from (3.10) relative to the initial estimates of range and velocity difference toanchor nodes, respectively. To determine RINS we use the INS specifications, and todetermine ?2drift, we use a self-estimation of the error in the drift velocity estimationintroduced next.52Chapter 3. Spatially Dependent Underwater Navigation3.3.2 Drift Velocity EstimationIn this section we describe the process of obtaining estimates v?driftk as a combina-tion of vanc,driftk measurements, which is then integrated into the measurement vector(3.13). Our drift velocity estimator requires ranging measurements ?dk? = mToFk c?k?1,assumed to be correct. However, we require only a coarse range estimation, mainlyto weight drift velocities from different anchor nodes.Considering the possibility of weakly correlated motion of nodes, we restrict theuse of drift velocities reported from anchor nodes. First, accounting for time changesin the ocean current, temporal restriction is performed by defining a time window,Twin (say 60 seconds), and considering only velocities of anchor nodes whose packetswere received in the last Twin sec. Second, spatial restriction is applied by using aCI, ?rk, indicating whether to use a velocity estimate received from a certain anchornode at time instance tk. This is formalized through the setKk = {k? | tk ? Twin ? tk? ? tk ? ?1,k? = 1} , (3.20)which contains the time instances for which drift velocities reported from anchornodes can be used. Furthermore, we use a second CI, ?dk , which evaluates the accuracyof estimation v?driftk and is incorporated into (3.12).Next, we present three schemes for fusing vanc,driftk measurements. Then, we for-malize the CIs ?rk and ?dk .Nearest NeighborAssuming that the spatial correlation of ocean current decreases with range, thesimplest method to obtain v?driftk is by choosing it to be the velocity of the anchornearest to the TN. Accordingly, we identifyk? = argmink??Kk?dk?? , (3.21)and setv?driftk = vanc,driftk? . (3.22)The main drawback of this method is that not all drift velocity information availablefrom anchor nodes is used. Thus, it is sensitive to noise in estimations vanc,driftk , andto irregularities of the ocean current.Weighted SuperpositionIn the weighted superposition method, velocities of anchor nodes are combined suchthatv?driftk =?k??Kk ?k?vanc,driftk??k??Kk ?k?, (3.23)53Chapter 3. Spatially Dependent Underwater Navigationwhere ?k? is a weight function.Since spatial correlation of ocean current depends on both range and depth (cf.[100]), a pragmatic choice is a normalized weight function?k? =???dk??maxk?Kk(?dk?)????, (3.24)where ? is a pre-determined exponent. However, since ocean current irregularities(e.g., turbulence) occur at small regions [100], anchor nodes located in close prox-imity to each other should be given smaller weights. Thus, the spatial density ofanchor nodes should also have an impact. Following [113], we suggest the alternativeweighting function??k?,k =???dk??maxk?Kk(?dk?)????(1 + hk?,k) , (3.25)which takes into account the locations of the TN and the anchor nodes. In (3.25),hk?,k =1?j?Kk,j 6=k? ?dj??j?Kk,j 6=k?1?dj??(1?(ranck? ? rk)T (rancj ? rk)?dk???dj?). (3.26)The exponent ? in (3.24) and (3.25) is adapted to the expected noise level of vanc,driftk .Our simulation results showed that when noise in estimates vanc,drift is high, goodperformance is obtained for ? = 0, whereas a value ? = 4 should be used for relativelyaccurate vanc,driftk estimations.Least SquaresAssuming that ocean current changes linearly in space, estimating the drift velocityof the TN can also be interpreted as estimating two planes, one each for the x-and y-coordinates of the velocity. Enumerating the elements in Kk from (3.20) ask1, k2, . . . , kLk where Lk = |Kk|, we formulate the problem as the linear combination?????xanck1 yanck1 ?anck1 1xanck2 yanck2 ?anck2 1... ... ...xanckLk yanckLk?anckLk 1?????? ?? ?P????ax ay a?bx by b?cx cy c?dx dy d?????? ?? ?C=?????vx,anc,driftk1 vy,anc,driftk1 v?,anc,driftk1vx,anc,driftk2 vy,anc,driftk2 v?,anc,driftk2... ...vx,anc,driftkLk vy,anc,driftkLkv?,anc,driftkLk?????? ?? ?V,(3.27)where the coefficients of C describe the two planes. Solving for C yieldsC =(P TWP)?1P TWV , (3.28)54Chapter 3. Spatially Dependent Underwater Navigationwhere W is a diagonal weighting matrix whose k th coefficient is ?k from (3.25). Weuse a coarse estimate of the location of the TN to calculate the velocity, such thatv?driftk =(xk?1, yk?1, ?k?1, 1)?C , (3.29)and xk?1, yk?1, and ?k?1 are the previous course estimation of the location of the TN.3.3.3 Confidence Index (CI)Utilizing the spatial dependencies between the motions of the TN and anchor nodeshas a great potential for improving UT. However, since in some cases the spatialcorrelation of ocean current may be weak, there is a need to limit the use of v?driftkthrough a CI. Considering the likely large errors in the TN velocity estimation ifspatial correlation is weak, we use two types of CIs. The first, ?rk, identifies anchornodes with whom spatial dependency of motion is weak, and is incorporated in theestimation methods using the set Kk from (3.20). The second, ?dk , is a measure forthe homogeneity of the current velocity field around the TN.CI for Correlation with Drift Velocity of a Single AnchorIn the above three schemes to evaluate v?driftk , only velocities of anchor nodes whoselast packet was received at time instance tk, k ? Kk, are considered for estimatingv?driftk (see (3.21), (3.23), and (3.27)). Assuming that spatial correlation of oceancurrent degrades with range, relative depth, and relative velocity of the anchor andTN, ?rk is a function of the distance of the TN to the anchor node, the differencebetween the distances of the TN and the anchor to the sea bottom, ?zbottom, and themeasured Doppler shift, ?fk from (3.10). To formalize this, we use three thresholdvalues Thr, Thz, and ThD, and set?rk =[1 if |dk| ? Thr ? |?zbottom| ? Thz ? ?fk c?k?1fc cos ?k?1 ? Thd0 otherwise]. (3.30)We suggest determining thresholds Thd and Thz by training on a set of trajec-tories obtained from real data, or, if not available, simulated by a numerical oceancurrent model (e.g., SHYFEM [109]) for the expected bathymetry of the environ-ment. However, a more educated guess can be made for Thr. In case the bathymtryis known, we can calculate the range for which the velocity of the water current canbe considered dependent. Otherwise, we use the Rossby radius of deformation, Dr,which is the range from a certain location at which the gravitational tide and low-related ocean current considerably change [100]. Since the effect of the gravitationalforce on ocean current is a dominant factor in determining the spatial correlationbetween the motion of the TN and the anchor, we set Thr = Dr. The Rossby radius55Chapter 3. Spatially Dependent Underwater Navigationof deformation is a function of the water depth, p, earth gravity, g, and the Coriolisforce parameter, f0, at the current latitude. For shallow water it is calculated as [100]Dr =?gpf0. (3.31)Since neighter Dr from (3.31) nor Thd and Thz are directly related to the velocity ofthe TN, and so are Thd and Thz, and since only a coarse estimation of the distancedk is needed, we consider ?rk from (3.30) to be an unbiased CI.CI for Detecting Uncorrelated MotionOur second type of CI enables self-evaluation of the estimation v?driftk . Let vk =[vxk , vyk ]T be the true velocity of the TN, and v?driftk (1? 2) be the first two elements ofvector v?driftk . To evaluate the validity of the assumption of spatially correlated oceancurrent for both speed and direction, we use the p-relative distance,ev(k) =?vk ? v?driftk (1? 2)?p?vk?p + ?v?driftk (1? 2)?p(3.32)with p = 2, as the figure of merit. Error (3.32) is a normalized measure combiningerrors in both speed and direction, whose value is 1 if the vectors point in oppositedirections and 0 if the vectors are the same.Our aim is to obtain a CI that detects large errors (3.32). To this end, we useprevious location estimates and anchors? drift velocities and find an error predictionfor a newly drift velocity information vanc,driftLk . Since a large variability of the driftvelocity field around the TN reflects poor spatial dependency of the ocean current,for such error prediction we use the variance of anchor nodes drift velocities. Theweighted variance of velocities is calculated in two steps. First, the weighted meanvelocity vector is calculated by?k =1LkLk?i=1vanc,driftki ?ki , (3.33)where ?k is the weight function from (3.24) or (3.25). Then, the weighted variancevector is computed by?2k =1LkLk?1?i=1(vanc,driftki ?ki ? ?k)2, (3.34)where the square is performed element-wise. The normalized variance is then??2k =??2k???2k?. (3.35)56Chapter 3. Spatially Dependent Underwater NavigationSince spatial dependency of ocean current should be fixed or change slowly overtime [100], we combine previous variances ??2k? , k? ? Kk, in vectors?k? =[??2k? ? ?dk?, ?dk?,??dk?, ??2k? ,???2k? , 1]T, (3.36)where ?dk? is used to match the contribution of the different velocities to the CIwith their contribution to v?driftk . Using vectors ?k? , we form a matrix of reliabilityindicators, ?k =[?k1 , . . . ,?kLk?1]T. Then, introducing ev = [ev(k1), . . . , ev(kLk?1)]Twe calculate?k =(??Tk)?1?kev , (3.37)and form the error predictione?v(Lk) = ?TLk?k . (3.38)Prediction e?v(Lk) is compared with a threshold The to form the CI?dk =[1 e?v(Lk) ? The0 otherwise]. (3.39)Similarly to thresholds Thd and Thz from (3.30), we suggest calculating The bytraining on a set of modeled trajectories.3.4 ResultsIn this section, we show and discuss the performance of our DD-UT scheme in sim-ulations and two sea trials. We compare the following velocity estimation methods:1) nearest neighbor (NN ) from Section 3.3.2, 2) weighted superposition (WSP) fromSection 3.3.2 with weighting function (3.24), 3) weighted superposition with spatialdirection consideration (WSPS ) from Section 3.3.2 with weighting function (3.25), 4)least squares (LS ) from Section 3.3.2 by replacing W from (3.28) with the identitymatrix, 5) and weighted least square (WLS ) from Section 3.3.2. We also compareperformance of the EKF and the UKF when only INS and ToF measurements are inuse and when the sound speed is considered fixed, e.g., [39]. The simulation resultsare also compared with the CRLB (3.18). We consider both evk from (3.32) and thedistance of the estimated location (x?, y?) to the true location,edk =?E[(x?k ? xk)2 + (y?k ? yk)2], (3.40)for tracking performance. Note that edk from (3.40) can readily be compared with thesquare root of J1,1(k) + J3,3(k) from (3.15).57Chapter 3. Spatially Dependent Underwater Navigation(a)0.6 0.70.8 0.91? Speed [m/s] (x?axis)Speed [m/s] (y?axis) Time [sec]TNAnchor 1Anchor 2Anchor 3Anchor 4(b)Figure 3.1: Simulated scenario: (a) simulated velocity field at depth 20 m, (b) simu-lated speeds of the anchor nodes and TN.3.4.1 SimulationsOur simulation environment includes a single TN and L anchor nodes. To simulatethe drift motion of nodes as well as the communication link between the anchornodes and the TN, we have developed a MATLAB-based hybrid simulator combiningnumerical models for both ocean current and power attenuation in water. In thiswork we are mostly concerned with tracking in regions of shallow water and in timesteps of a few seconds. For this reason, we have chosen the SHYFEM [109], whichis designed to resolve the hydrodynamic equations for coastal seas and other smallbasins. To model power attenuation in communication links, we use the Bellhopray-tracing numerical model (cf. [2]). The simulator requires a bathymetry map,latitude information, SSP, and initial location of nodes, and produces time-varyingtrajectories of nodes based on a generated current velocity field, as well as time-varying transmission loss values for the channel between the different nodes. Forsimplicity, we assume nodes are not self-propelled4. Example for the current velocityfield and the resulting speed of four network nodes are shown in Figures 3.1a and3.1b, respectively.The structure of the simulated channel is a square area of 4 ? 4 km2 with waterdepth of 100 m, and the bathymetry map includes one or two underwater hills ofuniformly randomly generated width and depth of 3000 m and 2000 m, respectively.Initially, we place nodes uniformly at random in a smaller region of 1 ? 1 km2 onthe water surface and let them drift for 20 min according to the simulated currentvelocity field, where the TN dives at a speed of 0.05 m/sec. We use two sound speed4For a more complex motion pattern, equation (3.2) can be used.58Chapter 3. Spatially Dependent Underwater Navigation(a)0 0.2 0.4 0.6 0.8 D  ?n=0.05 m/sec?n=0.01 m/sec?n=0.2 m/secTh2=0.1Th2=0.2Th2=0.3(b)Figure 3.2: (a) Mean of ev(k) from (3.32) as a function of number of anchor nodes,(b) PD vs. PF for different ?2anc and The values.profiles: one that matches model (3.4) and has a value of 1512 m/sec on the watersurface, and another which has a fixed value of 1512 m/sec. We consider a carrierfrequency of 15 kHz, and the model is set for location 49o16?13.33??N , 126o16?6.4??W(i.e., near Vancouver, BC). We let the anchor nodes transmit in a simple TDMAnetwork, with a time frame of L time slots of duration 10 sec. In its designated timeslot, each anchor transmits a data packet including its 3-D coordinates and its driftvelocity. We assume packets are received error-free as long as the signal-to-noise ratio(SNR) is above 15 dB. The SNR is calculated based on the output transmission lossfrom our simulator for a common power source level of 140 dB//?Pa@1m, bandwidthof 1 kHz, symbol duration of 1 msec, and an ambient noise level of 50 dB//?Pa/Hz.We first investigate the performance of our velocity estimate v?driftk from (3.12) andthe CI ?dk from (3.39). Tracking performance follows next.Velocity Estimate (simulations)In Figure 3.2a, we show the effect of the number of anchor nodes on the velocityestimation. Results are averaged over 81 scenarios of different bathymetry maps and1000 simulation runs for each scenario. For all methods, performance improves withthe number of anchor nodes. As expected, for large L, the performance of the WLSis better than that of the LS method. This improvement confirms our assumptionof range related spatial correlation of the ocean current. However, when L ? 5 noimprovement is observed. One reason for this is the sensitivity of the WLS methodto scenarios where a cluster of anchor nodes is formed and the velocity plane can betilted further due to noises at the measured anchors? locations. The range relatedspatial correlation is also the reason for the better performance of the WSP and WSPSmethods compared to that of the NN. However, the spatial direction considered in59Chapter 3. Spatially Dependent Underwater Navigationthe weighting function of the WSPS method does not seem to have a large impacton performance. We observe that for L < 8, the performances of the NN, WSP, andWSPS methods are better than those of the WLS or LS. This is because of the largeramount of information required for the latter to estimate matrix C from (3.27). Inthe following, we show results only for the WSP method.In Figure 3.2b, we show the detection probability, PD, vs. the false alarm prob-ability, PF, for the CI ?dk from (3.38). To calculate PD and PF, we set a boundaryev(k) = 0.1, such that a correct detection is declared when ev(k) ? 0.1 and ?v ? The,or when ev(k) ? 0.1 and ?v ? The. We compare results for three threshold val-ues, The (see (3.38)). Based on the results of Figure 3.2b, in the following we useThe = 0.2.Tracking (simulations)For tracking purposes, we follow the generated velocity field to calculate the time-varying location of the TN. To test the convergence of the tracking scheme, at thebeginning of each simulation run the TN is given an initial SSV estimate, a?0 (see(3.3)), which includes zero-mean Gaussian noise whose covariance matrix is suchthat the SNR is 10 dB and the signal is regarded as the elements of the true SSVa0. We compare performances of our DD-UT tracking method, tracking without driftvelocity estimation (No Drift), tracking without drift velocity estimation and Dopplershift measurements (No Drift+Doppler), and the latter scheme but without trackingthe sound speed (No Drift+Doppler+Speed). We measure performance using theEuclidian distance edk from (3.40). Since in our system measurement noise componentsin yk from (3.13) have different units, to show effect of measurement error we set theelements of Rmeasure based on a measurement SNR defined asMSNR = E [h(a)2i ](?measurei )2 , (3.41)where h(a)i and ?measurei are the ith element of h(a) from (3.13) and the diagonal ofRmeasure, respectively. We note that the values considered for the MSNR are takenfrom real INS systems and the results obtained in our sea trials (they are on the orderof 50 dB, see [34] and Chapter 4).We start by showing a tracking example for the simulated scenario presented inFigures 3.1a and 3.1b for MSNR = 40 dB. In the simulated scenario, anchor nodes 4and 3 are located roughly 200 m and 700 m away from the TN, respectively, whileanchor nodes 2 and 1 are located more than 1.5 km away. As a result, we observesimilarities between the speeds of the TN and anchor nodes 4 and 3. The scenario in-cludes two sudden changes for the speed of the TN in the x direction at time instances760 sec and 990 sec. To show the effect of link communication errors, we simulatedfailures for all packets received by the TN between time instances 400 sec and 500 sec.In Figure 3.3b, we show tracking performance using the UKF as a function of time,60Chapter 3. Spatially Dependent Underwater Navigation0 200 400 600 800 1000 120015101512151415161518152015221524Time [sec]Propagation Speed [m/sec]  True 1True 2UN?DPUN?DP (mismatch)No Drift+Doppler(a)0 200 400 600 800 1000 12000510152025303540Time [sec]ed k [m]  DD?UT (WSP)DD?UT (WSP,mismatch)No DriftNo Drift+DopplerNo Drift+Doppler+Speed(b)Figure 3.3: Simulated scenario: (a) speed of the TN, (b) tracking error edk from (3.40)where we used the WSP drift velocity estimation method for our DD-UT scheme.When a change in the velocity of the TN occurs, an increase in edk is observed, fol-lowed by a recovery process. Since the DD-UT scheme uses more information, itconverges roughly 30 sec before the other schemes. Moreover, the convergence is fora slightly lower error edk than that of the reference methods. Comparing the effectof adding Doppler shift information, larger errors and slower recovery is recordedwhen Doppler shift measurements are not in use (No Drift+Doppler) and the veloc-ity changes. In addition, due to the change in the sound speed with depth (roughly9 m/sec over the simulation time), a deterioration of performance of up to 5 m existswhen the sound speed is considered fixed (No Drift+Doppler+Speed). As expected,errors accumulate in time when communication link failure occurs and tracking isperformed solely based on INS measurements. Also here, recovery is faster using theDD-UT scheme. To comment on the sensitivity of our protocol to a mismatchedmodel for the SSP, in Figure 3.3b we also show results (DD-UT (mismatch)) of theDD-UT scheme where the SSM is based on (3.4) but the actual SSP is fixed (whichalso affects the Bellhop-based simulated power attenuation). While slower recoveryfrom velocity changes or communication link failures is observed, performance onlyslightly decreases and results are better than without tracking the sound speed. Toemphasize this, in Figure 3.3a we show tracking performance of c?k, where curvesTrue 1 and True 2 represent the SSP used in (3.4) and the fixed one, respectively.We observe that when the SSP matches (3.4), the estimated c?k closely follows thetrue one. However, inaccuracies exists when Doppler shift measurements are not inuse (No Drift+Doppler) and the additional information extracted from (3.9) is notavailable. When the SSP is fixed and the SSM is mismatched, performance decreasesbut the estimated sound speed is still within 1 m/sec from its true value.Next, we show statistical tracking results. We generate 81 bathymetry maps61Chapter 3. Spatially Dependent Underwater Navigation0 5 10 15 20 25 3000. k > x)  DD?UT (UKF)DD?UT (EKF)No DriftNo Drift+DopplerNo Drift+Doppler+SpeedCRLB (average)(a)35 40 45 50 55 60 65 700246810121416Measurement SNR [dB]ed k [m]  DD?UT (UKF)DD?UT (UKF,mismatch)DD?UT (EKF)No DriftNo Drift+DopplerNo Drift+Doppler+SpeedCRLB(b)Figure 3.4: Tracking performance (simulations): (a) empirical C-CDF forMSNR=50dB, (b) edk as a function of MSNR (thick line shows results for the CRLB).and for each realization we conduct 1000 simulation runs. In each simulation, wedetermine the initial location of the network nodes uniformly at random, and generatenew noise realizations. We note that since the scenarios generated include speed anddirection changes (much like the example shown in Figure 3.1b), we cannot determinea point in time for which tracking converges. Instead, considering convergence timeof up to 100 sec from the start of each simulation, we take the median of all edkresults obtained between time instances 100 sec and 1200 sec. In Figure 3.4b, weshow the effect of the MSNR. The results indicate a relatively moderate effect ofthe measurement noise on performance for the MSNR range considered. Hence,as argued above, the dominant effect in tracking is the ability to accurately modelthe motion of the TN. As expected, performance improves the more information isused. We observe that estimating the drift velocity has more benefit than utilizingDoppler shift measurements. We note that performance of the UKF are notablybetter than that of the EKF, and that this performance gain is more significant forlow MSNR. This is mainly due to the first order approximation of the EKF [108] andthe fast changes in the TN speed and direction relative to the time step interval ofthe filter which are known to cause instabilities [107]. This is emphasized by the goodperformance of the UKF even for a mismatched SSP. The need to track the soundspeed is demonstrated by the significant performance gain of the No Drift+Dopplerscheme compared to that of the No Drift+Doppler+Speed. In Figure 3.4b, we alsoshow the square root of the CRLB J1,1(k)+ J3,3(k) from (3.15). We observe that theCRLB is well approached by our DD-UT scheme. To comment on the variations of theperformance results, in Figure 3.4a we show the empirical complementary cumulativedensity function (C-CDF) of edk for MSNR= 50 dB, as well as the CRLB for reference.We observe small variations of edk for our DD-UT scheme using the UKF. The results62Chapter 3. Spatially Dependent Underwater Navigation?100 0100 2003000200040006000020406080100120 x [m]y [m] time [min]Boat 1Boat 2(a)2000 40006000 8000010002000300002000400060008000 UTM Location (x?axis)UTM Location (y?axis) Time [sec]Anchor 1Anchor 2Anchor 3TN(b)Figure 3.5: Node locations in Cartesian coordinates: (a) Singapore sea trial, (b) Israelsea trial.verify our conclusions from the average performance shown in Figure 3.4b.3.4.2 Sea TrialsDue to the complex sea environment and our reliance on models for the SSM, sensornoise, and on the physical phenomena of spatial correlation of the ocean current, oursimulation performance requires verification in a sea environment. For this reason,we have conducted two sea trials in the different bathymetry channel structures of theMediterranean Sea and the Indian Ocean. The former was performed in August 2010at Haifa, Israel, and included three vessels, representing three mobile nodes, whichdrifted for more than 2 hours. Water depth was around 40 m and the height of thesea waves was around 0.1m. The three nodes deployed transducers at depth of 10 m,and transmitted data packets every 3 minutes using a TDMA protocol includingthe nodes? 2-D UTM coordinates (which was measured at rate of 1 sec using GPSreceivers). The received packets were used to calculate the ToF (applying the methoddescribed in Chapter 4), and the Doppler shift (using the method described in [111]).No acceleration measurements were taken during this sea trial, and instead we use theGPS readings to calculate mINSk (see (3.5)). The time-varying location of the threenodes is shown in Figure 3.5b. The second sea trial was conducted in November2011 at the Singapore strait with water depths of 15 m and ocean wave height ofapproximately 0.5 m. The experiment lasted for more than one hour and includedtwo drifting boats. At each boat, we obtained 3-D acceleration measurements ata rate of f = 4.8 Hz using an Libelium Wasp Mote?s on-board accelerometer, andToF measurements were taken at each node every 20 sec using underwater acousticmodems, manufactured by Evologics GmbH, which were deployed at a depth of 5 m.Throughout the experiment, the locations of the boats were monitored using GPSreceivers at rate of 3 sec. The boats? locations are shown in Figure 3.5a.63Chapter 3. Spatially Dependent Underwater NavigationTable 3.1: Drift velocity estimation results from the Israel and Singapore sea trials.NN WSP LSSea Trial Measure N-I W-I N-I W-I N-I W-IIsrael E{|vk ? v?driftk (1? 2)|} 0.03 0.11 0.03 0.11 0.03 0.24E{|?k ? ??driftk |} 0.16 0.37 0.09 0.25 0.07 0.28Singapore E{|vk ? v?driftk (1? 2)|} 0.09 0.16 - - - -E{|?k ? ??driftk |} 0.17 0.22 - - - -For both sea trials, we use the GPS readings to calculate the drift velocity of theanchor nodes, vanc,driftk , and as the ground truth for the position and velocity of theTN.Velocity Estimate (sea trial)In Table 3.1, we compare the mean of errors |vk ? v?driftk (1 ? 2)| (in m/sec) and|?k ? ??driftk | (in radians) for the NN, WSP, and LS methods described in Section 3.3.To comment on the robustness to motion instabilities, we present results when alldata is considered (W-I ), and when disregarding data with motion irregularities (N-I ). For the Israel sea trial, motion irregularities are considered around time instances2400 sec, 5400 sec, and 7200 sec, and for the Singapore sea trial around time instances100 sec, 1500 sec, and 2900 sec. We note that all the above motion irregularities aredetected by our CIs, ?dk and ?rk, and both ?dk and ?rk are 1 in other time instances.For both sea trials, we observe good estimation results when motion is stable, andmore noisy estimations but still within acceptable range when motion irregularitiesare considered. The results imply that the WSP method outperforms both NN andLS methods.Tracking (sea trial)In this section, we show tracking performance for the two sea trials. Since we usedcommercial GPS receivers whose expected accuracy was ?5 m, we consider a trackingresult for which edk ? 10 m as accurate. In both sea trials, the depth of the transducerswas fixed. Thus, we do not track the sound speed and instead use a predefined soundspeed and modify the SSM (3.4) accordingly. In the Israel sea trial, we have measureda sound speed of c = 1550 m/sec which reduced by 2 m/sec along the water columnof 40 m. In the Singapore sea trial, we rely on yearly measurements showing a fixedsound speed of 1540 m/sec. In addition, in the latter sea trial we did not have accessto Doppler shift measurements, and vector yk from (3.13) is modified to not includemeasurement mDopplerk from (3.10). In the following, tracking starts given an initialestimate a0 (e.g., from a UWL process) such that ed0 = 10 m, and for the Israel sea64Chapter 3. Spatially Dependent Underwater Navigation0 500 1000 1500 2000 2500 3000 3500 400005101520Time [sec]Euclidian Error [m]  DD?UT (UKF)DD?UT (EKF)No Drift (UKF)(a)0 1000 2000 3000 4000 5000 6000 70000510152025Time [sec]ed k [m]  DD?UT (WSP)DD?UT (NN)DD?UT (LS)No DriftNo Drift+Doppler(b)Figure 3.6: edk from (3.40) vs. time: (a) Singapore sea trial, (b) Israel sea trial.trial c?0 = 1545 m/sec. We next show results for all the acquired data (i.e., withmotion irregularities) and incorporate both types of CIs introduced in Section 3.3.3.Tracking results for the Singapore sea trial are shown in Figure 3.6a. For allmethods, convergence is reached after roughly 200 sec (i.e., using 10 received packetsfrom the anchor). We observe several cases where performance degrades (e.g., aroundtime instances 500 sec, 2000 sec, and after 2800 sec). As the effect is similar to theone observed in Figure 3.3b, these performance fluctuations are explained by bothToF inaccuracies (due to the shallow water environment) and velocity changes (asseen in Figure 3.5a). Similar to the results in Figure 3.4b, better performance isobtained by the UKF compared to the EKF. As seen in the figure between timeinstances 2000 and 2500, the No Drift scheme sometimes achieves better results thanour DD-UT scheme. However, most of the time significant performance gain of upto 5 m is obtained by the DD-UT scheme compared to the No Drift one.In Figure 3.6b, we show tracking performance for the Israel sea trial. For all meth-ods, a sudden spike in tracking error occurs at around 2400 sec. This error is dueto the loss of communication in the network that occurred between time instances2400 sec and 3200 sec. The similar decrease in performance at around 4000 sec isexplained by a sudden change of velocity. Both faster recovery and absolute perfor-mance improvement are observed when drift velocity estimation is used. Moreover,performance significantly improves when Doppler shift measurements are utilized.Comparing the three methods of velocity estimation5, similar to our simulation re-sults, best performance is obtained by the weighted superposition scheme for whichthe tracking error converges to less than 5 m.5We note that the WLS method yielded almost the same results as the LS method65Chapter 3. Spatially Dependent Underwater Navigation3.5 ConclusionsIn this chapter, we considered the problem of UT, where nodes experience irregulardrifting motion. Assuming spatial correlation of the ocean current, we suggested threemethods to estimate the drift velocity of the TN by superimposing drift velocitiesreported by the anchor nodes. This augments the amount of information available forthe TN as an unbiased velocity estimate. To combat errors due to weakly correlatedmotion of nodes, we proposed two types of unbiased confidence indexes. Our schemealso incorporates sound-speed tracking and Doppler shift measurements availablefrom received packets, which, due to the uncertainty of the sound speed and thecontinuous motion of nodes in the channel, is a challenging task. We implementedtracking using the UKF and the EKF, and evaluated performance using numericalmodels for ocean current and power attenuation in the ocean. The results indicatea large gain of our scheme compared to reference approaches which do not considerdrift velocity estimation, Doppler shift measurements, or sound speed uncertainties,and showed that the CRLB is well approached by our scheme. The results fromtwo sea trials for different bathymetry channel structure conducted in Israel and inSingapore support the findings from simulations.66Chapter 4LOS and NLOS Classification forUWLIn the previous chapters, we have presented our approach for UWL and UT. Asexpected and observed in Figures 2.6 and 3.4b, localization accuracy depends onthe measurement noise from internal and external sources. In this chapter, we fo-cus on ranging noise, and specifically on the problem of mistaking NLOS-related ToFmeasurements as LOS measurements. Several works suggested ways to avoid misiden-tification of NLOS and LOS links. In [114], direct sequence spread spectrum (DSSS)signals, which have narrow auto-correlation, are transmitted to allow better separa-tion of paths in the estimated channel response. Averaging ToF measurements fromdifferent signals is suggested in [115], where results show considerable reduction inmeasurement errors. In [15], NLOS-related noise in the UAC is modeled using the Ul-tra Wideband Saleh-Valenzuela (UWB-SV) model, and multipath noise is mitigatedusing the approach introduced in [116]. A way to identify NLOS measurements is pre-sented in [95], where assuming that NLOS-based measurements have larger variancethan LOS-based measurements, measurements which increase the global variance arerejected. In [117], localization accuracy is improved by selecting ToF measurementsbased on minimal statistical mode (i.e., minimal variance and mean). Alternatively,the authors in [118] suggested a method for reducing the effect of NLOS-based noiseby assigning each measurement with a weight inversely proportional to the differencebetween the measured and expected distances from previous localization. However,no systematic way has been suggested to classify NLOS- and LOS-related ToF mea-surements. Instead, we take a more rigorous approach and estimate the distributionof the ToF measurements.The intuition behind our approach is that the continuous motion of nodes in theUAC changes causes shift in the arrival times and energy of signals received throughdifferent propagation paths, causing link variations. This diversity can be exploitedby obtaining multiple propagation delay (PD) measurements and classifying theminto classes of LOS, SNLOS and ONLOS (referring to Figure 1.4, recall SNLOSrefer to sea surface and bottom reflections and ONLOS to reflection off an object). Indoing so, we also take into account the effect of mobility on distance. The proposedclassification can improve the accuracy of UWL by rejecting or correcting NLOS-related PD measurements to obtain a single ToF estimation, or by using them tobound range estimation.To implement our scheme we present a two-step classification algorithm. We67Chapter 4. LOS and NLOS Classification for UWLfirst identify ONLOS-related PD-measurements by comparing PD-based range esti-mations with range estimations obtained from received-signal-strength (RSS) mea-surements. Considering the difficulty in acquiring an accurate attenuation model,our algorithm requires only a lower bound for RSS-based distance estimations. Afterexcluding PD measurements related to ONLOS, we apply a constrained expectation-maximization (EM) algorithm (cf. [91]) to further classify the remaining PD mea-surements into LOS and SNLOS. Through a clustering of PD measurements we mit-igate changes in propagation delay due to mobility of nodes. The EM algorithmalso estimates the statistical parameters of both classes, which can be used to im-prove the accuracy of UWL. Results from extensive simulations and three sea trialexperiments in different areas of the world demonstrate the efficacy of our approachthrough achieving a high detection rate for ONLOS links and good classification ofnon-ONLOS related PD measurements into LOS and SNLOS. To the best of ourknowledge, no prior work considered a machine learning approach for NLOS andLOS classification of multiple PD measurements. Moreover, link classification forranging was not investigated for the special characteristics of the UAC.It should be noted that while our approach can also be adapted to other typesof fading channels, it is particularly suited for UWL for the following reasons. First,our algorithm relies on significant power absorption due to reflection loss in ONLOSlinks, which are typical in the underwater environment. Second, we assume that thedifference in propagation delay between signals traveling through SNLOS and LOSlinks is noticeable, which is acceptable in the UAC due to the low sound speed inwater (approximately 1500 m/sec). Third, our algorithm is particularly beneficial incases where NLOS paths are often mistaken for the LOS path, which occurs in UWL,where the LOS path is frequently either not the strongest or non-existent. Last,we assume that the variance of PD measurements originating from SNLOS links isgreater than that of measurements originating from LOS, which fits channels withlong delay spread such as the UAC.The remainder of this chapter is organized as follows. Our system model and as-sumptions are introduced in Section 4.1. In Section 4.2, we present our approach toidentify ONLOS links. Next, in Section 4.3, we formalize the EM algorithm to classifynon-ONLOS related PD measurements into LOS and SNLOS. Section 4.4 includesperformance results of our two-step algorithm obtained from synthetic UAC envi-ronments (Section 4.4.1) and from three different sea trials (Section 4.4.2). Finally,conclusions are offered in Section System Setup and AssumptionsReferring to Figure 1.4, our system comprises of one or more transmitter-receiverpairs, (u, aj), exchanging a single communication packet of N symbols or impulsesignals, from which a vector X = [x1, . . . , xN ] of PD measurements xi, and corre-68Chapter 4. LOS and NLOS Classification for UWLsponding measured time ti, is obtained using detectors such as in, e.g., [44, 46, 47].We model xi such thatxi = xLOS + ni , (4.1)where xLOS is the PD in the LOS link, and ni is the measurement noise. We note thatdue to the mobility of nodes, xLOS is not strictly constant during the measurementinterval, and this motion bounds the accuracy of ranging.We focus on transmission over short range (on the order of a few km), for whichrefraction of acoustic waves is negligible and propagation delay in the LOS link ison average shorter than in the NLOS links. We assume successively transmittedsignals for PD measurements are separated by guard intervals such that ni in (4.1)can be assumed i.i.d. For each measurement xi a PD-based estimate, dPDi , is obtainedby multiplying xi with an assumed propagation speed, c. In addition, based on anattenuation model for an LOS link, we obtain RSS-based range estimates, dRSSi , i =1, . . . , N , from the received signals.In the following, we introduce our system model for obtaining RSS-based rangemeasurements as well as the assumed PDF for PD measurements.4.1.1 RSS-Based Range MeasurementsLet dLOS denote the distance corresponding to xLOS, i.e., dLOS = xLOSc. For thepurpose of obtaining RSS-based range measurements, we use the popular model [5]TLLOS(dLOS) = PL(dLOS) + AL(dLOS) +  , (4.2)where PL(dLOS) = ? log10(dLOS) is the propagation loss, AL(dLOS) = ?dLOS1000 is theabsorption loss, ? and ? are the propagation and absorption coefficients, respectively,and  is the model noise assumed to be Gaussian distributed with zero mean andvariance ?. Considering the simplicity of the model in (4.2), we do not directlyestimate dRSSi but rather estimate a lower bound dRSS,LBi , for which we apply upperbounds for ? and ? in (4.2) according to the expected underwater environment.For an ONLOS link with distance dONLOS = dONLOS,1 + dONLOS,2, where dONLOS,1and dONLOS,2 are the distance from source to reflector and from reflector to receiver,respectively6, we assume that the power attenuation in logarithmic scale is given by[5]TLONLOS(dONLOS) = TLLOS(dONLOS,1) + TLLOS(dONLOS,2) + RL , (4.3)where RL is the reflection loss of the reflecting object, whose value depends on thematerial and structure of the object and the carrier frequency of the transmittedsignals. Since RL is often large (see examples in [5]), and due to the differencesbetween models (4.2) and (4.3), we further assume thatTLONLOS(dONLOS) TLLOS(dONLOS) . (4.4)6Referring to the ONLOS link between node pair (u, a2) in Figure 1.4, dONLOS,1 = d21 anddONLOS,2 = d22.69Chapter 4. LOS and NLOS Classification for UWL4.1.2 PDF for PD MeasurementsSince we assume changes in xLOS are bounded by a small transmitter-receiver motionduring the time X is obtained, we can model the PDF of the noisy measurement xias a mixture of M = 3 distributions, corresponding to LOS, SNLOS, and ONLOSlinks, such that (assuming independent measurement noise samples in (4.1))p(X|?) =?xi?XM?m=1kmp(xi|?m) , (4.5)where ? = [?1, k1, . . . ,?M , kM ], ?m are the parameters of the mth distribution, andkm (M?m=1km = 1) is the a-priori probability of the mth distribution. Clearly, p(X|?)depends on multipath and ambient noise in the UAC, as well as on the detector usedto estimate xi. While recent works used the Gaussian distribution for p(xi|?m) (cf.,[86] and [10]), since multipath and ambient noises are hard to model in the UAC,we take a more general approach and model it according to the generalized GaussianPDF [119], such thatp(xi|?m) =?m2?m?(1?m)e?(|xi??m|?m)?m(4.6)with parameters ?m = [?m, ?m, ?m]. We associate the parameter vectors ?1, ?2,and ?3 with distributions corresponding to the LOS, SNLOS, and ONLOS links,respectively. Thus, by (4.1), ?1 = xLOS. Without prior knowledge of the actualdistribution of PD in the LOS and NLOS links, the use of parameter ?m in (4.6) givesour model a desired flexibility, with ?m = 1, ?m = 2, and ?m ? ? corresponding toLaplace, Gaussian, and uniform distribution, respectively. The flexibility and fit ofmodel (4.6) is demonstrated using sea trial results in Section 4.4.2.Following [95] and [117], we assume that PD measurements of NLOS links increasethe variance of the elements of X. Thus, if ?1, ?2, and ?3 are the respective variancesof measurements related to the LOS, SNLOS, and ONLOS links, then we have?1 < ?m, m = 2, 3. (4.7)Since, for the PDF (4.6),?m = (?m)2?(3?m)?(1?m) , (4.8)and by (4.8), ?m does not change much with ?m, constraint (4.7) can be modified to?1 < ?m, m = 2, 3. (4.9)70Chapter 4. LOS and NLOS Classification for UWLFurthermore, let TLIR be the assumed length of the UAC impulse response, whichis an upper bound on the time difference between the arrivals of the last and firstpaths. Then, since ?1, ?2, and ?3 in (4.8) capture the spread of measurements relatedto the LOS, SNLOS, and ONLOS links respectively,??m < TLIR, m = 1, 2, 3 . (4.10)Moreover, the propagation delay through the LOS link is almost always shorter thanthose for any NLOS link7. Hence, we have?1 < ?m < ?1 + TLIR, m = 2, 3. (4.11)Together with assumption (4.7), assumption (4.11) manifests the expected differencesbetween the PD in the LOS and NLOS links. Clearly, the more separable PD mea-surements from LOS and NLOS links are (i.e., the propagation delay difference islarger), the better the classification will be. Since the channel impulse response islonger for deeper channels, classification accuracy is expected to improve with depth.4.1.3 Remark on Algorithm StructureWe offer a two-step approach to classify PD measurements into LOS, SNLOS, andONLOS. First, assuming large attenuation in an ONLOS link, we compare PD-basedand RSS-based range estimates to differentiate between ONLOS and non-ONLOSlinks. Then, assuming PDF (4.6) for PD measurements, we further classify non-ONLOS links into LOS and SNLOS links.The reason for separating classification of ONLOS and SNLOS links is insufficientinformation about the distribution of the two link types. For example, delay inONLOS links may be similar to or different from that of SNLOS links. In the formercase, classification should be made for M = 2 states, while for the latter threestates are required. Since a mismatch in determining the number of states maylead to improper classification, we rely on the expected high transmission loss inONLOS links to first identify these links. Furthermore, a separate identification ofONLOS links can be used as a backup to our LOS/NLOS classifier. That is, wecan still identify the link as ONLOS even when the channel is fixed, and thus PDmeasurements originate from a single link-type. In the following sections, we describeour two-step approach for classifying PD measurements.4.2 Step One: Identifying ONLOS LinksConsidering (4.4), we identify whether measurement xi ?X is ONLOS-related basedon three basic steps as follows:7We note that in some UWACs, a signal can propagate through a soft ocean bottom, in whichcase SNLOS signals may arrive before the LOS signal [5]. However, such scenarios are rare and weassume that on average relation (4.10) holds.71Chapter 4. LOS and NLOS Classification for UWL? Estimation of dPDiWe first obtain the PD-based range estimation as dPDi = c ? xi.? Estimation of dRSS,LBiNext, assuming knowledge of the transmitted power level, we measure the RSSfor the ith received signal/symbol, and estimate dRSS,LBi based on (4.2), replac-ing ? and ? with upper bounds ?UB and ?UB, respectively.? ThresholdingFinally, we compare dPDi with dRSS,LBi . If dRSS,LBi > dPDi , then xi is classified asONLOS. Otherwise, it is determined as non-ONLOS.Note that the use of the above step Thresholding relies on assumption (4.4). Toclarify this, consider an ONLOS link. The RSS-based range estimation, dRSS,LBi , isobtained from an upper bound for an attenuation model (4.2), i.e., from applying anattenuation model for an LOS link to an ONLOS link. Since the latter is expectedto have a much larger power attenuation than the used model, it follows that dRSS,LBiwould be much larger than dPDi . Similarly, consider a non-ONLOS link (i.e., LOS orSNLOS). Here, since we use an upper bound for the attenuation model, we expectdRSS,LBi to be smaller than dPDi .Next, we analyze the expected performance of the above ONLOS link identifica-tion algorithm in terms of (i) detection probability of non-ONLOS links, Prd,non?ONLOS,and (ii) detection probability of ONLOS links, Prd,ONLOS. To this end, since explicitexpression for dLOS cannot be obtained from (4.2), in the following, we use the upperbound d?RSS,LB such thatlog10(d?RSS,LB) =TL?UB. (4.12)We note that (4.12) is a tight bound when the carrier frequency is low or when thetransmission distance is small.4.2.1 Classification of non-ONLOS LinksFor non-ONLOS links, we expect dRSS,LBi ? dLOS. Thus, since by bound (4.12),Pr(dRSS,LBi ? dLOS) ? Pr(d?RSS,LBi ? dLOS), and substituting (4.2) in (4.12), we getPrd,non?ONLOS ? 1?Q((?UB ? ?) log10 (dLOS)? ?dLOS1000?), (4.13)where Q(x) is the Gaussian Q-function.72Chapter 4. LOS and NLOS Classification for UWL4.2.2 Classification of ONLOS LinksWhen the link is ONLOS, we expect dRSS,LBi ? dONLOS. Then, substituting (4.3) in(4.12), and since Pr(dRSS,LBi ? dONLOS) ? Pr(d?RSS,LBi ? dONLOS), we getPrd,ONLOS ? Q(?UB log10 (dONLOS)? ? log10 (dONLOS,1dONLOS,2)? ?dONLOS1000 ? RL?).(4.14)Next, we continue with classifying non-ONLOS links into LOS and SNLOS links.4.3 Step 2: Classifying LOS and SNLOS LinksAfter excluding ONLOS-related PD measurements in Step 1, the remaining elementsof X, organized in the pruned vector Xex, are further classified into LOS (m = 1)and SNLOS (m = 2) links and their statistical distribution parameters, ?m, areestimated. Before getting into the details of our LOS/SNLOS classifier, we firstexplain its basic idea.4.3.1 Basic IdeaThe underlying idea of our approach is to utilize the expected variation in link typeof PD measurements due to mobility of nodes at sea. After identifying ONLOSlinks, this variation means that our set includes PD measurements of different valuesand link types. This allows us to use a machine learning approach to classify themeasurements into two classes, LOS and NLOS. For this purpose, we use the EMalgorithm. While using EM to classify measurement samples into distinct distribu-tions is a common approach, here the distribution parameters in (4.6) should alsosatisfy constraints (4.10), (4.9), and (4.11), where the two latter constraints introducedependencies between the parameters of the LOS and NLOS classes. Furthermore,we incorporate equivalence constraints to group measurements of similar values intoclusters which elements are classed to the same link type, thereby mitigating shiftsin the value of xLOS due to nodes? mobility. As we show later on, this result in anon-convex maximization of the log-likelihood function. For this reason, we presenta heuristic sub-optimal algorithm.In the following, we start by formalizing the equivalence constraints, and formu-lating the log-likelihood function. Next, we formulate a constrained optimizationproblem to estimate the distribution parameters, and present our heuristic approachto efficiently solve it. Given this estimate, we calculate the posterior probability ofeach PD measurement belonging to the LOS and SNLOS class, and classify the ele-ments of Xex accordingly. Finally, we describe how the initial solution, required forthe EM algorithm, is obtained and calculate the hybrid Crame?r-Rao bound to boundthe performance of our classifier.73Chapter 4. LOS and NLOS Classification for UWL4.3.2 Equivalence ConstraintsIn setting equivalence constraints, we assume that the identity and delay of the dom-inant channel path, used for PD detection, is constant within a given coherence time,Tc, and that for a bandwidth B of the transmitted signal, system resolution is lim-ited by ?T = 1B . PD measurements satisfying equivalence constraints are collectedinto vectors ?l, l = 1, . . . , L, where L denotes the number of such equivalence sets.Each PD measurement is assigned to exactly one vector, i.e., ?l have distinct ele-ments. To formalize this, we determine xi (recall that measurement xi correspondsto measurement time ti) and xj being equivalent, denoted as xi ? xj, if|ti ? tj| ? Tc (4.15a)|xi ? xj| ? ?T . (4.15b)To illustrate this, let xi, xj, and xn correspond to the same class (either LOS orNLOS), such that xi ? xj and xj ? xn. Then, although due to motion of nodes,xi and xn may not satisfy condition (4.15b), since ?l, l = 1, . . . , L, are distinctvectors, all three measurements xi, xj, and xn are grouped into same vector ?l andare further classified to the same state. That is, vectors ?p and ?q are merged ifthey have a common element. To form vectors ?l, l = 1, . . . , L, we begin with |Xex|(|?| symbolizes the number of elements in vector ?) initial vectors of single PDmeasurements, and iteratively merge vectors. This process continues until no twovectors can be merged. As a result, we reduce the problem of classifying xi ? Xexinto classifying ?l, which account for resolution limitations and node drifting.4.3.3 Formalizing the Log-Likelihood FunctionLet the random variable ?l be the classifier of ?l, such that if ?l is associated withclass m, m ? {1, 2}, then ?l = m. Also let ? = [?1, . . . , ?L]. Since elements in Xexare assumed independent,Pr(?l = m|?l,?p) =kpmp(?l|?pm)p(?l|?p)=kpm?xi??lp(xi|?pm)?2j=1 kpj?xi??lp(xi|?pj). (4.16)Then, we can write the expectation of the log-likelihood function with respect to theconditional distribution of ? given Xex and the current estimate ?p asL(?|?p) = E [ln (Pr(Xex,?|?)) |Xex,?p] =2?m=1[L?l=1Pr(?l = m|?l,?p)?xi??lln p(xi|?m) +L?l=1Pr(?l = m|?l,?p) ln km],(4.17)where lnx = loge x is the natural logarithmic function.74Chapter 4. LOS and NLOS Classification for UWLAssuming knowledge of ?p, ?p+1 is estimated as the vector of distribution param-eters that maximizes (4.17) while satisfying constraints (4.9), (4.10) and (4.11). Thisprocedure is repeated for Plast iterations, and the convergence of (4.17) to a localmaximum is proven [91]. Then, we calculate Pr(?l = m|?l,?Plast) using (4.16), andassociate vector ?l with the LOS path ifPr(?l = 1|?l,?Plast) > Pr(?l = 2|?l,?Plast) , (4.18)or with an SNLOS path otherwise. Estimation ?Plast and classifications ?l could beused further to improve the accuracy of UWL, e.g., [95, 23]. We observe that the twoterms on the right-hand side of (4.17) can be separately maximized, i.e., given ?p,we can obtain ?p+1m from maximizing the first term, and kp+1m from maximizing thesecond term. Thus (see details in [91]),kp+1m =1LL?l=1Pr(?l = m|?l,?p), m = 1, 2 . (4.19)In the following, we describe the details of our classification procedure for theestimation of ?m, followed by a heuristic approach for the initial estimates ? Estimating the Distribution Parameters ?1 and ?2To estimate ?m, we consider only the first term on the right-hand side of (4.17),which for the PDF (4.6) is given byf(?m, ?m, ?m) =L?l=1Pr(?l = m|?l,?p)?xi??lln ?m?ln(2?m)?ln ?(1?m)?(|xi ? ?m|?m)?m.(4.20)Then, considering constraints (4.9), (4.10) and (4.11), we find ?p+1m by solving thefollowing optimization problem:?p+11 ,?p+12 = argmin?1,?2?2?m=1f(?m, ?m, ?m) (4.21a)s.t. : ?1 ? ?2 ? ?1 + TLIR (4.21b)?m??????(3?m)?(1?m) ? TLIR ? 0 , m = 1, 2 (4.21c)?1 ? ?2 ? 0 . (4.21d)We observe that convexity of f(?m, ?m, ?m) depends on ?m. In Appendix A, wepresent an alternating optimization approach (cf. [120]) to efficiently solve (4.21).Next, we present an algorithm to obtain the initial estimation, ?0, whose accuracyaffects the above refinement as well as the convergence rate of the EM algorithm.75Chapter 4. LOS and NLOS Classification for UWL4.3.5 Forming Initial Estimation ?0Our algorithm to estimate ?0 is based on identifying a single group, ?l? , whoseelements belong to the LOS class with high probability, i.e., Pr (?l? = 1) ? 1. Thisgroup is then used as a starting point for the K-means clustering algorithm [91],resulting in an initial classification ?l for ?l, l = 1, . . . , L, to form two classified setsXexm , m = 1, 2. Finally, we evaluate the mean, variance, and kurtosis of the elementsin vector Xexm , denoted as E [Xexm ], Var [Xexm ], and K [Xexm ], respectively, to estimate?0 using the following properties for distribution (4.6):|Xexm ||Xex| = km , E [Xexm ] = ?m ,Var [Xexm ] =?2m?(3?m)?(1?m) ,K [Xexm ] =?(5?m)?(1?m)?(3?m)2 ?3 .(4.22)Since we assume that ?1 < ?2 (see (4.9)), we expect small differences between mea-surements of the LOS link, compared to those of SNLOS links. We use this attributeto identify group ?l? by filtering Xex and calculating the first derivative of the sortedfiltered elements. Group ?l? corresponds to the smallest filtered derivative.4.3.6 DiscussionWe note that the constraints in (4.21) do not set bounds on the values of ?1 and ?2,but rather determine the dependencies between them. This is because, apart fromthe value of TLIR and distribution (4.6), we do not assume a-priori knowledge aboutthe values of km and ?m, m = 1, 2. Without node motion, all elements of Xex belongto one class, but our classifier might still estimate both k1 and k2 to be non-zero,resulting in wrong classification into two classes. In this case, using the average ofthe elements of Xex might give a better estimation of dLOS than ?1.To limit this shortcoming of our classifier, we assume that ?1 and ?2 are distinct ifXex is indeed a mixture of two distributions. To this end, in the last iteration, Plast,we classify Xex as a single class (of unknown type) if the difference |?Plast1 ? ?Plast2 | issmaller than a threshold value, ?v (determined by the system resolution for distinctpaths). Then, if required, we find the distribution parameters of the (single) classby solving a relaxed version of (4.21), setting k1 = 1 and k2 = 0. Nevertheless, wemotivate relevance of our classifier in Section 4.4.2 by showing that scenarios in whichXex is indeed a mixture of two distributions are not rare in real sea environments.4.3.7 Summarizing the Operation of the ClassifierWe now summarize the operation of our classification algorithm, whose pseudo-code is presented in Algorithm 2. First, we evaluate dPDi and dRSS,LBi (lines 1-2). IfdRSS,LBi > dPDi , we classify xi as ONLOS; otherwise, we classify it as non-ONLOS(lines 3-5) and form the vector of non-ONLOS PD measurements, Xex, and groups76Chapter 4. LOS and NLOS Classification for UWLAlgorithm 2 Classifying X1: dPDi := c ? xi2: Calculate dRSS,LBi using RSS measurements, ?UB, ?UB and model (4.2)3: if dRSS,LBi > dPDi then4: Classify xi as ONLOS link5: else6: Exclude ONLOS measurements to form vector Xex and groups ?l satisfying(4.15)7: Estimate ?08: for p := 2 to Plast do9: Calculate kpm, m = 1, 2 using (4.16) and (4.19)10: for i := 1 to Nrepeat do {alternating maximization to solve (4.21) (see Ap-pendix A)}11: Estimate ?p,im , m = 1, 2 and set ?p,i+1m :=?p,im , ?p,i+1m :=?p,im , ?p,i+1m :=?p,im12: end for13: m = 1, 2: ?pm:=?p,Nrepeatm , ?pm:=?p,Nrepeatm , ?pm:=?p,Nrepeatm14: end for15: if |?Plast1 ? ?Plast2 | > ?v then16: Calculate Pr(?l = m|?l,?Plast) and ?l, m = 1, 2, l = 1, . . . , L using (4.16),(4.18)17: else18: Vector Xex consists of a single class. Repeat steps 7-14 for k1 = 1, k2 = 019: end if20: end if?l, l = 1, . . . , L (line 7). Next, we form the initial solution, ?0m (line 7), and run theEM algorithm for Plast iterations (lines 8-14). The procedure starts with estimatingkpm (line 9), followed by an iterative procedure to estimate ?pm for a pre-definednumber of repetitionsNrepeat (lines 10-13). After iteration Plast, we check if vectorXexconsists of two classes (line 15), and determine classifiers ?l, l = 1, . . . , L (line 16);otherwise Xex is classified as a single class (of unknown type), and, if estimating ?mis required, we repeat the above procedure while setting k1 = 1, k2 = 0 (line 18).The software implementation of the above algorithm can be downloaded from [96].Since the data for step 2 in Algorithm 2 is already available through the detectionof each symbol, and since the complexity of the EM algorithm is O (NPlast) (cf.[91]), the complexity of our algorithm is O (NPlastNrepeat). We also note that the EMalgorithm, as well as the alternate maximization process described in Appendix A,provably converge to a local maximum of the log-likelihood function (4.17). In thefollowing, we provide the hybrid Crame?r-Rao lower bound (HCRLB) as a benchmarkfor our classifier.77Chapter 4. LOS and NLOS Classification for UWL4.3.8 Deriving the HCRLBConsider the vector of measurements Xex whose elements are drawn from distribu-tions (4.6) withM = 2 classes (we assume that ONLOS measurements have correctlybeen identified). Our classifier estimates the vector ? = [?1, ?1, ?1, k1, ?2, ?2, ?2] =[?1, . . . , ?7]. We observe that constraints (4.11), (4.9), and (4.10), introduce depen-dencies between pairs (?1, ?5), (?2, ?6), (?r, ?r+1), r = 2, 6, respectively. Thus, wecannot use the conventional Crame?r-Rao Bound to lower bound the variance of anyunbiased estimator of ?. Instead, we apply the HCRLB considering ?1 as a deter-ministic and ?r = [?2, . . . , ?7] a vector of random variables having prior distributions,respectively. The HCRLB is given by [121]EXex,?r|?1[(?Plast ? ?) (?Plast ? ?)T]? H?1(?1) , (4.23)where H(?1) ? <7?7 is the hybrid Fisher information matrix8 (HFIM). Let %i be theclassifier of xi (i.e., %i = ?l if xi ? ?l). Then, the (j, q)th element of the HFIM isH(?1)j,q = E?r|?1 [F (?r, ?1)j,q] + E?r|?1[? ?2??j??qlog p(?r|?1)], (4.24)whereF (?r, ?1)j,q = EXex|?r,?1???|Xex|?i=1?2??j??qlog k%ip(xi|?%i)?? . (4.25)Solving (4.24) requires the calculation ofp(?r|?1) = p(k1)p(?2|?1)p(?2|?1, ?2)p(?1|?1)p(?1)p(?2) . (4.26)Since, as discussed in Section 4.3.6, we do not assume further knowledge aboutthe values of k1 and ?m, m = 1, 2, accounting for constraints (4.7)-(4.11) we as-sume p(?2|?1) is uniform between ?1 and ?1 + TLIR, p(?2|?1, ?2) is uniform be-tween ?1 and TLIR??????(1?2)?(3?2) , p(?1|?1) is uniform between 0 and TLIR??????(1?1)?(3?1) , andp(?m), m = 1, 2, is uniform between 1 and a deterministic parameter, G. Further-more, we assume p(k1) is uniform between 0 and 1. Exact expressions for (4.24) aregiven in Appendix B. For the numerical results presented in the following section weevaluate the HCRLB through Monte-Carlo simulations considering the above uniformdistributions.8Note that while the EM algorithm works on vectors ?l, the actual inputs to our classifier arePD measurements. Thus, in forming the HCRLB, we use xi rather than ?l.78Chapter 4. LOS and NLOS Classification for UWL4.4 Performance EvaluationIn this section, we present results from both computer simulations and sea trials todemonstrate the performance of our classification algorithm. The results are pre-sented in terms of detection probabilities of LOS, SNLOS, and ONLOS links. Inaddition, we measure estimation errors |?pm ? ?m|, |?pm ? ?m|, and |?pm ? ?m|. Wecompare our results to the HCRLB presented in Section 4.3.8, as well as to severalbenchmark methods. The purpose of the simulations is to evaluate the performanceof our classifier in a controlled environment, while results from sea-trial measurementsreflect performance in actual UWACs.4.4.1 SimulationsOur simulation setting includes a Monte-Carlo set of 10000 channel realizations,where two time-synchronized nodes, uniformly randomly placed into a square area of1 km, exchange packets. The setting includes two horizonal and two vertical obsta-cles of length 20 m, also uniformly randomly placed into the square area, such that aLOS always exists between the two nodes. In each simulation, we consider a packetof 200 symbols of duration Ts = 10 msec and bandwidth B = 6 kHz transmitted ata propagation speed of c = 1500 m/sec. To model movement in the channel (dealtwith by forming groups ?l), during packet reception the two nodes move away fromeach other at constant relative speed of 1 m/sec, and dLOS is considered as the LOSdistance between the nodes when the 100th symbol arrives.In our simulations, we use model (4.1) to obtain setX as follows. For each channelrealization and node positions, we find the LOS distance between the two nodes,and determine ?1 = xLOS. Based on the position of nodes and obstacles, we identifyONLOS links as single reflections from obstacles and determine ?3 as the average delayof the found ONLOS links. We use TLIR = 0.1 sec and based on constraint (4.11), werandomize ?2 according to a uniform distribution between ?1 and ?1 + TLIR. For theother distribution parameters ?, we determine ?m, m = 1, 2, 3 as an integer between1 and 6 with equal probability (i.e., G = 6 in (4.26)), and ?m, m = 1, 2, 3 according to(4.8) with ?m uniformly distributed between 0 and (TLIR)2, preserving ?1 < ?2. Basedon model (4.5), we then randomize xi, i = 1, . . . , 200 using distribution (4.6) and auniformly distributed km, m = 1, 2, 3 between 0 and 1, while keeping3?m=1km = 1and setting k3 = 0 if no ONLOS link is identified. Considering the discussion inSection 4.3.6, we use ?v = 1 mc as a detection threshold to check if measurementsin vector Xex correspond to a single link. Additionally, for forming groups ?l (see(4.15)), we use an assumed coherence time T?c = a ? Ts, where a ? {1, 5, 10}, and aquantization threshold ?T = 0.16 msec based on the bandwidth of the transmittedsignals. Note that since the distance between nodes changed by 2 m during receptionof the 200 symbols, if a > 2 m?T ?c ? 8.3, condition (4.15b) is irrelevant, whereas a = 179Chapter 4. LOS and NLOS Classification for UWL10 12 14 16 18 2000. probability?UB  Pd,ONLOSPd,ONLOS (analysis)Pd, non?ONLOSPd, non?ONLOS (analysis)(a) (b)Figure 4.1: Classification results: (a) Prd,non?ONLOS and Prd,ONLOS vs. ?UB, (b) Em-pirical detection probabilities of LOS and SNLOS.results into single-element vectors ?l.To simulate channel attenuation (4.2), we use ? = 15, ? = 1.5 dB/km (consideringa carrier frequency of 15 kHz [5]), and set  to be zero-mean Gaussian with variance5/dB2//?Pa@1m. We use a source power level of 100 dB//?Pa@1m and a zero-mean Gaussian ambient noise with power 20 dB//?Pa@1m, such that the SNR atthe output of the channel is high. Attenuation in LOS and SNLOS links is determinedbased on (4.2), while for ONLOS links we use (4.3) and set RL = 10 dB//?Pa@1m.To obtain the lower bound on RSS-based distance, dRSS,LBi , i = 1, . . . , 200, we use theattenuation model in (4.2) with ?UB = 20 and ?UB = 2 dB/km. An implementationof the simulation environment can be downloaded from [96].First, in Figure 4.1a we show empirical detection probabilities for ONLOS andnon-ONLOS links as a function of ?UB, as well as corresponding results using bounds(4.14) and (4.13). We observe a good match between the empirical results and theanalytical bound for Prd,ONLOS, and that Prd,ONLOS is hardly affected by ?UB. How-ever, Prd,non?ONLOS increases dramatically with ?UB, and the corresponding bound in(4.13) is less tight. This is because choosing ?UB < ? might lead to dRSS,LB > dLOSand neglectance of ? in (4.13) causes analytical inaccuracies. For Prd,ONLOS, however,the large RL is more significant than the effect of ?UB.In Figure 4.1b, we show empirical detection probabilities9 for LOS (LOS (EM))and SNLOS (SNLOS (EM)) links, the total detection probability (ALL (EM)), whichis calculated as the rate of correct classification (of any link). Also shown are classi-fication performance using only the initialization process (init), i.e., before the EMalgorithm is employed, as well as the results for classification without prior identifi-cation of ONLOS links (No ONLOS ID), i.e., without the first step of our algorithm.For the latter, we consider two cases: i) M = 2 and ii) M = 3, where in the9We note that detection probabilities are calculated only when vector X consists of both LOSand SNLOS related PD measurements; classification cannot be made otherwise.80Chapter 4. LOS and NLOS Classification for UWL0 5 10 15 20 25 300. Pr(? err<e)e [m]  ?1Plast (Tc=Ts)?1Plast (Tc=5Ts)?1Plast (Tc=10Ts)E(xi)min(xi)OutlierHCRB~~~Figure 4.2: Empirical C-CDF of ?err from (4.27).second case ONLOS links are considered as a separate class. We observe that theconstrained EM algorithm achieves a significant performance gain compared to theK-means algorithm, used in the initialization process. Results show that for the for-mer, the detection rate is more than 92% for both LOS and SNLOS. We also observea performance degradation when the first step for ONLOS identification is not per-formed. This degradation is more significant when ONLOS links are considered asSNLOS links, i.e., when M = 2. Please refer to the discussion in Section 4.1.3, forexplanations of this result.In Figure 4.2, we show the empirical complimentary cumulative distribution(C-CDF) of?err = |cx?? dLOS| , (4.27)where x? is i) ?Plast1 , ii) the average of the elements in X (E(xi)), iii) the minimumof X (min(xi)), or iv) the average value of X after removal of outliers, as suggestedin [95] (Outlier). Results for x? = ?Plast1 are shown for T?c ? {Ts, 5Ts, 10Ts}. Theresults in Figure 4.2 are also compared with the HCRLB presented in Section 4.3.8.We observe that the Outlier method outperforms the naive approaches of using theaverage or minimum value of X, where the latter performs extremely poorly for largevalues of ?err. However, the use of our classifier improves results significantly. Forexample, the proposed classifier achieves ?err ? 7 m in 90% of the cases, comparedto 11.2 m when using the Outlier method, and the results are close to the HCRLB.Such an improvement immediately translates into better localization performance asPD estimation errors significantly decrease. Comparing results for different values ofT?c, we observe that using equivalence constraints (i.e., T?c > Ts), performance slightlyimproves compared to the case of T?c = Ts. However, a tradeoff is observed as resultsfor T?c = 5Ts are marginally better than for T?c = 10Ts. This is because of erroneous81Chapter 4. LOS and NLOS Classification for UWL0 2 4 6 8 number, pc|?p 1?? 1|[m]0 2 4 6 8 1023456Iteration number, pc|?p 1?? 1|[m]0 2 4 6 8 1000.511.5Iteration number, p|?p 1??1|[m]0 2 4 6 8 number, p|kp 1?k|[m]Figure 4.3: Estimation error of LOS and SNLOS distribution parameters vs. EMiteration number.assignments to vectors ?l for over-estimated coherence time, T?c. This effect becomesmore significant when in addition to node movements also the channel changes (whichis included in the sea-trial results further below).Convergence of the EM iterative procedure is demonstrated in Figure 4.3, wherewe show average estimation errors of the distribution parameters of the LOS classas a function of the EM iteration step number. We observe that estimates stabilizeafter 10 iteration. While improvement compared to the initialization process (seeSection 4.3.5) is shown for all estimations, the impact of the EM algorithm is mostpronounced for the estimation of k1, which greatly affect classification performance.This improvement is also observed in Figure 4.1b.4.4.2 Sea TrialsWhile our simulations demonstrate good classification performance for our algorithm,the tests relied on the distribution model (4.6), and upper bound on transmission lossmodels (4.2) and (4.3), which might not be faithful representations of realistic UWACsand PD estimators. Thus, we present classification results for UWACs measuredduring three sea trials conducted in Israel and Singapore. One of these experimentswas conducted in a harbor environment to test only ONLOS classification, while theother two were in shallow water to test LOS and SNLOS classification. To acquirePD measurements from recorded sea-trial data, we used the phase-only-correlator(POC) detector as described in [47]. For the ith received signal, xi is estimated asthe first peak at the output of the POC that passes a detection threshold.82Chapter 4. LOS and NLOS Classification for UWL(a) (b)Figure 4.4: Israel harbor experiment: (a) location (picture taken from Google mapson Sep. 09), (b) results for ONLOS link classification.Classifying ONLOS linksIn this section, we show the performance of ONLOS link identification for anexperiment conducted at the Haifa harbor, Israel, in May 2009. The experimentincluded four vessels, each representing an individual node in the network. Here weconsider a subset of the recorded data for which nodes were static. In each vessel,a transceiver was deployed at a fixed depth of 3 m, at a water depth of around6 m. The four nodes were time synchronized using GPS and transmitted with equaltransmission power at a carrier frequency of 15 kHz. Referring to Figure 4.4a, node2 was placed at a fixed location 2A, while nodes 1, 3 and 4 sent packets to node2 while moving between various locations, creating a controlled environment of fivenon-ONLOS and four ONLOS communication links with a maximum transmissiondistance of 1500 m. For each link, (2, j), j ? {1,3,4}, we evaluated (i) dPD as theproduct of an assumed propagation speed of 1550 m/sec and the position of thefirst peak of the POC for the synchronization signal of each received packet, and (ii)dRSS,LB, employing an energy detector over the synchronization signal and using (4.2)for ?UB = 2 db/km and ?UB = 20. We note that results only changed slightly whenalternative methods for obtaining dRSS,LB and dPD were applied.In Figure 4.4b, we present values of dRSS,LB and dPD for each of the 9 commu-nication links. Applying our proposed ONLOS link identification method, all fourONLOS links were correctly classified and there was no false classification of non-ONLOS links. In particular, we observe that for all ONLOS links, dPD is much lowerthan dRSS,LB. Since the latter was obtained from model (4.2) (i.e., a model for LOS)and we assumed spherical propagation (i.e., ?UB = 20 in (4.2)), which is a very looseupper bound on power attenuation in the UAC (e.g., [5], [86]), this difference vali-dates our assumption that the RL level of the reflecting objects (which could havebeen harbor docks, ship hulls, etc.) are sufficiently high to satisfy assumption (4.4).83Chapter 4. LOS and NLOS Classification for UWLClassifying non-ONLOS linksNext, we present results from two separate experiments conducted in open sea:(i) the first along the shores of Haifa, Israel, in August 2010 and (ii) the second in theSingapore straits in November 2011, with water depths of 40 m and 15 m respectively.This is done to demonstrate our classifier?s performance in different sea environments.As communication links were all non-ONLOS links in both experiments, Xex = Xand we only present results for LOS/SNLOS classification.The first sea trial included three vessels, representing three mobile nodes, whichdrifted with the ocean current at a maximum speed of 1 m/sec, and were time-synchronized using the method described in Chapter 2. Throughout the experiment,the node locations were measured using GPS receivers (whose accuracy was up to?5 m), and the sound speed was measured to be c = 1550 m/sec with deviationsof no more than 2 m/sec across the water column. Each node was equipped witha transceiver, deployed at 10 meters depth, and transmitted more than 100 datapackets which were received by the other two nodes. Each packet consisted of 200direct-sequence-spread-sequence (DSSS) symbols of duration Ts = 10 msec and aspreading sequence of 63 chips was used.Table 4.1: Israel sea trial: distribution of estimated values of ?Plastm , m = 1, 2.Measure ? = 1 ? = 2 ? = 3 ? = 4 ? = 5 ? = 6?Plast1 , Tc = Ts 11% 7% 1.8% 1.8% 0% 77%?Plast1 , Tc = 10Ts 16% 11% 1% 1% 0% 67%?Plast2 , Tc = Ts 0% 54% 9% 5% 5% 24%?Plast2 , Tc = 10Ts 0% 57% 6% 5% 5% 25%An estimation parameter of interest is ?Plastm , which determines the type of dis-tribution of the mth class. In Table 4.1, we show the distribution of ?Plast1 and ?Plast2for different values of T?c. As the results are similar for both T?c = Ts and T?c = 10Ts,this implies that clustering PD measurements in vectors ?l does not affect the esti-mated type of distribution. We also observe that the LOS class seems to lean towards?Plast1 = 6, which implies a uniform distribution, while SNLOS measurements clusteraround ?Plast2 = 2, which corresponds to the normal distribution.In Figure 4.5, we show the empirical C-CDF of?err = |cx?? E(di)| , (4.28)where E(di) is the mean of the GPS-based transmitter-receiver distance during thereception of each packet, x? is either ?Plast1 , the average of the PD measurement in X(E(xi)), the minimum of X (min(xi)), or the average of the obtained PD measure-ments after removal of outliers, i.e., the method described in [95] (Outlier).Results84Chapter 4. LOS and NLOS Classification for UWL0 5 10 15 20 25 300. Pr(?err <e)e [m]  ?1Plast (Tc=Ts)?1Plast (Tc=5Ts)?1Plast (Tc=10Ts)E(xi)min(xi)Outlier~~~Figure 4.5: Empirical C-CDF of ?err from (4.28), T?c = 10Ts.are shown for T?c = aTs, where a ? {1, 10, 20}. Assuming GPS location uncertaintiesof 5 m, we require ?err to be below 6 m. Results show that ?err for x? = min(xi) islower than for x? = E(xi) and almost the same as the results for the Outlier method.However, proposed classifier achieves always the lowest error, which is smaller than6 m in more than 90% of the cases (compared to 55% for x? = min(xi)). Comparingresults for the different values of T?c, we observe that a notable advantage for T?c = 5Ts.Since in the sea trial, during packet reception nodes were almost static, this differenceis due to the time varying channel conditions.The second sea trial included two UWAC modems, manufactured by EvologicsGmbH, which were deployed at a depth of 5 m. One of them was suspended from astatic platform and the other from a boat anchored to the sea bottom. Throughoutthe experiment, the boat changed its location, resulting in three different transmitter-receiver distances which were monitored using GPS measurements (whose accuracywas on average ?1 m). Measurements xi ? X were obtained every 6 sec. Foreach transmission distance, the boat remained static for 20 min, allowing around200 measurements xi at each node. In this experiment, a propagation speed ofc = 1540 m/sec, as measured throughout the year in the Singapore straits [86],was considered.In Figure 4.6, since in the second sea trial the boat moved around its anchor whileX was obtained, we show the histogram of?erri = cxi ? di (4.29)for a single vector X, where di is the GPS-based transmitter-receiver distance mea-sured at time ti (i.e., when xi is measured), with mean and variance of E(di) =324.1 m and Var(di) = 3 m2, respectively. We also plotted cE(xi) ? E(di) and85Chapter 4. LOS and NLOS Classification for UWL?10 ?5 0 5 10 15 20 25 30 3500.  [m]  LOSSNLOSE(xi)min(xi)Theoretical PDF (?1)Theoretical PDF (?2)Figure 4.6: Histogram of ?erri from (4.29). Bin width 0.3 m, E(di) = 324.1 m.cmin(xi)?E(di) as well as PDFs (4.6) of the LOS and SNLOS classes for estimation?Plast , for which c?Plast1 ? E(di) = 0.1 m and c?Plast2 ? E(di) = 18.4 m. We estimated?Plast1 = 1 and ?Plast2 = 6, which matches the narrow and the near uniform distri-butions observed for the LOS and SNLOS classes, respectively. We note the goodfit between the shape of the estimated PDF and the histogram for both classes. Inaddition, we observe that estimation ?Plast1 gives much better results than the naiveapproach of taking the average or minimum value of X.Table 4.2: Singapore sea trial: cx??E(di)E(di) .Average distance [m] x? = ?Plast1 x? = ?Plast2 x? = E(xi) x? = min(xi)83 0.007 0.29 0.19 0.07324 0.0017 0.05 0.01 0.15584 0.0018 0.03 0.02 0.002In Table 4.2 we present results of the ratio cx??E(di)E(di) for the three locations of theboat, averaged for the two nodes, for x? = ?Plast1 , ?Plast2 , E(xi),min(xi). We observethat min(xi) usually, but not always, results in better propagation delay estimationthan E(xi), which in turn always results in better estimation than ?Plast2 , as expected.However, best results are obtained for c?Plast1 ?E(di)E(di) with average of 0.7 m compared tomore than 10 m for the other methods.The results in Figures 4.5, 4.6, and Table 4.2 show a significant differences of up to30 m between range measurements. Since motion of nodes was limited during the timeeach set of measurements X was obtained in both sea trials, this variation is due toa large difference between the delays in the LOS and SNLOS links, and validates our86Chapter 4. LOS and NLOS Classification for UWL10 20 30 40 50 600. [m]EmpricalP(? e?x)  W=10 (sync)W=10 (?1)W=30 (sync)W=30 (?1)Figure 4.7: Localization error, ?e, as a function of the number of received packets,W .assumptions (4.7) and (4.11). Moreover, since model mismatch of (4.6) would haveconsiderably affected the accuracy of estimating ?Plast1 , the good estimation results inFigure 4.5 and Table 4.2, as well as the distribution of ? in Table 4.1, validate thechoice of model (4.6) in two different sea environments (Israel and Singapore).Finally, we present the effect of our classifier on localization accuracy. We userecordings of PD measurements obtained from the first sea trial for the localizationmethod described in Chapter 2. This method time-synchronizes and localizes nodesusing PD measurements from anchors. The results are shown in terms of the distanceerror, ?e, of the estimated location for ranging using i) the estimated ?Plast1 value (forT?c = 5Ts), and ii) a single PD measurement obtained from the output of the POC fora chirp signal transmitted at the prefix of each packet (sync). The results are shownin Figure 4.7 for localization using W = [10, 30] packet exchanges (see Chapter 2 fordetails). Note that the large errors are due to GPS location uncertainty, which weused as reference and which for this sea trial corresponds to a localization error of upto 15 m. Using our classification approach, we observe a significant improvement ofup to 10 m in localization accuracy.4.5 ConclusionsIn this chapter, we utilize the variation of PD measurements due to continuous motionof nodes at sea and classify the former into three classes: LOS, SNLOS, and ON-LOS. We presented a two-step classifier which first compares PD-based and receivedsignal strength based ranging to identify ONLOS links, and then, for non-ONLOS87Chapter 4. LOS and NLOS Classification for UWLlinks, classifies PD measurements into LOS and SNLOS paths, using a constrainedexpectation maximization algorithm. We also offered a heuristic approach to effi-ciently maximize the log-likelihood function, and formalized the Crame?r-Rao Boundto validate the performance of our method using numerical evaluation. As our classi-fier relies on the use of simplified models, alongside simulations, we presented resultsfrom three sea trials conducted in different sea environments. Both our simulationand sea trial results confirmed that our classifier can successfully distinguish betweenONLOS and non-ONLOS links, and is able to accurately classify PD measurementsinto LOS and SNLOS paths.88Chapter 5A Machine Learning Approach forUnderwater DROur UT scheme presented in Chapter 3 relies heavily on speed and orientation mea-surements from on-board INS producing acceleration measurements. To this end, weaim to obtain a set of distance and heading measurements between each two loca-tions for which the tracked node receives a communication packet from its neighboranchor nodes. Using acceleration measurements, this procedure is preformed throughDR. As illustrated in Figure 1.5, at the presence of ocean waves these measurementsneed to be projected to the horizontal plane by compensating for the time-varyingpitch angle. The current methods discussed in Section 1.1.3 perform such projectionthrough direct measurement of the TN orientation. However, this approach limits theresolution of DR navigation, as measurements are filtered over the period of severalocean waves [54]. Moreover, due to energy constraints, gyrocompass are not always inuse and orientation measurements may not be available. A different approach may beto directly project acceleration measurements using the principal component analysis(PCA) (cf. [122, 123]). PCA gives the axis coordinate system (or the transformationmatrix to that system) along whose axes the variation of change is smallest. If thevessel acceleration is constant in a certain plane, PCA projection aligns accelerationmeasurements with that plane. The underlining hard assumption of this method isa large variance of acceleration measurements in the y and z axes and a fixed ac-celeration in the x axis. In the absence of alternative approaches to compensate forthe time-varying pitch angle with no orientation measurements, we use the so-calledPCA method as a benchmark.In this chapter, we offer a machine learning approach to compensate for the pitchangle using a single 3-D acceleration sensor. Our method, denoted as the DR-navigation-using-a-single-accelerometer (DR-A), is based on the observation that,due to ocean waves, the vessel pitch angle is periodic in nature. The intuition behindour method is that, when the vessel pitch angle is fixed, direction can be determinedwithout using orientation measurements. Hence, by identifying classes of accelera-tion measurements such that in each class the pitch angle is approximately the same,we can readily project acceleration measurements into a reference coordinate system.While our method can be used also for AUVs submerged deep at sea, it is mostlydesignated to compensate for wave induced motions. The main contribution of ourwork is therefore in obviating the need to compensate for the vessel time-varyingpitch angle via direct measurement of the vessel orientation using dedicated hard-89Chapter 5. A Machine Learning Approach for Underwater DRCombine per?state projected measurementsEstimate heading angleClasify measurements to M pitch?states Per?state: compansate on pitch angleIntegrate measurements to estimate distanceAlign measurements with vessel motion to compansate on heading angle Per state: estimate pitch angleFigure 5.1: Flow chart for the DR-A algorithm.ware, e.g., gyrocompass, without setting hard limitation on the vessel motion. OurDR-A method is executed sequentially. First, we estimate the vessel heading angleand project acceleration measurements such that these are aligned with the vessel mo-tion. Next, we classify the projected measurements into pitch-states of similar pitchangles. This is performed using a constraint EM algorithm. Third, per pitch-state, weproject acceleration measurements (whose pitch angles are similar) to compensate onthe vessel pitch angle. After this step, the vessel?s projected local coordinate systemis considered aligned with the the vessel heading direction and the East-North-Upcoordinates system. Finally, we integrate the projected measurements to evaluatethe distance traveled by the vessel. A flow chart of the above process is given inFigure 5.1.The remainder of this chapter is organized as follows. Our system model andassumptions are introduced in Section 5.1. In Section 5.2, we present the steps ofour DR-A method. Section 5.3 includes performance evaluation of our algorithm insimulations (Section 5.3.1) and using realistic data obtained during a designated seatrial (Section 5.3.2). Finally, conclusions are offered in Section System ModelOur system consists of a three-axis accelerometer device attached to a vessel, whichproduces N acceleration measurements during a set period of time, [tstart, tend], wheretend ? tstart is expected to be in the order of 10 seconds. We assume that at timetstart, the vessel?s initial speed and heading with respect to a reference coordinatesystem (e.g. UTM) is given as vi, and ?init, respectively. Our objective is to trackthe vessel heading angle between time instances tstart and tend, as well as to estimate90Chapter 5. A Machine Learning Approach for Underwater DRthe distance traveled by the vessel during the considered time period10, d?i,j. This isrequired for compensation of nodes? mobility for localization purposes.Let an,x, ?n, and ?n, n = 1, . . . , N be the vessel?s acceleration along the vesselheading direction, the vessel heading direction with respect to the reference coor-dinate system, and the vessel orientation (i.e., the direction in which the vessel?sbow is pointing) with respect to its heading direction ?n, respectively. We assumethat the change in ?n is only due to timely changes in ?n. That is, that during pe-riod [tstart, tend] the vessel?s orientation with respect to the reference system does notchange. In addition, we assume both an,x and ?n are slowly time-varying, such thatthe considered time period can be divided into W = tend?tstartTc time slots of durationTc (representing the coherence time of the system), in each of which Nslot = NTctend?tstartacceleration measurements are acquired, where in each time slot w, ?n and an,x areassumed fixed and equal ?w and aw,x, respectively. For simplicity, we assume the ves-sel?s motion is perfectly correlated with ocean waves such that the vessel roll anglecan be neglected. However, extension is suggested also for the case of time-varyingpitch and roll angles (see Section 5.2.5).In the wth time slot, on time tn, n = 1, . . . , Nslot, tstart ? tn ? tend, the ac-celerometer device produces a three-axis acceleration measurement vector, a?n =[a?n,x, a?n,y, a?n,z], at local coordinates, which are grouped into a matrix A?. Vectora?n is a projection of a vector an = [an,x, an,y, an,z]T representing the vessel?s accelera-tion in a 3-D coordinate system referred to as the horizontal plane. The coordinatesof the horizontal plane are defined so that the x axis is aligned with the vessel?sheading direction, assuming there is no movement in the y axis (since within thetime slot the heading is assumed fixed), and the z axis is as in the East-North-Upcoordinates system. Thus, the horizontal plane is separately defined for each timeslot of duration Tc with assumed fixed heading and acceleration. Referring to theillustration on Figure 1.5, the projection from an into a?n is modeled by a rotat-ing vector, [an,x, an,y, an,z]T about its y-axis by the vessel time-varying pitch angle,?n, then its z-axis by angle ?n, and adding a zero-mean Gaussian noise, en, with aper-axis standard deviation of ?3 m/(seconds)2, so that:??a?n,xa?n,ya?n,z?? =??cos ?n 0 sin ?n0 1 0? sin ?n 0 cos ?n????cos?n ? sin?n 0sin?n cos?n 00 0 1????an,xan,yan,z??+??en,xen,yen,z?? .(5.1)We note that while an,y is assumed zero, an,z can be non-zero. This is due to the?up and down? movements of the vessel with the ocean waves. However, we expecta small value for an,z. This is required to solve an ambiguity in estimating the pitchangle11. In fact, we are interested in cases where |an,x| >> |an,z|. Otherwise, the10Throughout this chapter upper case bold symbols represent matrices, bold symbols representvectors, ?? represents the measurement of true parameter ?, and ?? represents the estimation of ?.11This assumption is validated using a realistic wave model as well as results from a sea trial.91Chapter 5. A Machine Learning Approach for Underwater DRvessel is moving in almost fixed speed, vi, and projection is not required. However,it is important to note that by (5.1), even when an,z is zero, compensation over both?n and ?n is required.For each time instance tn, we aim to estimate ?n and ?n, and to project thevessel?s local coordinate system about the z-axis followed by its y-axis. The firstprojection converts the set of measurements A? into a projected set A?h with elementsa?hn. The second projection further converts the set of measurements into a projectedset A?h,p with elements a?h,pn . Since after the second projection the local coordinatesystem is expected to be aligned with the horizontal plane, we can readily integrateelements a?h,pn to estimate d?i,j. Furthermore, since the vessel?s orientation with respectto the reference coordinate system is assumed fixed during [tstart, tend], such projectionallows us to estimate the per-time slot change in the vessel?s heading direction withrespect to the initial heading, ?init.By (5.1), the set of measurements A? are affected by the pitch angle of the vessel.Much like the ocean waves, the vessel pitch angle is periodic in nature and likely,?pi4 < ?n <pi4 . However, being induced from ocean waves, we do not assume afixed period for the vessel pitch angle. Given this periodicity, we can identify timeinstances for which the vessel pitch angle is approximately the same. This observationsets the stage for classifying measurements into pitch-states of assumed fixed pitchangle, given the following model.Let A?(w) with elements a?n(w) = [a?n,x(w), a?n,z(w)]T , n = 1, . . . , Nslot be the set of2-D acceleration measurements acquired during the wth time slot, w = 1, . . . ,W , andsorted by their measurement time. We consider a Gaussian mixture with M pitch-states for the distribution of A?(w) such that for?(w) = {?1,x(w),?1,z(w), k1(w), . . . ,?M,x(w),?M,z(w), kM(w)},P (A?(w)|?(w)) =?a?n(w)?A?(w)M?m=1km(w)Pm(a?n,x(w)|?m,x(w))Pm(a?n,z(w)|?m,z(w)) ,(5.2)where ?m,x(w) =[?m,x(w), ?2m,x(w)], and ?m,z(w) =[?m,z(w), ?2m,z(w)], are the dis-tribution parameters of the mth pitch-state with mean ?m,x(w) and ?m,z(w), andvariance ?2m,x(w) and ?2m,z(w), respectively. km(w) (M?m=1km(w) = 1) is the a-prioriprobability of the mth pitch-state. Model (5.2) is used to classify acceleration mea-surements into pitch-states using a constraint EM algorithm. For clarity, in the fol-lowing we drop the time slot subindex, w, and consider projection of measurementsacquired during a single time slot.92Chapter 5. A Machine Learning Approach for Underwater DR5.2 The DR-A MethodRefereing to model (5.1), in the DR-A method we estimate angles ?n and ?n to projectmeasurement in A? into the horizontal plane and obtain an estimation for an,x, n =1, . . . , Nslot. While the orientation angle, ?n, is assumed fixed during the time slot,it is not the case for the pitch angle, ?n. For this reason, we separately compensatethe vessel heading and pitch angles. The former is done jointly for all measurementsacquired during a single time slot, resulting in a projected set A?h. For the latter,we use machine learning approach to classify acceleration measurements into statesof similar pitch angles, and compensate the pitch angle to form a projected set A?h,pfor every state, considered aligned with the horizontal plane. Finally, we combineprojected measurements of all time slots, and, using the initial (given) velocity vi,integrate them over the time period [tstart, tend] to obtain d?i,j. In the following sectionswe describe in details the steps of our method.5.2.1 Forming A?h: Estimation of the Heading AngleBefore forming classes of similar pitch angles, we project a?n ? A?, n = 1, . . . , Nslotto form a?hn = [a?hn,x, a?hn,y, a?hn,z], for which a?hn,z = a?n,z and (if the vessel?s pitch angleis zero) a?hn,x aligns with the heading of the vessel. This projection is performed asfollows.Refereing to Figure 1.5, ?n denotes the angle between the heading direction of thevessel, ?n, and the accelerometer?s local x-axis. Since in every time slot the vessel isassumed moving in a fixed heading, without measurement noise, there should be noacceleration caused by the vessel motion along the axis which is perpendicular to theheading direction. Therefore, we expecta?n,x sin?n ? a?n,y cos?n ? 0 . (5.3)We look for estimation ??n = ?? which minimizesN?n=1(a?n,x sin?? a?n,y cos?) by,tan ?? =N?n=1a?n,yN?n=1a?n,x. (5.4)Once ?? is determined through (5.4), we project measurements in A? and form matrixA?h. This is performed by multiplying a?n ? A?, n = 1, . . . , Nslot with the rotationmatrix??cos ?? sin ?? 0? sin ?? cos ?? 00 0 1?? . (5.5)93Chapter 5. A Machine Learning Approach for Underwater DRIn the wth time slot, the estimated angle ??w from (5.4) is compared with ??w?1to estimate the heading direction of the vessel, ?w, assumed fixed in each time slot.Let ??w be the change in the heading direction of the vessel between the w ? 1thtime slot and the wth one. Then, ?w = ?w?1???w. Recall we assume the directionof the vessel?s bow with respect to the reference coordinate system (e.g. UTM) doesnot change during the considered time period, [tstart, tend]. Thus, ???w = ??w ? ??w?1,and??w = ??w?1 ????w , (5.6)where ??0 = ?init.5.2.2 Forming A?h,p: Estimating the Time-varying PitchAngleAfter forming matrix A?h, we estimate the vessel pitch angle to form matrix A?h,p,which will be used to calculate d?i,j. Since the vessel pitch angle is time-varying, dif-ferent from estimation (5.4), elements of A?h cannot be directly projected to A?h,p. Forthis reason, traditionally, a direct measurement of the vessel orientation is used via,e.g. gyrocompass, which may be unavailable or too noisy. In this section we describean alternative approach, where based on the observation that the vessel pitch angleis periodic in nature, we form matrix A?h,p by grouping acceleration measurements toclasses of similar pitch angles.Based on model (5.2), to identify measurements of similar pitch angles we use aconstraint EM algorithm and classify the elements in A?h into M? pitch-states, whereM? is a pre-defined number of states. For an assumed coherence time, T?c, classificationis performed separately for each time slot. Since the effect of the pitch angle is similarin the x and z axes, classification is performed jointly for both axes.In classifying A?h, we can use side information in the form of positive constraintsfor measurements which must belong to the same pitch-state, and negative constraintfor measurements which must be classified into different pitch-states, as described inthe following.Formulating Positive ConstraintsPositive constraints allow us to mitigate measurement noise by relaxing the element-wise clustering problem, and instead clustering sets of measurements. Since thevessel pitch angle is continuous, we limit positive constraints to consecutive measure-ments, a?hn, a?hn+1, . . . , a?hn+? of similar values, where ? is limited. To formulate positiveconstraint, let Vpos be a predefined multiplication of the sensitivity level of the ac-celerometer device being used. Also let Tp be a pitch-coherence time used as an94Chapter 5. A Machine Learning Approach for Underwater DRupper bound for the time period over which positive constraints can be defined fortwo acceleration measurements. Define relation an ? an? if|an,x ? an?,x| < Vpos (5.7a)|an,z ? an?,z| < Vpos (5.7b)|tn ? tn?| ? Tp , (5.7c)otherwise an = an? . We classify measurements a?hn and a?hn? into the same pitch-state ifa?hn ? a?hn? , and if there exist no element a?hj , such that tn < tend < tn? and a?hn = a?hj ora?hn? = a?hj . Since the vessel pitch angle is affected by ocean waves, we set Tp = 12fwave ,where fwave is the fundamental frequency of the ocean waves, which can be estimatedusing, e.g. cyclostationary analysis (cf. [124]). Positive constraints are used to formmatrixes ?l, l = 1, . . . , L, each including a chain of consecutive measurements whichpair-wise are classified into the same pitch-state.The above definition of positive constrains guarantees that ?l are disjoint ma-trixes. We obtain ?l by grouping consecutive acceleration measurements satisfyingthe above constraints in disjoint matrixes such that a new matrix is formed every timepositive constraints are not met for two consecutive measurements. For each vector?l we assign classifier ?l = {1, . . . , M?} such that all elements in ?l are classified intothe same ?l pitch-state. To this end, we reduce the problem of classifying a?hn ? A?hinto classifying ?l.Formulating Negative ConstraintsNegative constraints reflect the expected change in the vessel pitch angle. Since thelast element of ?l and the first element of ?l+1 do not satisfy (5.7), negative con-straints are formed as the complementary of positive constraints. More specifically,negative constraints ensure that two consecutive subsets ?l and ?l+1 cannot sharethe same pitch-state. Interestingly, since the rank of vectors ?l, l = 1, . . . , L islimited by Tp, if Tp < T?c (recall T?c is the duration of each time slot) then negativeconstraints renders L ? 2. We represent negative constraints by operator??l,?l+1 ={1 ?l = ?l+10 otherwise}, l = 1, . . . , L . (5.8)Shental [125] suggested formalizing negative constraints by a directed Markovgraph, where in our case classifier ?l is a hidden (decision) node, connected to both ?l?1and ?l+1, as well as to an observation node, a?hn ??l. Since the pitch angle associatedwith ?l+1 depends on the pitch angle associated with ?l, hidden nodes form adirected chain from parent, ?l, to child, ?l+1, and from hidden nodes to observationnodes, as illustrated in Figure 5.2. This directed chain is a form of a Bayesian belief95Chapter 5. A Machine Learning Approach for Underwater DR?l?1 ?l+1?l?l+1?l?1 ?lFigure 5.2: Graph representation for positive and negative [126], where for Y being the set of classifiers ?l, l = 1, . . . , L (with ?0 = ?),we obtain the joint distributionP(Y|A?h,?)=L?l=1P(?l|?l?1,?, A?h). (5.9)The relation in (5.9) would be used to formulate the likelihood function to determine?l using a constraint EM algorithm, as described next.Formulating the Likelihood FunctionConsidering both positive and negative constraints, the data likelihood function forthe event of correct classification of the elements of A?h isP (A?h,Y|?) = 1c1L?1?l=1(1? ??l,?l+1)L?l=1?a?hn??lP (?l|?)P (a?hn,x|?l,?)P (a?hn,z|?l,?) , (5.10)where c1 =M???1=1? ? ?M???L=1L?1?l=1(1? ??l,?l+1)L?l=1P (?l|?).For classifying subsets?l, we use the EM algorithm to iteratively maximize (5.10).In the pth iteration, we obtain estimation ??p of ?, with elements ??pm,x, ??pm,z, ??pm,x,??pm,z, and k?pm, m = 1, . . . , M? . For the Gaussian mixture model (5.2), given ??p we96Chapter 5. A Machine Learning Approach for Underwater DRobtain [91]??p+1m,? =L?l=1P (?l = m|A?h, ??p)?a?hn,???la?hn,?L?l=1P (?l = m|A?h, ??p), ? ? {x, z} (5.11a)??p+1m,? =L?l=1P (?l = m|A?h, ??p)?a?hn,???l(a?hn,? ? ??p+1m)2L?l=1P (?l = m|A?h, ??p), ? ? {x, z} . (5.11b)Furthermore,k?p+11 , . . . , k?p+1M? = argmaxk1,...,kM?log(1c1)+M??m=1log(km)L?l=1P (?l = m|A?hx, A?hz , ??p) (5.12a)s.t.M??m=1km = 1 . (5.12b)Since c1 is a function of km (recall km = P (?l = m|??p)), it is hard to maximize(5.12). Instead, we approximate c1. Assuming negative constraints are mutuallyexclusive, c1 ? (1?M??j=1k2j )L?1 [125]. Clearly, this approximation does not hold in ourcase. However, since our Markov graph is sparse, this assumption has little effect onperformance (as our numerical simulations show). From (5.12) and using a lagrangemultiplier, we get?2(L?1)k?p+1m +P (?l = m|A?hx, A?hz , ??p)(1?M??j=1(k?p+1j )2)k?p+1m+(2L?1)M??j=1(k?p+1j )2?1 = 0 .(5.13)The expression in (5.13) can be solved for k?p+1m either by approximatingM??j=1(k?p+1j )2 asM??j=1(k?pj )2 (and k?pj is known from previous iteration), or using alternating optimizationtechnique (cf. [120]). Equations (5.11a), (5.11b), and (5.13), are used to determine??p+1, which in turn is used for the next EM iteration till convergence of (5.10) isreached12.12Note that the EM algorithm is proven to converge to a local maxima of the log-likelihoodfunction [91].97Chapter 5. A Machine Learning Approach for Underwater DRIn the last EM iteration, plast, we determine classifiers ?l, l = 1, . . . , L of vectors?l by numerically solving?l = argmax??l[P (??l = m|A?hx, A?hz , ??plast)], (5.14)and construct matrix A?hm, m = 1, . . . , M? including elements a?hn for which ?l = mand ?n = ?m.Considering model (5.1), to project the elements in matrix A?hm project onto A?h,pm ,we estimate a solution ??m by multiplying a?hn ? A?hm, n = 1, . . . , N with the rotationmatrix??cos ??m 0 ? sin ??m0 1 0sin ??m 0 cos ??m?? , (5.15)Observing model (5.1), we note that when the noise vector en is zero and headingcompensation is ideal, multiplying a?hn ? A?hm by the matrix in (5.15) gives the vector??ah,pn,x(??m)ah,pn,y(??m)ah,pn,z(??m)?? =??an,x cos (??m ? ?m) + an,z sin (?m ? ??m)an,yan,x sin (??m ? ?m) + an,z cos (??m ? ?m)?? . (5.16)Since an,z can be non-zero, ??m cannot be estimated following the same approach as in(5.4). Unfortunately, (5.16) sets a degree of freedom in choosing ??m. Instead, since weassumed an,x >> an,z (see Section 5.1), the term an,x (cos (??m ? ?m) + sin (??m ? ?m))is approximated by ah,pn,x(??m) + ah,pn,z(??m). Since ah,pn,x(??m) + ah,pn,z(??m) achieves its max-imum for ??m ? ?m = pi4 when an,x > 0, and for ??m ? ?m =pi4 + pi when an,x < 0, weset??m,1 = argmax??m?n: a?hn?A?hmah,pn,x(??m) + ah,pn,z(??m)?pi4??m,2 = argmax??m?n: a?hn?A?hmah,pn,x(??m) + ah,pn,z(??m)?pi4? pi . (5.17)From the two solutions in (5.17), we choose the one satisfying condition?pi4 < ??m <pi4 ,and using (5.16) form projection ah,pn,x, considered aligned with the horizontal planealong the vessel heading direction. Finally, we combine projected measurements fromall time slots and pitch-states in matrix A?h,p.Due to the dependency between hidden nodes ?l, the difficulty in (5.11), (5.13),and (5.14) lies in calculating P (?l = m|A?hx, A?hz , ??p). We next describe an efficientway to obtain the posterior probabilities.98Chapter 5. A Machine Learning Approach for Underwater DRFinding the Posterior ProbabilityFinding the posterior probability is simple when only positive constraints are imposed.Here, P (?l = m|A?h, ??p) = P (?l = m|?l, ??p), and since measurements in A?h areassumed independent (see (5.2)),P (?l = m|?l, ??p) =k?pmP (?l|?pm)P (?l|??p)=k?pm?a?hn??lP (a?hn,x|?pm)P (a?hn,z|?pm)?M?j=1 k?pj?a?hn??lP (a?hn,x|?pj)P (a?hn,z|?pj). (5.18)However, at the presence of negative constraints, ?l depends on other hidden nodes,andP (Y|A?h, ??p) =L?1?l=1(1? ??l,?l+1)L?l=1?a?hn??lP (?l|a?hn,x, ??p)P (?l|a?hn,z, ??p)c2, (5.19)wherec2 =M???1=1? ? ?M???L=1L?1?l=1(1? ??l,?l+1)L?l=1?a?hn??lP (?l|a?hn,x, ??p)P (?l|a?hn,z, ??p) .Here, the posterior probability can be obtained by marginalizing the joint probability(5.19). However, in general, this is an NP-hard problem (with similarities to the graphcoloring problem) with complexity O(M?L?1)[126]. Instead, since the Markov graphillustrated in Figure 5.2 is a directed chain, belief propagation techniques can beused to significantly reduce complexity to O (LM2) [126]. The general idea in beliefpropagation is based on observation (5.9), that assuming P (?l|?l?1) is known, beliefBEL?l(m) = P (?l|A?h, ??p) can be exactly calculated by receiving belief BEL?l?1(m)from parent ?l?1 and likelihood P (A?h|?l+1, ??p) from child ?l+1. Following [125], weuse Pearl?s belief propagation algorithm for trees [126], as presented in the following.In Pearl?s algorithm, each hidden node l exchanges ?messages? ??l(m) and pi?l(m)with his parents and children, respectively. We start by initializing lists pi?l(m) =??l(m) = 1, ?l,m, l = 1, . . . , L, m = 1, . . . , M? . Upon activation, each hidden node,?l, receives pi?l?1(m) and ??l+1(m) from its parent and child, respectively. It thencalculates??l(m) =M??n=1??l+1(n)?a?h??lP(?l = n|?l?1 = m, a?hn,x, a?hn,z, ??p)(5.20a)pi?l(m) =M??n=1pi?l?1(n)?a?h??lP(?l = m|?l?1 = n, a?hn,x, a?hn,z, ??p)), (5.20b)99Chapter 5. A Machine Learning Approach for Underwater DRwhere pi?0(m) = 1 (recall ?0 = ?), and setsBEL?l(m) =??l+1(m)pi?l(m)M??j=1BEL?l(j). (5.21)Next, hidden node ?l sends ?message?pi?l (m)M??j=1pi?l (j)to its child, ?l+1, and??l (m)M??j=1??l (j)to itsparent, ?l?1. Since our network is a directed Markov chain, we execute (5.20) and(5.21) for the sequence ?1 ? ?2 ? ? ? ? ?L, and reach convergence after L steps.Initial Estimation ??0The EM algorithm in (5.11) and (5.12) requires initialization of ??0. With no priorknowledge of the effect of ocean waves on acceleration, we use the K-means clusteringalgorithm (cf. [91]) to initially classify elements in each time slot into M? pitch-statesand form matrixes A?hm. Similar to the EM algorithm, the K-means algorithm isexecuted jointly for A?hx and A?hz . After this initial classification, based on the statisticalmean and standard deviation of elements a?hn,x, a?hn,z ? A?hm we calculate ??0m,x, ??0m,z, and??0m,x, ??0m,z, m = 1, . . . , M? , respectively, and k?0m is estimated as the ratio between rank|A?hm| and the number of elements in each time slot.5.2.3 Distance EstimationAfter projecting vector A? into A?h,p with elements a?h,pn,x, n = 1, . . . , N , consideredaligned with the vessel heading direction (see Section 5.2.1) and horizontal plane(see Section 5.2.2), we can readily estimate the distance traveled by the vessel attime period [tstart, tend], di,j. Given the initial velocity vi at time instance tstart, weobtain estimation d?i,j by integrating the projected acceleration measurements overthe period [tstart, tend]. First, we obtain the mean velocity by,v?i,j = vi +12N?n=2a?h,pn,x(tn ? tn?1) . (5.22)Then, we set d?i,j = v?i,j(tend ? tstart).5.2.4 Summarizing the Operation of the DR-A MethodWe now summarize the operation of our DR-A method. Referring to the pseudo-codein Algorithm 3, we first form vectors A?w, w = 1, . . . ,W for W = d tend?tstartT?c e time100Chapter 5. A Machine Learning Approach for Underwater DRslots (line 1). For each wth time slot, we estimate ?n and ?w, and project accelerationmeasurements in A?w into A?h,w (line 3). To assist classification of pitch-states, we setpositive and negative constraints to form subsets ?l and ?l, respectively (lines 4-11).Next, we perform initial classification (line 12) to calculate ??0 (line 13), and performplast EM iterations to classify ?l (lines 14-18). For each wth time slot and mthpitch-state, we project elements in matrix A?h,wm to compensate the vessel pitch angle(line 19), and group the projected elements to form vector A?h,p (line 21). Finally, weevaluate distance d?i,j (line 22).Algorithm 3 Evaluate d?i,j from vector A?1: Divide A? into W time slots A?w2: for w := 1 to W do {do for each time slot}3: Estimate ?n using (5.4) and ?w using (5.6), and project A?w into A?h,w using(5.5)4: l := 1, ?l ? a?h,w1 , ?l := ?5: for n := 1 to |A?h,w| ? 1 do6: if a?h,wn,x ? A?h,w and a?h,wn+1,x ? A?h,w satisfy positive constraints then7: ?l ? a?h,wn+18: else9: l := l + 1, ?l ? a?h,wn+1, ?l?1 ? (n, n+ 1)10: end if11: end for12: classify A?h,w using the K-means algorithm to initially form matrixes A?h,wm13: ??0m,x := E[A?h,wm,x], ??0m,z := E[A?h,wm,z], ??0m,x = E[(A?h,wm,x ? ??0m,x)2],??0m,z = E[(A?h,wm,z ? ??0m,z)2], k?0m =|A?h,wm |Nslot{initial estimation}14: for p := 0 to plast ? 1 do {EM iterations}15: Iteratively calculate (5.21) to obtain P (?l = m|A?h,w, ??p)16: Solve (5.11) and (5.13) to obtain ??p+117: end for18: Classify subsets ?l using (5.14) and form A?h,wm , m = 1, . . . , M?19: Project elements in matrixes A?h,wm using (5.17)20: end for21: group all projected measurements to form vector A?h,p22: Evaluate d?i,j using (5.22)The DR-A algorithm is designed for the case where an estimate of the distancetraveled by the vessel in the last tend ? tstart seconds is required. However, a mod-ification can be made to incorporate such recursive operation by re-estimating thedistance and heading once a newly single or a small number of acceleration measure-ments are acquired. Here, the summations and multiplications in (5.4), (5.9), (5.11)101Chapter 5. A Machine Learning Approach for Underwater DRand (5.20) are stored and recalculated only for the newly acquired measurements.5.2.5 DiscussionTime-varying Roll AngleIn this chapter, we specifically assumed the vessel roll angle is fixed. However, dueto ocean waves, in certain cases the roll angle can also be time-varying. While theroll angle is expected to change much slower than the pitch angle, the former maystill change within a single time slot. As a result, our assumption that (per timeslot) changes in acceleration are only due to the time-varying pitch angle, does notalways hold and classification to pitch-states cannot be made. A possible solution tothis problem would be to identify the frequency of change of the vessel roll angle andto define shorter time slots for which both acceleration in the horizontal plane andvessel roll angle can be considered fixed. Classification of acceleration measurementsis then performed for each of these (shorter) time slots. Since changes in the vesselroll angle also affects acceleration in the projected y-axis (which otherwise would beclose to zero), the rate of change in the vessel roll angle can be estimated by observingperiodic changes in the y component of A?. Clearly, this approach introduces morenoise in estimating di,j since classification is based on fewer measurements.ComplexityDR navigation is a task performed online. Thus, complexity is of interest. When agyrocompass is used and both ? and ?m are directly measured, DR involves multi-plications (5.5) and (5.15), and after accumulating N measurements, equation (5.22)is executed. In our case, the heading angle is estimated through (5.4), and thepitch angles by solving (5.21), (5.11) and (5.13). Referring to the discussion in Sec-tion 5.2.2, the above procedure is performed for each pth EM iteration and wthtime slot. Hence, the overhead complexity of the DR-A algorithm over using a gy-rocompass is O (LM2plastW ), where W = d tend?tstartT?ce and L ? NW . In our numericalsimulations and sea trial, convergence of the EM algorithm was reached after roughlyplast = 10 iterations, and we used M ? 10. Using an Intel Core Duo CPU with a 2.66GHz processor, this allowed a processing time of less than a second.Choosing the number of pitch-states MThe EM algorithm requires a pre-defined number of states, M . As the wave heightand its effect on the vessel pitch angle are hard to evaluate prior to data collection,determining M in an optimized fashion is a difficult task, which is beyond the scopeof this work. However, an educated guess can be made using tree decision algorithmsto determine the number of pitch-states as the one that maximises the amount ofavailable information, i.e., the entropy [127]. This is evaluated using the observation102Chapter 5. A Machine Learning Approach for Underwater DRthat projection accuracy increases with M , but as M increases less information isavailable per-state and classification performance decreases. We next explore thesetradeoffs.5.3 Performance EvaluationWe now evaluate the performance of our DR-A algorithm. The results are presentedin terms of ?err = |d?i,j ? di,j| and ?angle = |??n??n|. Since the DR-A method is basedon the Gaussian mixture model (5.2) as well as on the assumption that per-time slotacceleration in the horizontal plane, vessel heading direction, and vessel roll angle arefixed, to validate simulation results we also present results based on data collectedfrom a real sea environment.5.3.1 Simulation ResultsOur simulation setting includes a Monte-Carlo set of 10000 channel realizations. Ineach simulation, a vessel moves for 60 seconds in the x ? y plane with initial speeduniformly distributed between [0, 5] m/seconds. The vector of acceleration in thehorizontal plane, an,x, n = 1, . . . , N , is sampled at rate 0.1 seconds (i.e., N = 600),and generated as zero-mean colored Gaussian process with standard deviation of1 m/(seconds)2 and a cross-correlation factor between adjacent samples of e?0.1Tc ,where Tc = 6 seconds. Likewise, the vessel heading, ?n is generated uniformly be-tween [0, 2pi] with a similar cross-correlation factor between adjacent samples. Fur-thermore, for every simulation trial, the (fixed) vessel orientation angle with respectto the reference coordinate system is uniformly randomized within the interval [0, 2pi].Based on the latter and ?n, we form vector ?n, n = 1, . . . , N . Note that the initialspeed and heading direction are known.Let h(x, y, t) be the time domain t function for the height of the sea surface for amodeled three-dimensional ocean wave in the x ? y plane. To simulate wave-basedacceleration in the vertical plane, for tn being exactly in the middle of the timeperiod before a local maxima and after a local minima of h(x, y, t), we uniformlyrandomize sample an,z between [0.01, 0.05] g. Similarly, an?,z is generated uniformlybetween [?0.05,?0.01] g for tn? exactly in between a local maxima and a local minima.Acceleration then changes linearly with time such that it reaches zero at both localmaxima and minima of h(x, y, t). Since the derivative of h(x, y, t) is also the slopeof the wave surface, the pitch angle ?n at time sample tn and coordinates (xn, yn) iscomputed from tan ?n = ??tnw(x, y, tn). Using ?n and ?n and based on model (5.1),we form the vector of acceleration measurements, A?.Current literature offers multiple models for the wind-based ocean surface wavefunction h(x, y, t) (e.g. [128, 129, 130],). In our simulations we use the analyticalwave model offered in [130]. We note that similar results were obtained also for other103Chapter 5. A Machine Learning Approach for Underwater DR0 2040 6080 100050100?4?20246x [m]y [m]Wave elevation [m]Figure 5.3: Example of a modeled wave in the x? y plane. t = 10 seconds.wave models. For the ith wave frequency and jth directional angle, let ?i, ?i, and?i,j be the spreading directional angle, wave frequency, and an initial phase angle,respectively. The wave height is modeled ash(x, y, t) =I?i=1J?j=1?2S(?i)??i??jcos(cix cos ?j + ciy sin ?j ? ?it? ?i,j) , (5.23)where ci = ?2ig is the wave number, ?? and ?? are the increments of angles ? and ?, re-spectively, and we use the directional spectrum function S(?) = b1g2?5 exp[?b2(gU?)4]with b1 = 8.1 ? 10?3, b2 = 0.74, and a wind speed U = 5 knots. For each chan-nel realization, parameters ?i, ?i, and ?i,j are uniformly randomized in intervals[1, 5] rad/seconds, [0, 2pi] rad, and [0, 2pi] rad, respectively, and we use I = 10, J = 10,?? = 0.4 rad/seconds, and ?? = pi5 rad. An example for h(x, y, t) for t = 10 secondsis shown in Figure 5.3.Since current methods for DR navigation use both acceleration and orientationmeasurements, we benchmark our algorithm by showing results of ?err when an idealgyroscope is used, i.e., perfect compensation of the vessel pitch and heading an-gles (Ideal-Gyro), and when orientation measurements are noisy (Noisy-Gyro). Inaddition, we compare results of DR-A with a direct integration of acceleration mea-surements with no heading and pitch compensation (Naive), and with an alternativemethod in which after heading estimation, using the PCA method, per time slot weobtain measurements aligned with the horizontal plane (PCA). We also demonstratetradeoffs between complexity and performance by replacing the constraint EM algo-rithm with i) the initial K-means classifier (K-means), ii) a simple slicing classifier(Slice), and iii) non-constraint EM (NC-EM ). For the Ideal-Gyro and Noisy-Gyromethods, we estimate an,x by multiplying a?n with matrices (5.5) and (5.15) for themeasured heading and pitch angles, ??i,j and ??n, respectively. For the former we use104Chapter 5. A Machine Learning Approach for Underwater DR10?5 10?4 10?3 10?2 10?1 100 10100. [rad]Empirical Pr(? angle ? x)  1/?=50dB1/?=30dB1/?=20dB1/?=10dBFigure 5.4: C-CDF results of ?angle.??n = ?n and ??n = ?n, while for the latter we set ??n = ?n+ e?n and ??n = ?n+ e?n, wheree?n is a zero-mean Gaussian noise with variance ? rad2, which is the same variance con-sidered for the acceleration measurement noise. In the following, results for the DR-Amethod are shown for plast = 10 EM iterations and using Vpos = 0.05 m/seconds2 forthe positive constraints in (5.7).In Figure 5.4, we show the complementary cumulative density function (C-CDF)of ?angle using estimation (5.4) for different values of 1? . We observe that reasonableperformance are obtained for relatively low noise values (around 20 dB). Next, weshow tradeoffs of performance vs. the number of pitch-states, M? , and the assumedcoherence time, T?c. In Figure 5.5a we show performance of the four consideredclassifying method in terms of ?err for M? ? {2, 10, 20} and 1? = 20 dB. We observethat for the Slice method performance are not linear with M? . This is due to the factthat in the Slice method measurements are classified to all assumed M? pitch-states,and thus, for each pitch-state, fewer measurements are available affecting accuracyof estimation (5.17). While accuracy increases with M? for the DR-A, NC-EM, andKmeans (which allow empty pitch-states), we observe that little is gained for M? > 10.Next, for M? = 10, in Figure 5.5b we show ?err as a function of the assumed coherencetime, T?c, which is used to obtain W time slices of assumed fixed acceleration in thehorizontal plane. Here we observe a slight performance degradation for mismatchcoherence time (i.e., when T?c 6= Tc = 6 seconds). When T?c < Tc, this is because fewermeasurements are available to estimate the pitch angle in (5.17), while for T?c > Tc,performance degrade since our assumption of fixed acceleration in the horizontal plane(required for classification) does not hold. Interestingly, we observe that performanceare less affected in the latter case. That is, having enough statistics to estimatethe pitch angle is more important, as was also observed for the Slice method inFigure 5.5a. In the following we use M? = 10 and T?c = Tc.In Figure 5.6, we show average results of ?err for the considered classification105Chapter 5. A Machine Learning Approach for Underwater DRM=2 M=5 M=10 M=200510152025? err [m]  DR?ANC?EMKmeansSlice(a)T_c=3sec T_c=6sec T_c=12sec024681012141618? err [m]  DR?ANC?EMKmeansSlice(b)Figure 5.5: Average results of ?err as a function of (a) M? (for T?c = Tc), (b) T?c (forM? = 10). Tc = 6 seconds.methods and the benchmark methods as a function of 1? . We observe a significantperformance degradation for the Noisy-Gyro method compared to the Ideal-Gyro one.We consider this performance gap as the maximal gain available for using our method.We also observe that for the Noisy-Gyro method, performance is not linear with 1? (inthe logarithmic scale). This is because the noisy orientation measurements introducenon-Gaussian noise to the projected acceleration measurements. As expected, per-formance for the Naive approach is poor, and is in fact fixed for different noise values.The latter is due to the periodic nature of the vessel pitch angle, which averages outpositive and negative acceleration measurements in the x axis. Comparing the per-formance of the PCA method to those of our method, we observe that PCA is betterthan the Slice method, mostly due to the naive classification performed in the Slicemethod which is largely affected by measurement noise. However, using the betterclassification capabilities of the EM and K-means algorithm, we observe considerableperformance gain compared to the PCA method. This is due to the underlying as-sumption in PCA of the variance of acceleration measurements, which might not holdfor all modeled ocean waves. As expected, performance of the EM algorithm, whichis matched to the Gaussian mixture model in (5.2), outperforms that of the K-meansalgorithm, at a cost of complexity13. Moreover, significant improvement is achievedusing our DR-A method compared to that of the non-constraint EM algorithm, NC-EM. From Figure 5.6, we observe that the performance of our DR-A method is closeto that of the (unrealistic) Ideal-Gyro method. Thus, we conclude that, withoutusing orientation measurements, the DR-A method almost entirely compensates thevessel?s heading angle and time-varying pitch angle. To comment on the distribution13We note that both the EM and the K-means algorithms where processed in real-time.106Chapter 5. A Machine Learning Approach for Underwater DR10 15 20 25 30 35 40 45 5010?310?210?1100101102103? err [m]1/? [dB]  DR?ANC?EMKmeansSlicePCAIdeal?GyroNoisy?GyroNaiveFigure 5.6: Results of ?err as a function of 1? . M? = 10, T?c = Tc.0 5 10 15 20 25 30 35 40 4500. [m]Empirical Pr(? err ? x)  DR?ANC?EMKmeansSlicePCAIdeal?GyroNoisy?GyroFigure 5.7: C-CDF results of ?err. 1? = 20 dB, M? = 10, T?c = Tc.of the performance, in Figure 5.7 we show the C-CDF of ?err for 1? = 20 dB. Resultsshow that the above conclusions, drawn for the average ?err results, hold true for allsimulated scenarios.In the following we present results of offline processing of 3-D acceleration mea-surements obtained in a sea trial.5.3.2 Sea-Trial ResultsIn this section, we describe results of our DR-A method obtained from real sea en-vironment. The sea trial was conducted on Nov. 2011 in the Singapore Strait. Theexperiment lasted for two hours and included two boats. During the experiment,the waves height was about 0.5 m and the boats drifted with the ocean current,which was about 0.7 m/seconds. At each boat, we obtained around N = 33.5 k 3-Dacceleration measurements using the Libelium Wasp Mote?s on board accelerometer107Chapter 5. A Machine Learning Approach for Underwater DR?50 0 50 100 150 200 250 300020406080100120x [m]time [min]  Boat 1Boat 2(a)0 500 1000 1500 2000 2500 3000 3500 4000 4500020406080100120y [m]time [min]  Boat 1Boat 2(b)Figure 5.8: Sea trial: nodes location in Cartesian coordinates. (a) x-axis. (b) rate of f = 4.8 Hz, and used its serial port for data logging purpose and offlinedecoding. Throughout the experiment, the location of the boats was monitored usingGPS receivers at rate of 3 seconds and with expected accuracy of 5 m. The boatsGPS-based location in the x and y axis are shown in Figures 5.8a and 5.8b, respec-tively. From the figures we observe that, as a result of the ocean current, the boatschanged their heading direction. However, other than around time t = 25 min (whereboat 2 had to maneuver around an obstacle), this heading change is slow and fitsour underlying assumption. Furthermore, from the figures we observe a slow changein the boats? speed (with variance of 0.1 m/seconds2), which allows using time slicesof assumed fixed acceleration in the horizontal plane. In Figure 5.9, we show themeasured acceleration along the x axis as a function of earth gravity, g (the resultsfor the projected accelerations are discussed further below). We observe that accel-eration measurements follow a wave pattern, and that both frequency and amplitudeof these waves are different for the two boats. The periodic nature of the measure-ments shown in Figure 5.9 emphasize the need for compensating on the vessel pitchangle, as direct orientation measurements may be too noisy. Moreover, due to theobserved fast time-varying measurements (caused by ripples), mitigating the effect ofthe vessel?s pitch angle using filtering is not possible without loss of resolution.First, in Figure 5.10a we show C-CDF performance of the heading estimate forthe two boats, where the vessel heading direction with respect to the UTM coordinatesystem is calculated based on the boats? GPS-based location. Results are comparedfor consecutive time slots of duration Tslot such that NTslotf estimations of ?angle areobtained. Since accuracy of estimation (5.4) improves with the number of measure-ments but decreases if the heading angle changes within the time slot, results tradeofffor Tslot. We observe for all cases best results are obtained for Tslot = 200 seconds,where the error is below 0.02 rad in more than 90% of cases. Due to the sensitivity108Chapter 5. A Machine Learning Approach for Underwater DR0 10 20 30 40 50?0.05?0.04?0.03?0.02?0.0100.010.020.03Time (sec)Acceleration x?axis (g)  Boat 1 (projected)Boat 1 (measured)Boat 2 (projected)Boat 2 (measured)Figure 5.9: Sea trial: measured and projected acceleration along the x axis relativeto g for M? = 5 and T?c = 40 seconds. Boat 1.0 0.01 0.02 0.03 0.04 0.05 0.0600. [rad]Empirical Pr(? ? ? x)  Tslot=60secTslot=120secTslot=200secTslot=240sec(a)0 2 4 6 8 10 1201234567Derivative of heading angle [deg/sec]? ? [deg]  Boat 1Boat 2(b)Figure 5.10: Sea trial: (a) C-CDF results of ?angle for the two boats, (b) ?angle vs.the accumulated change of the boat?s heading angle within the time slot, Tslot =300 seconds.109Chapter 5. A Machine Learning Approach for Underwater DR0 2 4 6 8 10 12 1400. [m]Empirical Pr(? err ? x)  M=2,Tc=20secM=8,Tc=40secM=5,Tc=60secM=5,Tc=40secFigure 5.11: Sea trial: C-CDF results of ?err for the two boats. Tslot = 200 secof our scheme to changes of the vessels? heading angle within the time slot, furtherincrease of Tslot reduces accuracy. This is shown in Figure 5.10b, where ?err is pre-sented as a function of the accumulated change of the boat?s heading angle within thetime slot for Tmathrmslot = 300 seconds. For both vessels we observe a considerableincrease in ?err whenever the accumulated change in heading direction is more than5 degrees. A possible way to limit such inaccuracies is to detect significant headingchanges using e.g. a compass, and to set uneven time slots such that the headingangle is roughly fixed within each time slot.In Figure 5.9, for the first 50 seconds of the experiment, we show the measured andprojected acceleration along the x axis, where the latter are obtained using M? = 5and T?c = 40 sec. We observe that the projected measurements are almost constant,which matches the expected slow change of the boats? acceleration in the horizontalplane. Finally, in Figure 5.11 we present C-CDF results of ?err, comparing estimationd?i,j to the GPS-based distance for time slots of duration Tslot = 200 sec and fordifferent values of M? and T?c. For each time slot, the initial speed vi is calculatedbased on the first two GPS-based locations of the boats. We observe that in morethan 96% of cases ?err is lower than the expected error for M? = 5 and T?c = 40 sec.Considering this result and the low estimation error observed for the heading angle,we conclude that when the boats? heading is constant, our method fully compensatesfor the vessel?s time-varying pitch angle using only a single accelerometer device.5.4 ConclusionIn this chapter, for DR navigation of a vessel whose motion is affected by the oceanwaves, we proposed a method to estimate the vessel heading and the distance traveledby the vessel using only a single 3-D accelerometer. This is required when measure-ment of the vessel orientation using a gyrocompass for example, is unavailable or110Chapter 5. A Machine Learning Approach for Underwater DRtoo noisy to directly compensate for the vessel pitch and heading angles. Using only3-D acceleration measurements, the major challenge in such calculation is the wave-induced vessel?s time-varying pitch angle. Considering this problem, based on theperiodic nature of the vessel pitch angle, we described a machine learning classifica-tion approach that forms classes of acceleration measurements for which the pitchangle is similar. For each class, our method estimates the vessel pitch angle, andprojects the available acceleration measurements into the horizontal plane. The pro-jected measurements are then used to estimate the distance traveled by the vesselvia simple integration. Since our method relies on models for the distribution ofacceleration measurements, alongside simulations, we presented results from a seatrial conducted in the Singapore strait. Both our simulation and sea trial resultsconfirmed that at a cost of increased complexity, our method accurately estimatesorientation and distance using only a single accelerometer device.111Part IISpatial Reuse MAC techniques forUWANs112Chapter 6Time and Spatial ReuseHandshake Protocol for UWANsUsing the UWL and location tracking capabilities developed in Part I, we now moveon to describe location-dependent MAC protocols for UWANs. In this chapter, weconsider the case of UWANs which support peer-to-peer communication betweenany pair of one-hop neighbor nodes, i.e., nodes which are in the communicationrange of each other. Our main contribution is a distributed CA handshake-basedMAC protocol that makes use of joint time and spatial reuse. This protocol willbe referred to as the joint time and spatial reuse (TSR) handshake protocol. Ourapproach utilizes nodes? location information and exploits the long propagation delayin UWAC channels as well as the (possible) sparsity of UWAN topologies to improvechannel utilization in handshake-based MAC protocols. Our protocol is specific forUWANs for the following reasons: First, it utilizes the long propagation delay inthe UAC. Second, while not limited to, our protocol works best in sparse networks,which in the UAC is often the case due to the high attenuation and the existenceof obstacles. Third, our protocol considerably reduces packet collisions, which is ofinterest in UWAC where nodes have a limited energy supply. Last, our protocolrelies on relatively moderate to long data messages, which due to the relatively lowbit rates is the case in UWAC.The remainder of this chapter is organized as follows. System model and ob-jectives are introduced in Section 6.1. In Section 6.2 we formalize the problem ofmaximizing channel utilization in CA scheduling, and in Section 6.3 we describe thedetails of a distributed sub-optimal solution for this problem. Simulation results arepresented in Section 6.4, and conclusions are offered in Section System Model and ObjectivesWe are interested in a CA handshake-based resource allocation protocol that achievesboth high MAC throughput and low scheduling delay, while limiting primary con-flicts, defined as simultaneously arriving (i.e., overlapping) packets from differentsenders at a common receiver. Considering the possible effect of remote interferenceon the signal-to-interference-plus-noise ratio (SINR), and thus on the effectiveness ofRTS/CTS transmission [131], we assume a packet is lost if the SINR at the receiver issuch that the packet error probability is above a required level. Since it is difficult to113Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsonline predict the SINR and since nodes may not be aware of transmissions outsidethe communication range, in the TSR protocol, we avoid primary conflicts only withnodes whose transmissions surely interfere with the reception and whose transmissionscheduling is known, and possible collisions with other sources of interferences needto be tolerated. To formalize this, let the network be described by the undirectedgraph G(N ,K) with the set N of vertices, representing nodes, and the set K of edges,representing communication links. Also let Kj be the list of nodes sharing a commu-nication link with node j. For a node j, we avoid primary conflicts with the conflictset Ij of nodes located within the interference range of j, such that Ij ? Kj. Thatis, if the interference range is larger than the communication range, we have Ij = Kj.Set Kj is obtained by including all nodes whose packets are successfully decoded byj. Furthermore, using an attenuation model, the interference range, common for allnodes, is a-priori calculated as the maximal range for which the interference-to-noiseratio (INR) is above a threshold TINR. Thus, upon obtaining Kj, node j can calculateits conflict set, Ij.Let T pdj,j? denote the propagation delay in link (j, j?)14. We assume that a node jobtains T pdj,p , p ? Kj, with a certain accuracy bounded by ttol. Considering possibleoutdated propagation delay information in the network, we focus on scenarios wherenodes are static or their motion is limited by ttol (for example, nodes which track theirtime-varying locations and share them across the network). We consider a UWANin which a node j ? N has a message i of duration15 Tmsgi,j,j?  Tpdj,j? to transmit tonode j? ? Kj, and j? may or may not respond with its own message to j. We considerapplications with heavy network load for short period of times in which several CScan exist simultaneously. In our setting, nodes need not be aware of the number ofnodes in the network, packets arrive randomly, and the identity of the destinationnode, j?, may change over time. Thus, although we consider static or slowly movingnodes with respect to ttol, the network topology may change dynamically.The above setup restricts our protocol to a class of applications where nodesare static or slowly moving with respect to ttol, duration of transmitted message ismoderate to long, and communication can be either two-way (symmetric or non-symmetric) or one-way. Such applications may include submerged buoys, divers, orunderwater structures, involving command and control or data retrieval. We identifytwo existing applications supporting this kind of setup. The first is a study of themigration and survival of marine animals, implemented by Kintama-Research basedin Vancouver Island, Canada [132]. Kintama has several acoustic arrays deployedin the Pacific Ocean near and north of Vancouver Island. Each array is comprised14We indicate the communication partner of node x as x?. Note that x? can be different for adifferent CS.15Note that the restriction on Tmsgj,j? is because when messages are short, due to the long channelreservation process, there is little benefit in using spatial reuse techniques for scheduling simultaneoustransmissions.114Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsof tens of underwater buoys spaced by hundreds of meters. Kintama holds periodicmaintenance missions, during which a separate connection to each acoustic sensoris setup in order to collect data and update its software. However, by forming anetwork between the array elements and routing data between sensors, efficiencymay significantly increase, saving valuable time and effort. In this kind of setting,two-way or one-way communication of long packets is required between the networknodes.A second practical example is a system called ?Deep-Link?, which includes up to15 nodes and is used for command and control, surveillance, and diver-safety pur-poses in three navies. Nodes in the Deep-Link system are moving while continuouslytracking their location using gyrocompass and DVL. This location is periodicallyshared across the network (see system specification in [133]). While often, due tonodes motion, location information of nodes in the Deep-Link system propagatestoo slowly in the network, there are scenarios where nodes remain static or slowlymove while exchanging large image and voice files are exchanged (either one-way ortwo-way) between nodes, in possibly sparse network setting. The Deep-Link appli-cation sets limits on the end-to-end transmission delay, and energy supply is limited.Thus, throughput and delay are of interest. Moreover, in the Deep-Link system, thenetwork may dynamically change (i.e., different transmitter-receiver pairs, changeof destination nodes, nodes leaving or entering the network, and nodes rebooting).Therefore, in cases where moderate-to-large files are exchanged and propagation de-lay information is reliable, handshake-based approach for scheduling transmissions intwo-way (symmetric or asymmetric) or one-way communication that utilizes networkresources is required for the Deep-Link system.In the following subsections, we formalize our objectives.6.1.1 MAC ThroughputDenote M succj,j? (W ) the set of indices of (original and relayed) unicast messages nodej ? N successfully transmits to node j? ? Kj during the time interval of W seconds,and let Li indicate the length of message i. The per-link MAC throughput is definedas?through,linkj,j? (W ) =?i?Msuccj,j?(W )LiW, (j, j?) ? K . (6.1)Consequently, the average per-link MAC throughput is given by?through(W ) = 1|K|?(j,j?)?K?through,linkj,j? (W ) , (6.2)where |X| is the cardinality of set X.115Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs6.1.2 FairnessAssuming equal message generation rate across the network, fairness can be measuredby comparing the MAC throughput of nodes in (6.1). Applying the widely used Jain?sfairness index [134], we have the fairness measure?fair,through(W ) =1|K|(?(j,j?)?K?through,linkj,j? (W ))2?(j,j?)?K(?through,linkj,j? (W ))2 . (6.3)6.1.3 Scheduling DelayWe only consider the portions of link delay that are affected by the MAC protocol,which we denote as scheduling delay. The MAC protocol affects link delay by allowingnodes to transmit (original or relayed packets) at specific times. Denote sRTS,initj,j?,i thetime node j ? N tries to reserve the channel to transmit message i to node j? ? Kj, andsfinishj,j?,i the time node j? successfully received message i from node j. Then, schedulingdelay is defined as?delay(W ) =1|K|?(j,j?)?K1|M succj,j? (W )|?i?Msuccj,j?(W )(sfinishj,j?,i ? sRTS,initj,j?,i ? Tmsgi,j,j?). (6.4)For clarity, in the following we drop the message subindex and consider the schedulingand transmission of a single message.6.2 Maximizing Channel Utilization inHandshake ProtocolsIn the TSR protocol we make use of both time and spatial reuse techniques to max-imize channel utilization. Following [69], if two-way communication is required, weachieve time-reuse by allowing both nodes j ? N and j? ? Kj to simultaneously ex-change messages. As illustrated in Figure 6.1, this is performed by dividing messagesinto a series of packets and utilizing the long propagation delay to allow simultane-ously packet transmission, thus improving channel utilization as only a single initial-ization process is required per CS. Furthermore, by scheduling simultaneous trans-missions from different CSs, we achieve spatial reuse even for one-way or asymmetriccommunication. In the following, we combine this time reuse with spatial-reuse tech-niques to enable simultaneous transmissions in neighbor CSs, defined as CSs whosenodes can construct a connected conflict sub-graph. In traditional handshake-basedprotocols, nodes detecting an RTS and its corresponding CTS packet should stay116Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsNT RTS CTSp?pjj?Info (p? p?) Info (p?? p) Info (j ? j?) Info (j? ? j)xsRTSj,j?sCTSj,j?sj,j?Figure 6.1: Illustration of channel reservation process (note that the first data packetof node j is smaller than the rest).silent for the entire CS. Furthermore, there are cases where a node should remainsilent when detecting only the RTS or CTS packets, e.g., when the destination nodeis expected to transmit an acknowledgment packet. Thus, channel utilization greatlydecreases with node density. Utilizing both time and spatial reuse allows us to alle-viate this shortcoming.A CS Cj,j?, (j, j?) ? K, is defined by three characteristic parameters referred to asthe CS parameters : 1) sj,j?, 2) dj,j? and 3) tj,j?, where sj,j? is the time node j transmittedits first data packet to node j?, dj,j? is the duration of a single packet transmitted fromj to j?, and tj,j? is the time difference between the starting transmission times ofconsecutive packets, referred to as the cycle time of the message. Consequently,sfinishj,j? = sj,j? + (Ncyclej,j? ? 1)tj,j? + dj,j?, (j, j?) ? K , (6.5)where N cyclej,j? = dTmsgj,j?dj,j?e is the number of cycles in the CS Cj,j?. Our protocol is basedon scheduling CSs. To form the CS Cj,j?, nodes j and j? determine the CS parameters,while avoiding primary conflicts, and transmit data packets of duration dj,j? once inevery tj,j? seconds starting from time sj,j?.In the following we identify three types of primary conflicts: 1) when a new CS in-terferes with active CSs, 2) when transmissions from active CSs interfere transmissionof a new CS, and 3) interference within the CS.117Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs6.2.1 Types of Primary ConflictsConflict type 1 - Interference to active CSsConsider the two CSs Cp,p? and Cj,j?, such that p ? Ij. In conflict type 1, packetsfrom node j arrive at node p while the latter is receiving packets from node p?. Thisscenario is illustrated in Figure 6.2a. To avoid such interference, j should scheduleits transmissions such that its packets arrive at p while p is not receiving from p?.Conflict type 2 - Interference from active CSsConflict type 2 involves packet transmission from node j to node j? while j? experiencesinterferences from neighbor CSs, as illustrated in Figure 6.2b.Conflict type 3 - Interference within the CSIn this type of conflict, a packet from node j arrives at node j? while the latter istransmitting to j. Due to the half-duplex property of the acoustic transducers, j?would not be able to detect the packet of j and it would be lost. This is illustrated inFigure 6.2c. Similarly, node j might transmit its own packet while receiving a packetfrom j?, as illustrated in Figure 6.2d. Avoiding such a conflict, j should considertransmissions from j? while scheduling its own transmissions.Conflict types 1 and 2 are caused by interference to and from neighbor CSs, whileconflict type 3 is caused by synchronization problems with the destination node.We note that when scheduling transmissions, all types of primary conflicts shouldbe taken into account. Next, we formalize constraints to avoid the above primaryconflicts.6.2.2 Formalizing ConstraintsWe start with formalizing general constraints for tj,j? and dj,j?, which apply to allthree scenarios discussed above. Avoiding primary conflicts of type 3, a new datapacket cannot be transmitted before the destination node received the previous datapacket. Moreover, avoiding primary conflicts of type 1 and 2, tj,j? should be an integermultiple of cycle times of neighbor CSs, otherwise primary conflicts avoided in certainCS cycles might still exist in later cycles, resulting in packet collisions. Let R be theset of nodes already participating in CSs or seeking to reserve the channel. Then, foran integer n, the above constraints on tj,j? can be formalized bydj,j? + Tpdj,j? + ttol ? tj,j? = n? tp,p? ?p ? R ? (Ij ? Ij?), p 6= j, j? . (6.6)Assuming the nodes in R form a connected conflict graph (otherwise the networkis divided into sub-networks, whose scheduling is performed separately), we observe118Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs{ {Xpcycle n2cycle n1tp?,pp?jj?T e?p,p,p?,n1T b?p,p,n2(a) Illustration of primary conflict of type 1X{{jq?p?qpj?cycle nqcycle npT bp,j?,nqT ep,j?,p,nq(b) Illustration of primary conflict of type 2X{ {j?jcycle 0 Te?j,j,j?,0 cycle 1tj?,jT b?j,j,1(c) Illustration of primary conflict of type 3X{jcycle 0j?T b?j,j,0(d) Illustration of primary conflict of type 3Figure 6.2: Illustration of different types of primary conflicts.119Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsthat constraint (6.6) is satisfied by settingtj,j? = maxp(dp,p? + T pdp,p?)+ ttol ?p ? R . (6.7)That is, we adopt a common cycle time within the network. While the solution in(6.7) may not be the optimal one to minimize scheduling delay, it is the simplest anda more fair solution.Next, as illustrated in Figure 6.1, in order for two nodes j and j? to simultaneouslytransmit in a CS, the duration of their packets should be smaller than T pdj,j? . Thus,we apply the following constraint to the packet duration:dj,j? ? Tpdj,j? ? ttol . (6.8)We now continue to formalize specific constraints to avoid the three types ofprimary conflicts described in Section 6.2.1 when scheduling transmissions in the CSCj,j?. For convenience, considering nodes p and q such that q ? Ip, we define thevariable T bp,q,np,p? as the time that the np,p?th packet from node p arrives at node q, i.e.,T bp,q,np,p? = sp,p? + Tpdp,q + np,p?tp,p? , (6.9)and the related timeT ep,q,j,np,p? = Tbp,q,np,p? + dj,j? . (6.10)Formalizing Conflict Type 1Avoiding conflict type 1 (see Figure 6.2a), the packets of node j should arrive atnode p before or after those transmitted from node p?. Let n?p,j be the index ofthe first packet transmitted from p? which possibly experiences interference from thetransmissions of j. Assuming j is ready to transmit in time sinitj,j? , forxnp,p?,p,j = T bp?,p,np,p?+1 ?(sinitj,j? + dj,j? + Tpdj,p), (6.11)n?p,j can be found asn?p,j = argminnp,p?(xnp,p?,p,j) , (6.12a)s.t. xnp,p?,p,j ? 0 . (6.12b)Obtaining n?p,j ?p ? R ? Kj, p 6= j?, from (6.12), constraint 1 is formalized assj,j? ? Tep?,p,p?,n?p,j? T pdj,p + 2ttol, (6.13a)sj,j? + dj,j? ? Tbp?,p,n?p,j+1? T pdj,p ? 2ttol. (6.13b)120Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsFormalizing Conflict Type 2To formalize constraint 2, illustrated in Figure 6.2b, we schedule the transmissionsof node j such that its packets arrive at node j? when the latter is not experiencinginterference from nodes in Ij?. To this end, we find nodes p? ? R and q? ? R, whosetransmissions are the first and last to possibly interfere the reception of j?s firstpacket at j?, respectively (note that it is possible that p? = q?), and correspondingpacket indices n??p?,j ? Ncyclep? and n??q?,j ? Ncycleq? , according to(p?, q?, n??p?,j, n??q?,j)= argmin(p,q,np,p?,nq,q?)T bq,j?,nq,q? ? Tep,j?,p,np,p?, (6.14a)s.t. T ep,j?,p,np,p? + 2ttol ? sj,j? + Tpdj,j? ? Tbq,j?,nq,q?? 2ttol , (6.14b)T ep,j?,p,np,p?+1 ? 2ttol > sj,j? + Tpdj,j? , (6.14c)T bq,j?,nq,q??1 + 2ttol < sinitj,j? + Tpdj,j? , (6.14d)p, q ? R ? Ij? , (6.14e)n??p,p? ? Ncyclep? , n??q,q? ? Ncycleq? . (6.14f)Using the solutions from (6.14), we set the following constraintssj,j? ? Tep?,j?,p?,n??p?,j? T pdj,j? + 2ttol, (6.15a)sj,j? + dj,j? ? Tbq?,j?,n??q?,j? T pdj,j? ? 2ttol . (6.15b)Formalizing Conflict Type 3Next, referring to Figure 6.2c, we formalize constraint 3. Assuming sinitj,j? = sinitj?,j , i.e.,both nodes j and j? are ready to transmit at the same time and that T pdj,j? = Tpdj?,j , weset the following conditionssj,j? + Tpdj,j? ? Tej?,j,j?,0 ? Tpdj,j? + ttol, (6.16a)sj,j? + dj,j? ? Tbj?,j,1 ? 2Tpdj,j? ? ttol . (6.16b)Similarly, we setsj,j? + dj,j? ? Tbj?,j,0 ? ttol . (6.17)Merging Constraints for the Different Types of Primary ConflictsFortunately, the four conditions (6.13), (6.15), (6.16) and (6.17) can be merged intotwo constraints. In order to avoid conflict of type 1 we should consider all neighborCSs. To formalize this, referring to constraint (6.13) we construct upper and lowerbound vector u1 and l1 with elements T ep?,p,p?,n?p,j?Tpdj,p +2ttol and T bp?,p,n?p,j+1?Tpdj,p?2ttol,121Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsrespectively, ?p ? R?Ij, p 6= j?. Furthermore, considering the other types of primaryconflicts and referring to (6.15), (6.16) and (6.17) we set the lower boundsl2 = T ep?,j?,p?,n??p?,j ? Tpdj,j? + 2ttoll3 = T ej?,j,j?,0 ? 2Tpdj,j? + ttol , (6.18)and the upper boundsu2 = T bq?,j?,n??q?,j ? Tpdj,j? ? 2ttolu3 = T bj?,j,1 ? 2Tpdj,j? ? ttolu4 = T bj?,j,0 ? ttol . (6.19)Then, the four constraints introduced above can be merged ontosj,j? ? max (l1, l2, l3)4= l (6.20a)sj,j? + dj,j? ? min (u1, u2, u3, u4)4= u , (6.20b)where (6.20a) and (6.20b) are performed element-wise.We next formalize an optimization problem taking all of the above constraintsinto consideration.6.2.3 Channel Utilization Maximization ProblemWe are interested in maximizing channel utilization by maximizing the packet du-ration, dj,j?, and minimizing the transmission starting time, sj,j?, for each CS whileavoiding packet collisions. Considering constraints (6.8) and (6.20), for a utility func-tion f(sj,j?, dj,j?), a minimum required packet duration, dmin (set by the packet headerduration), and a fixed time interval Toffset used to bound the waiting time sj,j? ? sinitj,j? ,we formalize the channel utilization maximization problem (CUMP)maximize?j?Rf(sj,j?, dj,j?) (6.21a)s.t. sj,j? ? l (6.21b)sj,j? + dj,j? ? u (6.21c)sj,j? ? sinitj,j? + Toffset (6.21d)dj,j? ? Tpdj,j? ? ttol (6.21e)dj,j? ? dmin , (6.21f)to obtain sj,j? and dj,j? ?j ? R, followed by a calculation of tj,j? using (6.7).We observe that solving (6.21) requires a centralized approach to obtain the pa-rameters of the CS Cj,j? ?j ? R, which significantly increases the communicationsoverhead. Therefore, we next describe our TSR protocol which offers a sub-optimaldistributed solution for the CUMP (6.21).122Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs6.3 The TSR Protocol - A Sub-OptimalApproachWe first relax (6.21) by considering synchronized communication in the CS Cj,j? suchthat sj,j? = sj?,j, dj,j? = dj?,j and tj,j? = tj?,j (however the numbers of packets transmittedby j and j? need not be the same). As a result, as long as constraints (6.8) and (6.6)are satisfied, conflict type 3 does not need to be considered. Moreover, we replacethe set R with a set Rj ?(Ij ? Ij?), which is the set of nodes who participate inactive CSs at time sRTS,initj,j? , which are neighbors to either j or j?, hereby schedulingone CS at a time (instead of scheduling all CSs together, as we did in (6.21)). Toformalize the TSR protocol we replace u and l in (6.21) with different bounds u? andl?, which unlike the former are not a function of the parameters of CS Cj,j? (a detaileddescription will be given in Section 6.3.2 below). Then, for a single CS Cj,j?, theCUMP (6.21) becomesminimizesj,j? ,dj,j?f(sj,j?, dj,j?) (6.22a)s.t. sj,j? ? l? (6.22b)sj,j? + dj,j? ? u? (6.22c)sj,j? ? sinitj,j? + Toffset (6.22d)dj,j? ? Tpdj,j? ? ttol (6.22e)dj,j? ? dmin . (6.22f)Since in (6.22a), sj,j? is minimized and dj,j? is maximized, regardless of the utilityfunction, the solution for (6.22) is given bysj,j? = l? (6.23a)dj,j? = min(T pdj,j? ? ttol, u?? l?), (6.23b)and we satisfy constraints (6.22d) and (6.22f) by verifying that sj,j? ? sinitj,j? + Toffsetand that dj,j? ? dmin. Otherwise, since constraints (6.22d) and (6.22f) are upper andlower limits on sj,j? and dj,j?, respectively, there is no feasible schedule for the CS Cj,j?and transmissions are deferred. Since n?p,j in (6.12), required for both u? and l? (aswe show further below), is a function of dj,j?, it might be hard to calculate dj,j? from(6.23b). Considering this problem, we suggest a heuristic approach that finds thelargest feasible dj,j? (whose effect on both throughput and scheduling delay is greaterthan sj,j?) using a bisection procedure over the range Tpdj,j? and dmin.Next, since the solution in (6.7) to obtain tj,j? requires a centralized approach inwhich dp,p? and T pdp,p? ?p ? R are known, we offer a modified solution that satisfies123Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs(6.6) by setting tj,j? to be the least common multiple (LCM) of neighbor CS?s cycletimes. To formalize this, let us denote the cycle time vector tj = [tp1,p?1 , . . . , tpI ,p?I ]with rational elements tpi,p?i , for nodes pi ? Rj, pi 6= j, j?, with I being the number ofsuch elements (note that tj = tj?). Also define ? j =[tj, Q(dj,j? + Tpdj,j? + ttol)](whereQ(x) is the nearest rational number of x such that Q(x) ? x), and let L(v) be theLCM of the elements of vector v, such that L(? j)L(tj) is an integer. Then, for an optimizedinteger n?j we settj,j? = n?j ? L(tj) , (6.24)and since a choice of L(? j) for tj,j? surly satisfies (6.6), we find n?j by solvingn?j = min(n) (6.25a)s.t. n? L(tj) ? dj,j? + Tpdj,j? + ttol (6.25b)n ? {1, . . . , L(? j)L(tj)} . (6.25c)Assuming that ?p ? Rj, parameters sp,p?, tp,p? and dp,p? are known to j at timesRTS,initj,j? (we qualify this assumption further below by introducing a mechanism inwhich nodes learn the CS parameters of their one-hop neighbors and synchronize thisdata with their destination node), node j can calculate u?, l? and n?j to solve (6.23)and (6.24). Thus, unlike (6.21), (6.22) can be solved distributly for a single CS Cj,j?.The TSR protocol includes a sequential procedure to schedule multiple CSs. Con-sider the sequence J = {j1, j2, . . . , jM}, of M nodes forming a fully-connectedconflict graph (i.e., jm ? Rjn , ?jm, jn ? J ) and wishing to reserve the chan-nel, enumerated in ascending order according to sRTS,initjm,j?m , such that CSs Cjm,j?m andCjn,j?n , ?jm, jn ? J , n 6= m are neighbor CSs (note that this setting does not meanthat the network is fully connected). First, node j1 determines the CS Cj1,j?1 pa-rameters using (6.23) and (6.24) for Rj1 = ?. Next, detecting the CS Cj1,j?1 at timesRTS,initj2,j?2 , node j2 determines the CS Cj2,j?2 parameters for the set Rj2 = {j1, j?1}.Finally, detecting transmissions of the previous CSs Cjm,j?m , m = 1, . . . ,M ? 1at time sRTS,initjM ,j?M , node jM determines the parameters of the CS CjM ,j?M for the setRjM = {j1, j?1, . . . , jM?1, j?M?1}. We note that in order to make the TSR a dis-tributed protocol, a node scheduling the parameters of its CS will use all availablenetwork resources. Thus, the TSR protocol is a greedy protocol and fairness in re-source allocation may be affected. We also observe the similarity of this approachto cognitive radio in which secondary users utilize available frequency bands withoutinterfering primary users [135]. Here, primary users may be CSs in progress whilesecondary users are newly established CSs, and the sensing step is the mechanismused to identify the parameters of active CSs.Consider the network topology in Figure 6.3a for the purpose of illustration ofour protocol, where x ? Ip, p ? Ij, and x? ? Ij?. The propagation delay in all links124Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsj xpp?j? x?(a) (b)Figure 6.3: Illustration of packet exchange assumed to be equal to T pd. We start with node p transmitting N cyclep packetseach of duration T pd to node p?. In this case, for a time window of T = N cyclep T pd,MAC throughput is simply 1. Next, we allow p? to transmit the same amount of datato p. This is possible if packet transmissions are spaced by at least T pd seconds,as suggested in [69] and illustrated in Figure 6.3b. Since both nodes can transmitN cyclep /2 packets during the time window T , neglecting channel reservation time,MAC throughput remains the same. We now consider the case where node j tries toestablish two-way CS Cj,j?, transmitting the same amount of information as in Cp,p?.By implementing our protocol we allow j and j? to transmit together with p and p?.Since transmissions in the CS Cj,j? are only limited by the CS Cp,p? as illustrated inFigure 6.3b, MAC throughput for a time window of T = N cyclep T pd is expected toincrease to 2. Finally, we consider the case of CS Cx,x? joining CSs Cp,p? and Cj,j?.Avoiding interference, nodes x and x? schedule their transmissions according to (6.23)and (6.24) such that their transmissions do not interfere Cp,p? and Cj,j?. This processis illustrated in Figure 6.3b, where dx,x? and sx,x? are set such that packets from xarrive at p and j while they are transmitting and at x? while it is not experiencinginterference from j?, and such that packets from x? arrive at j? while it is transmittingand at x while it is not experiencing interference from j and p. Numerical results(see Section 6.4 below) show that for the latter case MAC throughput for the timewindow T increases to 2.5.125Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsData packet transmission in the CS Cj,j? is preceded by channel reservation processbased on exchanging RTS, CTS and notification (NT) control packets of fixed sizes,dRTS, dCTS and dNT, respectively, between j and j?. The RTS packet is transmitted bynode j for the process of initializing channel reservation and includes a temporal setof parameters for the CS Cj,j?, determined by j. The CTS packet, including the finalparameters of the CS Cj,j?, is transmitted by node j? to synchronize the parametersof the CS Cj,j? with node j, and to let node p ? Kj?, p 6= j update its Rj database.Finally, the NT packet, which also includes the final CS parameters, is transmittedby node j to notify node p ? Kj, p 6= j? of the CS Cj,j? parameters, immediatelyfollowed by N cyclej =Tmsgj,j?dj,j?data packets of duration dj,j? in time cycles of tj,j? seconds,while node j? starts transmitting its N cyclej? at the instant when j transmits its NTpacket (note that the duration of the first data packet from j is dj,j? ? dNT). We notethat in the TSR protocol the RTS and CTS packets need to be scheduled to avoidprimary conflicts with neighbor CSs. However, the NT packet is not treated as aseparate packet and is transmitted just before the first data packet of node j. Thisprocess is illustrated in Figure Priority of Control PacketsA common problem in handshake-based protocols (e.g., [68],[69]) are collisions result-ing from two neighbor CSs trying to reserve the channel at the same time. Consider-ing this problem, in TSR we apply a priority mechanism for incoming packets. Thepriority mechanism gives advantage to a node which is in a more advanced stage ofits channel reservation process. Consider nodes j and p, which are in the process ofchannel reservation to establish CSs Cj,j? and Cp,p?, respectively. The following rulesapply:1. If node j sends an RTS packet at time Tj and is waiting for a CTS responsewhile detecting an RTS packet sent from node p at time Tp16, node j will stopits channel reservation process if Tj > Tp. Channel reservation of j would alsostop if j receives a CTS packet or a data packet from node p while waitingfor a CTS packet. However, if j receives an RTS packet from node p aftertransmitting its own CTS packet, node j will ignore the received RTS packet.2. If node j sends a CTS packet at time Tj and detects a CTS packet sent fromnode p at time Tp, node j will avoid transmitting its data packets if Tj > Tp.Similarly, if node j sends a CTS packet to node j? at time Tj and detects a datapacket from node p with sp,p? = Tp, node j will delay its data packet transmissionif Tj > Tp.16Note that since we assume that node j is aware of T pdj,p , it is capable of estimating Tp.126Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsWe note that if node j stops its channel reservation process due to detection ofpackets from node p, it will restart the process once the parameters of the newlyestablished CS Cp,p? are included in Rj. We also note that if j cancels its datapacket transmission, node j? may continue transmitting if its transmissions do notcollide with transmissions from the newly established CS Cp,p?. The above prioritymechanism ensures interference-free schedule in neighbor CS Cp,p? and Cj,j? if these CSsare connected via at least one communication link, otherwise collisions may occur.Next, we describe the mechanism by which nodes j and j? schedule their RTS andCTS packets and share information of neighbor CSs with minimum communicationoverhead to readily solve (6.23) and (6.24).6.3.2 Scheduling Control PacketsWe observe that when Ij 6= Ij?, node j might not be able to resolve conflict type 2without exchanging information with node j? to solve (6.23) and (6.24). Therefore,the objective of the channel reservation phase is twofold: 1) to allow nodes j and j? toreserve link (j, j?) and 2) to synchronize information of neighbor CSs between j andj? with minimum communications overhead.Avoiding interference to neighbor CSs, nodes j and j? should schedule the trans-mission of their RTS and CTS packets17 while avoiding conflict types 1 and 2. Dif-ferent from data packets, control packets are transmitted only once and have a fixedpre-determined duration. Thus, only the transmission times, sRTSj,j? and sCTSj,j? for theRTS and CTS control packets, respectively, need to be determined.Scheduling RTSWe start with scheduling the transmission time of the RTS packet from node j tonode j?. As in the process of scheduling data packets, described in Section 6.2.2,?p ? Rj, using (6.12) we find index n?RTSp,j of a packet transmitted from node p? tonode p that possibly collides with the RTS packet from j by replacing sinitj,j? and dj,j?in (6.11) with sRTS,initj,j? and dRTS, respectively. Then, avoiding conflicts of type 1 werequiresRTSj,j? ? Tep?,p,p?,n?RTSp,j? T pdj,p + 2ttol , (6.26a)sRTSj,j? ? Tbp?,p,n?RTSp,j +1? dRTS ? T pdj,p ? 2ttol . (6.26b)Next, in order to avoid primary conflicts of type 2 (see Section 6.2.2) we obtain nodespRTS, qRTS and corresponding indices n??RTSpRTS,j, n??RTSqRTS,j of packets whose transmissions17Recall that the NT control packet is appended to the first data packet of node j, and thereforeneed not be separately scheduled.127Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsmight interfere the reception of the RTS packet at node j?, by replacing set R withset Rj and sinitj,j? with sRTS,initj,j? in (6.14). Then, as in (6.15), we requiresRTSj,j? ? TepRTS,j?,pRTS,n??RTSpRTS,j? T pdj,j? + 2ttol (6.27a)sRTSj,j? ? TbqRTS,j?,n??RTSqRTS,j? dRTS ? T pdj,j? ? 2ttol . (6.27b)Define vectors uRTS1 and lRTS1 with elements uRTS1 (p) and lRTS1 (p) ?p ? Rj, respec-tively, such thatlRTS1 (p) = T ep?,p,p?,n?RTSp,j ? Tpdj,p + 2ttol , (6.28a)uRTS1 (p) = T bp?,p,n?RTSp,j +1 ? Tpdj,p ? dRTS ? 2ttol , (6.28b)and letlRTS2 = T epRTS,j?,pRTS,n??RTSqRTS,j? T pdj,j? + 2ttol , (6.29a)uRTS2 = T bqRTS,j?,n??RTSqRTS,j? T pdj,j? ? dRTS ? 2ttol . (6.29b)Then, constraints (6.26) and (6.27) can be merged ontolRTS 4= max(lRTS1 , lRTS2)? sRTSj,j? ? min(uRTS1 , uRTS2) 4= uRTS . (6.30)Hence, if uRTS ? lRTS, node j sets sRTSj,j? = lRTS, otherwise it waits a backoff timeof Toffset seconds (with possibly different bounds lRTS and uRTS) before trying toreschedule the transmission of its RTS packet.Scheduling CTSSince node j might not be aware of all neighbor CSs of node j?, it might wronglyidentify nodes pRTS and qRTS used in (6.27). However, since conflicts of type 2 donot interfere neighbor CSs (see Figure 6.2b) the effect might be the loss of the RTSpacket, which can then be retransmitted. However, since transmission of a CTSpacket does not require feedback to start data packet transmission, unlike schedulingRTS packets, CTS scheduling must be collision-free. Avoiding information exchangeof neighbor CSs between j and j?, which renders large communication overhead, in thefollowing we describe a mechanism to obtain collision-free CTS transmission basedon sharing bounds of scheduling the CS Cj,j?.Our approach is based on the observation that due to the min/max operationsin (6.20), which set the limitations on sj,j? and dj,j?, only the scheduling bounds needto be shared by nodes j and j?. After scheduling its RTS packet, node j determinestemporary parameters for the CS Cj,j?, s?j,j?, d?j,j? and t?j,j? by solving a version of (6.23)128Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsand (6.24) for u? = min(u1, u2) and l? = max(l1, l2) for sinitj,j? = sRTSj,j? +Tpdj,j? , and replacingR with a temporary set R?j ? Ij including all neighbor CSs node j is aware of at timesRTS,initj,j? . Next, j transmits the temporary CS parameters to its destination node j?along with the upper bound u?, and waits for the CTS response from j? within the timewindow[sRTSj,j? , u?+ Tpdj,j? + Toffset]. In turn, j? extracts the temporary CS parametersand u? from the received RTS packet and is thereby aware of the scheduling limitationsset by the neighbor CSs of node j. Hence, j? refers to these limitations as a time framefor scheduling its CTS packet transmission and to later set the parameters of the CSCj,j?. More specifically, j? determines sCTSj,j? as in (6.30) replacing dRTS with dCTS andsRTS,initj,j? with sCTS,initj,j? = s?j,j? + k1 ? t?j,j?, where k1 ? {0, . . . , bu?+Toffset?s?j,j?t?j,j?c} is theminimum integer for whichsCTSj,j? ? u?+ k1 ? t?j,j? ? dCTS , (6.31)and can be found in an iterative procedure.The final parameters of the CS Cj,j? (which may be different from the temporalparameters set by node j) are determined by node j?. Since j? determines the CSparameters for both j and j?, it must 1) ensure CA transmission and reception ofpackets at node j and 2) allow CA transmission and reception of packets at node j?.The first condition is satisfied by scheduling transmission of data packets within thelimitations set by node j. Since the first data packet is transmitted after j receivesthe CTS packet of j?, we setsinitj,j? = s?j,j? + k2 ? t?j,j? , (6.32)where k2 = dsCTSj,j?+dCTS+Tpdj,j??s?j,j?t?j,j?e. In addition, ensuring data packet transmissionwithin the backoff time of node j, we requiresj,j? ? s?j,j? + k3 ? t?j,j?sj,j? + dj,j? ? u?+ k3 ? t?j,j? (6.33)for at least one integer k3 ? {0, . . . , bu?+Toffset?s?j,j?t?j,j?c}. Since sCTSj,j? and sj,j? are notrestricted to the time proposed by node j, bounds (6.31) and (6.33) offer some flexi-bility in scheduling CTS and data packet transmission, respectively, while satisfyingprimary conflicts of node j.The second condition is satisfied by calculating the bounds u? and l? in (6.23) notonly for data packets transmitted from j? but also for data packets transmitted fromj. That is, j? calculates upper bound vectors u?1,j and u?1,j?, and lower bound vectors129Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsl?1,j and l?1,j? with elementsu?1,j(p) = T ep?,p,p?,n?p,j ? Tpdj,p + 2ttolu?1,j?(p) = Tep?,p,p?,n?p,j?? T pdj?,p + 2ttoll?1,j(p) = T bp?,p,n?p,j+1 ? Tpdj,p ? 2ttoll?1,j?(p) = Tbp?,p,n?p,j?+1 ? Tpdj?,p ? 2ttol (6.34)?p ? Rj, p 6= j, j?, and boundsu?2,j = T bq?,j?,n??q?,j ? Tpdj,j? ? 2ttolu?2,j? = Tbq?,j,n??q?,j?? T pdj,j? ? 2ttoll?2,j = T ep?,j?,p?,n??p?,j ? Tpdj,j? + 2ttoll?2,j? = Tep?,j,p?,n??p?,j?? T pdj,j? + 2ttol , (6.35)for set R?j? ? Ij? including all neighbor CSs j? is aware of at time sinitj,j? . Then, theparameters of the CS Cj,j? are determined at node j? by replacing bounds u? and l? withu? = min(u?+ k3 ? t?j,j?, u?1,j, u?1,j?, u?2,j, u?2,j?)l? = max(s?j,j? + k3 ? t?j,j?, l?1,j, l?1,j?, l?2,j, l?2,j?), (6.36)and solving (6.23) to obtain sj,j? and dj,j?. Next, tj,j? is obtained by adding t?j,j? to tjand solving (6.24).The final parameters of the CS Cj,j? are available to j and to nodes in Kj?Kj? bypiggybacking them, along with the number of data packets j and j? wish to transmit,Ncycle,j =Tmsgj,j?dj,j?and Ncycle,j?, respectively, on the CTS packet of j? and on the NTpacket of node j, which, as noted above, is appended to the first data packet of j.Having both Ncycle,j and Ncycle,j?, allows nodes to further utilize the channel whencommunication is asymmetric, as reflected in (6.14f). In addition, we allow nodesoverhearing data packets to estimate the parameters of neighbor CSs even whencontrol packets are lost. This is performed by detecting the arrival time, packetduration, and transmission cycle, of decoded data packets. However, when (controlor data) packets from nodes outside the communication range but still affecting SINRare not detected, collisions may occur. This problem is not unique to the TSR andappears in any handshake-based protocol which relies on RTS/CTS exchange to alertnearby nodes (e.g., [68],[69]). To limit the effect of such interference, direct-sequence-spread-spectrum (DSSS) signals with different pseudo-random sequences allocated toeach node (often used in UWAC to mitigate inter-symbol-interferences [9]) can be130Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsPreamblePreamblePreamblesourceIDDestinationIDsequence (source)sourceIDDestinationIDsequencesourceIDDestinationIDsequenceRTS PacketData PacketCTS and NT Packets(destination)Packetnumber Datasj,j? dj,j? tj,j?Npck Npckd?j,j? t?j,j? u?s?j,j?Figure 6.4: Structure of RTS, CTS, NT, and data packets.used to significantly decrease the interference range. The structures of the RTS,CTS, NT, and data packets are shown in Figure 6.4. A flow chart describing theprocess of scheduling RTS and CTS packets, as well as determining the CS Cj,j?parameters, is offered in Figure 6.5. Furthermore, a software implementation of theTSR protocol can be downloaded from [96].Finally, a word on complexity and communications overhead of the TSR protocolis in order. While the steps of our protocol may seem complex, we note that bothj and j? schedule the parameters of the CS Cj,j? by solving a number of closed formequations, using up to three iterative processes. In addition, for each CS, the com-munications overhead is limited to transmission of the CS parameters piggyback onthe RTS, CTS and NT control packets.6.4 ResultsFor the purpose of comparing the performance of the TSR protocol to benchmark pro-tocols we choose the TDMA, Slotted floor acquisition multiple access (FAMA) [60],adaptive propagation-delay-tolerant MAC protocol (APCAP)18 [68], and the bidirec-tional concurrent MAC (BiC-MAC ) [69] protocols. The TDMA is an interference-free protocol best suited for static networks with heavy load, while Slotted-FAMAcombines TDMA and handshake-based scheduling to allow some network dynamics.We choose the APCAP and BiC-MAC protocols for their usage of timing-advancetechniques, utilizing the long propagation delay in the channel. The source code ofour implementation of the three benchmark protocols as well as the TSR protocolis available from [96]. We compare the four protocols in terms of throughput (6.2),18We note that due to high collision rate in APCAP occurring when a node overhears anotherRTS packet while waiting for CTS response, we had to slightly modify APCAP and rather thantransmitting the data message according to the time suggested by the destination node, we alsoconsidered scheduling constraints known to the source at the time CTS is received.131Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsYes!No!Cancel CTS transmissionYes!schedule?Valid CTSNo!Cancel CTS transmissionYes!No!Transmit RTS with temporal CS parameters and u? from (6.23)and dj,j? ? dmin ?Is sj,j? ? sinitj,j? + ToffsetCalculate CS parameters using (6.23) and (6.36)k1 : k1 + 1 k1 ? u?+Toffset?s?j,j?t?j,j? ?Calculate sCTSj,j? as done for sRTSj,j? , also checking (6.31)Set sCTS,initj,j? = s?j,j? + k1t?j,j?Set sinitj,j? = sRTSj,j? + T pdj,j?Set sRTSj,j? using (6.30)k1 = 1Set sinitj,j? using (6.32)Transmit CTS with final CS parametersSchedule initial CS parameters, s?j,j?, d?j,j? and t?j,j? using (6.23) for Rj ? Kj ? IjFigure 6.5: Scheduling of RTS and CTS and determining of CS parameters in theTSR protocol.132Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANsfairness (6.3), and scheduling delay (6.4).6.4.1 Simulation SettingIn our simulations, we generated a Monte-Carlo set of 10000 channel realizations,where for each one, N = {6, 10, 15} nodes are uniformly placed in a square area of5?5 km2 at a fixed depth of 40 m for a 50 m long water column. In each realization,the channel includes four horizontal obstacles and one vertical obstacle at uniformlydistributed positions and with lengths uniformly distributed in [100, 200] m. For eachnode pair, we calculate the Euclidian distance, and set transmission loss to infiniteif an obstacle blocks the line-of-sight. A packet is decoded correctly if the SINR issuch that the packet error probability (with no error-correction-code) is below 10?4and a BPSK modulation is considered, otherwise collisions occur and all collidingpackets are lost. The SINR is calculated taking into account all signals arriving tothe receiver. We regard a packet as lost if its destination node experiences interference(of any portion) from another packet, i.e., we look at the worst-case SINR over theperiod of the packet. In addition, we consider transmission of a data message assuccessful only if all its packets are successfully received by the destination node.The received power of each packet is calculated for a common power source level of155 dB//?Pa@1m, and using the Bellhop ray-tracing model (cf. [2]) for a flat sandsurface, carrier frequency of 15 kHz, and sound speed of 1540 m/sec. For the abovenumbers, and based on the Bellhop attenuation model, the obstacle- and interference-free maximum transmission range is about 2 km. Note that this range may decreasedue to effect of interferences on SINR.To show the effect of long interference range compared to the communicationrange, we present simulation results with and without the use of DSSS signaling. Forthe former, we use different pseudo-random sequences with Lc = 15 chips allocatedto each node, and consider a cross correlation factor of 1Lc between arriving signals,which limits the interference range. We measure the network performance for a fixedtime interval of W = 1000 seconds, during which each node is assigned with originaldata messages of length 100 kbit to be transmitted to one of its one-hop neighbornodes (in smaller packets of size dj,j?), and the arrival of messages is modeled as aPoisson process with a mean arrival rate of 0.01 1sec , which is regenerated for eachchannel realization and for each node. This results in the transmission of on average60 data messages for each channel realization. Such messages can accommodate anysmall-scale image file (e.g., the Deep-Link application) or reasonable set of collecteddata (e.g., the Kintama application). If a node j has more than one neighbor node,destination node, j?, is chosen uniformly at random for each message.Following the list of commercial UWAC modems in [9], we consider a transmissionrate of 10 kbps, and use a data packet header of 500 bits (mostly for the preamblesequence, e.g., in the Evologics modem [9]), such that, for TSR, the average ratiobetween the number of header and information bits per data packet (see Figure 6.4)133Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs0 0.20.4 0.60.8 Rmsg?through ? delay / Tmsg (source) No DSSSWith DSSSFigure 6.6: Average of ?through from (6.2) and ?delayTmsgj,j?from (6.4) as a function of Rmsg =Tmsgj?,jTmsgj,j?for TSR with and without DSSS.was measured to be about 10%. Note that, while it is not always the case, j? mightalso have a message to transmit to node j. For TDMA, we choose time slot durationof Tslot = 6.2 sec, which for the maximal range of?2?5 km, allows data transmissionof 1.6 sec per time slot. For the TSR protocol, we assume a perfect propagation delayestimation (i.e., ttol = 0), and use TINR = 0 dB for the INR threshold. The sourcecode for the simulation environment is also available at [96].6.4.2 Simulation ResultsFirst, we consider two-way communication and explore the effect of asymmetric trans-mission and interference range on throughput and delay of TSR. In Figure 6.6, weshow the average of ?through from (6.2) and of ?delay from (6.4) as a function of thesymmetry rate, Rmsg =Tmsgj,j?Tmsgj?,j, both with and without the use of DSSS signaling. Boththroughput and delay performance increase when DSSS is used to limit interferencerange. This is because shorter interference range result in higher network sparsity,and thus potential higher gain from spatial reuse. Moreover, from Figure 6.6, we ob-serve that naturally, since amount of transmitted data increases with Rmsg, so is delay.However, since TSR aims to maximize channel utilization, throughput also increaseswith Rmsg. In the following, we consider common message duration for all nodes fortwo-way or one-way communication, where the former occurs opportunistically whenboth j and j? have a message to transmit to each other.Figure 6.7 shows the empirical C-CDF of ?fair,through from (6.3) for the five simu-134Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs0.2 0.4 0.6 0.8 Pr(? fair ? x)  TSRBiC?MACSlotted?FAMATDMAAPCAPFigure 6.7: Empirical C-CDF of ?fair,through in (6.3) for the TSR, TDMA, Slotted-FAMA, BiC-MAC, and APCAP protocols. |N | = 6.lated protocols. As expected, TDMA, which allocates equal number of time slots foreach node, is the fairest protocol. From the handshake-based protocols, we observethat the fairness indices of the TSR and the BiC-MAC protocols are higher than thoseof the Slotted-FAMA and APCAP. This is due to the time reuse in both protocolsthat allows both nodes j and j? to transmit during the CS Cj,j?, while Slotted-FAMAand APCAP give priority to the node which first reserves the channel. We observethat the fairness index of the TSR is lower than that of BiC-MAC. This is becausethe low node density in our simulation model causes large variations in propagationdelays, thus variation of the elements of tj is large. Since the CS cycle is proportionalto the LCM of tj [see (6.24)], in TSR, fewer CSs could occur simultaneously, affectingfairness.Figure 6.8 shows the empirical CDF of ?delay from (6.4) for the five protocols. Wenote that the delay shown in the x-axis is normalized by Tmsgj . Although TDMA isinterference-free, its delay is significantly higher. This is because, in TDMA, eachmessage is divided into 6 time slots, transmitted |N |Tslot apart. Due to the relativelylong time slot, delay is also high in Slotted-FAMA, which channel reservation processdepends on TDMA. We observe that the scheduling delay of the TSR is considerablylower than those of the BiC-MAC and APCAP protocols. This is due to the time andspatial reuse in the TSR protocol that allow simultaneous transmission of neighborCSs.Next, we compare ?through from (6.2) for the five protocols. Figure 6.9a shows em-pirical C-CDF results without using DSSS signaling. We observe that performance ofTDMA, which includes many empty time slots if network traffic is low, is the lowest.135Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs0 5 10 15 20 25 3000. / Tmsg(source)Empirical Pr(? Delay ? x)  TSRBiC?MACSlotted?FAMATDMAAPCAPFigure 6.8: Empirical CDF of ?delay in (6.4) for the TSR, Slotted-FAMA and BiC-MAC protocols. |N | = 15.Furthermore, APCAP, which allows simultaneous channel reservation for neighborCSs, achieves better throughput performance than Slotted-FAMA, but lower perfor-mance than BiC-MAC for high throughput values. The latter is because at highernetwork traffic rates (and potentially higher throughput), there is a higher probabil-ity for the destination node to have a message to transmit to the source node, whichin BiC-MAC, can be done simultaneously. We observe that throughput results ofTSR outperform those of the benchmark protocols, except for very low throughputvalues. This is due to the channel utilization maximization performed by the TSRprotocol. Such channel utilization is possible in TSR by dividing messages into datapackets. While such division increases the overhead due to the packet header (seeFigure 6.4) on throughput, it has the positive effect of possible simultaneous trans-missions from nearby nodes. To quantify this, in Figure 6.9b we show the empiricalC-CDF results for ?through when DSSS signaling is used, and thus interference rangeis much shorter (usually shorter than the communication range). From Figures 6.9aand 6.9b, we observe a large variance for the results of the TSR protocol. This ismainly because, being a greedy suboptimal time- and spatial-reuse protocol, the per-formance of TSR depends on the network topology and the order of incoming packets.Comparing results of Figures 6.9a and 6.9b, we observe that results are the same forthe Slotted-FAMA and the TDMA protocols. We also observe, that performance im-proves for the APCAP and BiC-MAC protocols, mainly since using these protocols,packet collisions occur when interference range is longer than the communicationrange. However, the most significant improvement is observed in the TSR protocol,which due to the shorter interference range, can simultaneously schedule more CSs.Finally, we evaluate effect of network size. Let ?(W, |N )| be a performance mea-136Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs0 0.02 0.04 0.06 0.08 0.1 0.1200. Pr(? through ? x)  TSRBiC?MACSlotted?FAMATDMAAPCAP(a)0 0.02 0.04 0.06 0.08 0.1 0.1200. Pr(? through ? x)  TSRBiC?MACSlotted?FAMATDMAAPCAP(b)Figure 6.9: Empirical C-CDF of ?through from (6.2) for the TSR, TDMA, Slotted-FAMA, APCAP, and BiC-MAC protocols. |N | = 6. (a) without DSSS signaling, (b)with DSSS signaling.sure (?through(W ), ?delay(W ), or ?fair,through(W )) for |N | network nodes. In Figure 6.10,we show?change(|N | = 6, 10, 15) =?(W,10)?(W,6) +?(W,15)?(W,10)2, (6.37)which serve as an indicator of the scalability of the different protocols, and optimally,?change ? 1. From Figure 6.10, we observe that similar to the results shown inFigure 6.7, the effect of |N | on the fairness index is lowest using TDMA and Slotted-FAMA. However, comparing results for throughput and delay, we observe that forTSR ?change(|N | = 6, 10, 15) is close to 1, and the effect of the network size is muchlower than for the other four protocols. Thus, in terms of scalability, TSR is close tooptimum [62].From the results of our simulations we observe that at the cost of fairness in re-source allocation, throughput and scheduling delay are considerably improved usingthe TSR compared to the TDMA, Slotted-FAMA, APCAP, and the BiC-MAC proto-cols. Furthermore, in TSR we observe a much smaller effect of the number of networknodes on both throughput and delay. Comparing the results shown in Figure 6.6 tothose in Figures 6.8 and 6.9a, this performance gain of TSR is achieved even whencommunication is asymmetric. Our protocol is thus an effective solution that tradesoff fairness with throughput and delay. The improvement in throughput and schedul-ing delay are achieved by the TSR protocol at only a small cost of communicationsoverhead, as only the CS parameters are exchanged between the transmitting nodes,and the protocol is fully distributed.137Chapter 6. Time and Spatial Reuse Handshake Protocol for UWANs  TSR  BiC?MAC  FAMA   APCAP   TDMA change(|N|={6,10,15})  ?through?delay?fairFigure 6.10: ?change(|N | = 6, 10, 15) from (6.37).6.5 ConclusionsIn this chapter, we considered the problem of designing a handshake-type protocolfor UWAN supporting CA unicast communications. We formalized the problem ofresource assignments to nodes to maximize the per-link channel utilization whileavoiding mutual access interference within the communication range, and suggesteda sub-optimal distributed protocol to solve it. Our protocol combines spatial reuseand timing advance techniques to utilize the long propagation delay in the channeland the expected sparsity of the network graph. We described the process of channelreservation and distributed scheduling while keeping communications overhead ata minimum. By means of simulation results, we demonstrated that at the cost offairness in resource allocation for large transmission ranges, our protocol outperformsexisting handshake protocols in terms of per-node throughput and scheduling delay.138Chapter 7Robust Spatial Reuse Schedulingin UWANsTo complete our solution to transmission scheduling in UWANs, we now considerthe problem of resource assignment through broadcast scheduling in UWANs whichsupport frequent transmission of broadcast packets, i.e., packets that need to bereceived by all nodes in the network. This is required for sharing of navigationinformation, simultaneous control of several systems, sending distress signals, etc.A practical example is the ?Deep-Link? system [133], which supports a network ofup to 15 nodes for command and control and divers safety purposes and includesperiodic transmission (once every minute) of broadcast packets including localizationcoordinates. Another specific example is transmission of data from moving AUVs to asurface station. In this scenario, each node broadcasts its packets to all its neighborswhich on-the-fly decide whether to relay these packets.Considering the problem of low channel utilization of contention-based schedulingalgorithms for high-rate UWANs, we propose a spatial-reuse TDMA scheduling al-gorithm. Spatial-reuse scheduling algorithms assume accurate topology information,such that possible network sparsity is used to increase throughput by allowing si-multaneous transmissions (e.g., [136]). However, this assumption may be violated inUWANs, where node movements render time-varying topology or topological informa-tion is temporary unavailable due to high packet loss rate. As a result, several nodesmight temporary hold conflicting topology information leading to packet collisions.Previous works on wireless mesh networks attended to this problem by developingalgorithms to ensure fast propagation of topology variations across the network (e.g.[137]). Unfortunately, in UWAC such an approach might be too slow due to thelong propagation delay. Uncertainty of topology information in topology-dependentscheduling can be regarded as a problem of robustness since we require a certainminimum performance to be achieved even under topology mismatch. The authorsof [138] addressed this problem making the assumption that a probabilistic modelfor the uncertain topology parameters is available. A different approach is the use oftopology-transparent scheduling which does not depend on the instantaneous networktopology. Topology-transparent scheduling was pioneered in [139], which suggested aschedule based on the maximal degree of the network graph and an upper bound onthe number of conflicts between any two nodes regardless of network topology. Caiet al. [140] generalized this algorithm and reduced the number of conflicts.In this chapter, our goal is to reconcile the seemingly conflicting requirements139Chapter 7. Robust Spatial Reuse Scheduling in UWANsof high channel-resource utilization and robustness to network-topology informationuncertainty. To this end, we combine the concepts of topology-transparent andtopology-dependent scheduling. The former element ensures that topology infor-mation mismatch does not cause an uncontrolled amount of packet collisions. Thelatter component allows us to make use of additional spatial reuse in case of reliabletopology information. To guarantee delivery of broadcast packets in (possibly) sparsenetworks, our algorithm includes packet flow control. Flow control also integrates acertain amount of fairness into our system by ensuring that improved aggregate net-work throughput reflects in increased throughput for each node. We present simula-tion results for typical UWAC environments as well as for network topologies recordedin sea trial experiments, and compare the performance of our algorithm with that oftwo spatial-reuse topology-dependent algorithms and two topology-transparent algo-rithms for both fixed and time-varying topologies. The results demonstrate that ouralgorithm provides a favorable tradeoff between network throughput and robustnessto outdated topology information due to topology changes, while also achieving fair-ness in terms of per-node throughput. The motivation for our algorithm is topologyuncertainties, which are common in UWAC due to permanent motion of nodes andphenomena like shadowing and transient ambient noise [5].The remainder of this chapter is organized as follows. System model and designobjectives are introduced in Section 7.1. In Section 7.2, we first formalize the BSPand present a topology-dependent scheduling algorithm, based on which we developthe proposed mixed topology-transparent/dependent approach. In Section 7.3, wedescribe our approach to obtain the topology and conflict matrixes. Simulation resultsare presented and discussed in Section 7.4, and conclusions are drawn in Section PreliminariesIn this section, we introduce the system model and the objectives for resource allo-cation considered in this work.7.1.1 System ModelWe consider UWANs with a fixed small to moderate number of nodes N , say N < 50,distributed over an area of a few square kilometers. Each node is given a uniqueidentification number and can be a source, relay, or destination node for a givenmessage. We require only a coarse periodic time-synchronization between the nodesto establish a network-wide TDMA frame structure; that is, node clock offset andskew should be negligible compared to the propagation delay, which is on the order of1 to 3 seconds for distances of 1 to 4 km. The applications supported by the UWANgenerate high network traffic in the form of periodic broadcast packets (i.e., messagesfrom a single node to all other nodes) relayed by a common routing mechanism across140Chapter 7. Robust Spatial Reuse Scheduling in UWANsthe network (e.g. minimal hop-distance, greedy routing, etc.). We further assumeheavy network traffic, and link this model to the Deep-Link system, where nodesperiodically share their location information with the rest of the network nodes.7.1.2 Objectives of Resource AllocationWe measure the performance of our scheduling algorithm in terms of throughput,scheduling delay, and fairness in resource allocation, as described in the following.ThroughputDefine yi,j(T ) as the number of broadcast packets originated by node i and receivedby node j in T time slots, referred to as original packets. Considering broadcastpackets, the throughput of node i is given by [141]?through,node(i) =1T (N ? 1)N?j=1j 6=iyi,j(T ) , (7.1)where we assume that the observation window T is much larger than the TDMAframe length L. The per-node throughput is defined as?through =1NN?i=1?through,node(i) . (7.2)Scheduling DelayWe define scheduling delay as the delay between the time an original packet (i.e.,not routed) is delivered to the MAC layer at its source and the time it is received atits destination (which may be several hops away). For the latter, since we considerbroadcast packets, we take the average reception time. As such, scheduling delayincludes the end-to-end transmission and queuing delay, and the waiting time for atransmission time slot. To formalize this, let Tschedule(n, j, i) be the scheduling delay(measured in number of time slots) for message i, i = 1, . . . ,Mn, transmitted fromsource n to destination j, where Mn is the total number of messages transmitted bynode n. The average scheduling delay for the network is then expressed by?delay =1N(N ? 1)N?n=1N?j=1,j 6=n1MnMn?i=1Tschedule(n, j, i) (7.3)time slots.141Chapter 7. Robust Spatial Reuse Scheduling in UWANsFairnessSince we assume nodes can always transmit a packet, fairness is measured by compar-ing the differences in node-wise throughput. More specifically, we apply the widelyused Jain?s fairness index [134] to throughput (7.1) and measure fairness by?fair,through =1N(N?i=1?through,node(i))2N?i=1[?through,node(i)]2. (7.4)Towards the goal of achieving fairness, we formalize resource-allocation constraintsthat guarantee node i a minimal number of di time slots per TDMA frame for trans-mission [81]. That is, defining xi as the number of time slots assigned to node iwithin a TDMA frame, we havexi ? di , i = 1, . . . , N . (7.5)Since our algorithm should guarantee delivery of broadcast packets in (possibly)sparse networks, we include constraints to control flow of packets in the network.To this end, given multihop routes established by a routing algorithm, constraint(7.5) can be used to respect traffic-flow control and thus avoid bottleneck nodes.Specifically, by defining routing variables ?i,j, i, j = 1, . . . , N , with ?i,j = 1 if node iis a relay for node j?s broadcast packets and ?i,j = 0 otherwise (note that ?i,i = 1),anddi =N?j=1gj?i,j , (7.6)node i is guaranteed to transmit gi original packets per TDMA frame through con-straint (7.5)19. Note that both gi and di are defined per frame and thus do notrepresent delay requirements but rather fairness constraints. Consequently, onlyafter transmitting gi original packets, and relaying awaiting packets in its routingqueue, node i may utilize its additional time slots in the TDMA frame and broadcastadditional original packets.Next we formalize the BSP to optimize our objectives under the above fair-ness/flow constraint.19Note that if ?i,j is not given (e.g., AUVs reporting to a surface station), flow control is preservedby pre-defining parameters di.142Chapter 7. Robust Spatial Reuse Scheduling in UWANs7.2 Formalizing the BSP7.2.1 Basic ApproachBefore getting into the details, in the following we describe the basic approach ofour algorithm. We are interested in a resource allocation algorithm, for which flowcontrol (7.5) is preserved, and a favorable tradeoff between throughput (7.2) andscheduling delay (7.3) is achieved making use of topology information. This is ac-complished through tracking topology changes and applying a topology-dependentschedule which adapts to these changes. Considering the problem of slow propaga-tion of topology information in an UWAN of moving nodes, and thus the occurrenceof outdated topology information, our algorithm should accommodate such topologyuncertainties while nodes update their topology. This is required to avoid cases where,due to topology uncertainties, the network collapses and is unable to recover from atopology change. We refer to this objective as short-term robustness. The result isa algorithm that adjusts to topology changes to improve performance while reducingscheduling conflicts in the case of temporarily outdated topology information.The output of our algorithm is an N ? L spatial-reuse TDMA (STDMA) binaryscheduling matrix M such that node i, 1 ? i ? N , is allowed to transmit a singlepacket in time slot j, 1 ? j ? L, if and only if M i,j = 1, and L is the number of timeslots in each TDMA frame. Flow control is enforced through pre-defined gi in (7.6)or di in (7.5) to achieve fairness in resource allocation (7.4). Note that since both Land ?i,j from (7.6) are time-varying, so is matrix M . Thus, M is re-calculated eachtime a topology change is detected.Our algorithm is general in the sense that it can operate for a variety of multiplepacket reception (MPR) scenarios. This includes, for example, systems with idealMPR that can resolve all collisions of received packets (due to DSSS), MPR up toa maximal number of simultaneously received packets, MPR depending on receivedsignal strength for packets from different users (to account for near-far effects), andsystems without MPR. Each of these scenarios gives rise to a conflict graph usedin our scheduling algorithm. The conflict graph is represented as an N ? N binarymatrix Q, with elements qi,j, such that qi,j = 1 if and only if nodes i and j must nottransmit simultaneously. For example, usually acoustic transducers are half-duplex,and therefore, since we consider broadcast packets, we do not allow nodes which areconnected through one-hop links to transmit simultaneously, i.e., we respect primaryconflicts [77] and set qi,j = 1 when nodes i and j are one hop apart20.Since both ?through and ?delay depend on the network topology, it is hard to op-timize them directly for broadcast packets. However, since in our algorithm flowcontrol is treated as a problem constraint, sufficient time slots for relaying incoming20We note that this constraint can be relaxed for non-broadcast packets or if the long propagationdelay in the channel is utilized for simultaneous transmission and reception. However, the latterwould require tracking the time-varying location of each node.143Chapter 7. Robust Spatial Reuse Scheduling in UWANsmultihop packets are available, and channel utilization and thus availability of timeslots to nodes is proportional to throughput. In addition, for a given L, channel uti-lization is inversely proportional to scheduling delay. Therefore, following, e.g., [82]and [81], instead of direct optimization of ?through and ?delay, we maximize channelutilization defined as?avail =1NLN?i=1xi . (7.7)We account for topology variations due to both link instabilities, i.e., flickeringand node movements. The former is dealt with by conservative approach to de-termine network topology, and for the latter we combine topology-transparent withtopology-dependent schedules. The input to our algorithm is the time-varying net-work topology, which for a given MPR model, is used to construct the conflict ma-trix, Q. The more limited the MPR, the less sparse is Q, and channel utilizationdecreases. Since our system requires broadcast scheduling to cope with high networkpacket transmission rate, and flow control to realize successful delivery of broadcastpackets, possibly with delay constraints21, we modify the BSP described in [82, 81]and [80] to include flow control. In the following, we first consider the maximizationof (7.7) under constraint (7.5) assuming network topology information is available,which we refer to as the topology-dependent BSP (T-BSP). This not only providesa benchmark case, but the formulation we propose also sets the stage for the robustBSP (R-BSP) presented thereafter.7.2.2 Formalizing the T-BSPFollowing [81] and towards trading throughput (7.2) with scheduling delay (7.3), wefirst minimize the frame length L under fairness/flow constraints and then maximizechannel utilization (7.7) for a given L. Different from [81], which considered di = 1 ?iin (7.5), we avoid bottleneck nodes by allowing possibly different minimal numbersof packet transmission per-TDMA frame as determined by (7.6). Furthermore, while[81] obtained a collision-free schedule through problem constraints, we avoid schedul-ing conflicts by first constructing all feasible time slot allocations and then choosingthe sequence of allocations that leads to maximum channel utilization. This struc-ture of successively solving two sub-problems to obtain the T-BSP schedule allows usto readily combine topology-dependent and topology-transparent scheduling in theR-BSP formulation considered next.First, based on the conflict matrix Q, we find the set of possible node assignmentsto a time slot by the columns of the binary matrix I ? {0, 1}N?K such that for columnj, In,j = Im,j = 1 only if qn,m = 0, i.e., nodes n and m can transmit in the sametime slot, where K is the number of possible such node assignments. The T-BSP21For example, the Deep-Link system [133], requires that navigation information is shared acrossthe network at least once in every minute.144Chapter 7. Robust Spatial Reuse Scheduling in UWANsis then solved by associating each column j of I with a non-negative integer aj,representing how many times each combination of node assignments is used in theresulting schedule M . Mathematically, defining vector a = [a1, . . . , aK ]T , the vectorx = [x1, . . . , xN ]T of the number of time slots within a frame assigned to nodes isobtained byx = Ia . (7.8)Thus, (7.7) can be rewritten as (1 denotes the all-one column vector of appropriatelength)?avail =1NL1TIa . (7.9)Now, to minimize the frame length L given constraint (7.5) we formulate theminimum-frame-length problem (MFLP)mina1Ta (7.10a)s.t. Ia ? d (7.10b)a ? NK , (7.10c)whose solution aMFLP gives the frame lengthL = 1TaMFLP . (7.11)Finally, defining the vector of traffic demands d = [d1, . . . , dN ]T with di from (7.5)and using L from (7.11), the channel-utilization-maximization problem (CUMP) canbe written asmaxa1TIa (7.12a)s.t. Ia ? d (7.12b)1Ta ? L , (7.12c)a ? NK . (7.12d)The sequence of (7.10) and (7.12) solves the T-BSP. More specifically, if aCUMPis the solution of (7.12), the scheduling matrix M is constructed from columns of Iwith aCUMPj being the number of times the jth column Ij is used:M = [I1 . . . I1? ?? ?aCUMP1. . . IK . . . IK? ?? ?aCUMPK] . (7.13)We note that both (7.10) and (7.12) are instances of the cutting-stock problem (CSP),for whose solution optimized numerical methods exist, e.g., [142].Inspecting (7.12) and (7.10), we observe that we can restrict the K possible pat-terns as follows.145Chapter 7. Robust Spatial Reuse Scheduling in UWANsLemma 1 Considering the graph representation of the UWAN with nodes being ver-tices and communication links being edges of the graph, the only possible node assign-ments according to the MFLP and CUMP are maximal independent sets22 (MISs) ofthis graph.Proof 1 Let us consider two possible node assignment patterns p1 and p2, withp2 ? p1 = ei, for some i ? {1, 2, . . . , N}, and ei is the unit column vector whoseelements are all zero except the ith element which is equal to 1. Using p2 instead ofp1 as a column vector of I does not decrease the left-hand side of constraints (7.10b)and (7.12b) and the objective (7.12a). Hence, using p2 can only improve the solu-tion compared to using p1. Since because of scheduling constraints in Q, all possiblepatterns are independent sets of the graph specified by the conflict matrix Q, it is suf-ficient to consider independent sets with maximal cardinality, i.e., MISs, as columnsof I.Hence, to solve the T-BSP we first construct the MIS matrix I, using, for example,the algorithm described in [143]. Next, we enforce flow control using constraints(7.6), where ? is given by the routing mechanism. Finally, we form the CSPs (7.10)and (7.12) and solve them using, e.g., a branch-and-bound solver [142].Based on the above formalization of the T-BSP, we now proceed by combiningtopology-dependent with topology-transparent scheduling to enhance short-term ro-bustness to topology uncertainties.7.2.3 Formalizing the R-BSPWhile using T-BSP scheduling in UWANs is promising for increasing channel utiliza-tion and decreasing scheduling delay due to spatial reuse, it is sensitive to erroneoustopology information (as we will demonstrate by simulation results in Section 7.4).For example, consider two connected nodes that do not share the same frame lengthL due to flawed topology information. The result would be an almost random sched-ule and thus catastrophic packet collisions. Hence, a topology-independent framelength is necessary to achieve short-term robustness to uncertain topology informa-tion. To combine the benefits of both topology-transparent and topology-dependentschedules, we suggest a new approach that combines an underlying skeleton schedulewith a fixed frame length Lskel obtained from a topology-transparent schedule withthe use of topology information.Combining Topology-Transparent with Topology-Dependent SchedulingWe start from a topology-transparent schedule with an N ? Lskel skeleton matrix S,a-priori known to all nodes, whose element Si,j = 1 if and only if node i transmits22An independent set is a collection of vertices/nodes that can simultaneously transmit with noscheduling conflicts. A maximal independent set is an independent set with maximal size.146Chapter 7. Robust Spatial Reuse Scheduling in UWANsin time slot j (specific examples for S will be given in Section 7.2.3). First, foreach column j of matrix S we identify a unique slot node r(j). Slot nodes serve asreference nodes for conflict removal and will always transmit in their time slots. Forthis purpose, we rearrange S to form a matrix Smod such that Smodr(j),j = 1. We notethat the assignment of slot nodes should be fair, and ideally nodes will be selectedequally often as slot nodes. Algorithm 4 shows the pseudo-code of an Lskel-stepprocess in which slot nodes are selected in a round robin fashion to form Smod. Inthe lth step of Algorithm 4 slot node r(l) of the lth column of Smod is determined.To achieve fairness we start with i = l mod N (line 5) and continue with i = (i+1)mod N (line 15) until we find a column j in S which was not already assigned a slotnode and for which Si,j = 1 (line 8). This column becomes the lth column of Smod(line 9) and we set r(l) = i (line 10). The fairness property of this algorithm willbe demonstrated by numerical results in Section 7.4. Note that this rearrangementof S into Smod does not affect channel utilization (7.9) of the topology-transparentschedule and is performed a-priori as it does not require topology information.Algorithm 4 Rearranging topology-transparent schedule S into Smod1: U := ?2: for (l := 1 to Lskel) do3: {Determine the slot node}4: FLAG := 05: i := l mod N6: while FLAG = 0 do7: for (j := 1 to Lskel) do8: if (Si,j = 1 and j /? U) then9: Smodl := Sj {Smodl ,Sj are the lth and jth columns of Smod,S, respec-tively}10: r(l) := i11: U := {U , j}12: FLAG := 113: end if14: end for15: i := (i+ 1) mod N16: end while17: end forBased on the rearranged skeleton matrix Smod and the scheduling constraints ofthe conflict graph matrix Q, a matrix Iskel is constructed which replaces matrix Iin the CUMP (7.12). This procedure, whose pseudo-code is shown in Algorithm 5,makes use of topology information (which, if erroneous, leads to an increased collisionrate, but it does not cause a collapse of the schedule due to the underlying topology-transparent skeleton schedule and the pre-defined choice of slot nodes). Considering147Chapter 7. Robust Spatial Reuse Scheduling in UWANsthe jth column of Smod, a list Tj consisting of all (not necessarily maximal) inde-pendent sets of the network graph, satisfying all scheduling constraints in Q, whichinclude r(j) is formed (line 2). To increase channel utilization while preserving asmuch as possible the structure of the topology-transparent schedule, the independentsets in Tj which include the largest number of pre-assigned nodes, T modj , are appendedto Iskel (lines 3, 4 and 6). Since there may be multiple independent sets chosen fromTj for each column j of Smod, (i.e., |T modj | ? 1), the number of columns of Iskel, Kskel,is possibly larger than Lskel. Since the R-BSP draws its short-term robustness fromthe a-priori chosen frame size Lskel, to maintain the deterministic frame size, onlyone set of each T modj can be chosen to form the scheduling matrix M . This can beformulated by the constraintAa = 1 , (7.14)where A is an Lskel?Kskel 0/1-matrix such that An,m = 1 only if the mth column ofIskel was derived from the nth column of Smod.Algorithm 5 Determine Iskel from the skeleton schedule Smod and conflict matrixQ1: for (j := 1 to Lskel) do2: Tj : all independent sets satisfying scheduling constraints in Q, which includer(j)3: Pj : all nodes i for which Smodi,j = 14: T modj : sets from Tj that include the largest number of nodes from Pj5: end for6: Iskel := [T mod1 , . . . , T modLskel ]The example shown in Figure 7.1 illustrates the described process. We consider anetwork of N = 6 nodes represented by the undirected graph in Figure 7.1(a). Theskeleton matrix S is selected according to the orthogonal topology-transparent (OTT)schedule, discussed in the introduction and described in [140] (see Section 7.2.3 forfurther details), where the shaded entries represent slot nodes. It is first rearrangedinto Smod using Algorithm 4, such that the columns 1 to 9 in Smod are columns1,2,3,6,4,5,9,7, and 8 in S, as shown in Figure 7.1(b). Then, Iskel is formed byexpanding the columns of Smod utilizing the topology information according to Algo-rithm 5. Note that Iskel is recalculated at each node every time a topology change isdetected and would change accordingly. For the topology in Figure 7.1(a), there aretwo possible expansions for columns 5 and 8 of Smod. Finally, Figure 7.1(c) showsthe masking matrix A for this example.A Suboptimal R-BSPBefore proceeding with the R-BSP, we deviate to present a spatial reuse suboptimalschedule, referred to as the hybrid spatial-reuse time-division multiple access (HSR-148Chapter 7. Robust Spatial Reuse Scheduling in UWANsFigure 7.1: Example: (a) sample topology for a UWAN. (b) constructing matrix Iskelusing Algorithms 4 and 5 for the sample network. (c) masking matrix used in (7.14).TDMA), which implement the concept of a skeleton schedule. This would help todevelop the intuition required to formalize the R-BSP. This algorithm has two distinctadvantages: (i) it has polynomial worst case complexity (rather than exponentialcomplexity as the optimal solution), and (ii) it is amenable to analytical performanceevaluation.We start from a skeleton TDMA schedule with node i being the slot node in timeslot t = i. Then, additional nodes are added to each time slot. For this purpose, eachedge is assigned a unit weight and the shortest-path matrix, H, with elements hi,jbeing the minimal number of hops required for transmitting a packet from node i tonode j, is established running a polynomial-time shortest-path technique such as theDijkstra algorithm [144] on T . Since nodes at hop distance one from the slot nodecannot transmit, nodes at hop distance two from the slot node can safely use thetime slot, as long as nodes at hop distance three do not transmit and so on. Thus,nodes with even hop distance to the slot node are candidate joining nodes, whilenodes with odd hop distance to the slot node are set to be receiving nodes. In caseswhere nodes with even hop distance to the slot node are neighbors, only one of thesenodes can become a joining node. To resolve this conflict, each candidate joiningnode j is assigned a weight wj,t for slot t, and the candidate with the largest weightamong the competing nodes becomes the joining node. In order to achieve fairnessamong candidate joining nodes, wj,t are assigned afresh in each TDMA frame. Thisis accomplished by random generation of weights in each TDMA frame at all nodes,which use a common random-generator seed and reference time for updating weights.DefiningKj,t = {k ? Nnodes|cj,k = 1, ht,j = ht,k} (7.15)for j, t ? Nnodes, j 6= t, the proposed schedule for HSR-TDMA can be formalized as149Chapter 7. Robust Spatial Reuse Scheduling in UWANsfollows:Initialize It = {t} (skeleton TDMA schedule)(7.16a)If ((ht,j mod 2 = 0) ? (wj,t > wk,t ?k ? Kj,t)) then j ? It (j 6= t is a joining node)(7.16b)Adjusting Flow Constraints in Robust SchedulingRecall that di in (7.6) represents the minimum number of time slots for transmissionwhich should be assigned to node i per time frame. Due to the fixed skeleton time-frame, the fairness constraints (7.5) may not always be satisfiable, i.e., the problemmay be infeasible. For this reason, we relax the original problem by expanding thetime frame from Lskel to c ? Lskel slots. Consequently, (7.14) becomesAa = c ? 1 . (7.17)Note that parameter c does not affect delay in the network but rather ensures flowcontrol. Consider, for example, a demand in (7.6) of gi = 2 transmission slots per-TDMA frame in a fully connected network with Lskel = 4 time slots. Clearly, thisdemand is infeasible, but can still result a feasible schedule through (7.17) by settingc = 2.In the following we present a worst-case approach to determine c. Let vi be thepre-defined number of times that node i is selected as a slot node in one time frameof Lskel time slots. Since a slot node always transmits in its designated time slot andxi ? vi, constraint (7.5) for node i is surely satisfied within a maximum ofdiLskelvi? maxi(di)Lskelmini(vi)(7.18)time slots. Using the upper bound from the right-hand side of (7.18), we set c =dmaxi(di)mini(vi) e. To ensure the flow constraints from (7.6), we can useN?i=1gi for maxi(di) in(7.18).Formalizing the Robust Scheduling Optimization ProblemUsing (7.17) and (7.18), the CUMP R-BSP can be formalized asmaxa1TIskela (7.19a)Aa = c ? 1 , (7.19b)a ? NKskel . (7.19c)150Chapter 7. Robust Spatial Reuse Scheduling in UWANsSince Iskel =[T mod1 , . . . , T modLskel], the solution of (7.19) is aj(i) = c for j(i) being theindex of the column of T modi with the largest number of non-zero elements, i =1, . . . , Lskel, and aj = 0 for the remaining j. The scheduling matrix M is composedof the selected columns of Iskel as in (7.13). For the example given in Figure 7.1 wechoose columns 6 and 10 of Iskel, since their one-norms are higher than for columns5 and 9, respectively. Thus, while both T-BSP and R-BSP are NP-hard (since bothinvolve finding independent sets in the network graph), different from the T-BSP, theR-BSP schedule in (7.19) can be obtained without solving an optimization problem.While Algorithm 4 is performed only once, matrix Iskel is recalculated throughAlgorithm 5 every time a topology change is detected, and the R-BSP schedule (7.19)is updated. Hence, the only fixed element of R-BSP is the skeleton matrix Smod, andeven the schedule length may change (but not Lskel) if parameter c is updated dueto changes in the routing matrix in (7.6). The flow chart in Figure 7.2 summarizesthis process, and a software implementation of the algorithm can be downloadedfrom [96]. To provide an estimate for numerical complexity, we report that, using anIntel Core Duo CPU with a 2.66 GHz processor, the R-BSP schedule for 50 nodes istypically obtained in less than one second.A Fair R-BSP ScheduleWe note that the R-BSP in (7.19) can be modified to facilitate different objectivefunctions (7.19a). One example would be the case that fairness (7.4) is equallyimportant to channel utilization. Here, we conside equal-resource allocation fairnessto approximately equalize the number of resources assigned to users, which is regardedas the fairest resource assignment schedule [145]. Towards this objective we minimizethe sample variance of the slot assignments given byvar(x) = 1NN?i=1(xi)2 ?(1NN?i=1xi)2= 1NxTx?(1N1Tx)2. (7.20)Since x = Iskela [see (7.8)] and defining V =(Iskel)T Iskel? 1N(Iskel)T 1 ? 1TIskel, wehavevar(x) = 1NaTV a . (7.21)We use the expression from (7.21) to regularize the utilization objective (7.19a) withthe regularization weight ? and arrive at the fair R-BSP (FR-BSP):maxa(1cLskel1TIskela? ?aTV a)(7.22a)s.t. Aa = c ? 1 , (7.22b)a ? NKskel . (7.22c)151Chapter 7. Robust Spatial Reuse Scheduling in UWANsAlgorithm 1Algorithm 2ConstraintsSolve R?BSPwith maximal cardinalityoffline processfor every detected topology changeOnline process: re?calculatedNetwork graphMinimal number of time slotper frame diForm list of slot nodes r(j)Apply aj(i) := cSkeleton matrix S Rearrange skeleton matrix SmodConstruct matrix IskelConstruct matrix ADetermine cChoose set j(i) of T modjForm scheduling matrix MFigure 7.2: Flow chart to obtain the R-BSP scheduling matrix M .FR-BSP (7.22) is an integer geometric programming (GP) optimization problem andcan be sub-optimally solved in polynomial-time (using e.g., the simplex-like (integer)quadratic programming algorithm [146] or the branch-and-bound algorithm [142]).We note that the R-BSP in (7.19) is generic with regards to the topology trans-parent schedule S that is used. However, channel utilization, scheduling delay andshort-term robustness performances are affected by the specific choice of the skeletonschedule. Thus, we continue with considerations for selecting the skeleton scheduleand the description of two possible skeleton schedules used for numerical results inSection 7.4.Choosing a Skeleton ScheduleA skeleton schedule is a topology-transparent schedule with fixed frame length Lskel.A reasonable choice of such a schedule would be one that achieves high channelutilization while guaranteeing minimal packet collision rate. However, there are otherproperties that deserve consideration. Since we combine the skeleton schedule with152Chapter 7. Robust Spatial Reuse Scheduling in UWANstopology-dependent schedule, a high level of flexibility in allocating additional timeslots to nodes is also of interest. Moreover, to increase fairness (7.4), the skeletonschedule should allow a fair assignment of slot nodes using Algorithm 4. Anotherconsideration in choosing a skeleton schedule is its frame length Lskel, where a shortLskel decreases scheduling delay (7.3).Following the above considerations, a possible skeleton schedule is the conven-tional TDMA schedule with frame length Lskel = N in which node i is the slotnode for slot i. Here, although channel utilization is low, slot node allocation isfair. Another, more sophisticated topology-transparent schedule is the orthogonaltopology-transparent (OTT) schedule suggested in [140]. In the OTT schedule thetime frame is divided into v subframes, each of which consists of u time slots, and anode is assigned to transmit at least once in each subframe. Here, channel utilizationis higher compared to TDMA, but slot node allocation is less fair. The values uand v are assigned such that, for any conflict matrix, Q, it is guaranteed that nomore than x conflicts occur between any pair of nodes during a time frame of u? vtime slots. We consider the special case of x = 1 for which u = d12 +?14 +Ne andv = min(u,? + 1), where ? is the maximum degree of the network graph [140]. Inthe case that ? is unknown, we suggest using a mismatched version of the OTTschedule in which a pre-defined ?p replaces the true degree ?, which we refer to asmismatched OTT (M-OTT). Since v = min(u,? + 1) in OTT with x = 1 it followsthat v = u if ? ? u ? 1. Hence, in this case M-OTT and OTT become identicalschedules if ?p ? u? 1.To comment on the frequency of the event ? ? u? 1, let us consider the popularexample of a Bernoulli random graph with non-directed edge probability p, for whichthe node degrees are binomially distributed with parameters N ? 1 and p (cf. [147]).We can generate such a graph by adding outgoing (directed) edges from each vertexto every other vertex with probability p? = 1??(1? p). Denoting the outgoing-edgedegree of node i by ??i, then the C-CDF of ?? = maxi(??i) isPr (?? ? k) = 1? (Pr(??i < k))N = 1?(k?1?`=0(N ? 1`)(p?)`(1? p?)N?1?`)N. (7.23)Since the edge degree is lower bounded by the outgoing-edge degree, evaluating (7.23)for k = u?1 gives a lower bound on the probability that ? ? u?1. Figure 7.3 showsthe lower bound (7.23) for k = u? 1 as well as the empirical probability Pr (? ? k)as a function of p and several values of N . We observe that already with p = 0.5the Pr(?? ? u ? 1) and thus Pr(? ? u ? 1) is close to one, and hence a choice of?p = u? 1 for M-OTT would render it identical to OTT with high probability. Wereport that the same conclusion was drawn for a more realistic (and limited) set oftopologies obtained from both simulations and sea trial recordings, as described inthe following.153Chapter 7. Robust Spatial Reuse Scheduling in UWANs0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.500. ? u?1)  Empirical, N=8Lower bound, N=8Empirical, N=14Lower bound, N=14Figure 7.3: Probability (7.23) for k = u ? 1 and empirical probability of ? ? u ? 1when generating a Bernoulli random graph with N nodes and edge probability p.7.3 Obtaining the Topology MatrixThe optimal T-BSP and R-BSP schedules as well as the suboptimal HSR-TDMAone require knowledge of the MIS matrix I, obtained from conflict matrix Q. In thissection we describe a mechanism to construct Q for different MPR scenarios, andshare it across the network.7.3.1 Obtaining the Topology MatrixWe start with tracking and sharing the time-varying network topology. Networktopology is represented by an N?N matrix T with binary elements ti,j, representingexistence of a direct communication link between nodes i and j. Matrix T is sharedacross the network by nodes piggy-backing their connectivity lists (CLs) of one-hopneighbor nodes on broadcast packets (for example periodic navigation packets in theDeep-Link system [133]). Initially, we assume a fully connected network, i.e., T isthe all-one matrix. This way, initial transmissions are interference-free and nodescan start updating their topology matrix. Note that this initial schedule is updatedthrough executing Algorithm 5 and solving (7.19) every time a topology change isdetected. The mechanism to update the topology information is described in thefollowing.FlickeringConsidering the time-varying characteristics of the channel, we wish to avoid theflickering problem in which topology changes too fast to distribute across the network.154Chapter 7. Robust Spatial Reuse Scheduling in UWANsThus, links need to be stabilized. We account for the flickering problem by introducingcounters b1 and b2 used for adding and removing communications links, respectively.In R-BSP, since node j is a slot node at least vj times in a time frame, and vj ispre-defined (see Section 7.2.3), node i would remove j from its connectively list if itdid not receive a packet from j within the last Tremove,j = d b2vj e time frames. Similarly,in T-BSP, node i is guaranteed to transmit di packets per time frame, and thus, inT-BSP, Tremove,j = d b2dj e. On the other hand, i would add j to its connectivity listonly if it receives b1 successive packets from j.Applying the above sensitivity mechanism introduces a delay in the update ofCLs. The values of b1 and b2 can be regarded as the convergence parameters ofthe scheduling algorithm, since the process of recovery from topology changes doestake on the order of b1 and b2 time frames for adding and removing links, respec-tively. However, when topology changes faster than the convergence time of thealgorithm or when topology updates bearing packets are lost, CLs may be outdated,and scheduling conflicts may occur. Furthermore, multihop routes would break re-sulting in packet losses. To account for these fast topology variations, we extend thesensitivity mechanism beyond neighbor nodes such that if a node i did not receive apacket (via a single or multiple hops) from node j in b3 time frames, it refrains fromtransmitting in slot j. The value b3 trades off robustness to fast topology variations(increases with smaller b3) and availability. A pragmatic choice is b3 = ? ? b2, whereh is the maximal number of hops in the network.Denoting by Pe,pac(i, j) the packet error rate (PER) for the link between i andj, the probability for node i to receive k successive packets transmitted from nodej is psuc(i, j) = (1? Pe,pac(i, j))k. Hence we can lower bound the miss-detectionprobability, pmis, by choosing k such that psuc(i, j) < pmis. Since Pe,pac(i, j) is difficultto estimate before a link between nodes i and j has been established, a maximalexpected PER, pe,max, based on transmission range of the system can be used. Thus,as a pragmatic solution we suggest the selection of b1 such that(1? pe,max)b1 > 1? pmis, (7.24)where pmis is set according to the tolerated miss-detection rate in worst-case links.On the other hand, node j is removed from the CL of node i if node i did not receivea packet transmitted from j in the last b2 time frames. Since the probability ofreceiving at least one packet in k frames is given by 1 ? (Pe,pac(i, j))k, we adjust b2according to(pe,max)b2 < pdrop, (7.25)where pdrop represents an acceptable dropping probability for the expected worst-case link. Figure 7.4 shows b1 and b2 according to (7.24) and (7.25), respectively.We note that in our system only high values of pmis and pdrop are considered since (i)these apply for worst-case links and (ii) the expected value of Pe,pac(i, j) is high fortransmission ranges above 1 Km, which are of our interest.155Chapter 7. Robust Spatial Reuse Scheduling in UWANs400 600 800 1000 1200 1400 1600 1800 200011.522.533.544.555.56Transmission distance [m] ??>Convergance parameters b1, b 2 ???>  b1: 1?pmis=0.2b1: 1?pmis=0.9b2: pdrop=0.3b2: pdrop=0.1Figure 7.4: Convergence parameters b1 and b2 vs. transmission rangeSymmetryWhile we assume T is a symmetric matrix, in the underwater channel links betweennodes located at different depths might not be reciprocal due to different noise lev-els. Therefore, we apply a conservative strategy and locally replace all asymmetriccomponents ti,j 6= tj,i of T by ti,j = tj,i = 1 to force symmetry. Note that the sym-metrized connectivity matrix is generated locally, whereas the actual CLs giving riseto a (possibly) asymmetric T are shared throughout the network.7.3.2 Constructing the Conflict GraphIf the system has either ideal or no MPR capabilities, the conflict matrix Q is directlyobtained from matrix T . Specifically, considering primary conflicts, for the former weset Q = T , while for the latter Q = T ? T . However, as mentioned in Section 7.1.1,we can also represent conflict graphs for systems with limited MPR capabilities. Inparticular, in a system where MPR is limited to a pre-defined number of packets,Nlimit, we require?mqm,n ? Nlimit. A conflict graph for such system is constructed byrejecting independent sets in I which include more than Nlimit nodes connected to acommon node. Alternatively, a conflict graph for a more realistic system, where MPRability is determined by the relative distances of transmitters to a common receiver,is constructed by setting qi,j = 1 if nodes i and j are the interfered and jammer nodein a near-far scenario [148] as described in the following.In a near-far scenario, transmissions from nodes close to a receiver interfere trans-missions of farther nodes. One possible approach to reduce such interference is toinclude a desired SINR level as constraints in the scheduling optimization problem156Chapter 7. Robust Spatial Reuse Scheduling in UWANs(e.g. [149] and [74]). However, this requires distance evaluation to other nodes andan accurate propagation model for the estimation of the SINR. In case of a near-far,we define the receiver node as the center node, the closer nodes (which cause theproblem) as the interfering nodes, and the more distant nodes whose transmissionsare blocked as the jammed nodes. We identify the interfered and jammer nodes basedon the fact that, as a result of near-far, the interfered node appears to be connectedto the center node, but not vice-versa. That is, T becomes asymmetric. Unlike tem-poral instabilities of T due to flickering or short-term interference, asymmetry dueto the near-far effect is stable. Hence, the identities of the center, interfering, andjammed nodes can be detected from observing long-term asymmetric components ofT . In case a node cannot determine which of a set of nodes is the jammer node,it would assume all nodes in this set are jammers, and would avoid joining theirtransmissions. Furthermore, in case of multiple near-far scenarios, since symmetry ischecked per center node, separate a-symmetric components cannot be identified.7.4 Simulation ResultsIn this section we report simulation results to illustrate the performance of the pro-posed R-BSP scheduling with regards to 1) per-node throughput, 2) scheduling delay,and 3) fairness. In particular, we present results for the CUMP R-BSP schedule (7.19)and the FR-BSP schedule with ? = 1 (7.22) using two skeleton schedules: 1) the M-OTT and 2) the TDMA, and compare them with results for the T-BSP, HSR-TDMA(7.16), OTT from [140] and the conventional TDMA schedule. Furthermore, to showthe effect of the skeleton schedule, we also consider the schedule resulting from theCUMP in (7.12) when applying the frame length L = c ? Lskel, i.e., the R-BSP framelength, which we refer to as the CUMP schedule in the following.In our simulations, we implemented the mechanism described in Section 7.3, whichallows nodes to track the network time-varying topology and conflict matrixes. Byallowing nodes to move and measuring performance over time T , we show how eachalgorithm reacts to topology changes. Furthermore, while the above algorithms mayhave different TDMA frame-lengths, we always consider the same traffic generation.In particular, we require a minimal number of original packets per frame of gi = 1 ?i[see (7.6)] for fairness, and let nodes transmit up to N original packets per-TDMAframe. We apply the minimal hop-distance routing mechanism for all experiments.Given the topology matrix, this is obtained using the Dijkstra algorithm (cf. [144]).Since we consider broadcast packets, i.e., each packet is directed to all other net-work nodes, and since we consider half-duplex communication, primary conflicts arenot allowed in the network conflict matrix, Q. In our simulations we consider fourdifferent MPR scenarios: i) ideal MPR, ii) MPR of up to 2 overlapping receivedpackets (Limit MPR (Nlimit = 2)), iii) MPR of up to 3 overlapping received packets(Limit MPR (Nlimit = 3)), and iv) no MPR capabilities (No MPR). For the above157Chapter 7. Robust Spatial Reuse Scheduling in UWANsfour scenarios, we neglect interference from nodes located more than two hops away.This is considered since unlike for terrestrial radio-frequency communication, whereconcurrent transmission of nodes three or more hops away may notably decrease theSINR at the receiving node [149], such degradation is usually negligible in UWACdue to the significant effect of the channel absorption loss. We used two approachesto obtain network topologies in our simulations. First, a model-based topology wasgenerated based on an attenuation model. The model-based simulations are used tosimulate movements of AUVs and divers in a near-shore or harbor environment, asconsidered in the Deep-Link application. The main focus of these simulations is tocompare short-term robustness performance. Since model-based topologies might betoo simplified, we also use a time-varying topology recorded in a sea trial, where wetested our algorithm also for the realistic case of MPR limited by the relative dis-tance between sources and destination (i.e., the near-far problem). In the followingwe present results of both simulations.7.4.1 Model-Based TopologyFor model-based topologies, we generated a Monte-Carlo set of 1000 topologies withN = 8 nodes, and measured the network performance for each topology in a fixedinterval of T = 1000 time slots with duration of 5 seconds, considering transmittedpackets of duration 1.49 seconds, maximal transmission range of 5 km, sound speedof 1500 m/sec, and time-synchronization uncertainties up to 10 msec [14]. We placednodes according to a uniform distribution in a square area of size 5 km ? 5 km.This area included four horizontal obstacles and one vertical obstacle at uniformlydistributed positions within the square area, with lengths being uniformly distributedin [100, 200] m. In our setting, a link exists if no obstacle obstructs the line-of-sightpath and the expected error rate for packets of 100 bits and BPSK communication isbelow 10?4. The effect of topology variations on system performance was investigatedfor each topology by allowing nodes to move during the network operation (the effectof link flickering is considered in the sea-trial-based topologies, described in the nextsection). At the start of the simulation, each node was assigned with a motion vectorwith uniformly distributed speed and direction of [?5, 5] knots and [0, 360] degrees,respectively, and sustained the same course. If a node reaches an obstacle, a newrandomized direction is determined, away from the obstacle. We note that the aboveparameters reflect the expected packet length and node mobility in the Deep-Linkapplication, where longitude and latitude information are shared in the network andAUVs or divers are assumed moving in a fixed course and speed to explore a near-shore or harbor environment, which often leads to sparse topologies (for further detailssee [133]).While there exist several tools to simulate an underwater channel, e.g., the Bellhopsimulator [2], their run-time is rather slow. Since we require a large number of channelrealizations, we used the popular transmission loss model (which implies a carrier158Chapter 7. Robust Spatial Reuse Scheduling in UWANs0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.0900. Prob(? through ? x)  OTTM?OTT (?=3)M?OTT (?=4)M?OTT (?=6)M?OTT (?=8)Figure 7.5: C-CDF of ?through from (7.2) for matched and mismatched OTT andstatic model-based topology.frequency of about 30 kHz) [5, Ch. 5]TL(r) = 20 log10( r1 m)+ 3 r1 kmdB, (7.26)where r is the transmission distance. We consider a source level of 155 dB//?Pa@1m,a noise level of 50 dB//?Pa/Hz, DSSS signals with Lc = 31 chips, a packet size of100 bits, a transmission rate of 100 bps, and a required packet error rate of 10?4.Based on these parameters, the maximal hop distance, dhop, is approximately 2000 m.Furthermore, assuming a normalized cross correlation of 1Lc for different pseudo-random sequences, we get negligible interference (i.e., more than 10 dB below thenoise level) from transmissions of nodes located more than 3200 m from the receiver,i.e., 1.6 ? dhop. This justifies our assumption above for neglecting interference fromnodes located more than two hops away.Following the discussion in Section 7.2.3 we choose the value ?p = u? 1 for thepre-defined graph degree of the M-OTT. The suitability of this choice is verified inFigure 7.5 showing the empirical C-CDF of the measured per-node throughput (7.2)for the OTT and M-OTT schedules for static model-based topologies (i.e., nodes didnot move after setting up the network topology). The results show that M-OTT withthe pre-determined value ?p = 3 achieves practically the same performance as OTT.Since u = 4 for networks with N = 8 and x = 1, ?p = 3 for M-OTT in the following.We start with comparing the measured per-node throughput (7.2). For the caseof static nodes, Figure 7.6 shows the empirical C-CDF of throughput of the R-BSPschedule for the different MPR scenarios. Additionally, we show throughput resultsfor the TDMA schedule. We observe that the performance of R-BSP with ideal159Chapter 7. Robust Spatial Reuse Scheduling in UWANs0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.1800. Prob(?through ? x)  Ideal MPRLimited MPR (Nlimit=2)Limited MPR (Nlimit=3)No MPRTDMAFigure 7.6: C-CDF of ?through from (7.2), for static model-based topologies and dif-ferent MPR scenarios.MPR is almost identical to that of a system with limited MPR and Nlimit = 3, andthat only a small performance degradation occurs when Nlimit = 2. Furthermore,we observe that while performance for a system without MPR capabilities decreasesnotably compared to that of a system with MPR, significant spatial reuse gain overconventional TDMA is still achieved. However, the effect of simultaneous transmis-sions on SINR is expected to grow with N . Thus, we conclude that, for small N ,the proposed spatial-reuse schedule is beneficial regardless of the MPR capabilities.For clarity and simplicity, in the following we focus on the case of ideal MPR. InFigure 7.7a we compare per-node throughput for the different considered schedulingalgorithms when nodes are static. Considering, for example, a per-node throughputof 0.1 as a desired quality of service (QoS), we observe that using OTT and TDMA,the desired performance is hardly reached for all topology configurations23. However,by applying spatial reuse, the desired QoS is achieved in more than 50% of all topol-ogy configurations using the R-BSP approach. Furthermore, comparing performanceof R-BSP to that of T-BSP we observe clear throughput advantages for R-BSP. Thisresult is expected since, while R-BSP uses a fixed frame length, T-BSP minimizesframe length, which tradeoffs channel utilization with scheduling delay. The CUMPschedule, which applies the same frame length as R-BSP, achieves a notably higherthroughput than R-BSP. This, however, comes at a considerable cost in schedulingdelay and fairness as will be discussed below. We observe that the R-BSP schedulewith TDMA skeleton achieves higher throughput than HSR-TDMA, which also uses23We note that since we regard throughput as a measure of successfully received packets, whichmay involve routing, it is not identical to channel utilization and thus throughput of TDMA is notlimited to 1N .160Chapter 7. Robust Spatial Reuse Scheduling in UWANs0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.1600. Prob(? through ? x)  TDMAOTTHSR?TDMAT?BSPCUMPR?BSP(TDMA)R?BSP(M?OTT)FR?BSP(M?OTT)(a)0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.1600. Prob(? through ? x)  TDMAOTTHSR?TDMAT?BSPCUMPR?BSP(TDMA)R?BSP(M?OTT)FR?BSP(M?OTT)(b)Figure 7.7: C-CDF of ?through from (7.2) for model-based topologies. (a) static (nooutdated topology). (b) dynamic (slowly propagating topology)a skeleton TDMA schedule. This is due to the channel utilization maximization andflow control in R-BSP that is not part of the HSR-TDMA schedule. Comparingperformances of the variants of R-BSP, we observe that since CUMP R-BSP directlymaximizes channel utilization, it achieves higher throughput than FR-BSP. In addi-tion, since channel utilization of the M-OTT schedule is better than that of TDMA(see Section 7.2.3), throughput performance of R-BSP using M-OTT as a skeletonschedule is slightly better than when using TDMA.Next, in Figure 7.7b we show throughput performance when nodes in the model-based simulated environment are allowed to move and thus topology is dynamic.Compared to the results for static topologies in Figure 7.7a, throughput performanceof the T-BSP schedule dramatically decrease, while a negligible performance degrada-tion is observed for the R-BSP. This is because of the short-term robustness of R-BSPwhich allows maintaining a certain level of performance until topology changes areupdated. We also observe that although HSR-TDMA includes a TDMA skeletonschedule, its throughput performance also decreases when mobility is allowed. Thisis because time-slot assignment in HSR-TDMA is based on hop-distance to the slotnode, which is more sensitive to topology uncertainties. This result demonstratesthe effectiveness of the proposed combination of topology-transparent and topology-dependent scheduling for R-BSP to cope with uncertain topology information, whileproviding high throughput by adapting to topology changes and exploiting the (pos-sible) sparsity of the network. Since throughput performance degradation is alsoobserved for the CUMP schedule, whose throughput is now lower than that of theR-BSP schedule, we conclude that R-BSP is able to overcome one of the main lim-itations of spatial-reuse scheduling (e.g., T-BSP, CUMP and HSR-TDMA), namelysensitivity to outdated topology information, while achieving higher throughput thanpure topology-transparent scheduling.Figure 7.8 shows the empirical CDFs for ?delay from (7.3) of the different schedules161Chapter 7. Robust Spatial Reuse Scheduling in UWANs0 10 20 30 40 50 60 7000. Prob(?delay? x)  TDMAOTTHSR?TDMAT?BSPCUMPR?BSP(TDMA)R?BSP(M?OTT)FR?BSP(M?OTT)Figure 7.8: CDF of ?delay from (7.3) for static model-based topologies.for static model-based topologies. Since scheduling delay is strongly connected to thenumber of time slots a node is assigned to, a significantly lower delay is obtained forthe T-BSP and the R-BSP schedules using M-OTT as a skeleton schedule comparedto the conventional TDMA and the OTT schedules. Comparing delay performanceof R-BSP with M-OTT to that of CUMP we observe that although both scheduleshave the same frame length, due to the skeleton schedule used in R-BSP its delayis significantly lower. However, since the frame length is directly minimized in theT-BSP schedule (see (7.10)), it achieves a slightly lower scheduling delay in almostall topologies than R-BSP with M-OTT skeleton schedule. We observe that delayperformance of FR-BSP and CUMP R-BSP with M-OTT skeleton are almost thesame. While delay performance of R-BSP with TDMA skeleton and HSR-TDMA arealmost the same, since in M-OTT nodes are assigned to transmit in more time slotsthan in TDMA, better delay performance is obtained comparing R-BSP with M-OTTto R-BSP with TDMA. We do not show results for scheduling delay for a dynamictopology, since we only consider successfully received packets for scheduling delay(7.3) and no retransmission mechanism in case of packet collisions. Thus, outdatedtopology information leading to packet collision has little influence on schedulingdelay.7.4.2 Sea-Trial-Based TopologyWhile the model-based simulation, introduced above, include node mobility and thustopology uncertainties, the considered movements may be too artificial. For thisreason, in the following we also consider topologies obtained from communicationlinks recoded in a sea trial conducted in May 2009 in the Haifa harbor. The sea162Chapter 7. Robust Spatial Reuse Scheduling in UWANs(a)1234234112 43Topology 1 Topology 2 3Topology 321234 2 431Topology 4 Topology 5 Topology 641(b)Figure 7.9: Structure of Sea Trial: (a) satellite picture of the sea trial location (picturetaken from Google maps on September 29, 2009). (b) recorded network topologies.trial included four vessels, which moved between the harbor docks in a slow speed ofabout 1 m/sec. The different locations of the nodes during the sea trial are marked inFigure 7.9a, where, for example, node 1 moved between points 1A, 1B, 1C, and 1D,at which it stayed for some time. The topology structures of the network as recordedduring the sea trial are shown in Figure 7.9b, where first the nodes communicatedin a fully connected network (i.e., Topology 1), then formed Topology 2, and so onuntil the nodes formed the chain Topology 6 where node 1 is not connected. Notethat the difference between Topologies 4 and 5 is the distance between nodes 1 and2.As in the Deep-Link application, during the sea trial, each node broadcastedits time-varying location coordinates to the rest of the network nodes every singleminute, which we adopt as the duration of the time slot. This motion of nodes andcommunication type represent the practical scenario of divers moving in a near-shoreenvironment with obstacles and broadcasting their location coordinates to all othernodes for safety reasons and command and control. The four nodes transmitted ata power such that given the small dimensions of the harbor (1500 m at its longestaxis) connectivity is mainly determined by the structure of the harbor and existingobstacles. Based on received packets and using a flickering-mitigation mechanism tostabilize network topology, each node identified its list of one-hop neighbor nodesand piggy-backed it on its broadcast packets to create a shared network topology.Given the measured network topology, conflict matrix Q was obtained considering asystem with Nlimit = 3, while satisfying primary conflicts and accounting for possiblenear-far problems. For the latter, referring to Figure 7.9a, near-far problem occurredwhen nodes 1, 2, and 4 were located at 1A, 2A, and 4A, respectively. Using themechanism described in Section 7.3, our algorithm resolved this problem and limitedscheduling such that nodes 1 and 4 cannot transmit simultaneously.163Chapter 7. Robust Spatial Reuse Scheduling in UWANs50 100 150 200 250 3000. 1?>2Topology 2?>3Topology 3?>4Topology 4?>5Topology 5?>6Time slotThroughput  TDMAT?BSPR?BSP(M?OTT)Figure 7.10: Results of ?through from (7.2) for topologies recorded in the sea trial andT = 10 time-slots. Each vertical line represents the time a topology change startsaffecting results.In Figure 7.10, we show the throughput (7.2) during the sea trial as functionof time, where each throughput measurement is averaged over a sliding window ofT = 10 time slots. For clarity, we present result only of TDMA, T-BSP, and R-BSPwith OTT skeleton. The results reflect exactly what has been recorded during thesea-trial, including the sharing of topology information, and thus include the effectof topology mismatch. The straight lines in Figure 7.10 mark the time a topologychange starts affecting the throughput results, and the labels for topologies matchthe topologies shown in Figure 7.9b. The effect of a topology change is evident by thenetwork recovery time and the absolute throughput decrease. The former is measuredby the difference from the time topology changes until it is updated and throughputconverges, and the latter by the difference between the throughput once the changeoccurs and after topology updates. From Figure 7.10, we observe that compared toperformance of T-BSP, effect of topology changes on throughput of R-BSP is muchlower. Consider, for example, Topology 4 recorded from time slot number 150 until210. Here, for T-BSP, throughput drops to 0.14 until it converges to 0.26 (i.e., adifference of 0.12) after roughly 40 time slots. However, for R-BSP, the throughputdifference is only 0.03 and network recovers after less than 20 time slots.In Figure 7.11, we show scheduling delay performance for the sea-trial-based topol-ogy. As for the simulation-based topologies, we again distinguish between static anddynamic topologies. The latter is similar to the time-varying topologies consideredfor Figure 7.10, and the former is emulated by assuming that all nodes share thesame (and correct) topology information. The value of this static-topology case isto show results for measured and thus realistic topologies which complement those164Chapter 7. Robust Spatial Reuse Scheduling in UWANsStatic Topology Dynamic Topology8101214161820? delay  TDMAOTTHSR?TDMAT?BSPCUMPR?BSP(TDMA)R?BSP(M?OTT)FR?BSP(M?OTT)Figure 7.11: ?delay from (7.3), for static and dynamic sea-trial-based topologies.for simulation-based topologies in the previous section. We observe that when topol-ogy is dynamic, scheduling delay of T-BSP, CUMP and HSR-TDMA considerablyincreases compared to the case of static topology. However, delay performances ofthe topology-transparent algorithms and the three variants of the R-BSP algorithmhardly change, which demonstrates their short-term robustness to topology varia-tions.In summary, considering the results for the different performance criteria for bothmodel-based and sea-trial-based topologies, we conclude the proposed R-BSP pro-vides a favorable tradeoff of throughput and scheduling delay, together with flowcontrol and a high short-term robustness to outdated topology information.Finally, a word on communication overhead is in order. While topology-transparentand random-access scheduling algorithms (e.g., handshake and Aloha) are fully dis-tributed, both R-BSP and T-BSP are centralized solutions as they require topologyinformation of the entire network. However, the actual calculation of the schedule isperformed locally. Furthermore, as these algorithms support transmission of broad-cast packets, and topology information is piggy-backed on broadcast packets, theoverhead for each packet is limited to N ? (N ?1) bits. This overhead can be furtherreduced by transmitting only updates of topology information.7.5 ConclusionsIn this chapter, we considered the problem of scheduling in high-traffic UWANs sup-porting transmission of broadcast packets. We formalized the problem of resourceassignments to nodes to maximize channel utilization under certain fairness/flow con-165Chapter 7. Robust Spatial Reuse Scheduling in UWANstrol. Considering the challenges of resource assignment for time-varying topologies,we suggested combining topology-transparent with topology-dependent schedulingto improve short-term robustness to inaccurate or outdated topology information.We presented two robust scheduling algorithms to maximize channel utilization andto improve fairness. By means of simulation results, we demonstrated that our ap-proach outperforms existing topology-transparent algorithms in terms of throughputand scheduling delay by reusing topology information. Furthermore, we showed thatcompared with an optimized topology-dependent schedule, short-term robustness totopology variations is significantly improved, while scheduling delay is only slightlyincreased. Further work will include a utilization of the long propagation delay in thechannel by scheduling transmissions within time slots to allow simultaneous trans-missions from neighbor nodes, while avoiding scheduling constraints.166Chapter 8Adaptive Error-Correction CodingScheme for UWANsThe spatial-reuse TDMA scheduling protocol offered in the previous chapter usestopology information in the form of connectivity and conflict matrices. While thelatter requires location information to evaluate whether a node is within the inter-ference range, only a rough location estimation is required and the full localizationcapability developed in Part I is not used. To complement this, in this chapter we uti-lize propagation delay information to improve reliability in TDMA UWANs throughadaptive channel coding. While the existing literature of adaptive transmissions inUWANs presented in Section 1.2.2 demonstrated significant improvement in networkthroughput and latency, we argue that there is room for further improvement byobtaining channel state information (CSI) in the form of distance to nearby nodes.Since in slotted scheduling, the guard interval is usually dimensioned according tothe modem?s maximal detection range (which for UWANs corresponds to a propa-gation delay on the order of a few seconds for a typical interference range of a fewkilometers [5]), each (re)transmission includes a sizeable overhead. Thus, consider-ing that actual propagation delay for specific communication links is often notablyshorter than the maximal expected delay, we suggest improving link reliability byutilizing the often over-sized guard interval in a time slot. In particular, assumingthat the propagation delays to nodes within the interference range of a transmittingnode are known (e.g., from frequent packet exchange, such as from navigation pack-ets in Deep-Link), our scheme opportunistically includes extra parity symbols in thedata packet if the guard interval is longer than needed for interference-free transmis-sion. Since extending the code length trades off reliability and energy consumptionfor transmission, we optimize the number of parity symbols used, considering bothsingle packet transmission and packet retransmission with IR-HARQ. We note thatcompared to conventional adaptive coding, where CSI usually is given in the form ofa link quality parameter like SNR, one novel aspect of our approach lies in the directuse of ranging information as part of the CSI. Such adaptation of coding rate basedon delay has not been considered before.We present two possible implementations for our adaptive coding approach, onebased on a bank of codes and another one based on rateless codes. For both schemes,we include the case of ranging information being available only at the transmitterside, thus obtaining range-based adaptive coding with no communication overhead.We present simulation results for typical underwater acoustic environments as well167Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsas experimental results from a sea trial. The results demonstrate that, when ranginginformation is available (e.g., the Deep-Link application), our protocol provides sig-nificant gains compared to the performance of fixed coding schemes in both reliabilityand transmission energy consumption.The remainder of this chapter is organized as follows. The details of the sys-tem model are introduced in Section 8.1. In Section 8.2, we describe our adaptivecoding approach for both single packet transmission and IR-HARQ. Two possibleimplementations schemes of the proposed adaptive coding method are introducedin Section 8.3. Simulation and experimental results are presented and discussed inSection 8.4, and conclusions are drawn in Section System ModelWe consider slotted UWANs where node i is assigned with messages of K informationsymbols to transmit to its designated receiver j. The considered scenario accommo-dates unicast communication, and besides slotted transmissions, we set no limitationon the scheduling protocol. We define the link interference range as the distance upto which transmissions significantly affect the signal-to-interference-plus-noise ratio(SINR) at an unintended receiver. Due to the large attenuation in the underwa-ter acoustic channel (cf. [5]) we assume that the per-link interference range can bebounded by the detection range of synchronization signals, whose energy is usuallymuch larger than that of information bearing signals. We assume periodic packetexchange between nodes, such that by estimating the time-of-flight [150] of receivedsynchronization signals, each node is aware of the distance to nodes located withinits interference range.Let dmax be the maximal interference range of the system. Furthermore, for timeslot t, let dt,i be the maximum distance of node i to nodes within its interferencerange which are scheduled to receive in time-slots t and t+ 1. Clearly,dt,i ? dmax , (8.1)and thus often the guard interval could be reduced while still ensuring that packetsare received interference-free. Using knowledge of dt,i, our goal is to optimize time slotutilization of node i. The optimization aims to strike a balance between reliability ofand energy consumption for transmission.8.2 The Adaptive Coding SchemeLet us first consider the transmission of a single packet, i.e., no ARQ is applied. Ifa fixed-rate error-correction code is used, K information symbols are encoded intoNmin coded symbols. Nmin is determined assuming dt,i = dmax and thus the full guard168Chapter 8. Adaptive Error-Correction Coding Scheme for UWANs0 200 400 600 800 1000100101102?t,i [m]g coding  pRS=0.05pRS=0.08pRS=0.12pRS=0.15Figure 8.1: Gain gcoding from (8.5) as a function of ?t,i from (8.2).interval is needed for interference-free scheduling. However, assuming that node i hasan accurate estimate of the range difference?t,i = dmax ? dt,i , (8.2)we can shorten the guard interval and transmit up toNmaxt,i = bNmin +?t,iTs ? cc (8.3)symbols without causing interference to other unintended receivers. In (8.3), Tsand c are the symbol period and propagation speed, respectively. Hence, denotingby Nactualt,i the number of actually transmitted symbols transmitted at time t fromsource i, then Nmin ? Nactualt,i ? Nmaxt,i .Next, we demonstrate the gain that can be achieved by adaptive coding in termsof the packet-error-rate (PER) and the energy consumption for transmission. Thisnot only highlights the possible improvements by better utilizing the time slot, butalso sets the stage for the following optimization of Nactualt,i .8.2.1 Gain of Adaptive CodingWe use the example of an (K,N) Reed-Solomon (RS) code [151] to analyze theperformance improvements due to adaptive coding.PER GainLet N ? be the number of transmitted symbols after puncturing N?N ? symbols of theoriginal RS code. Denoting by pRS the RS symbol error probability before decoding,169Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsthe packet error probability (PER) after decoding is given bypRSpacket(N ?) =N ??k=b(N ??K)/2c+1(N ?k)(pRS)k(1? pRS)N ??k . (8.4)Let us consider the PER when the receiver obtains N ? = Nactualt,i demodulated sym-bols, and compare it to the case of coding with Nmin. By (8.4), the PER of theseschemes is pRSpacket(Nactualt,i ) and pRSpacket(Nmin), respectively. Thus, in terms of successrate, the gain of the adaptive punctured RS coding scheme over the fixed code isgcoding =1? pRSpacket(Nactualt,i )1? pRSpacket(Nmin). (8.5)Note that metric gcoding from (8.5) is meaningful only in the case of poor performanceof the non-adaptive coding scheme, which requires an ARQ protocol and is the caseconsidered.In Figure 8.1, for Ts = 0.01 sec, c = 1500 m/sec, we show gcoding from (8.5) forNactualt,i = Nmaxt,i , K = 54, and Nmin = 63, as a function of ?t,i from (8.2), and forseveral values of pRS. We observe that gcoding is significant and fast increasing with?t,i and pRS. We note that for large ?t,i the PER of the adaptive coding schemebecomes extremely small, and gcoding converges to 1/(1 ? pRSpacket(Nmin)) as observedin Figure 8.1.Energy Consumption for TransmissionSince instead of Nmin symbols, we opportunistically transmit Nactualt,i symbols perpacket, the potential gain of the adaptive coding scheme over the fixed code in termsof PER is achieved at the cost of higher energy consumption for per-packet trans-mission. This may seem to be a challenge for UWAC networks, where often energyresources at (battery-operated) network nodes are limited. However, considering thelow reliability in UWAN links, and accordingly the energy spent for successfully re-ceived data packets, the improved error correction capability of the adaptive codingscheme may ultimately reduce energy consumption for transmission, as we discussnext.Let ppacket(N) be the error rate of a packet transmitted using an (K,N) error-correction code. Then, a successful transmission requires on averageM(N) = 11? ppacket(N)(8.6)packet transmissions. Furthermore, denoting by S and Th the transmit power and du-ration of the packet header and pre-ample sequence, respectively, the average energy170Chapter 8. Adaptive Error-Correction Coding Scheme for UWANs0 200 400 600 800 1000100101102103?t,i [m]g energy  pRS=0.05,Th=0.05pRS=0.08,Th=0.05pRS=0.12,Th=0.05pRS=0.15,Th=0.05pRS=0.15,Th=0.5Figure 8.2: Gain genergy from (8.7) as a function of Th and ?t,i from (8.2). Non-erasurechannel.consumption for one successful packet transmission is M(N) ?S(NTs+Th). To quan-tify the advantage of our adaptive coding approach in terms of transmission-energyconsumption we consider the ratiogenergy =M(Nmin) ? (NminTs + Th)M(Nactualt,i ) ? (Nactualt,i Ts + Th). (8.7)We note that genergy in (8.7) increases with Th, and is influenced by Nactualt,i throughthe energy consumption term PNactualt,i Ts and the average number of packet trans-missions M(Nactualt,i ), where the latter depends through (8.6) on the packet error rate(PER) ppacket(Nactualt,i ). Hence, M(Nactualt,i ) decreases with Nactualt,i , while the energyconsumption term increases for larger Nactualt,i .To shed some light on the value of genergy from (8.7), we consider the exampleof the RS code used already in Section 8.2.1. In Figure 8.2, we show genergy from(8.7) as a function of ?t,i (8.2) and Th, and the same set of parameters consideredin Section 8.2.1. In particular, Nactualt,i = Nmaxt,i . We note that while genergy increaseswith Th, due to the low transmission rate this increase is not significant. As expected,we observe that the curves have a distinct maximum, reflecting the trade-off betweenlarger transmission energy and lower PER for increasing Nmaxt,i . We note that genergyincreases with larger symbol-error rate pRS, as it emphasizes the error-rate gain ofadaptive over fixed-rate coding. Furthermore, we observe that the ratio genergy islarger than one in a wide range of distances ?t,i for pRS ? 0.08. Hence, adaptivecoding consistently provides a gain in energy consumption in such unreliable com-munication channels, which are typical for UWANs.Considering the convergence of gcoding from (8.5) to a constant gain value as shown171Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsin Figure 8.1, and the non-monotonic behavior of genergy from (8.7) as can be seenfrom Figure 8.2, we note that the choice of Nactualt,i = Nmaxt,i can be improved upon,especially for large values of ?t,i. In particular, to limit energy consumption, weoptimize Nactualt,i , as described in the following.8.2.2 Optimization of N actualt,iThe channel between transmitter i and receiver j at time t is characterized by itscapacity Ct,i,j, whose unit is bit per coded symbol. Assuming that channel conditionsdo not change much within a packet transmission, the receiver can likely successfullydecode after Nactualt,i transmitted symbols ifCt,i,jNactualt,i ? (1 + ?)KL , (8.8)where L is the byte size of coded symbols and ? accounts for the gap to capacity usingpractical codes. Hence, by estimating Ct,i,j transmitter i can determine the numberof symbols required for successful decoding. Combining (8.8) with adaptation basedon interference range, for a single packet transmission we haveNactualt,i = min((1 + ?)KLCt,i,j, Nmaxt,i). (8.9)While for the transmission of the first packet, Nactualt,i ? Nmin (see Section 8.2), forlater packets Nactualt,i according to (8.9) could be below Nmin, which would lead to anoverall energy savings compared to the fixed-rate coding scheme.As an example of obtaining Nactualt,i , we consider the M -ary symmetric channel(MSC) and the M -ary erasure channel (MEC). The former model is a good fit forthe RS code discussed in Section 8.2.1, and the latter is used for rateless Fountaincodes, discussed further below. For the case of RS coding and the MSC, we haveM = 2L symbols and the capacity isCt,i,j = L?H(pRSt,i,j)? pRSt,i,j log2(M ? 1) , (8.10)where H(?) is the binary entropy function. For the MEC model with symbol erasureprobability pet,i,j, we haveCt,i,j = L(1? pet,i,j). (8.11)For (8.10) and (8.11), estimates p?RSt,i,j and p?et,i,j of the symbol error and erasure rates,respectively, are required. The process of obtaining these estimates is described nextfor both single and multiple packet transmissions.Single Packet TransmissionIf a feedback channel exists (as assumed in [89]), the receiver can measure the chan-nel conditions (e.g., from a received request-to-send packet) and report Ct,i,j to the172Chapter 8. Adaptive Error-Correction Coding Scheme for UWANstransmitter, which then directly calculates Nactualt,i from (8.9). Otherwise, since bothpRSt,i,j from (8.10) and pet,i,j from (8.11) can be represented as a function of the SNR,snrt,i,j, we use the distance information available at the transmitter and an attenua-tion model to obtain an estimate for snrt,i,j and calculate Ct,i,j under the assumptionof small deviation of the SNR from its nominal value.Multiple Packet TransmissionIn a communication session between nodes i and j, multiple packets may be transmit-ted and acknowledgments are received for successful packets. By knowing the numberof symbols needed for a previous successful transmission, and assuming channel con-ditions do not change much between consecutive packets, the transmitter can reverse(8.9) to estimate Ct,i,j. In the case of unsuccessful (and thus unacknowledged) previ-ous packets, we gradually update the assumed channel conditions. For an unsuccessfulpacket m? 1 transmitted at time tm?1, if Nactualtm?1,i < Nmaxtm?1,i we havepRStm?1,i,j > p?RStm?1,i,j ,petm?1,i,j > p?etm?1,i,j . (8.12)Thus, we monotonically increase p?RSt,i,j or p?et,i,j till a threshold is reached or the num-ber of retransmitted packets exceeds a maximum P , after which failure is declaredand the packet is dropped. Given distance information between i and j, dtm,i, theabove threshold can be calculated from an upper bound on the signal attenuation(e.g., Chapter 4). Note that the above process does not involve direct estimate oflink quality and does not require additional communication overhead other than ac-knowledgments, which are already part of any ARQ protocol.We observe the similarities in the problem of increasing p?RSt,i,j or p?et,i,j, and thecongestion avoidance mechanism of the TCP-IP protocol [152]. In TCP-IP, conges-tion avoidance is required to manage failures in packet transmission by changing thecongestion window, such that for each unacknowledged packet the maximal windowsize is halved and the window size is reduced to its initial value. Adopting the samestrategics, we setp?RStm,i,j = p?RStm?1,i,j ? xMSC ,p?etm,i,j = p?etm?1,i,j ? xMEC , (8.13)where xMSC > 1 and xMEC > 1 control the trade-off between energy consumption fortransmission and the number of packets needed till successful decoding, i.e., networklatency. An illustration of the above procedure is presented in Figure Extension to IR-HARQThe process of optimizing Nactualt,i is extended next to use in the IR-HARQ protocol(cf. [85]). In the IR-HARQ protocol, instead of packet-wise decoding, the designated173Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsFigure 8.3: Illustration of the procedure of updating channel conditions for multiplepacket transmission.receiver accumulates all demodulated symbols from previous packets. In turn, thesource keeps transmitting packets until an acknowledgement of successful decodingis received. In this section, we describe how our adaptive coding scheme can beembedded in such protocol.Consider unsuccessful transmission of previous packets, n = m?, . . . ,m ? 1. As-suming channel conditions do not change much from packet m? to m, we modify (8.9)intoNactualtm,i = min????(1 + ?)KL? Ctm,i,jm?1?n=m?Nactualtn,iCtm,i,j, Nmaxtm,i????, (8.14)and Ctm,i,j is updated using the same process illustrated in Figure 8.3 for multiplepacket transmission. Similar to the case of multiple packet transmission discussedin Section 8.2.2, the initial estimate Ctm? ,i,j required to calculate Nactualtm? ,i , is set bythe number of symbols,m??1?n=m??Nactualtn,i , needed for successful decoding of a previousmessage accomplished after m? ?m?? packet transmissions.8.3 ImplementationWe now describe practical implementation schemes for our adaptive coding approach.LetNmax = Nmin + dmaxTs ? c. (8.15)174Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsFigure 8.4: Illustration of adaptive coding implementation for single packet trans-mission.Since Nmin and Nmax are set by the maximal and minimal propagation delay of thesystem, respectively, by (8.3), Nmin ? Nmaxt,i ? Nmax. While node i has knowledge of?t,i and thus can calculate Nmaxt,i to set Nactualt,i according to (8.9) or (8.14), this maynot be the case for its receiver j, who is aware of only Nmin, Nmax, and K. This isbecause node j may not be aware of the distance of node i to all nodes within itsinterference range. Considering this problem, one possibility for node i is to transmitthe value Nactualt,i as a separate header packet. If it is undesirable to transmit this sideinformation, which of course takes away from the available guard time for sendingextra parity symbols, the iterative decoding scheme illustrated in Figure 8.4 can beapplied for the case of a single packet transmission. In this case, the receiver makesmultiple decoding attempts with the first attempt starting after receiving enoughinformation bits to satisfy (8.8). If decoding fails (e.g., the cyclic-redundancy check(CRC) did not pass), receiver j makes another attempt after having obtained at leastone more demodulated symbol. Decoding attempts are stopped when a post-amblesignal to mark the position of the last symbol in each packet is detected or when atmost M try = Nmax ? (1 + ?)K + 1 decoding attempts are made.Next, we suggest two implementation examples for our adaptive coding approach.Bank-of-CodesThe first implementation uses a pre-defined bank of up to Nmax ? (1 + ?)K codes,which can be a set of either optimized codes for different rates or punctured codes.For the latter, we apply an (K,N) mother code, where N is pre-defined at bothtransmitter and receiver. Since Nactualt,i ? Nmaxt,i , for a single packet transmission,175Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsN ? Nmax, while for IR-HARQ, N ? P ? Nmax (recall P is the maximum allowednumber of packet retransmissions). At its designated time slot t, node i transmitsNactualt,i symbols by puncturing N ?Nactualt,i symbols of the codeword, following a pre-defined puncturing pattern, which, in the case of an IR-HARQ, is different for everypacket transmission.Rateless CodesThe second implementation example is based on Fountain codes [153]. At time t, thetransmitter generates a codeword whose length corresponds to Nactualt,i symbols. Dueto the rateless nature of Fountain codes, generation of any number of parity symbolsis easily facilitated, and the process is similar in both single packet transmission andIR-HARQ. No side information is needed at the receiver assuming that a commonseed for the random generation of the columns of the generator matrix is used. Thesame adaptive coding and successive decoding procedure can be applied to variantsof Fountain codes, most notably Raptor codes [154]. For Raptor codes, we use an(K,Nouter) outer error-correction code and an inner (Nouter, Nactualt,i ) Fountain code,where Nouter = ? ?K and ? is a design parameter controlling the maximal probabilityof the failure of the inner Fountain decoding.With regards to Fountain codes, using LT Fountain codes [155] has a benefit ifthe transmitter-receiver link can be modeled as an erasure channel. In this case,message passing decoding is alike successive cancelation, and additionally demodu-lated symbols available at the m-th decoding attempt can be used directly to improvethe result from the (m ? 1)-st decoding stage (see [153]). Here, decoding with andwithout knowledge of Nactualt,i are in fact identical, and thus there is no complexityoverhead due to the iterative decoding procedure from Figure 8.4. However, since inunderwater acoustic communication transmission rate is on the order of a few kbpsand packets are small [9], we expect K to be on the order of a few tens to thousandsymbols. Therefore, since popular LT and Raptor codes perform well only for largecode word lengths, for our numerical results we apply the Fountain coding schemedescribed in [156], where good performance results are obtained for information wordlengths as low as K = 100, at the cost of somewhat increased decoding complexity.When the channel cannot be modeled as an erasure channel, the integration of newlyarrived samples into message-passing decoding is somewhat more complicated. Forthis case, favorable decoding schedules are described in [157] and [158].DiscussionComparing the above Bank-of-Codes and Rateless coding schemes, we note that forthe former, since often there are restrictions for the code design parameters24, Nmay be much greater than Nmax (for a single packet transmission) or P ? Nmax (for24For example, for Reed-Solomon codes N must be equal to 2n ? 1 for some integer n [151].176Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsIR-HARQ), and encoding and decoding complexity may be greater than that of therateless scheme. However, in the Bank-of-Codes scheme, the punctured or pre-definedcode can specifically be optimized for a rate and thus achieve better performance thanthe rateless code.8.4 Performance Results and DiscussionWe now evaluate the performance of our adaptive coding scheme in terms of thePER, energy consumption for transmission, and throughput using numerical simula-tions. Furthermore, to show the effect of a realistic sea environment, we also presentresults from a sea trial, where we implemented the punctured RS scheme in an actualunderwater acoustic modem (namely, the Deep-Link modem).8.4.1 SimulationsSettingOur simulation setting includes a Monte-Carlo set of 10000 channel realizations. Foreach channel realization, four nodes are uniformly randomly placed in a square areaof 2000 ? 2000 m2 at a fixed depth of 40 m for a 50 m long water column. Thenodes operate for 100 sec in a TDMA network. Since in this paper, we are moreinterested in showing the possible gain of using our adaptive coding scheme ratherthan the absolute decoding capability, for simplicity in our simulations we adopt abinary erasure channel (BEC) model (i.e., MEC with M = 2) with binary phase shiftkeying (BPSK) modulation. The symbol-erasure probability is determined based onthe transmitter-receiver link distance, d. More specifically, for each d, we calculatethe receiver-side SNR using the Bellhop ray-tracing simulator (cf. [2]) for a flatsand surface, a common power source level of 130 dB//?Pa@1m, and a noise levelof 50 dB//?Pa/Hz. Considering the large set of channel realizations, instead ofrunning Bellhop for the entire bandwidth, we used the Bellhop results for the carrierfrequency, which was set to 15 kHz. The channel erasure rate is then determined fromthe calculated SNR considering the BPSK modulation. The output of the Bellhopsimulator in terms of the transmission loss as a function of range is given in Figure 8.5.From the figure we observe that for different ranges we may get the same transmissionloss and thus channel erasure rate, which is due to the shadowing characteristics ofthe underwater acoustic channel [5]. An approximate model of this transmission lossisTL = ? log10(d) + ?d/1000 , (8.16)where d is the transmission distance, ? is the propagation loss with typical valuesbetween 10 and 30 [5], and ? is the absorption loss which for a carrier frequency of15 kHz is roughly 2 dB/km [5]. To allow channel changes (which affects Ct,i,j from(8.8)), during the network operation we let the nodes drift between the transmission177Chapter 8. Adaptive Error-Correction Coding Scheme for UWANs0 1000 2000 3000 4000 50002030405060708090100range [m]Transmission loss [dB]Figure 8.5: Transmission loss vs. range. Output from the Bellhop simulator [2].of packets, and calculate the snr and the pe, accordingly. Drift motion is simulatedusing the Shallow Water Hydrodynamic Finite Element Model (SHYFEM) oceancurrent model [109]. The model is set for location 49o16?13.33??N , 126o16?6.4??W (i.e.,near Vancouver, BC), and a channel structure with two underwater hills at depth30 m located at both corners of the considered square area.The transmitter sends short information messages of K = 456 bits with a trans-mission rate of 500 bps, Th = 0.1 sec, and an original code rate of K/Nmin ? 0.9.The duration of the time slot is determined according to a maximal detection rangeof 1500 m and a propagation speed of 1500 m/sec. Hence, using the adaptive cod-ing scheme, at most, i.e., for dt,i = 0 m, 1000 coded symbols can be transmitted toform a coding rate of K/Nmax ? 0.45. Packets are retransmitted until successfulreception is obtained at the intended receiver. This scenario mimics the exchangeof navigation packets in the Deep-Link system [133]. During the network operation,out of the four nodes, we choose a transmitter and receiver, and set Nactualt,i accordingto the maximal distance of the transmitter from its intended receiver and the nodesscheduled to transmit in time slots t and t + 1. While due to strong multipath andclock offsets ranging errors are expected, in Chapters 2 and 4 we have shown thatthese errors can be limited to a few meters. Hence, given the low transmission rate,the effect of an overestimated interference range would be a minor interference of 1-3symbols colliding with a later packet. For this reason, we assume that the interferencerange is accurately estimated at the transmitter. Nevertheless, due to the simulateddrift motion and the fact that dt,i is estimated before the actual transmission, smallinaccuracies in the estimation of dt,i do exist.We evaluate performance of IR-HARQ using the adaptive coding scheme with fullyutilized time-slot (FIR-HARQ), and IR-HARQ using optimized number of symbols178Chapter 8. Adaptive Error-Correction Coding Scheme for UWANs0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.4500. probabilityPER  F?RS (burst)P?RS (i.i.d)P?RS (burst)FountainRaptor RSFigure 8.6: PER as a function of channel erasure rate.(OIR-HARQ) To show the effect of using the IR-HARQ we also show results fora single packet transmission with a fixed coding gain (Single). For the consideredschemes, the maximal number of packet retransmissions allowed until a message isdeclared failed is P = 5. For the OIR-HARQ, the threshold for the updating of p?et,i,j(see Section 8.2.2) is calculated from model (8.16) for ? = 30 and ? = 3 as an upperbound for power attenuation in the channel. Similarly, we use ? = 10 and ? = 1.5as a lower bound on power attenuation to calculate the initial condition p?et1,i,j at thebeginning of the network operation, and ? = 0.1 for the ratio of required informationbits in (8.8). As a worst case scenario for the comparison with the fixed-rate code,we assume acknowledgments are always received.For the case of a single packet transmission (denoted above as Single), we demon-strate the gain of the adaptive coding scheme by showing performance of differentcoding implementations: RS (fixed (F-RS) and punctured (P-RS)) with coded wordof 8 bits, Fountain [156], and Raptor codes using an RS outer code (we note that sim-ilar values were obtained for Raptor codes using a low-density parity check (LDPC)outer code). As performance of the RS scheme varies greatly with the erasure pat-terns, we show performance results for both i.i.d. and burst-wise erasures. Theformer is motivated by the ambient noise in the channel, and the latter by temporar-ily correlated waves and ships-induced noises [5]. Finally, for the Raptor codes weuse ? = 1.2 (see Section 8.2). A software implementation of these protocols can bedownloaded from [96].179Chapter 8. Adaptive Error-Correction Coding Scheme for UWANs0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.4500. probabilityChannel Utilization  F?RS (burst)P?RS (i.i.d)P?RS (burst)FountainRaptor RSFigure 8.7: Channel utilization as a function of channel erasure probability (for ?t,i ?650 m).ResultsWe start off by comparing performance of the adaptive coding scheme to the fixedcoding scheme for a single packet transmission, where for the former we transmitNmaxt,i symbols and for the latter we transmit Nmin symbols. In Figure 8.6, we showthe PER as a function of the erasure probability of the channel. For each valueof erasure probability, we average the PER for the cases where the actual erasureprobability is within a range of 0.02 from the one indicated through a marker inFigure 8.6. First, we observe that the performance of the RS scheme for burst-wiseerasures is significantly better than that for i.i.d. erasures. This is due to the binary(BPSK) transmission that leads to more erroneous RS symbols (recall we used acoded word of 8 bits) and emphasizes on the suitability of RS coding in burst-noisechannels. However, from Figure 8.6 we also see that even for i.i.d. erasures, thedifferent adaptive coding schemes significantly outperform that with the fixed-rateRS code. The implementation with Fountain and Raptor codes25 shows its advantagefor memoryless channels (i.i.d. erasures26), and again greatly outperforms the fixed-rate coding scheme.Next, we investigate channel utilization, defined as the rate of successful packets,for the different adaptive schemes. Since performance changes with both channelerasure probability and ?t,i from (8.2), in Figures 8.7 and 8.8 we show channelutilization as a function of the channel erasure probability and ?t,i, respectively.The former figure is obtained by calculating channel utilization for cases where ?t,i25The results of the Raptor codes are superimposed to the one for fountain codes.26We note that for rateless codes similar results where obtained for the case of burst-type erasures.180Chapter 8. Adaptive Error-Correction Coding Scheme for UWANs0 200 400 600 800 1000 120000.,iChannel Utilization  F?RS (burst)P?RS (i.i.d)P?RS (burst)FountainRaptor RSFigure 8.8: Channel utilization as a function of ?t,i (for erasure probability of roughly0.21).is within the range of 640? 64 m, and the latter for cases where the channel erasureprobability is within the range of 0.21 ? 0.02. Note that since we consider fournodes and TDMA, channel utilization is bounded from above by 14 . However, itcan considerably degrade if retransmissions are needed. For example, as also shownby the results in Figure 8.6, for the considered erasure rate in Figure 8.8, only afew packets were properly decoded using the fixed RS code and channel utilizationis almost zero. From both figures, we observe a significant gain of the adaptivecoding schemes over the fixed-rate RS scheme. From Figure 8.8, it can be seenthat, as expected, performance improves as ?t,i increases. As in Figure 8.6, the bestperformance is achieved by the punctured RS scheme for burst-wise erasures withonly a very small performance loss for the Fountain and Raptor coding schemes.In fact, from Figures 8.7 and 8.8 we observe that for these schemes starting from?t,i ? 150 m and channel erasure rate of up to 0.3, channel utilization is maximal,i.e., no retransmissions are required.We now compare performance of the considered three protocols, namely: Single,FIR-HARQ, and OIR-HARQ. Due to the small difference between performance ofthe adaptive coding schemes, in the following we present results of only the binaryFountain code implementation. In Figure 8.9, we show the error ?p(m) = |pe ? p?e|as a function of packet number m for different values of xBEC. Since motion in oursimulations is restricted to drifting, pe does not change rapidly, and ?p(m) reflectsconvergence of estimate p?e. Since we bound the increase of p?e, ?p(m) decreasesfast after three packet transmissions. We also observe that the initial error (i.e.,?p(1)) increases with xBEC. This is because the number of transmitted symbols tilldecoding increases with xBEC, and the former is used to determine the initial p?e.181Chapter 8. Adaptive Error-Correction Coding Scheme for UWANs1 2 3 4 510?410?310?210?1100Packet number? p  XBEC=1.5XBEC=1.2XBEC=1.1Figure 8.9: Error ?p(m) as a function of packet number m. (Note that values in they-axis are reversed).Clearly, ?p decreases for smaller xBEC values. This means less transmitted symbolsper packet, but at the cost of transmitting more packets. However, as observedin Figure 8.9, the difference is not significant. To determine the effect of xBEC onnetwork latency, in Figure 8.10 we show a histogram of the number of packets neededtill decoding is possible. We observe that failure rate of the Single scheme is fargreater than that of the IR-HARQ schemes. In fact, no failures are detected forthe FIR-HARQ scheme, which utilizes the entire time slot. As expected, latencydecreases for higher values of xBEC. However, the latter characteristic comes atthe cost of energy consumption for transmission, which improves as the number oftransmitted symbols needed for successful decoding, Nfinal =P?m=1Nm, decreases. Thisis observed in Figure 8.11, where we show the complementary density function (CDF)of Nfinal. We note the large variance of Nfinal for the FIR-HARQ method, for whichthe number of redundancy symbols greatly increases as more packets are required fordecoding. Due to the adaptive transmission in the OIR-HARQ schemes, their Nfinal,and thus energy consumption for transmission, is significantly lower than the FIR-HARQ scheme. Here, we observe that Nfinal does not change much for xBEC = 1.5and 1.2, which implies that our adaptive coding scheme is not very sensitive to thechoice of this parameter.Finally, in Figure 8.12 we show the CDF of the network goodput, defined as thenumber of delivered information bits during the network operation of 100 sec. Asexpected, goodput of the IR-HARQ schemes is considerably higher than that of theSingle scheme. We also note that goodput is maximal for the FIR-HARQ scheme (atthe cost of energy-consumption for transmission). However, not much difference is ob-182Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsFail   1    2    3    4    5 numberHistogram of network latency  SingleFIR?HARQOIR?HARQ (XBEC=1.5)OIR?HARQ (XBEC=1.1)Figure 8.10: Histogram of network latency in terms of number of packets needed tilldecoding.400 600 800 1000 1200 1400 160000. [symbols]Empirical Pr(N final ? x)  FIR?HARQOIR?HARQ (XBEC=1.5)OIR?HARQ (XBEC=1.2)OIR?HARQ (XBEC=1.1)Figure 8.11: CDF of the number of symbols transmitted till successful decoding,Nfinal.183Chapter 8. Adaptive Error-Correction Coding Scheme for UWANs0 10 20 30 40 50 6000. [symbols/sec]Empirical Pr(Goodput ? x)  SingleFIR?HARQOIR?HARQ (XBEC=1.5)OIR?HARQ (XBEC=1.2)OIR?HARQ (XBEC=1.1)Figure 8.12: CDF of network goodput.served comparing performance of FIR-HARQ and OIR-HARQ with xBEC = 1.5. Bythese results, we argue that utilizing the time slot to adaptively adjust the code ratedecreases network latency and increases network goodput. Furthermore, optimizingthe coding rate in an IR-HARQ scheme significantly reduces energy consumption fortransmission at a small cost in network goodput.8.4.2 Sea Trial ResultsTo measure the performance of our adaptive scheme in a realistic sea environment,in November 2009 we conducted an experiment in the Haifa harbor, Israel. Theexperiment included three Deep-Link modems, statically deployed from the harbordocks as shown in Figure 8.13. The distance was 340 m between nodes 1 and 2 (Link1), 780 m between nodes 1 and 3 (Link 2), and 910 m between nodes 2 and 3 (Link3). The modems used RS codes with flexible parameters. Erasure decoding wasperformed, where erasures were declared based on thresholding the received signalsamples. Using this capability, we tested both the fixed and punctured RS codingschemes. During the experiment, the three nodes periodically broadcasted shortpackets of 200 bits at a rate of 300 bps in a TDMA scheduling scheme, where ineach time frame first node 1 transmits, then node 2, and then node 3. Each packetincluded a header of 0.67 sec for a synchronization signal and preamble sequence,and each time slot included a guard interval accounting for possible clock drifts anda maximal propagation delay of 1 sec. The latter was determined according to thesize of the harbor, which was roughly 1500 m. We compared the performance of asingle packet transmission using the punctured RS scheme with a fixed RS code ofrate 4/5, such that the duration of the time slot was roughly 2.5 sec, and at most,184Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsFigure 8.13: Satellite picture of the experiment location (picture taken from GoogleEarth on July 23, 2012.) The three locations of the nodes are marked.i.e., for dt,i = 340 m, coding rate of the punctured RS scheme was 0.41.The experiment included two parts each lasting for one hour. In the first partwe measured performance of the fixed RS coding scheme, and in the second part thepunctured RS coding scheme was tested. Signals were transmitted at a low sourcelevel of 130 dB//?Pa@1m, and as in our simulations we used model (8.16) to estimatethe symbol error rate and the capacity required for evaluation of Nactualt,i .In Figure 8.14, we show the packet success rate, Psuccess, for the three links. Similarto the simulated results in Figure 8.6, we observe a significant gain of the adaptiveover the fixed coding scheme, which is 14% on average. The success rate increasesalso for Link 1, where transmission distance is short and thus the PER has been loweven for fixed-rate coding. We can thus conclude that the proposed adaptive codingscheme is indeed a viable approach to increase network goodput and decrease energyconsumption in a realistic UWAN.8.5 ConclusionsIn this paper, we suggested an adaptive coding approach to improve the packet er-ror rate in a time-slotted UWAC network. Different from usual adaptive coding ap-proaches, our approach uses range information as the basis for adaptation of the coderate. This allows us to exploit the difference between the worst-case and the actuallyrequired guard time. By optimizing the number of parity check symbols transmittedin both single packet transmission and multiple packet transmission using IR-HARQ,we managed to control the trade-off between goodput and energy consumption for185Chapter 8. Adaptive Error-Correction Coding Scheme for UWANsLink 1 (340 m) Link 2 (780 m) Link 3 (910 m)0.50.550.60.650.70.750.80.850.90.951P success  Punctured RSFixed RSFigure 8.14: Packet success rate for the three links from the sea trial.transmission. We described two implementations for our approach, using puncturedand rateless codes. By means of analysis and simulation results, we demonstrated theadvantages of our adaptive coding scheme over fixed-rate error correction in terms ofpacket error rate, transmission energy consumption, and throughput. The simulationresults were verified in a sea trial.186Part IIISummary of Thesis and FurtherResearch187In this thesis, we explored the problems of UWL and spatial-reuse MAC design forUWANs. We offered localization and tracking solutions that combat the continuousand irregular motion of nodes in the channel, lack of time-synchronization betweenthe network nodes, uncertainties in propagation speed information, and the effect ofmeasurement errors. We then used the developed localization capability to designspatial-reuse scheduling algorithms for both unicast and broadcast transmissions anda location-dependent adaptive coding technique. The proposed methods were testedin a developed simulator combining numerical models for both ocean current andpower attenuation in the channel. The results were verified in four sea experimentsof different channel bathymetry structures, using both industry and self-developedunderwater acoustic modems. We now summarize the contributions of the thesis andpropose possible future research directions.? In Chapter 2, we have described a new algorithm for joint time-synchronizationand localization for UWANs. Our algorithm is based on packet exchanges be-tween anchor and unlocalized nodes, makes use of INS measurements to obtainaccurate short-term motion estimates, and exploits the permanent motion ofnodes. Our solution also allows self-evaluation of the localization accuracy. Us-ing simulations, we have compared our algorithm to two benchmark localizationmethods as well as to the Crame?r-Rao bound. The results demonstrate thatour algorithm achieves accurate localization using only two anchor nodes andoutperforms the benchmark schemes when node synchronization and knowledgeof propagation speed are not available. Moreover, we have reported results ofa sea trial where we validated our algorithm in open sea.? In Chapter 3, we have presented a new UT scheme which considers sound speeduncertainties, incorporates Doppler shift measurements, and utilizes (possible)spatial correlation of ocean current to estimate the drift velocity of the TN asa combination of the drift velocities of anchor nodes. The latter is a distinctlynew feature of our UT approach, which increases resilience to water currentirregularities. We have also offered two types of unbiased confidence indexesaimed to control the use of drift velocity estimation. To evaluate the perfor-mance of our UT scheme, we have employed a hybrid simulator that combinesnumerical models for the ocean current and the signal-power attenuation inthe ocean. We have also reported results from two sea trials conducted in theMediterranean Sea and in the Indian Ocean. By tracking the sound speed, andutilizing Doppler-shift measurements and drift velocity information of anchornodes, accuracy is significantly improved.? In Chapter 4, we have utilized variations of ToF measurements due to mobilityof nodes and have presented an algorithm to classify the former into LOS andNLOS links. First, by comparing signal strength-based and ToF-based rangemeasurements, we have identified object-related NLOS links, where signals are188reflected from objects with high reflection loss, e.g., ships hull, docks, rocks,etc. In the second step, excluding ToF measurements related to ONLOS links,we have used a constrained expectation-maximization algorithm to classify ToFmeasurements into two classes: LOS and sea-related NLOS, and to estimatethe statistical parameters of each class. Results from simulations and threesea trials demonstrate a high detection rate of ONLOS links, and accurateclassification of ToF measurements into LOS and SNLOS.? In Chapter 5, we have pointed out the problem of DR navigation for vesselslocated close to or on the sea surface, where, due to ocean waves, the vesselpitch angle is fast time-varying and its estimation via direct measurementsof orientation is prone to drifts and noises. We have suggested a method tocompensate on the vessel pitch angle using only a single acceleration sensor.First, our method classifies acceleration measurements into states of similarpitch angles. Then, for each class, we project acceleration measurements intothe reference coordinate system along the vessel heading direction, and obtaindistance estimations by integrating the projected measurements. Results inboth simulated and actual sea environment demonstrate good DR performanceusing only acceleration measurements.? In Chapter 6, we have utilized the long propagation delay in the UAC andthe (possible) sparsity of the network topology, and have formalized conditionsfor which a node can transmit unicast packets even when it is located withinthe communication range of a node participating in an active communicationsession. We have considered these conditions as design constraints and havepresented a distributed CA handshake-based MAC protocol, which, by jointlyapplying spatial and time reuse techniques, greatly improves channel utilizationat the price of some reduction in fairness in resource allocation.? In Chapter 7, we have addressed the problem of spatial-reuse scheduling inUWANs that support frequent transmission of broadcast packets and requirerobustness to inaccurate topology information. We have derived a broad-cast scheduling algorithm that combines topology-transparent and topology-dependent spatial-reuse scheduling methodologies to achieve high throughputin static and dynamic topology scenarios. Results show that our schedulingalgorithm achieves a favorable tradeoff between network throughput and ro-bustness to outdated topology information due to topology changes, and thatit also achieves fairness in terms of per node throughput.? In Chapter 8, we have proposed a new adaptive coding method to maximizegoodput in TDMA UWANs through time and spatial reuse by exploiting thesurplus guard time that occurs for individual links for improving transmissionreliability. In particular, using link distances as side information, transmitters189utilize the available portion of the time slot to adapt their code rate and in-crease reliability. Since increased reliability trades off with energy consumptionfor transmission, we have modified the code rate, considering both single andmultiple packet transmission using the IR-HARQ algorithm. For practical im-plementation of this adaptive coding scheme we have considered punctured andrateless codes. Simulation and sea trial results demonstrate the gains achievedby our coding scheme over fixed-rate error-correction codes in terms of boththroughput and consumption of transmitted energy per successfully deliveredpacket.The following are suggestions for further research.1. In Chapter 3, we have exploited spatial dependencies between the motion ofnodes to offer an unbiased velocity estimate which increases the reliability ofthe motion model. The performance gap observed in Figure 3.4b relative tothe Crame?r-Rao Lower Bound was explained by the mismatch in the assumedcovariance matrix for both model and measurement noise, as well as due to anon-linear spatial correlation of the ocean current. We believe that by applyingBayesian learning techniques both challenges can be overcome.2. In Chapter 6, we have presented a handshake-based MAC protocol that care-fully schedules transmissions to maximize the use of network resources by uti-lizing the long propagation delay in the channel. While the latter was alsoutilized in Chapter 8 by means of adaptive coding, the focus here was on relia-bility rather than throughput maximization. Hence, a possible extension of thiswork is a propagation delay-dependent approach for contention-free schedulingand for broadcast communication, i.e., a modification of the algorithms sug-gested in Chapter 7 to also utilize the long propagation delay.3. In Chapter 8, we have suggested a heuristic algorithm to trade off reliability andenergy consumption for time-slotted transmission of short packets by adaptivelychanging the channel coding rate. Potentially, by optimizing the number ofparity symbols used, this tradeoff can be greatly improved. This would resultin a new ARQ scheme that may be of interest to any energy constraint system.In addition, the rateless coding approach adopted in Chapter 8 relied on amodel of binary erasure channel for the received symbols. By combining belief-propagation methods and interference identification techniques, still for shortpackets, more realistic non-erasure channel models can be considered.4. 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TLIR ? ?1 ? ?p+1,n2?p+1,n+11 ? ?2 ? ?p+1,n+11 + TLIR0 ? ?1 ? min????p+1,n2 , TLIR??????(1?p+1,n1)?(3?p+1,n1)????p+1,n+11 ? ?2 ? TLIR??????(1?p+1,n2)?(3?p+1,n2) .The above equations can be evaluated numerically by first finding the set of206Appendix A. Alternating Optimization Approach for Solving (4.21)possible solutions for ?p+1,n+1m , ?p+1,n+1m , and ?p+1,n+1m , solving???mf(?m, ?p+1,nm , ?p+1,nm ) =L?l=1Pr(?l = m|?l,?p)?xi??l|xi ? ?m|?p+1,nm ?1?p+1,nm(?p+1,nm)?p+1,nm? Sgn(xi ? ?m) = 0???mf(?p+1,n+1m , ?m, ?p+1,nm ) =L?l=1Pr(?l = m|?l,?p)?xi??l? 1?m+ ?p+1,nm |xi ? ?p+1,n+1m |?p+1,nm(?m)?p+1,nm +1= 0???mf(?p+1,n+1m , ?p+1,n+1m , ?m) =L?l=1Pr(?l = m|?l,?p)?xi??l1?m+1?2m?(1?m)?(|xi ? ?p+1,n+1m |?p+1,n+1m)?mlog(|xi ? ?p+1,n+1m |?p+1,n+1m)= 0 ,where Sgn(x) is the algebraic sign of x, and ?(?) is the digamma function, i.e., the firstderivative of log ?(?), that satisfy the above constraints. However, for integer ?p+1,nm ?5 and approximating Sgn(xi??m) with Sgn(xi??p+1,nm ), both ???mf(?m, ?p+1,nm , ?p+1,nm )and ???mf(?p+1,n+1m , ?m, ?p+1,nm ) can be solved analytically.Finally, in [120], it was proven that alternating maximization converges if for eachalternation, problem constraints are handled internally (see also results in Figure 4).207Appendix BExpressions for the HCRBDenoting bi,m = xi - ?m and R = 4 ? (m? 1), for (4.24) we haveF (?r, ?1)j,q =???????????????????????????????????????????????? ?m??m?1m|bi,m|?m?2[?m ? 1 + 2|bi,m|?(bi,m)], j = R + 1, q = R + 1;??2mSgn(bi,m)|bi,m|?m?1???m?1m , j = R + 1, q = R + 2;Sgn(bi,m)[???mm |bi,m|?m?1 + ?m???mm log( 1?m )|bi,m|?m?1]+kmSgn(bi,m)?m???mm |bi,m|?m?1 log |bi,m|, j = R + 1, q = R + 3;??2m???m?1m |bi,m|?m?1Sgn(bi,m), j = R + 2, q = R + 1;1?2m? (?m + 1)?m|bi,m|?m???m?2m , j = R + 2, q = R + 2;|bi,m|?m???m?1m + ?m???m?1m |bi,m|?m log |bi,m|?|bi,m|?m?m???m?1m log ?m, j = R + 2, q = R + 3;|bi,m|?m?1Sgn(bi,m)( 1?m )?m [?m log |bi,m|?m + ?m], j = R + 3, q = R + 1;|bi,m|?m???m?1m [?m log|bi,m|?m + |bi,m|?m?1], j = R + 3, q = R + 2;? 1?2m ?1?4m??( 1?m )? (|bi,m|?m )?m(log |bi,m|?m )2 ? 2?3m?(1?m ), j = R + 3, q = R + 3;? 1k2m , j = R + 4, q = R + 4;0, otherwise,where ?(?) is the Dirac delta function, and ?(?) and ??(?) are the digamma andtrigamma functions, i.e., the first and second derivative of log ?(?), respectively.Furthermore, defining a1,m = ?(1?m), a2,m = ?(3?m), and a3,m = a1,2a2,2 , we obtain?2??j??qlog p(?r|?1) =???????????????????????????????1(TLIR?a3,2??1)2, j = 2, q = 2;?0.5(?2)?2TLIRa?0.53,2(TLIR?a3,2??1)2(3a3,2a2,2 ??(3?2)+??(1?2)a2,2), j = 2, q = 7;12?41(???( 1?1 ) + 9??( 3?1 ))? 1?31(?( 1?1 )? 3?(3?1 )), j = 3, q = 3;?0.5(?2)?2TLIRa?0.53,2(TLIR?a3,2??1)2(3a3,2a2,2 ??(3?2)+??(1?2)a2,2), j = 7, q = 2;???2[0.5TLIR(?2)?2(a3,2)?0.5TLIR?a3,2??1(3a3,2??(3?2)a2,2 +??(1?2)a2,2)], j = 7, q = 7;0, otherwise,where ??(?) is the first derivative of ?(?).208


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