Statistical Quality-of-Service AwareAdaptive Transmission for Free SpaceOptical Communication SystemsbyMd. Zoheb HassanM.A.Sc., The University of British Columbia, 2013B.Sc., Bangladesh University of Engineering and Technology, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)May 2019c© Md. Zoheb Hassan, 2019ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Statistical Quality-of-Service Aware Adaptive Transmission for Free Space Optical Communication Systems submitted by Md. Zoheb Hassan in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering (ECE) Examining Committee: Victor C. M. Leung, Electrical and Computer Engineering, UBC Co-supervisor Md. Jahangir Hossain, School of Engineering, UBC Okanagan Campus Co-supervisor Shariar Mirabbasi, Electrical and Computer Engineering, UBC Supervisory Committee Member Lukas Chrostowski, Electrical and Computer Engineering, UBC University Examiner Clarence De Silva, Mechanichal Engineering, UBC University Examiner Additional Supervisory Committee Members: Lutz Lampe, Electrical and Computer Engineering, UBC Supervisory Committee Member Julian Cheng, School of Engineering, UBC Okanagan Campus Supervisory Committee Member iiAbstractDespite the growing attention for free space optical (FSO) networks, state-of-the-art literature lacksappropriate adaptive transmission (AT) schemes that can exploit the stochastic propagation channel ofthe FSO networks and guarantee delay quality-of-service (QoS) in the link-layer. Specifically, weather-induced channel impairments not only affect the error-rate or outage probability but also increasethe end-to-end queueing-delay of the FSO network. This dissertation aims to improve QoS-awarethroughput of the terrestrial FSO communication systems by designing innovative AT schemes. Thekey goal of the developed AT schemes is to maximize the supportable arrival rate while ensuring theQoS in terms of certain delay-bound violation probability constraints.We first analyze the effective capacity (EC) of terrestrial FSO communication systems. We deriveaccurate closed-form expressions of the achievable EC by considering several FSO channel impairments.Through asymptotic analysis, we reveal insights on the EC increment. Next, we present delay-QoSaware discrete-rate AT schemes for FSO communication systems with parallel optical beams and av-erage/peak transmit power constraints. Our results suggest that to improve the delay-throughputtrade-off, only suitable optical channels need to be activated. Simulation results demonstrate thatjoint adaptation of transmission parameters of the active optical beams improve throughput of theFSO communication systems in the strict statistical-QoS constraints.Subsequently, we develop AT schemes for FSO backhaul/fronthaul networks. We first study ATschemes for buffer-aided parallel decode-and-forward relaying assisted hybrid radio-frequency (RF)/FSObackhaul networks. Two different hybrid RF/FSO system configurations are considered, and ATschemes for both configurations are developed. These schemes maximize the arrival rate subject tothe total queue-occupancy constraint. Next, we develop delay-QoS aware joint power allocation andrelaying link selection for amplify-and-forward relay assisted uplink FSO fronthaul networks. Finally,we investigate joint FSO fronthaul and millimeter-wave access link optimization for the downlink cloudsmall cell network subject to end-to-end queue-length-bound violation probability constraints. Exten-sive simulations are performed to evaluate the performance of the proposed AT schemes by consideringseveral FSO channel impairments and statistical-QoS requirements. Simulation results demonstratethat our proposed AT schemes substantially improve the statistical-QoS aware arrival rate in the FSObackhaul/fronthaul networks.iiiLay SummaryProvision of ubiquitous backhaul connectivity is a key requirement for ultra-dense 5G networkarchitecture. Thanks to optical-fiber-like data-speed with rapid deployment and freedom from spec-trum licensing, free space optical (FSO) links are capable of complementing optical fiber based back-haul/fronthaul networks. For satisfying the tremendous data-rate demand in 5G communications, FSObackhaul/fronthaul networks need to support an extreme high data arrival rate. Data buffering, whichenables temporarily storing arrived data at the transmitting-end, is inevitable for improving reliabilityof FSO backhaul/fronthaul networks against weather-induced impairments. Nevertheless, data buffer-ing results in long queuing-delay which is detrimental to real-time traffic. We aim to improve themaximum supportable arrival rate to the FSO communication network subject to delay-bound vio-lation probability constraint. Towards this objective, we develop adaptive transmission schemes forseveral terrestrial FSO systems. Through extensive simulations, we demonstrate the efficiency of theproposed adaptive transmission schemes for FSO communication networks.ivPrefaceThis thesis is based on the research conducted under the joint supervision of Professor VictorC. M. Leung and Professor Md. Jahangir Hossain. For all the chapters, I conducted the requiredliterature review and developed the research ideas. I carried out the required mathematical analysisand performed simulations. Moreover, I preprepared the related manuscripts. My supervisors helpedme to validate the analytical and simulation results, and improve the presentation of the manuscripts.All the manuscripts were also co-authored by Professor Julian Cheng who is also a member of mysupervisory committee. Professor Cheng helped me to improve the system models as well as theoverall presentation of the manuscripts.Following is the list of the journal and conference publications related to the chapters of the thesis.Both published and submitted journal articles are provided in this list.Published and Submitted Journal PapersJ1. M. Z. Hassan, M. J. Hossain, J. Cheng, and V. C. M. Leung, “Effective capacity of coherentPOLMUX OWC impaired by atmospheric turbulence and pointing errors,” IEEE/OSA J. Lightw.Technol., vol. 34, no. 21, pp. 5007-5022, Nov. 2016 (part of Chapter 3).J2. M. Z. Hassan, M. J. Hossain, J. Cheng, and V. C. M. Leung, “Delay-QoS aware power allocationand adaptive modulation for dual channel coherent OWC,” IEEE/OSA J. Opt. Commun. Netw.,vol. 10, no. 3, pp. 138-151, Mar. 2018 (part of Chapter 4).J3. M. Z. Hassan, M. J. Hossain, J. Cheng, and V. C. M. Leung, “Statistical delay-QoS aware jointpower allocation and relaying link selection for free space optics based fronthaul networks,” IEEETrans. Commun., vol. 66, no. 3, pp. 1124-1138, Mar. 2018 (part of Chapter 6).J4. M. Z. Hassan, M. J. Hossain, J. Cheng, and V. C. M. Leung, “Adaptive transmission for coherentOWC with multiple parallel optical beams,” IEEE Photonics Technol. Lett., vol. 30, no. 12, pp.1119-1122, June 2018 (part of Chapter 4).J5. M. Z. Hassan, M. J. Hossain, J. Cheng, and V. C. M. Leung, “Joint FSO fronthaul and millimeter-wave access link optimization for cloud small cell networks: A Statistical-QoS aware approach,”accepted for publication at IEEE Trans. Commun. (part of Chapter 7).J6. M. Z. Hassan, M. J. Hossain, J. Cheng, and V. C. M. Leung, “Hybrid RF/FSO backhaul networkwith statistical-QoS aware buffer-aided relaying,” submitted to a journal for potential publication(part of Chapter 5).vPrefaceReferred Conference PublicationsC1. M. Z. Hassan, V. C. M. Leung, M. J. Hossain, and J. Cheng, “Delay-QoS aware adaptive re-source allocation for FSO fronthaul networks,” IEEE Global Commun. Conf. (GLOBECOM),Singapore, 2017, pp. 1-6 (part of Chapter 6).C2. M. Z. Hassan, V. C. M. Leung, M. J. Hossain, and J. Cheng, “Statistical delay aware joint powerallocations and relay selection for NLOS multi-channel OWC,” IEEE Global Commun. Conf.(GLOBECOM), Washington, DC, 2016, pp. 1-6 (part of Chapter 6).C3. M. Z. Hassan, V. C. M. Leung, M. J. Hossain, and J. Cheng, “Effective capacity performanceof coherent POLMUX OWC with power adaptation,” IEEE Global Commun. Conf. (GLOBE-COM), San Diego, CA, 2015, pp. 1-7 (part of Chapter 3).viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xviiiChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Application of terrestrial FSO technology for 5G backhaul/fronthaul network . . 21.1.2 Challenges for FSO Communications and Thesis Objective . . . . . . . . . . . . 41.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.1 Channel Capacity of FSO Communications . . . . . . . . . . . . . . . . . . . . . 71.2.2 QoS-aware Adaptive Transmission for FSO Communications . . . . . . . . . . . 81.2.3 Cooperative FSO and Hybrid RF/FSO Systems . . . . . . . . . . . . . . . . . . 91.2.4 FSO Based Backhaul and Fronthaul Networks . . . . . . . . . . . . . . . . . . . 121.3 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Chapter 2: FSO System Models, Channel Models, and Statistical-QoS Constraints . 192.1 Preliminary of FSO Systems Based on Detection Techniques . . . . . . . . . . . . . . . . 192.1.1 Coherent FSO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1.2 SIM FSO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2 Statistical Model of FSO Channel Impairments . . . . . . . . . . . . . . . . . . . . . . . 232.2.1 Statistical Model of Atmospheric Turbulence Fading . . . . . . . . . . . . . . . . 232.2.2 Atmospheric Attenuation and Geometric Loss . . . . . . . . . . . . . . . . . . . . 262.2.3 Statistical Model of Pointing Error . . . . . . . . . . . . . . . . . . . . . . . . . . 27viiTABLE OF CONTENTS2.3 Preliminary of Statistical-QoS Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . 282.3.1 Statistical-QoS constraints for single-hop fading channel . . . . . . . . . . . . . . 292.3.2 Statistical-QoS constraint for dual-hop fading channel . . . . . . . . . . . . . . . 332.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Chapter 3: Effective Capacity of Coherent POLMUX OWC Impaired by Atmo-spheric Turbulence and Pointing Errors . . . . . . . . . . . . . . . . . . . . 353.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . . . . . . . . 353.2 System and Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.1 POLMUX OWC System With Coherent Detection . . . . . . . . . . . . . . . . . 363.2.2 Statistical Model of Channel Impairments . . . . . . . . . . . . . . . . . . . . . . 383.3 Effective Capacity with Only Atmospheric Turbulence . . . . . . . . . . . . . . . . . . . 393.3.1 Independent Power Adaptation Scheme . . . . . . . . . . . . . . . . . . . . . . . 393.3.2 Joint Power Adaptation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.4 Effective Capacity with Atmospheric Turbulence and Misalignment Fading . . . . . . . 473.4.1 Independent Power Adaptation Scheme . . . . . . . . . . . . . . . . . . . . . . . 473.4.2 Joint Power Adaptation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Chapter 4: Delay-QoS Aware Joint Adaptive Modulation and Power Allocation forMultichannel Coherent OWC System . . . . . . . . . . . . . . . . . . . . . 594.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . . . . . . . . 594.2 System Model and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.3 QoS-Aware AM and Power Allocation for Dual-Channel System with Average PowerConstraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.3.1 ICO with Average Transmit Power Constraint . . . . . . . . . . . . . . . . . . . 644.3.2 JCO with Average Transmit Power Constraint . . . . . . . . . . . . . . . . . . . 684.3.3 Computational Complexity of ICO and JCO . . . . . . . . . . . . . . . . . . . . 724.4 QoS-Aware AM and Power Allocation for Multi-beam System with Peak Transmit PowerConstraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.4.1 System Model and Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . 724.4.2 Independent Channel Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 734.4.3 Joint Channel Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.4.4 Independent Channel Optimization with Beam Selection . . . . . . . . . . . . . . 764.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.5.1 AT For Dual-Channel System With Average Power Constraint . . . . . . . . . . 774.5.2 AT For Multi-Channel System With Peak Power Constraint . . . . . . . . . . . . 824.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Chapter 5: Hybrid RF/FSO Backhaul Network with Statistical-QoS Aware Buffer-aided Parallel Relaying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85viiiTABLE OF CONTENTS5.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . . . . . . . . 855.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.2.1 Overview of the Considered System Configurations . . . . . . . . . . . . . . . . . 865.2.2 Channel Model and CSI Requirements . . . . . . . . . . . . . . . . . . . . . . . . 895.3 Optimal AT for Single-Carrier Hybrid RF/FSO System . . . . . . . . . . . . . . . . . . 895.3.1 AT over RF Links: Optimal Problem Formulation and Solution . . . . . . . . . . 905.3.2 AT over FSO Link: Optimal Optical Transmit Power Allocation at MBS . . . . 935.3.3 Maximum Supportable Arrival Rate . . . . . . . . . . . . . . . . . . . . . . . . . 955.4 Optimal AT for Multi-Carrier Hybrid RF/FSO System . . . . . . . . . . . . . . . . . . . 965.4.1 Optimal Power Allocation and Sub-channel Assignment for RF Transmission . . 965.4.2 Optimal STM Selection and Transmit Power Allocation for FSO Transmission . 985.4.3 Maximum Supportable Arrival Rate . . . . . . . . . . . . . . . . . . . . . . . . . 1025.5 Simulation Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Chapter 6: Statistical-Delay-QoS Aware Joint Power Allocation and Relaying LinkSelection for FSO Fronthaul Networks . . . . . . . . . . . . . . . . . . . . . 1106.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . . . . . . . . 1106.2 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116.2.2 Link Signal-to-Noise-Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1146.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1146.4 Joint Power Allocation and Relaying Link Selection . . . . . . . . . . . . . . . . . . . . . 1176.4.1 Transformation of the Optimization Problem . . . . . . . . . . . . . . . . . . . . 1176.4.2 Power Allocation and RRH-Relaying Link Assignments . . . . . . . . . . . . . . 1196.4.3 Semi-distributed JMCPARLS algorithm . . . . . . . . . . . . . . . . . . . . . . . 1226.4.4 Complexity of JMCPARLS algorithm . . . . . . . . . . . . . . . . . . . . . . . . 1236.5 Performance Evaluation and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1246.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Chapter 7: Joint FSO Fronthaul and Millimeter-Wave Access Link Optimization inCloud Small Cell Networks: A Statistical-QoS Aware Approach . . . . . 1337.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . . . . . . . . 1337.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1347.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1397.4 Proposed Fronthaul and Access Link Optimization . . . . . . . . . . . . . . . . . . . . . 1437.4.1 Solution to Sub-problem I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1437.4.2 Solution to Sub-problem II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1497.4.3 Convergence of the Proposed Scheme . . . . . . . . . . . . . . . . . . . . . . . . . 1527.5 Performance Evaluation and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1537.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160ixTABLE OF CONTENTSChapter 8: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1618.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1618.2 Concluding Remarks on the Accomplished Works . . . . . . . . . . . . . . . . . . . . . . 1628.3 Suggested Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1638.3.1 Secure and QoS-Aware Resource Allocation for Hybrid In-band Wireless/FSOBackhaul in HetNet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1648.3.2 QoS-Aware Joint Rate Adaptation and Trajectory Optimization for BA UAVRelays in FSO Backhaul Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 1658.3.3 QoS and Content Caching Aware Joint FSO Fronthaul and mmWave Access LinkOptimization in CScNet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1668.3.4 Robust and Learning-based Algorithm Design for QoS-provision in FSO Fron-thaul Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Appendix A: EC of Independent Power Adaptation of Coherent POLMUX OWCwith Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186Appendix B: EC of Joint Power Adaptation of Coherent POLMUX OWC with PhaseNoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188Appendix C: Proof of the Proposition 6.3.1 . . . . . . . . . . . . . . . . . . . . . . . . 190Appendix D: Proof of the Proposition 6.3.2 . . . . . . . . . . . . . . . . . . . . . . . . . 192Appendix E: Proof of the Proposition 7.4.1 . . . . . . . . . . . . . . . . . . . . . . . . . 193Appendix F: Proof of the Proposition 7.4.3 . . . . . . . . . . . . . . . . . . . . . . . . . 195Appendix G: List of Other Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . 197xList of TablesTable 6.1 Fronthaul cluster topologies used in Figure 6.9. . . . . . . . . . . . . . . . . . . . 131Table 7.1 Notations for the key parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 135xiList of FiguresFigure 3.1 EC comparison between the coherent POLMUX with joint and independentpower adaptation schemes over a Gamma-Gamma turbulence channel withoutpointing error (α = 4.43, β = 4.39) and with γp = 30 dB, 0o polarization controlerror, and perfect phase noise compensation. . . . . . . . . . . . . . . . . . . . . 51Figure 3.2 EC of coherent POLMUX with independent power adaptation scheme over aGamma-Gamma turbulence channel (α = 4.43, β = 4.39) with γp = 30 dB, 0opolarization control error, and imperfect phase noise compensation. . . . . . . . 51Figure 3.3 EC of coherent POLMUX with joint power adaptation scheme over a Gamma-Gamma turbulence channel (α = 4.43, β = 4.39) with γp = 30 dB, 0o polariza-tion control error, and imperfect phase noise compensation. . . . . . . . . . . . . 52Figure 3.4 Stringent statistical-delay constrained EC comparison between the coherent POL-MUX with joint and independent power optimizations in Gamma-Gamma tur-bulence without pointing error and with perfect phase noise compensation. . . . 52Figure 3.5 Stringent statistical-delay constrained EC comparison between the coherent POL-MUX with joint and independent power optimizations in misalignment-weakturbulence fading channel with δ = 0o, Ao = 0.75, and perfect phase noisecompensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Figure 3.6 Stringent statistical-delay constrained EC comparison between the coherent POL-MUX with joint and independent power optimizations in misalignment-strongturbulence fading channel with δ = 0o, Ao = 0.75, and perfect phase noisecompensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Figure 3.7 Stringent statistical-delay constrained EC comparison between the coherent POL-MUX with joint and independent power optimizations in strong Gamma-Gammaturbulence with 0o polarization control error and imperfect phase noise compen-sation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Figure 3.8 Power penalty factor (in dBm) of the independent power adaptation scheme withrespect to the joint power adaptation scheme in the stringent statistical-delayconstraints with σs/r = 1, δ = 0o, and perfect phase noise compensation. . . . . 54Figure 3.9 Stringent statistical-delay constrained EC comparison between the coherent POL-MUX with joint and independent power optimizations in Gamma-Gamma tur-bulence with 0o polarization control error and perfect phase noise compensationfor different link distances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 4.1 System block diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62xiiLIST OF FIGURESFigure 4.2 ESE comparison among different M -ary modulations with ICO, average transmitpower constraint, γc = 30 dB, and BERt = 10−6. . . . . . . . . . . . . . . . . . . 77Figure 4.3 ESE comparison among differentM -QAM based adaptive transmissions in Gamma-Gamma turbulence fading with average transmit power constraint, γc = 30 dB,and BERt = 10−6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 4.4 ESE comparison among different M -QAM based adaptive transmissions in K-turbulence fading with average transmit power constraint, γc = 30 dB, andBERt = 10−8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 4.5 ESE comparison between coherent M -PAM based ICO and JCO in K-turbulencefading (α = 1.99) with average transmit power constraint, imperfect phase noisecompensation, γc = 30 dB, and target BER = 10−8. . . . . . . . . . . . . . . . . 79Figure 4.6 Delay-bound violation probability of M -QAM based ICO and JCO subject toaverage transmit power constraint. . . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 4.7 ESE comparison among different AT schemes subject to peak transmit powerconstraint in strong turbulence fading and 650m long link. . . . . . . . . . . . . 83Figure 4.8 ESE comparison among QoS-aware AT schemes (proposed in Sections 4.4.2-4.4.4) for Pt = 0.16W in weak turbulence fading. . . . . . . . . . . . . . . . . . . 83Figure 4.9 ESE comparison among QoS-aware AT schemes (proposed in Sections 4.4.2-4.4.4) for Pt = 0.16W in strong turbulence fading. . . . . . . . . . . . . . . . . . 84Figure 5.1 Hybrid RF/FSO communication system with BA parallel RN(s). . . . . . . . . . 87Figure 5.2 Equivalent queue model for parallel relay network. . . . . . . . . . . . . . . . . . 89Figure 5.3 Maximum supportable arrival rate versus (vs.) QLB trade-off for SC hybridRF/FSO backhaul network with L = 3 RNs and β(m)SI = 10−4, ∀m. . . . . . . . . 104Figure 5.4 Maximum supportable arrival rate vs. RF transmit power for SC hybrid RF/FSObackhaul network with L = 3 RNs, Q(1)max = Q(2)max = 3000 bits, ζ1 = ζ2 = 10−3,and β(m)SI = βSI , ∀m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Figure 5.5 Maximum supportable arrival rate vs. weather-dependent FSO link attenua-tion for SC hybrid RF/FSO backhaul network with β(m)SI = 10−4, ∀m, Q(1)max =Q(2)max = 3000 bits, and ζ1 = ζ2 = 10−3. From left to right, the vertical dashedlines represent weather conditions with clear air, haze, light fog, moderate fog,and dense fog [108]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Figure 5.6 Maximum supportable arrival rate vs. weather-dependent FSO link attenuationfor MC hybrid RF/FSO backhaul network with L = 3 RNs, Q(3)max = Q(4)max =3000 bits, ζ3 = ζ4 = 10−3, and Nsc = 30 RF sub-channels. . . . . . . . . . . . . 106Figure 5.7 Maximum supportable arrival rate vs. QLB violation probability for MC hybridRF/FSO backhaul network with L = 3 RNs, Q(3)max = Q(4)max = 3000 bits, andNsc = 36 RF sub-channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Figure 5.8 Maximum supportable arrival rate vs. number of RF sub-channels in MC hybridRF/FSO network with L = 3 RNs, Q(3)max = Q(4)max = 3000 bits, ζ3 = ζ4 = 10−3. 107Figure 6.1 A block diagram of a single fronthaul cluster. . . . . . . . . . . . . . . . . . . . . 111xiiiLIST OF FIGURESFigure 6.2 EC comparison among JMCPARLS, ILO, and EPA/NRS schemes in atmo-spheric turbulence fading with {Pm} = 1 Watt, {Pl} = 1 Watt, and N = 2optical channels per RRH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure 6.3 EC comparison between JMCPARLS and EPA/NRS schemes in atmosphericturbulence fading and pointing error with {Pm} = 1 Watt, {Pl} = 1 Watt, andN = 2 optical channels per RRH. . . . . . . . . . . . . . . . . . . . . . . . . . . 125Figure 6.4 EC comparison between JMCPARLS and EPA/NRS schemes for different queue-length bounds in strong atmospheric turbulence fading with {Pm} = 1 Watt,{Pl} = 1 Watt, and N = 2 optical channels per RRH. . . . . . . . . . . . . . . . 125Figure 6.5 EC of the JMCPARLS scheme for different number of optical channels per RRHover atmospheric turbulence fading channels with {Pm} = 1 Watt and {Pl} = 1Watt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Figure 6.6 Delay-bound violation probability of the JMCPARLS, ILO, EPA/NRS schemesover atmospheric turbulence fading channels with {Pm} = 1 Watt, {Pl} = 1Watt, and N = 2 optical channels per RRH. . . . . . . . . . . . . . . . . . . . . 126Figure 6.7 EC of the JMCPARLS scheme for different number of apertures at the RRHswith {Pm} = 1 Watt, {Pl} = 1 Watt, and N = 4 optical channels per RRH. . . . 127Figure 6.8 EC of the JMCPARLS scheme for different coordinates of the RNs in strongatmospheric turbulence fading channel with {Pm} = 1 Watt, {Pl} = 1 Watt,and N = 2 optical channels per RRH. . . . . . . . . . . . . . . . . . . . . . . . . 127Figure 6.9 EC comparison between JMCPARLS and EPA/NRS schemes for different num-ber of RRHs, RNs, and ANs in strong atmospheric turbulence fading channelwith {Pm} = 1 Watt, {Pl} = 1 Watt, and N = 2 optical channels per RRH. . . . 128Figure 7.1 Schematic of downlink CScNet with FSO fronthaul and mmWave access links. . 136Figure 7.2 Data arrival rate comparison between the proposed and benchmark schemesconsidering 6 UEs in the access link and 2 FSO RNs (coordinates (in the unit ofmeters): [−500, 80] and [−500,−80]) in the fronthaul link without pointing error. 154Figure 7.3 Impact of misalignment in the FSO fronthaul link and imperfect instantaneousCSI acquisition on the data arrival rate of the proposed scheme considering 6UEs in the access link and 2 FSO RNs (coordinates (in the unit of meters):[−500, 80] and [−500,−80]) in the fronthaul link . . . . . . . . . . . . . . . . . . 155Figure 7.4 Impact of relay assisted FSO fronthaul on the data arrival rate of the proposedscheme considering 6 UEs in the access link and ideal alignment in the FSOfronthaul link. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Figure 7.5 Data arrival rate of the proposed scheme versus number of UEs in the accesslink considering 3 FSO RNs (coordinates (in the unit of meters): [−100, 80],[−100,−80], [−100, 0]) in the fronthaul link with perfect alignment. . . . . . . . 158Figure 7.6 Data arrival rate of the proposed scheme considering 6 UEs in the access linkand 2 FSO RNs (coordinates (in the unit of meters): [−500, 80], [−500,−80]) inthe FSO fronthaul link with perfect alignment. . . . . . . . . . . . . . . . . . . . 159xivLIST OF FIGURESFigure 7.7 Data arrival rate versus outer loop iteration number of the Algorithm 8 consider-ing 6 UEs in the access link and 2 FSO RNs (coordinates (in the unit of meters):[−500, 80], [−500,−80]) in the FSO fronthaul link with perfect alignment. . . . . 159xvList of AcronymsAcronyms Definitions5G Fifth GenerationAF Amplify-and-forwardALS Adaptive Link SchedulingAN Aggregation NodeAT Adaptive TransmissionAPT Acquisition-pointing-trackingAWGN Additive White Gaussian NoiseBA Buffer-aidedBBU Base Band UnitBER Bit-error-rateBPSK Binary Phase Shift KeyingCDF Cumulative Distribution FunctionCPVR Constant-power, Variable-rateC-RAN Cloud Radio Access NetworkCScNet Cloud Small Cell NetworkCSI Channel State InformationDF Decode-and-forwardEC Effective CapacityEPA/BS Equal Power Allocation with Beam SelectionEPA/NRS Equal Power Allocation with Nearest Relay SelectionESE Effective Spectral EfficiencyFD Full-duplexFSO Free Space OpticalGbps Giga-bits-per-secondGNC Global Network ControllerHetNet Heterogeneous NetworksHT Hybrid TransmissionHz HertzICO Independent Channel OptimizationICO/BS Independent Channel Optimization with Beam SelectionILO Independent Link OptimizationIM/DD Intensity Modulation with Direct DetectionIRI Inter-relay-interferenceJCO Joint Channel OptimizationxviList of AcronymsJMCPARLS Joint Multi-channel Power Allocation and Relay SelectionKKT Karush-Khun-TuckerLB Load-balancingLO Local OscillatorLOS Line-of-SightMBS Macro-cell Base StationMC Multi-carrierMHz Mega HertzM -PSK M -ary Phase Shift KeyingmmWave Millimeter-waveNBA Non buffer-aidedOFDMA Orthogonal frequency division multiple accessOOK On-off KeyingOWC Optical Wireless CommunicationsPDF Probability Density FunctionPLL Phase Lock LoopPOLMUX Polarization MultiplexingQAM Quadrature Amplitude ModulationQLB Queue-length BoundQoS Quality-of-serviceRF Radio FrequencyRN Relay NodeRRH Remote Radio HeadRV Random VariableSBS Small-cell Base StationSC Single-carrierSD Spatial DiversitySI Self InterferenceSIC Self Interference CancellationSIM Subcarrier Intensity ModulationSM Spatial MultiplexingSNR Signal-to-noise ratioSOP State of PolarizationSTM Spatial Transmission Mode SelectionTbps Tera-bits-per-secondTDMA Time Division Multiple AccessTS Transmission SlotUE User EquipmentVPVR Variable-power, Variable-rateWF Water-fillingxviiAcknowledgmentsI would like to express my sincere gratitude to my supervisor Prof. Victor C. M. Leung for hiscontinuous support, from his vast knowledge and experience, throughout my PhD career. I will continueto be inspired by his constant encouragement, dedication to research, and outstanding work ethics. Iam also extremely grateful to my co-supervisor Prof. Md. Jahangir Hossain for helping me in differentacademic and non-academic aspects during my stay at UBC Okanagan campus. Moreover, I wouldlike to express my deepest gratitude to Prof. Julian Cheng who is one of my supervisory committeemembers and was also my co-supervisor during my M.A.Sc. study. Both Profs. Hossain and Chengtaught me several research skills over these years, and always provided feedback on my works. Mysupervisors provided me the ultimate freedom to work on the topics of my interest, and helped meto grow as an independent researcher. They taught me how to come up with an interesting researchproblem and how to develop useful solutions. Their continuous guidance have made this dissertationa reality. I have been truly blessed by having the opportunity to work under the supervision of Prof.Leung, Prof. Hossain, and Prof. Cheng.I would like to thank Prof. Lutz Lampe and Prof. Shahriar Mirabbasi for their willingness toserve on my supervisory committee, and for providing me their valuable feedback, critical comments,and suggestions during my qualification exam. I am sincerely thankful to Prof. Steve Hranilovic forproviding several insightful comments as the external examiner of my thesis. I would also like to thankProf. A Bruce Dunwoody, Prof. Clarence De Silva, and Prof. Lukas Chrostowski for their willingnessto participate in my thesis examination committee.I am grateful to the University of British Columbia (UBC) for supporting my research through FourYear Doctoral Fellowship. In addition, I thankfully acknowledge the generous scholarships that I re-ceived from the electrical and computer engineering (ECE) department and the institute for computing,information and cognitive systems (ICICS) of UBC, Vancouver campus.Throughout this PhD journey, I have met with different people from both UBC Okanagan and UBCVancouver campuses. I am particularly grateful to my colleagues from the research groups of Prof.Leung, Prof. Cheng, and Prof. Hossain for sharing their valuable research and professional experienceswith me.Finally, I would like to thank my family members for keeping their faith in me. I am very thankfulto my parents and my sister for their patience, understanding, and encouragement. I am indeed gratefulto my wife for her unconditional love and encouragement in all these years. She always motivated meduring my good time and bad time. All of my achievements would not have been possible without thecontinuous support of my family members.xviiiChapter 1Introduction1.1 Background and MotivationFree space optical (FSO) communication (also known as optical wireless communication (OWC)) isa broadband wireless technology that provides a high speed connectivity between two nodes by trans-mitting modulated infrared or visible optical carrier through unguided medium [1–3]. FSO technologyoperates in several hundred terahertz (THz) frequency band, and it enjoys freedom from spectrumlicensing. Moreover, unlike RF transmission, FSO provides interference-free full-duplex (FD) connec-tivity. Due to narrow beamwidth, in general, FSO provides physical-layer data security from maliciouseavesdroppers. Unlike fiber optics technology, FSO system offers rapid deployment, and it can beefficiently used in the scenarios, such as during disaster recovery period and during the event of broad-casting concerts/sports, where temporary but high speed communication network needs to be rapidlydeployed. The history of FSO communications can be dated back to 1970s when the commercial laserswere developed for optical communications [4]. In the time-frame of 80s and 90s, FSO communicationsystem was mainly used for the deep-space applications and covert communications [5, 6]. Due to thematurity of the optoelectronic devices, FSO communications started to receive increasing attention forcivil applications from early 2000. In the last decade, FSO communication was used in several applica-tions, such as, cost effective solution to the “last-mile connectivity” problem, realization of high speedcampus wide local area network, high definition (HD) video transmission in wireless video surveillancenetwork, and rapid deployment of temporary communication infrastructure during disaster recoveryperiod [7]. In addition, in the recent years, FSO communication has gained significant attention forthe following applications: (i) backhaul/fronthaul in cellular network, (ii) unmanned-air-vehicle (UAV)communication, (iii) high speed connectivity between nodes in data-center, (iv) underwater sensor nodecommunication, and (v) data transmission in indoor wireless network through visible light carrier. In[8], a detailed classification of different FSO communication systems was presented. The FSO commu-nication system considered in this dissertation is known as the terrestrial FSO communication system.For the terrestrial FSO communication systems, the wavelength windows located near 850 nm, 1060nm, 1250 nm, and 1550 nm experience less than 0.2 dB/Km atmospheric attenuation [7]. Therefore,these wavelengths are suitable for the terrestrial FSO systems. Particularly, the 850 nm and the 1550nm wavelength windows are also extensively used in the optical fiber communications. Accordingly,due to the commercial availability of the optical communication components in the 850 nm and the1550 nm wavelength windows, most of the terrestrial FSO communication systems operate in the 850nm and the 1550 nm wavelengths. Note that, since the 1550 nm wavelength is less sensitive to thehuman eyes compared to the 850 nm wavelength, the 1550 nm wavelength is allowed to transmit around50 times more optical power than the 850 nm wavelength. For such a reason, the 1550 nm wavelengthis more appealing for long distance communications. Finally, the mid-infrared and long-infrared wave-11.1. Background and Motivationlengths also have the low atmospheric attenuation co-efficients. However, the optical communicationcomponents for such long wavelengths are not widely available similar to the near-infrared wavelengths.Terrestrial FSO communication system is usually employed for data transmission between two fixedpoints; it usually requires line-of-sight (LOS) link; and depending on weather condition, it providesdata transmission over medium-to-long distance (500m to several kilometers). International telecom-munication union (ITU) has provided several standards recommending the design of the terrestrialFSO applications [8]. In addition, several off-the-shelf commercial FSO products are available thatcan support few hundred Mega-bits-per-second (Mbps) to 10 Giga-bits-per-second (Gbps) terrestrialFSO link [9–12]. Several successful experiments were performed to demonstrate 10 Gbps to 100 Tera-bits-per-second (Tbps) data transmission over the terrestrial FSO links [13–15]. Moreover, giant techcompanies such as Facebook Inc. and Google Inc. have recently employed FSO based technology inorder to develop a reliable and high-speed communication system for providing Internet connectivityin the under-developed countries [16, 17]. Overall, the successful field-trials and commercial availabil-ity strongly support the commencement of the FSO technology in the future wireless communicationnetwork architecture.1.1.1 Application of terrestrial FSO technology for 5G backhaul/fronthaulnetworkCompared to today’s wireless communication network, the fifth generation (5G) wireless commu-nication network will feature explosive demand of bandwidth-hungry mobile data traffic along withmassive connectivity of exponentially increasing number of communication devices [18]. A recent data-traffic forecast, prepared by Cisco Inc., shows that by 2021 the number of mobile users will increaseseven fold compared to the mobile users of today’s network [19]. In addition, through the evolution ofso-called Internet of things (IoT), the number of connected devices will reach around 20 to 30 billionsby 2021 [20]. In order to meet such tremendous growth of mobile data traffic and devices, industryand academia have jointly identified the key-performance-indicator (KPI) of the 5G network commonlyrefereed as 5G requirements as follows: 1000 fold increase of mobile data traffic; 10 − 100 times moreconnected devices; 10 times improved energy consumption; less than 1 millisecond (ms) latency; and10 Gbps and 1 Gbps data rate for stationary and mobile users, respectively [21]. However, realizationof such requirements will require redesign of the current cellular network architecture through break-through concepts. The key players for the paradigm shift of network architectural design will be theacquisition of upper portion (beyond radio-frequency (RF)) of the electromagnetic spectrum for wire-less communications, development of spectrum-efficient modulation/coding/multiple-access technology,and network densification. Specifically, network densification through the massive deployment of low-power base stations (generally referred as small-cells) is a key enabler of 5G technology [22]. However,managing such large number of base stations is challenging for traditional network architecture. Cloudradio access network (C-RAN), originally proposed by China Mobile Inc., is an innovative network ar-chitecture to efficiently accommodate network densification. In C-RAN, only the radio functionality isincluded in the cell-site (commonly refereed as remote radio head (RRH) or remote radio unit (RRU)),and the other baseband signal processing functionalities are centrally performed in a cloud server,known as the base band unit (BBU) pool. Compared to the traditional cellular architecture, C-RAN21.1. Background and Motivationprovides improved resource optimization through cloud computing, advanced interference managementthrough collaborative signal processing, flexible upgrade of the required technology through software-defined networking, and enhanced energy-efficiency/spectrum-efficiency [23]. Besides centralization,heterogeneity through the deployment of base stations of different transmission power and transmis-sion range is an another important enabler of 5G RAN. Heterogeneous network (HetNet) offers trafficoff-loading from macro-cell to micro, pico, and femto cell base stations, and leads to the improvedspectral-efficiency [24]. By integrating the concept of C-RAN and heterogeneous network, novel RANarchitectures were proposed where multi-tier low-power base stations are managed by the centralizedBBU pool. Such architectures are known as heterogeneous cloud small cell network (HCsNet) or het-erogeneous C-RAN (H-CRAN), and they integrate the advantages of both C-RAN and HetNet withimproved mobility management [25, 26]. Nevertheless, provision of suitable backhaul/fronthaul tech-nology for the high-rate, cost-effective, and ubiquitous connectivity of the small cells with centralizedserver and/or macro-cell base station (MBS) remains an important challenge for dense 5G RAN. Notethat, the link between RRH and BBU pool in the conventional C-RAN architecture is refereed asfronthaul. On the other hand, the links between the small-cell and macro-base stations in HetNetare referred as backhaul. Without loss of generality, the notion of fronthaul and backhaul can beinterchangeably used in 5G RAN architecture [27].Due to the strict throughput (10 Gbps) and latency (on the order of 100µs) requirements of thebackhaul for 5G RAN, fiber optics is the most suitable backhaul technology for 5G RAN. Recently,fiber-to-the-home (FTTH) or fiber-to-the-building (FTTB) architecture, based on point-to-multi-pointpassive optical network (PON), has been introduced, and such FTTH network will constitute a majorportion of the backhaul network for 5G RAN. The performance comparison of different PON basedoptical fiber backhaul networks for 5G RAN can be found in [23, 27]. Nevertheless, expansion of FTTHbased backhaul network requires laying new fiber through trenching. Consequently, the network expan-sion for ultra-dense-networking scenario becomes a cost-prohibitive and daunting task. Specifically, atpresent, “the deployment of FTTH is scarce since only 15 countries of the whole world has more than15% FTTH penetration [27]”. In order to satisfy the backhaul demand of 5G RAN in the future ultra-dense-networking scenario, two different approaches are undertaken. The first approach investigatesthe development of distributed or semi-distributed RAN architecture by splitting the functionalitiesbetween RRH and BBU which leads to the reduced burden on the backhaul/fronthaul network [28].The second approach investigates new wireless backhaul technology, including sub-6 GHz wireless back-haul, in-band wireless backhaul, and millimeter-wave (mmWave), in order to enhance the scalabilityof the backhaul network in 5G RAN [29]. In particular, the backhaul network for 5G RAN will in-clude multiple technologies in a multi-hop fashion instead of a single standalone backhaul technology.As such, 5G RAN will be served by hybrid multi-hop backhaul network architecture [30]. In this re-gard, FSO communication emerges as a promising backhaul technology for 5G RAN. As a backhaultechnology, FSO can offer 10 Gbps data rate over 500 meter to several kilometers long distances [31].For example, the commercially available FSO transceiver, named as Artolink M1-10GE, developed byARTOLINK Inc., supports 10 Gbps full-duplex connectivity over 1.5 Km link length [12]. In [32],the authors reported an experimental demonstration of terrestrial FSO communications enabled byoptical repeater and wavelength division multiplexing (WDM) that could achieve 10 Gbps over 3.4 Km31.1. Background and Motivationlink length. Note that, high transmit power is usually required in order to mitigate the attenuationover several kilometers long link. However, due to the eye-safety issue, the transmission power in theFSO system is usually restricted within certain limits. Depending on the wavelength and type of lasertransmitter, such a transmission power limit can be from 10 milliwatt to 500 milliwatt. A detaileddescription of the eye-safety based transmit power restriction for the practical FSO transmitters canbe obtained from [33, Table 1.6]. Nevertheless, despite the limited transmission power budget, FSOcan be a suitable backhaul solution in the small cell network, thanks to the reduction of cell size in therange of few hundred meters. Moreover, by using high speed backup RF link, such as mmWave, thereliability of FSO based backhaul network can be further enhanced in the adverse weather conditions.Consequently, FSO based technology provides a meaningful solution to complement the optical fiberbased backhaul technology in the 5G RAN architecture.1.1.2 Challenges for FSO Communications and Thesis ObjectiveAlthough the terrestrial FSO communication systems feature several advantages over the RF wire-less technologies, terrestrial FSO communication systems are not currently as widespread as RF wirelesstechnologies. The reasons are three folds. First, up to now, the commercially available FSO transceiversare more expensive than the RF and/or microwave transceivers. Second, the strict requirements of hav-ing LOS links often times present hurdle for the widespread and cost-effective deployment of the FSOcommunication systems in the cellular network. Third, the reliability of any FSO communication sys-tem degrades due to the weather-induced channel impairments. Particularly, weather-induced perfor-mance degradation is the major challenge for terrestrial FSO communication based backhaul/fronthaulnetworks. The performance limiting factors for terrestrial FSO communications can be divided intothree categories, namely, atmospheric turbulence induced scintillation, weather-induced optical signalattenuation, and pointing error. The atmospheric temperature and pressure variation in the presenceof wind produce atmospheric turbulence (atmospheric turbulence can be considered as air pockets oreddies of different sizes). The propagation medium with atmospheric turbulence experiences randomrefractive-index fluctuations. The optical beam, transmitted through atmospheric turbulence, experi-ences random irradiance fluctuation, i.e., spatial and temporal intensity fading at the receiver. In aclear weather, the most detrimental atmospheric loss to the FSO communication system comes fromthe atmospheric turbulence induced scintillation. Typically, a deep fade can last up to 1-100 ms andresults in loss of 109 consecutive information bits for a transmission rate of 10 Gbps [1]. On the otherhand, weather-induced optical signal attenuation is mainly caused by absorption and scattering ofoptical signals by the atmospheric particles. In particular, severe weather conditions, such as densefog, cloud, and heavy snow, significantly limit the visibility of FSO communications. As a result, suchweather conditions present serious performance degrading factors for terrestrial FSO links. Finally,due to random building sways and/or mechanical vibrations present in the FSO system, the alignmentbetween transmitter and receiver in terrestrial FSO communications is hampered. Such a misalign-ment between transmitter and receiver is known as the pointing error. In addition to weather-inducedchannel fading and attenuation, pointing error is a major performance limiting factor for the terrestrialFSO communication systems.The aforementioned performance degradation factors result in link failure, and significantly degrade41.1. Background and Motivationthe achievable data rate over terrestrial FSO links. Thus, mitigation of such performance degradationfactors is crucial for the terrestrial FSO communication systems. In state-of-the-art-literature, severalsolutions were proposed in order to mitigate the aforementioned performance limiting factors (see [7]and references there in). Spatial diversity combining, enabled by multi-input multi-output (MIMO)transceiver architecture, substantially improves the symbol-error rate and outage probability in thepresence of strong atmospheric turbulence fading. Since atmospheric turbulence fading channel variesslowly, it is possible to obtain the channel state information (CSI) at the transmitter through feedbackfrom the receiver. Accordingly, adaptive transmission (AT) scheme, where different degrees-of-freedomof a communication system are adapted according to the channel conditions, provides an efficient tur-bulence fading mitigation solution. Cooperative communications and hybrid RF/FSO are two wellinvestigated solutions for enhancing reliability of terrestrial FSO communication systems. Cooperationthrough relays improves outage performance and enhances the coverage of FSO communication sys-tem. For FSO transmission, the attenuation due to rain can be on the order of 3 dB/Km. As a result,FSO transmission is usually unaffected by rain [7]. However, FSO transmission is severely affectedby the moderate to dense fog. On the other hand, the RF wireless technology, employing 10 GHz orhigher carrier frequency, is not affected by fog. However, such an RF wireless technology is adverselyimpaired by rain. As such, FSO and high speed RF transmission technologies experience complemen-tary weather-dependent channel adversity. Moreover, transmission over the RF link is not affected bypointing error and the RF link can be used to provide connectivity when the FSO link is temporar-ily blocked. Accordingly, hybrid RF/FSO system (where an RF link is used as a backup link to theexisting FSO link) enhances robustness of the FSO communication system in all weather conditions.In addition, it was experimentally shown that transmission over the long-infrared wavelength (10µm)through quantum-cascade laser allows to maintain satisfactory link quality even in the presence ofdense fog [34, 35]. Moreover, in state-of-the-art literature, several efficient beam acquisition-pointing-tracking (APT) methods were proposed in order to mitigate the pointing error for the terrestrial FSOcommunication systems [36].Due to the stochastic channel impairments, transmission data rate over FSO link fluctuates. Asa result, an FSO transmitter needs to store the arrived data that is not transmitted owing to thefluctuation of the instantaneous data rate over FSO link. Accordingly, introducing buffers at the FSOtransmitter prevents data loss, thanks to the data storage capability of the buffers. Data buffering isparticularly useful when FSO is used as a bridge to connect the fiber optic backhaul network with theaccess network, and large size data files (i.e., bulk traffic) are transmitted over FSO links. In this case,the arrived data from fiber optic network may not be immediately transmitted to the access link, anddata buffering is required in order to improve reliability of the FSO link. Thanks to the recent ad-vancement of the powerful and inexpensive storage technologies, buffers can be introduced at the FSOnodes without significantly increasing the implementation cost [110]. Nevertheless, for a communicationsystem over fading channel, data buffering provides an improved throughput at the cost of increasedqueuing-delay [37]. In 5G and beyond-5G network architectures, end-to-end latency is a critical per-formance metric. Specifically, end-to-end latency not only does impact user’s quality-of-experiencebut also (significantly) influences monetary profit of the high-frequency-trading organizations [38]. Ina multi-hop communication network, the accumulation of the queueing-delay at each hop constitutes51.1. Background and Motivationthe major component of the end-to-end latency. As a result, controlling queueing-delay is extremelyimportant for latency-sensitive applications. However, maintaining a deterministic queueing-delay overthe wireless fading channels is challenging. Moreover, compared to the average delay, distribution ofthe delay is more important for the real-time traffic in the 5G communications. Statistical quality-of-service (QoS), where the required queueing-delay bound is probabilistically guaranteed with the help oftail distribution of the queueing-length, is suitable for the transmission of real-time traffic over wirelessfading channels [40]. In this thesis, we develop novel approaches to provide statistical-QoS guaranteeover the terrestrial FSO communication systems. In general, the developed approaches are appropriatefor the delay-sensitive applications with the following attributes: (i) the applications have the queue-building traffic, (ii) the applications can work with variable data rate over the fading channels, (iii)the applications require certain delay-bound violation probability, and (iv) such delay-bound violationprobability can be satisfied by utilizing the tail distribution of the queueing-length. We emphasize thatseveral real-time applications have the aforementioned features. For example, interactive video confer-encing, real-time VoIP, smart grid control, and virtual reality applications require 0.3s, 50ms, 10ms,and sub-millisecond end-to-end latency with delay-outage probability of 0.1, 0.02, 10−2 to 10−5, and10−5 to 10−9, respectively [41, 42, 192]. In addition, some low-latency applications require high relia-bility as well. In FSO communication system, the reliability can be enhanced by providing redundantcommunication links between the source and destination nodes.For the best effort traffic, where data can wait for a long time in the buffer before getting transmit-ted, the maximum supportable arrival rate approaches ergodic capacity of the system. Consequently,in such a case, the system can achieve the ergodic channel capacity. On the other hand, real-time trafficusually has certain delay bounds, and such traffic can not wait for a long time in the buffer beforegetting transmitted. Consequently, the maximum supported arrival rate for such real-time traffic getsreduced. Therefore, an inherent delay-throughput trade-off is associated with data buffering. Themain aspect of this thesis is to exploit the degrees-of-freedom of the terrestrial FSO communicationsystems to improve the trade-off between the achievable throughput and statistical-delay requirements.Accordingly, we aim to develop innovative AT schemes over the terrestrial FSO communication sys-tems. We emphasize that in state-of-the-art literature, AT schemes were developed in order to mitigatethe deleterious impact of atmospheric turbulence fading and improve the average channel capacity ofthe FSO communication systems. However, such AT schemes do not provide any guarantee that thequeuing-delay at the transmitting-end is bounded. Since data traffic of various delay requirements istransmitted over terrestrial FSO communication systems, it is imperative to investigate AT schemesfor improving the throughput-delay trade-off in the buffer-aided (BA) terrestrial FSO communicationsystems.In this thesis, we consider statistical-QoS aware AT schemes for the following FSO networks: (i)point-to-point FSO communication system1 with multiple parallel optical beams; (ii) hybrid RF/FSObackhaul network with BA parallel relaying; and (iii) FSO based uplink and downlink fronthaul networkin C-RAN. Particularly, this thesis is built on the following five research objectives.1. Analyze the maximum achievable effective capacity (EC) of a dual channel FSO communication1The point-to-point terrestrial FSO communication system can be used in order to connect two outdoor access-pointsinstalled on top of two different buildings.61.2. Literature Reviewsystem employing coherent detection and polarization multiplexing (POLMUX) in the presenceof atmospheric turbulence fading and pointing error.2. Investigate delay-QoS aware joint adaptive modulation (i.e., discrete rate-adaptation with prac-tical modulation schemes) and power allocation for coherent FSO system with multiple paralleloptical beams.3. Develop statistical-QoS aware AT schemes for the hybrid RF/FSO backhaul network with BAparallel relaying.4. Develop delay-QoS aware joint adaptive power allocation and relaying link selection for the FSObased uplink fronthaul network in C-RAN architecture.5. Investigate joint fronthaul and access link optimization in cloud small cell network (CScNet)architecture by considering multi-user scenario (where the transmitted data of the user(s) mayhave different statistical-QoS constraints), FSO based fronthaul network, and mmWave basedaccess network.1.2 Literature Review1.2.1 Channel Capacity of FSO CommunicationsChannel capacity is an important information-theoretic performance metric in order to quantifythe achievable throughput over the fading channels. Channel capacity performance of the FSO com-munication systems over atmospheric turbulence fading channels is well investigated in state-of-the-artliteratures. The authors in [44, 45] studied the channel capacity of the coherent FSO communicationsystems with lognormal amplitude fluctuations and Gaussian phase fluctuations. The channel capacityof FSO communication system in low signal-to-noise ratio (SNR) regime over the Gamma-Gammaturbulence fading and over the M -turbulence fading channels were investigated in [46] and [47], respec-tively. The authors in [48] analyzed the achievable channel capacity of FSO communication systememploying different detection techniques. By employing equal-gain-combining (EGC), the authors in[49] evaluated channel capacity of an FSO communication system over independent but non-identicallydistributed MIMO channels. Recently, the authors in [50] investigated the impact of correlation of theMIMO transceiver branches on the achievable channel capacity of an FSO communication system. Thefollowing works analyzed channel capacity of an FSO communication system by considering the overallimpact of atmospheric turbulence fading and pointing error. The authors in [51] developed closed-formergodic capacity expressions for a coherent FSO communication system with heterodyne detection byconsidering the Gamma-Gamma turbulence and pointing errors with zero boresight error. By consid-ering pointing error with non-zero boresight error, the authors in [52] developed exact and asymptoticchannel capacity expressions for coherent and intensity modulated FSO systems over Gamma-Gammaturbulence channels. Moreover, the channel capacity of a MIMO FSO system considering zero bore-sight and non-zero boresight pointing errors was developed in [53] and [54], respectively. Note thatthe aforementioned works investigated the average channel capacity (also known as ergodic channelcapacity) of an FSO communication system. Since, the FSO communication systems experience slow71.2. Literature Reviewfading, ergodic capacity can be realized by using long interleaver and/or by transmitting long codeword[48]. Because of the slow variation of the channel compared to the transmitted symbol duration, aninterleaver of large depth (on the order of giga-byte) is required. The interleaver implementation issuefor a practical 5.4 Km OWC link was considered by the researchers at MIT Lincoln Lab [39], suggest-ing that it is possible to implement such a long interleaver for the practical OWC systems. However,note that, such an interleaver results in a long delay. Therefore, over FSO fading channels, data inter-leaving/interleaving can only be considered when the application can tolerate an arbitrary long delay.Outage capacity, which determines the maximum (constant) throughput of a communication systemsubject to certain outage probability, was also analyzed for FSO communications. Outage capacity isparticularly applicable when the transmitter does not have CSI, and it transmits by using a constantrate. In [55], the authors investigated outage capacity of FSO communication system by consideringlognormal turbulence fading, Gamma-Gamma turbulence fading, and zero boresight pointing error.Note that, both ergodic capacity and outage capacity do not consider the delay-bound violationprobability of the transmitted traffic. For fading channels, such a consideration is important, especiallywhen the transmitter employs data buffering for the real-time traffic. In this regard, in the existing RFwireless communication literatures, the concept of EC was introduced, and it is defined as the maximumconstant traffic arrival rate that a communication channel can support in order to guarantee a certainstatistical-delay constraint [56]. With a statistical-delay constraint, the delay-bound is guaranteedwith a certain violation probability [57, 58]. We emphasize that the conventional ergodic capacity ismeaningful for the best-effort traffic. In contrast, EC provides maximum achievable throughput subjectto given delay-constraint, and thus, it provides generalization of the ergodic capacity. Since FSOcommunication system is subject to time varying channel impairments, provision of such a statistical-delay constraint is appealing for practical FSO applications. On the other hand, recently multichannelcoherent transmission like POLMUX has been proposed in order to boost the transmission data rate.Accordingly, in Chapter 3, we analyze the achievable EC of coherent POLMUX FSO system consideringseveral channel impairments. Such an analysis provides insights to the statistical-QoS provisioningperformance of the coherent FSO communication systems.1.2.2 QoS-aware Adaptive Transmission for FSO CommunicationsSince atmospheric turbulence fading is a quasi-static channel, reliable estimates of the receivedCSI can be obtained at the transmitter through feedback from the receiver. Based on such CSI, thetransmitter can adapt the transmission parameters over the turbulence fading channels. Moreover, dueto large channel coherence time of atmospheric turbulence fading, an FSO communication system doesnot require the frequent adaptation of transmission parameters. Consequently, AT is a feasible fadingmitigation solution for the FSO communication systems. A brief review of the recent works on AT forFSO communication is presented as follows. Constant-power variable-rate (CPVR) AT schemes wereinvestigated by adapting the modulation orders over the lognormal and Gamma-Gamma turbulencefading channels in [59, 60]. Rate-adaptive transmission over FSO channels by employing adaptive low-density-parity-checking (LDPC) code was developed in [61]. Moreover, rate-adaptive transmission forMIMO FSO communications was analyzed in [62]. Due to the stochastic nature of turbulence fading andlink attenuation, received optical power also fluctuates. Consequently, for an average transmit power81.2. Literature Reviewconstrained FSO communication system, transmit power adaptation (along with rate adaptation) offersanother degree of freedom for performing AT over atmospheric turbulence fading channels. Consideringcontinuous rate adaptation and average transmit power constraint, several transmit power adaptationschemes were proposed for an FSO communication system [63]. Performance of transmit power andrate adaptation algorithms were studied for an FSO communication system subject to dynamic linkattenuation via experiment [64]. By utilizing practical modulations and average/peak transmit powerconstraints, joint transmit power and rate adaptation was proposed over the atmospheric turbulencefading channels [65]. AT scheme for parallel-channel FSO communication was also investigated. Adap-tive power allocation over an FSO communication system employing multiple parallel optical beams(via WDM) was proposed in [66]. By using the CPVR AT scheme, a threshold-based multiple op-tical signal selection scheme was proposed for an FSO communication system employing WDM overturbulence fading channel [67]. With capacity achieving code and average/peak intensity constraints,adaptive intensity allocation was proposed for an FSO communication system with multiple paralleloptical beams [68].Although, the aforementioned works improved spectral efficiency of the FSO communication sys-tems by employing rate and power/intensity adaptation, such works did not consider the link-layerQoS requirements for transmission parameter adaptation. Adaptive modulation (AM) was capitalizedin order to maximize the throughput of an FSO communication system supporting only the latency-tolerant traffic [69]. By integrating AM and automatic re-transmission request (ARQ) protocol, crosslayer performance analysis of an FSO communication system was performed, and delay performanceof an FSO communication system was investigated in terms of the number of required re-transmissions[70]. However, the authors in [70] did not provide any guideline for designing the AT scheme basedon the delay-QoS requirements. By using an average transmit power constraint, the authors in [71]proposed transmit power adaptation schemes in order to provide statistical-delay-bound guarantee tothe transmitted traffic in a coherent FSO communication system. However, the authors considered acontinuous transmission rate adaptation with an ideal AM and coding. Consequently, the AT schemesproposed in [71] only provide a theoretical upper bound of the statistical-delay-QoS aware throughputof a coherent FSO communication system. To the best of our knowledge, no prior work developedjoint rate-adaptation with practical modulation schemes and power allocation for FSO communicationsystem with statistical-QoS constraint. In order to fill such a gap, in Chapter 4, we develop delay-QoSaware AM and power allocation for an FSO communication system employing multiple parallel opticalbeams over turbulence fading channels.1.2.3 Cooperative FSO and Hybrid RF/FSO SystemsRelayed communication techniques are introduced in order to improve the error rate and/or out-age probability of the FSO communication systems over the fading channels. A relay assisted systemcan realize the virtual MIMO system by creating multiple independent fading channels, and can pro-vide the advantage of diversity combining. In addition, relay assisted transmission can also facilitatecommunication when the LOS link between the transmitter and the receiver of an FSO system isseverely impaired or blocked due to the presence of physical obstacles. Performance analysis of therelay assisted FSO communication system was presented in [72]. Multi-hop or serial relaying is an91.2. Literature Reviewefficient technology to enhance the coverage of FSO link. The end-to-end performance of the multi-hop relaying over FSO channels was analyzed in [73–75] and [76, 78] for the intensity modulated andcoherent FSO communication systems, respectively. In particular, [73–75, 77] considered amplify-and-forward (AF) relaying protocol, and [76, 78] considered decode-and-forward (DF) relaying protocol.The parallel relaying was also considered for the FSO communication system [79]. In the conventionalparallel relaying scheme, simultaneous activation of all the available relays in a given transmission slotis assumed. Such a relaying scheme does not require CSI at the transmitter. However, in practice,concurrent activation of multiple relays requires synchronization of the transmissions from multiplerelays to the destination. Accordingly, the design complexity is increased, especially when the numberof relays is large. In order to avoid the need of synchronizing the transmissions from multiple relays,the authors in [80] proposed several relay selection schemes where a single relay was activated in eachtransmission slot. Such relay selection schemes require CSI for all the available relay links in order toselect a suitable relay link. Moreover, in [81], it was analytically shown that for FSO communications,the selective relaying achieves improved diversity-gain. Recently, mixed RF/FSO relaying was intro-duced in order to facilitate radio over FSO (RoFSO) communications. The mixed RF/FSO relayingscheme facilitates the multiplexing of a large number of RF devices into a single FSO channel. Thus,in both uplink and downlink, mixed RF/FSO relay can transmit large number of RF messages. Therecent contributions on the performance of mixed RF/FSO relay system can be found in [82], [83],[84], and [85]. Besides, power allocation was also investigated for the cooperative FSO communicationsystem. Disjoint relay selection and power adaptation techniques were proposed for the relay assistedFSO communication systems in [80, 86]. It was shown in [86] that for an optimal performance of theconsidered FSO communication system, entire transmit power should be transmitted over the strongestlink between the transmitter and receiver. The strongest link between the transmitter and receiver wasselected from the direct link as well as all the available relaying links. Moreover, if a relaying link wasselected for data transmission, the total available power was optimally allocated between both hopsof the selected relaying link in order to minimize the error probability. A joint power adaptation andrelay selection scheme was proposed for a cooperative FSO network with a number of distributed FSOsource-destination node pairs, and these nodes perform data communications between them by usingeither the direct link or a two hop relaying link [87]. The proposed optimization problem maximizedthe overall network throughput subject to the transmit power, relay selection, and cost constraints. Amixed integer non-linear programming (MINLP) problem was formulated and centralized/distributedsolutions to the problem were obtained by using bipartite matching and convex optimization tech-niques. Besides, dynamically configurable FSO relaying was proposed in [88] in order to enhance therobustness of the cooperative FSO network against the weather-induced channel impairments.Hybrid RF/FSO transmission is another effective solution to improve the reliability of the FSOcommunication system impaired by harsh weather conditions. Specifically, hybrid RF/FSO capitalizesthe complimentary weather dependent performance of RF and FSO communications. The commercialFSO transceivers are often equipped with a backup RF channel which is used to transmit information(usually at a lower rate) when the FSO link becomes unavailable, and thus leads to an improvedreliability [89]. A brief review on the recent works of hybrid RF/FSO communication system is given asfollows. A practically efficient strategy for a hybrid RF/FSO communication system is to transmit same101.2. Literature Reviewpacket over the parallel RF and FSO links, and accept the packet at the receiver only from the morereliable link. Based on such an approach, the authors in [90] proposed a hard-switching scheme whereonly RF or FSO link is active in a given transmission slot. In contrast, both RF and FSO links are activein the soft-switching methods. Raptor and rateless encoding/decoding based soft-switching methodswere proposed in [91] and [92], respectively. Adaptive power control and adaptive link combiningwere investigated in order to improve outage probability of a hybrid RF/FSO communication system[93, 94]. By considering RF and FSO links as two independent parallel channels, a throughput optimaljoint encoding/decoding over RF and FSO links was developed [95]. Topology control, such as, jointoptimization of RF and FSO transmission power levels and FSO beamwidth, were also proposed fora hybrid RF/FSO mesh network [96]. Link layer performance of a hybrid RF/FSO communicationsystem was also investigated in the recent literature. In [97], the authors analyzed different cross layerperformance metrics of a point-to-multi point hybrid RF/FSO communication system. The authors in[98] developed a throughput-optimal stochastic optimization by deriving packet admission control andpower levels for both RF and FSO links. A hybrid RF/FSO system, similar to [98], was also consideredin [99], and joint RF/FSO link selection and power allocation were developed subject to the reliabilityguarantee of the transmitted traffic. In [100], the performance of hybrid RF/FSO communicationsystem with ARQ coding was analyzed, and an adaptive power allocation over both RF and FSO linkswas developed. The reliability of a hybrid RF/FSO communication system can be further enhanced byadding relay assisted transmission in a hybrid RF/FSO communication system. In [101], the authorsdeveloped game-theory based spectrum trading in order to improve the link availability of the FSOlink. In such a spectrum-trading scheme, the transmitter of an FSO link can borrow RF band from anearby RF transmitter when the FSO link degrades. Subsequently, the FSO transmitter simultaneouslytransmits over both FSO link and relay assisted RF link, and leads to an improved reliability. In [89],the authors proposed inter-relay cooperation by using relay-to-relay RF backup links in order to enhancethe outage performance of parallel relayed cooperative FSO communication system.The conventional FSO relaying immediately forwards the received data to the destination, and theachievable throughput of such a relaying is limited by the rate of weaker hop. In BA relaying, relaycan (temporarily) store the received data in the buffers. BA relays can choose whether to forward thereceived data or not, and such a degree-of-freedom improves the end-to-end throughput. BA relayingover fading channels was first proposed in [102]. Subsequently, several AT schemes, including adaptivelink selection and adaptive power allocation, were proposed for BA relaying in RF communications(see [103], [104] and the references therein). A detailed survey on the relay selection strategy for RFBA relaying was provided in [105]. Motivated by the success of BA relaying in RF communications,several recent works have considered BA relaying in FSO and hybrid RF/FSO communication systems.In [106], the authors investigated hybrid RF/FSO based backhaul link to support multiple RF users,and developed optimal RF transmission and reception scheduling of the mixed RF/FSO relay byconsidering delay requirements and CSI availability. Different end-to-end performance metrics of asimilar system were investigated in [107]. BA and non-buffer-aided (NBA) parallel relay selectionschemes were developed for the hybrid RF/FSO communication system in [108]. Due to the directivetransmission, FSO link offers FD connectivity without interference. Such a property was utilized in[109] in order to improve outage probability of an FSO link by introducing BA and UAV assisted111.2. Literature Reviewmobile relays. Finally, by utilizing Markov chain, cooperative relaying protocols were developed forBA parallel and multi-hop FSO relay systems in [110] and [111], respectively.For BA relaying, the improved end-to-end throughput and outage probability are achieved witha trade-off of increased link-layer delay. In 5G communications, the reliability of communicationbetween two nodes is often-times defined as the probability of transmitting certain amount of data fromsource to destination within a predefined time frame [112]. Consequently, for ensuring reliability in 5Gcommunications, it is important to simultaneously maximize the throughput and provide delay-boundguarantee. A heuristic protocol, that can maintain an average delay of the transmitted packets, wasproposed in [108]. In [106], the following two extreme cases were considered: (i) traffic can wait at therelay for an arbitrary long duration and (ii) traffic can not wait at the relay at all. However, for real-timetraffic, delay-bound is more meaningful than average delay, and real-time traffic often tolerate a certaindelay-bound violation probability. On the other hand, owing to the uncertainty in channel conditionscaused by multi-path path fading in RF and scintillation in FSO links, providing deterministic delaybound guarantee is challenging for a hybrid RF/FSO communication system. In this context, inChapter 5, we develop statistical-QoS aware AT schemes for a hybrid RF/FSO communication systemby utilizing BA parallel relaying. We investigate the following two scenarios. In the first scenario,we investigate FD transmission over both RF and FSO links while considering self-interference (SI)and inter-relay-interference (IRI) over the RF links. In the second scenario, we investigate multi-carrier transmission over both RF and FSO links where orthogonal-frequency-division-multiple-access(OFDMA) is used over the RF links, and multiple parallel optical beams are used over the FSO links.1.2.4 FSO Based Backhaul and Fronthaul NetworksBoth hybrid RF/FSO and cooperative communications are the potential candidates for improvingthe reliability of FSO based backhaul/fronthaul network [113]. By using graph theory, the authorsin [114] developed a cost-effective upgrading of the exiting optical fiber backhaul network by addinghybrid RF/FSO links subject to data-rate, connectivity, and reliability constraints. In [115], the sameauthors developed reliable and cost-effective backhaul network deployment by using hybrid RF/FSOand multi-connectivity (known as K-connectivity) for each base station. A similar problem was alsotackled in [116], where mirror assisted backhaul links are used to connect the distant non-line-of-sightbase stations. By using relay assisted hybrid RF/FSO backhaul links, adaptive resource allocationswere performed for enhancing sum throughput of an OFDMA cellular network [117]. The FSO backhaullink can be utilized for extending the existing fiber backhaul link in the dense networking scenario. In[118], a mixed FSO/fiber backhaul network was investigated, and the impact of the fiber non-linearityon the performance of mixed FSO/fiber network was analyzed. Recently, a steerable FSO transmissiontechnology was developed for the picocell backhaul network in [119]. Such a steerable FSO technologyenables a picocell to dynamically connect with the gateway through one or more hops and leadsto an improved reliability, thanks to the adaptive routing. Moreover, FSO based backhaul/fronthaultechnology was also considered for UAV-based cellular network [120, 121]. In order to efficiently performcommunication from terrestrial base station with multiple mobile UAV nodes over FSO backhaul, amulticast problem was formulated, and the solution to such a multicast problem was obtained via prizecollecting traveling salesman problem [122].121.3. Thesis ContributionsThe recent works investigating FSO based fronthaul for C-RAN are summarized as follows. In [123],the authors presented performance comparison of mmWave and FSO based fronthaul technologies forH-CRAN architecture. Joint time slot allocation and fronthaul compression were developed for hybridRF/FSO fronthaul link in C-RAN architecture [124]. Downlink optimization of RF/FSO fronthaulfor C-RAN was also investigated in [125]. Specifically, the authors optimized pre-coding, quantizer,and power allocation over RF links considering channel capacity constraint of the hybrid RF/FSOfronthaul link. In a recent work, joint optimization of the RF quantizers and the amplifier gains ofthe FSO links was investigated for C-RAN with mixed RF and FSO fronthaul networks [126]. Non-orthogonal-multiple access (NOMA) was also proposed for FSO fronthaul network. Note that, due tothe directivity of FSO links, FSO based fronthaul link requires large number of transceivers at thecentral node in order to maintain connectivity with the base stations in dense network. NOMA in FSOis used for multiple-access in uplink, and it allows two transmitters to simultaneously communicatewith one receiver. Hence, NOMA can potentially reduce the cost of FSO based fronthaul link. Theperformance of NOMA based FSO fronthaul in C-RAN architecture was investigated by consideringchannel aware decoding and joint channel/QoS-aware dynamic decoding in [127] and [128], respectively.Finally, in [129], the experimental demonstration of the FSO based fronthaul network was discussed.Despite the aforementioned progresses, state-of-the-art literature do not consider link-layer delay-QoS requirements for FSO based fronthaul network. As a notable departure from state-of-the-artliterature, in this thesis, we develop statistical-QoS aware AT scheme(s) for the FSO based fronthaulnetwork in C-RAN architecture. Specifically, in Chapter 6, we develop delay-QoS aware joint powerallocation and relaying link selection for an uplink FSO fronthaul network. In Chapter 7, we pro-vide statistical-QoS aware joint FSO fronthaul and mmWave access link optimization for the CScNetarchitecture.1.3 Thesis ContributionsThe key contribution of this thesis is to develop AT schemes that will ensure statistical-QoS guar-antee for the BA terrestrial FSO communication systems. Specifically, in this thesis, we make thefollowing three fold contributions.− Analysis of the EC of an FSO communication system: The main novelty of this contribution isthat it provides the exact closed-form expression(s) of the achievable EC considering atmosphericturbulence fading and pointing error. Through the derived expressions, the maximum achievablethroughput of an FSO communication system subject to certain statistical-QoS constraint can bequantified. The key findings of the analysis are as follows. First, this analysis reveals that for acertain relationship between two parameters of pointing error, namely, equivalent beamwidth andjitter standard deviation, the high SNR EC increment per dB average transmit power does not de-pend on the pointing error. Second, this work analytically quantifies the asymptotic performancegap between the independent and joint power adaptation schemes in the stringent statistical-delayconstraints. Third, this work shows that the delay limited capacity of the independent poweradaptation technique approaches zero in the strong turbulence regime (i.e., the atmospheric tur-bulence fading has K-distribution); however, the joint power adaptation technique can support131.3. Thesis Contributionsa finite delay limited capacity in the strong turbulence regime.− Development of the QoS-aware AT scheme(s) with practical modulations: The main novelty ofthis contribution is the development of statistical-QoS aware AT schemes for an FSO communica-tion system with the practical modulation schemes. The developed schemes improve the spectralefficiency of an FSO communication system by performing AM, power allocation, and adaptivebeam selection. Moreover, the developed schemes ensure certain statistical-QoS constraint forthe transmitted data. The key findings of this contribution are as follows. First, the proposedAT schemes achieve higher spectral efficiency in the strict statistical-QoS constraints and strongturbulence fading compared to the well-known AT schemes of the existing literature. Second,jointly adapting the transmission parameters of the active optical beams notably improves spec-tral efficiency in the presence of strict statistical-QoS constraints, especially for strong turbulencefading or a long transmission link.− Development of innovative resource allocation algorithms for FSO network(s): The primary fo-cus of this contribution is to ensure statistical-QoS for the FSO based backhaul/fronthaul net-works that can be used in the HetNet or C-RAN architectures. In this contribution, severaloptimization problems are proposed for the considered FSO networks. Such optimization prob-lems are formulated as MINLP problems. As a result, it is challenging to obtain the globaloptimal solutions to the considered optimization problems. In addition, the involved functionalform of the EC makes the formulated optimization problem(s) even more challenging to solve.Therefore, the key novelty of this contribution is to provide efficient solution to the proposed op-timization problems by merging the tools from Lagrangian dual decomposition, matching theory,and alternating optimization theory. We also develop innovative resource allocation algorithmsfor improving the delay-throughput trade-off of the considered FSO networks. The developedalgorithms are generic, i.e., they can be applied to any turbulence fading and/or pointing errormodel. The main significance of this contribution is that it provides some interesting insightsfor FSO based backhaul/fronthaul networks. To the best of our knowledge, such insights are notreported in the contemporary literature. The key findings of this contribution are summarizedas follows.– For an FSO backhaul network with BA parallel relaying, the optimal transmission strat-egy switches from BA all-active to BA selective relaying as the weather induced FSO linkattenuation increases.– For an FSO backhaul network with BA parallel relaying and multiple transmit/receive aper-tures at both hops, adaptive selection of the spatial transmission mode at both hops enablesthe network to support improved statistical-QoS aware arrival rate.– When the BA RRHs in the network have multiple FSO fronthaul links available, jointoptimization of these fronthaul links notably improves the EC of the RRHs, especially inthe presence of strong turbulence fading and large QoS-exponents.– For the downlink transmission in CScNet architecture with FSO fronthaul and mmWaveaccess links, the supportable QoS-aware arrival rate to the BBU pool can be substantially141.4. Thesis Organizationimproved by performing AT over both the fronthaul and access links under a joint optimiza-tion framework.Remark I: The FSO link attenuation due to fog can reach several hundred dB/Km, and conse-quently, maintaining connectivity by transmitting infrared optical beam(s) becomes impossible in thepresence of dense fog. Therefore, the fog induced link attenuation is a crucial challenge for an FSOnetwork. However, our proposed AT schemes do not mitigate the fog induced link attenuation. Theproposed AT schemes can primarily be applied to improve the delay-throughput trade-off of the FSOsystems in the clear weather by combating the short-term fading introduced by scintillation. In thepresence of severe fog, alternative communication channels, such as RF or mmWave, need to be usedin order to maintain the connectivity. However, in several places, the severe fog only occurs in aninfrequent manner. For example, based on the real-time climate data, it was shown in [101] that theprobability of occurring severe fog induced channel attenuation in the city of Edinburgh, UK, is quitelow (around 6 × 10−3). Obviously, in such a scenario, a standalone FSO communication system canachieve 99% link availability. Particularly, in such a case, during the clear weather condition, an FSOsystem can be operated with the proposed AT schemes. On the other hand, during the severe fog,such an FSO system can borrow an RF spectrum from the neighbor communication network in orderto maintain the connectivity. The aforementioned RF spectrum trading improves the capacity of thesystem in the adverse weather condition, and the interested readers are refereed to [101] for the detailsof the RF spectrum trading procedure between an FSO link and an RF link. We also emphasize thatdue to the fog, the achievable communication ranges in the FSO communication system vary accord-ing to the deployment scenario. For example, in the maritime deployment scenario, an FSO link cansupport 3 Km long communication range with 99.9% link availability [130]. On the other hand, in thedense urban deployment scenario, an FSO link can support 100 meter to 500 meter long communicationrange with 99% to 99.9% link availability [119, 129]. Note that, such a link availability is sufficient forpico-cell backhaul network. Finally, in the rural deployment scenario, LOS link is more likely available.Consequently, in the rural deployment scenario, FSO backhaul link can support communication rangeover a few kilometers [117]. Overall, depending on the deployment scenario, the communication rangeof the considered FSO communication systems of this thesis can be a few hundred meters to a fewkilometers.1.4 Thesis OrganizationThis thesis is organized into eight chapters. In what follows, we summarize the content of eachchapter.In Chapter 1, we present a brief background on the development of FSO based technology alongwith the competence of FSO technology for 5G backhaul/fronthaul network. The research objectivesof this thesis are also presented. A comprehensive review of the FSO communication literature relatedto this thesis is provided. Finally, the contributions of the overall thesis are summarized.Chapter 2 presents the required technical background for the entire thesis. We first introduce dif-ferent well-known detection techniques for FSO communications. Next, we present a brief review aboutthe statistical model(s) of atmospheric turbulence fading, geometric loss and atmospheric attenuation151.4. Thesis Organizationfor terrestrial FSO communications, and statistical model(s) of the pointing error due to misalignmentbetween transmitter and receiver. Finally, in order to facilitate the ensuing analysis of the thesis, wepresent some basic concepts of statistical-QoS for single hop and dual-hop communications over fadingchannels.In Chapter 3, we investigate the EC of an FSO communication system employing the coherentdetection and POLMUX over the Gamma-Gamma turbulence fading channels with pointing errors.We consider two different power adaptation techniques, namely, independent power adaptation andjoint power adaptation schemes. Closed-form EC expressions are developed for both power adaptationtechniques. Asymptotic analyses provide the increments of EC in the high SNR regimes, in both non-stringent and stringent statistical-delay constraints, for every 1 dB increase of the average transmitoptical power. In addition, the impact of non-ideal phase noise compensation is also investigated. Ouranalysis reveals the superiority of the joint power adaptation technique in order to support the stringentstatistical-delay constraints over the FSO channels impaired by the strong turbulence fading and/orpointing error. However, the numerical results demonstrate that the performance gap between the jointand independent power adaptation schemes is significantly reduced as the statistical-delay constraintsbecome loose and/or the channel impairments (i.e., turbulence fading and/or pointing error) becomeweak. This chapter has been included in a published journal article [71].In Chapter 4, we propose statistical-delay-QoS aware adaptive modulation (AM) and power allo-cation for multi-channel coherent FSO communication system over the atmospheric turbulence fadingchannels. For given statistical-delay constraints (i.e., link-layer delay bound and delay-bound viola-tion probability) and target bit-error-rate (BER) requirements, our proposed AM and power allocationmaximize the effective spectral efficiency (ESE) subject to the transmit power constraints. Specifically,for a dual-channel coherent FSO system, we develop AT scheme by employing independent and jointchannel optimizations subject to average transmit power constraint. Numerical results demonstratethat our proposed AM and power allocation significantly outperform the conventional AT schemes inthe strict statistical-delay constraints. Numerical results also depict superiority of the joint channeloptimization (JCO) in the strong turbulence fading and strict statistical-delay constraints. In addition,we develop statistical-delay-QoS aware AT schemes by considering the peak transmit power constraintfor a coherent FSO system employing multiple parallel optical beams. The proposed schemes jointlyperform AM, transmit power allocation, and beam selection by considering statistical-delay constraints.We investigate independent channel optimization (ICO), JCO, and independent channel optimizationwith beam selection (ICO/BS) techniques. Our analysis reveals insights to the performance of the de-veloped AT schemes for the stringent delay-QoS constraint in high and low SNR regimes. The materialspresented in this chapter have been included in two published journal articles [131, 132].In Chapter 5, we develop AT schemes over a hybrid RF/FSO backhaul network for connectingMBS with small-cell base station (SBS) through multiple parallel BA relay nodes. The developed ATscheme improves delay-throughput trade-off of backhaul network by capturing both RF and FSO linkqualities and QoS requirements of the transmitted data. The objective of this work is to maximizethe constant data arrival rate to the network such that the total queue occupancy in the networkis bounded with certain acceptable queue-length bound violation probability. We study two differentsystem configurations, such as, single-carrier and multi-carrier hybrid RF/FSO communication systems.161.4. Thesis OrganizationBy employing Lagrangian duality, QoS-aware transmit power allocations over both RF and FSO linksare developed. By utilizing adaptive power allocations, different transmission decisions are dynamicallyperformed according to RF and FSO link conditions. Several insights are presented by consideringspecial cases on link conditions and QoS requirements. Simulation results provide the following twoobservations: (i) compared to the standalone RF or FSO based BA adaptive relaying, the proposedscheme provides improved weather resilience; and (ii) compared to several conventional NBA and BAfixed relaying, the proposed scheme considerably improves the maximum supportable data arrival ratefor a hybrid RF/FSO backhaul network. This chapter has been included in a submitted journal article[133].In Chapter 6, we propose a statistical-delay-QoS aware joint power allocation and relaying linkselection scheme for uplink of a multichannel coherent FSO based fronthaul network. The RRHs in theconsidered fronthaul network are equipped with buffer for (temporarily) storing the arrived data, andour objective is to maximize the supportable arrival rate at the input of the RRHs’ buffer. Towards thisobjective, we propose an AT scheme that assigns suitable relays and aggregation nodes to the RRHs andallocates transmit power among the parallel optical beams transmitted from the RRHs. Specifically,the proposed scheme maximizes end-to-end EC of the RRHs over the FSO fronthaul network subjectto certain transmit power budgets at both RRHs and relay nodes. The joint power allocation andrelaying link selection are formulated as an MINLP problem. We obtain near optimal solution tosuch an optimization problem by using Lagrangian dual decomposition and minimum weight matchingtechniques. Our analysis reveals that in order to maximize the end-to-end EC of the RRHs, transmitpower allocation and relaying link selection should consider both statistical-delay-QoS requirements ofthe transmitted data and channel gains of the transmission links. Simulation results demonstrate thatour proposed scheme improves statistical-delay-QoS aware throughput in the presence of atmosphericturbulence fading and pointing error. This chapter has been included in a published journal article[134].In Chapter 7, we investigate resource optimization for the downlink CScNet architecture where theBBU pool communicates with BA SRRHs through FSO fronthaul, and SRRHs transmit to the userequipments (UEs) by using time division multiplexing based mmWave access links. The objective ofthis work is to maximize the supportable aggregate data arrival rate in the network by exploiting theinter-dependence of fronthaul and access links. Towards this objective, we consider maximum accept-able end-to-end queue-length bound violation probability constraints, load-balancing constraints in theaccess link, fronthaul link selection constraints, and transmit power budget constraints of fronthauland access links. Since the joint fronthaul and access link optimization is a non-convex and combinato-rial problem, we develop iterative solution by decomposing the original optimization problem into twosub-problems. The first sub-problem optimally obtains fronthaul and access link power allocation andfronthaul link selection by using Lagrangian dual decomposition and canonical one-to-one matchingtechniques. By employing Lagrangian dual decomposition and alternating optimization techniques,the second sub-problem obtains near optimal data arrival rate for each UE, UE-SRRH associations,fronthaul rate allocation among the transmitted data for the UEs, and transmission duration schedul-ing in the mmWave access links. An algorithm of polynomial complexity is developed in order todetermine the supportable aggregate data arrival rate by considering statistical-QoS requirements, and171.4. Thesis Organizationits convergence is proved. Simulation results depict that the proposed scheme substantially improvesthe supportable aggregate data arrival rate to the BBU pool over several benchmark schemes. Thischapter has been included in a journal article accepted for publication [135].Finally, Chapter 8 summarizes contributions of the entire thesis. In addition, potential futureresearch topics related to this thesis are also discussed in this chapter.18Chapter 2FSO System Models, Channel Models,and Statistical-QoS ConstraintsIn this chapter, we briefly review the conventional detection techniques for terrestrial FSO com-munications. We also review the existing mathematical models of the channel impairments for FSOcommunications. Finally, we discuss about the statistical-QoS constraints for wireless communicationsover fading channels.2.1 Preliminary of FSO Systems Based on Detection TechniquesFor the terrestrial FSO communications, on/off keying (OOK) based intensity modulation with di-rect detection (IM/DD) is widely used. OOK signaling with IM/DD and deterministic detection thresh-old provides a simple implementation for the transceivers in the FSO communication systems [137].However, due to the atmospheric turbulence fading, the OOK IM/DD with deterministic threshold suf-fers from the irreducible error floor. Adaptive detection thresholds are required in order to overcomesuch an irreducible error floor. On one hand, implementing adaptive detection threshold requires rapidchannel measurements and increases the system complexity, and on the other hand, the performanceof such adaptive detection threshold depends on the accuracy of CSI estimation. Maximum-likelihood(ML) sequence detection is another well-investigated solution for the OOK IM/DD system [7]. How-ever, optimal ML sequence detection requires joint temporal statistics of the turbulence fading [164].As an alternative to the aforementioned OOK IM/DD systems, two different detection techniques,namely, coherent detection and sub-carrier IM/DD (SIM), are well-investigated for the terrestrial FSOcommunication systems. In [138], an error-rate performance comparison between coherent and SIMFSO systems was presented. The channel of a coherent FSO system with heterodyne detection canbe modeled as a complex Gaussian channel [136]. Thus, the exact channel capacity of the coherentdetection can be obtained in closed-form expression [52], and such an expression is suitable for solvingthe considered optimization problems. In contrast, the expression of the exact channel capacity of theIM/DD (or SIM) systems lacks analytical tractability for the considered optimization frameworks. Ac-cordingly, for the analytical tractability of the proposed optimization frameworks, we employ coherentdetection technique for the considered FSO systems. However, for the completeness of this thesis, inwhat follows, we briefly review both coherent and SIM FSO systems.2.1.1 Coherent FSO SystemIn an FSO communication system with coherent detection, the information bit is modulated on thephase and/or amplitude of optical carrier for transmission. At the receiving-end, the received optical192.1. Preliminary of FSO Systems Based on Detection Techniquessignal is first coherently mixed with an optical beam generated by the local oscillator (LO), and thecombined optical beam is incident to the photodetector. For the optimal performance of the coherentreceiver, the polarization state of the received and LO’s optical beam should match, and the receivedphase noise should be perfectly compensated. A coherent FSO communication system experiencesphase noise introduced by both atmospheric turbulence and/or lasers. Without loss of generality, inthe subsequent analysis of this chapter, we assume that the polarization states of the received and LO’soptical beam are matched via polarization controller, and the phase noise is accurately compensatedbefore detection2. Such assumptions are common in the existing coherent FSO literature (see [43] andreferences therein). The electric field of the modulated optical carrier at the output of laser transmittercan be written asEt(t) = Eo exp (j(ωct+ φs + φt)) (2.1)where Eo is the amplitude of the transmitted electric field, ωc is the carrier frequency, φs is the phaseinformation associated with the selected modulation, and φt is the laser phase noise. In terms of theelectric field, the incident optical beam on the photodetector can be expressed asEr(t) = Es exp(j(ωct+ φs + φt + φa)) + ELO exp(j(ωLOt+ φLO)) (2.2)where Es and φa are the amplitude of the received electric field and phase noise introduced by atmo-spheric turbulence, respectively; ELO is the amplitude of the electric field of the optical beam generatedby the LO; ωLO is the LO frequency; and φLO is the LO phase noise. The incident optical power atthe photodetector, denoted as Pr(t), is expressed asPr(t) = Ps + PLO + 2√PsPLO cos (ωIF t+ φs + φn) (2.3)where Ps is the received optical signal power; PLO is the LO power; φn = φt+φa−φLO is the total phasenoise present in the received photocurrent; and ωIF = ωc−ωLO is the intermediate frequency where ωcand ωLO denote the carrier frequency and the LO frequency, respectively. The photocurrent generatedby the photodetector can be written as ir,c(t) = iDC + iAC(t) + nc(t) where iDC = R(Ps + PLO) andiAC(t) = 2R√PsPLO cos(ωIF t + φs + φn) are the direct current (DC) and alternating current (AC)terms, respectively; R is the responsivity of phtotodetector; and nc(t) is zero-mean additive whiteGaussian noise (AWGN) process with variance σ2c . In a photo-detection process, the noise can begenerated from a shot noise process induced by the received optical signal and background radiation,and/or thermal noise process. Hence, the noise variance is written as σ2c = σ2shot + σ2Th + σ2back whereσ2shot is the shot noise variance due to the received optical power; σ2Th is the thermal noise variance;and σ2back is the shot noise variance due to the received background radiation [138]. A typical coherentFSO communication system is operated with large LO power. Thus, PLO Ps is satisfied and theDC current at the output of photodetector is dominated by the term RPLO. Due to large LO power,the shot noise generated by LO dominates both thermal noise and background radiation induced shotnoise. Therefore, the noise variance for the generated photocurrent in a coherent FSO system is given2In the following chapter, we justify the practicality of the accurate phase noise compensation assumption for coherentFSO system. In Chapters 3 and 4, we evaluate the impact of uncompensated phase noise on the derived performancemetrics for a coherent FSO system. On the other hand, in Chapters 5, 6, and 7, we consider that phase noise in thecoherent receiver is accurately compensated.202.1. Preliminary of FSO Systems Based on Detection Techniquesby σ2c ≈ σ2shot = 2qRPLO4f , where q is the electronic charge, and4f is the noise equivalent bandwidthof photodetector. Note that, the transmitted information needs to retrieved from the AC current, i.e.,from iAC(t). The procedure for retrieving the transmitted information from the AC current is givenas follows [139]. At first, two down-conversion processes are applied on the AC current in order toobtain the in-phase and quadrature components of the baseband signal. By combining the in-phaseand quadrature components, the equivalent baseband signal is obtained. The equivalent basebandsignal is given asy1 =√2R√PsPLO exp(j(φs + φn)). (2.4)Phase noise compensation is applied on the equivalent baseband signal. Assuming that the phase noisecompensation circuit has an accurate estimation of the phase noise, the input signal to the detectormodule is obtained asy2 = y1e−jφn =√2R√PsPLO exp(jφs). (2.5)The received optical power Ps can be written as Ps = AI, where A is the photodetector area and I isthe received optical irradiance. Therefore, the instantaneous SNR at the input of detector module iswritten asγcoh =2R2PsPLO2qRPLO4f =RAq4f I = γcohI (2.6)where γcoh is the average SNR per symbol. Assuming the (average) transmit power of the consideredFSO system is Pt, the average received power, Ps, can be expressed as Ps = ∆LPt where ∆L is aconstant path-loss factor. The average SNR of the coherent OWC system can be written asγcoh =Rq4f∆LPt. (2.7)The expression of the incident electric field on the photodetector, given by (2.2), considers ideal tem-poral and spatial coherence between the received optical signal and LO’s output. Usually, atmosphericturbulence fading distorts the wavefront of the transmitted optical signal, and thus, it corrupts thespatial coherence between the received optical signal and LO’s output. Such a wavefront distortioncan be compensated by applying adaptive optics to the received optical signal prior to mixing withthe LO’s output [140, 141]. In addition, as explained in [140], when the receiver has multiple smallapertures such that the apertures’ sizes are smaller than the spatial coherence radius of scintillation,the atmospheric turbulence fading induced wavefront distortions are negligible. In such a case, effectivecoherent reception, i.e., temporal and spatial matching between the received optical signal and LO’soutput is achievable. In the considered coherent FSO system models of this thesis, it is assumed thattransceivers employ multiple small apertures and the divergence angle of the transmitted beam is small.As such, coherent reception, given by (2.2), is realizable. Moreover, due to the consideration of temporaland spatial coherence between the received optical signal and LO’s output, the resultant performancemetrics can be considered as the theoretical upper-bounds for the practical coherent terrestrial FSOcommunication systems.212.1. Preliminary of FSO Systems Based on Detection Techniques2.1.2 SIM FSO SystemA detailed description of the SIM FSO communication system can be found in [137, 142]. In aSIM system, information bit stream is first modulated on an RF sub-carrier by using a conventionalelectrical modulator. Both phase and/or amplitude modulators can be employed. The pre-modulatedRF sub-carrier then drives an optical source, such as, light-emitting diode and/or laser. Thus, theoutput intensity is modulated by the information carrying RF sub-carrier. Since, the input to anoptical source has to be non-negative, a DC-bias is added with the RF signal. The intensity modulatedoptical signal is transmitted in the atmosphere, and is incident to the photodetector of the receiver afterbeing collected by a receiving telescope. The electric current, generated by photo detection process, isgiven by [137, eq. (2.4)]ir(t) = RIP [1 + ξs(t)] + ns(t) (2.8)where s(t) is the pre-modulated RF signal; P is the given transmit power of the optical source; ξ isthe modulation index satisfying the condition −1 ≤ ξs(t) ≤ 1 in order to avoid overmodulation; I isa random variable (RV) corresponding to the received irradiance fluctuation caused by atmosphericturbulence; and ns(t) is the noise term and it is modeled as a zero-mean AWGN process with varianceσ2ns . Typically in a SIM system, two types of photodetectors, namely, positive-intrinsic-negative (PIN)and avalanche photodiode (APD), are used. Compared to a PIN photodetector, an APD photodetectoris suitable for the long range FSO communication systems since it provides an extra gain to the outputcurrent for the impact ionization effect. However, the impact ionization also increases the noise currentgenerated by the APD photodetector. As a result, for a given received optical power, the gain of anAPD photodetector needs to be optimized in order to maximize the received SNR [7]. In addition, inorder to facilitate the impact ionization, APD requires a higher reverse bias which eventually increasesthe circuit complexity and electrical power consumption. In a SIM FSO communication system, thenoise generated from the receiver depends on the type of the photodetector used in the system. Thenoise current generated from the PIN photodetector is dominated by the thermal noise. However,a PIN photodetector may also generate non-negligible shot noise when the background radiation issufficiently high. On the other hand, the noise current generated from the APD photodetector isusually dominated by the shot noise. In addition, depending on the load resistor, APD photodetectormay also add non-negligible thermal noise. Assuming a PIN photodetector is used, the noise varianceis obtained as σ2ns ≈ σ2back + σ2Th. The shot noise variance due to background radiation is given asσ2back = 2q∆fRIb where Ib is the background light irradiance, and the thermal noise variance is givenas σ2Th = 4kbTk/RL where kb is Boltzman constant, Tk is the temperature in Kelvin, and RL is theload resistance. By normalizing the power of s(t) to unity, the instantaneous SNR (per symbol) at theinput of electrical demodulator can be written asγSIM =(RPξ)224f(qRIb + 2kbTk/RL)I2 = γSIMI2 (2.9)where γSIM , (RPξ)224f(qRIb+2kbTk/RL) is the electrical SNR (per symbol) assuming unit mean receivedirradiance. Due to the requirement of DC bias, SIM system experiences poor efficiency. In addition,when the electrical coherent modulation scheme (such as M -ary phase shift keying) is used to pre-222.2. Statistical Model of FSO Channel Impairmentsmodulate the RF sub-carrier, performance of the SIM system depends on the phase noise at the receiver.Usually, SIM system requires (relatively) simple transceiver architecture. However, compared to thecoherent FSO communication system with homodyne/heterodyne detection, SIM system offers inferiorbit-error rate and data rate, as demonstrated by [138] and [48], respectively. Moreover, coherent FSOcommunication system with homodyne/heterodyne detection can provide higher ambient noise rejectioncapability, improved sensitivity, and power efficiency. Accordingly, the coherent FSO communicationsystems with homodyne/heterodyne detection are suitable for the long haul applications [43].2.2 Statistical Model of FSO Channel ImpairmentsDepending on the deployment scenario and weather condition, different FSO channel impairmentscan have different orders of impact. For example, in the night time and/or foggy weather condition,atmospheric optical signal attenuation will have the highest impact on the end-to-end performancemetrics. On the other hand, pointing error will have the crucial impact on the performance of thecommunication system if either transmitter or receiver is mobile. Finally, in the clear weather, atmo-spheric turbulence induced scintillation has the most severe impact, especially for the long distancecommunications. For short distance communications, i.e., for the link length smaller than 500 meter,scintillation usually has a little impact on the received average power [7]. However, scintillation resultsin random fluctuation of the transmission rate which may adversely impact the queueing-delay in thenetwork. Accordingly, for delay-sensitive applications, scintillation needs to be carefully considered.2.2.1 Statistical Model of Atmospheric Turbulence FadingAtmospheric turbulence induced scintillation is a stochastic process. Consequently, appropriatestatistical model is required in order to characterize performance of an FSO communication system inthe presence of atmospheric turbulence fading. Over years, several statistical models were proposed inorder to describe the scintillation. The log-normal distribution is an earlier fading model that workswell in weak turbulence condition. However, log-normal fading cannot describe the irradiance fluc-tuation caused by the moderate to strong turbulence fading. Different extensions of the log-normaldistribution, namely, log-exponential and log-Rice distributions were proposed in order to describe at-mospheric turbulence fading beyond the weak turbulence regimes. The K-distribution was proposedin order to describe the strong atmospheric turbulence fading for an FSO communication system.On the other hand, negative exponential distribution describes the atmospheric turbulence fading inthe saturation regime. The Gamma-Gamma distribution is a widely accepted atmospheric turbulencefading model, which can describe a wide range of turbulence fading regime (from weak to strong).Moreover, both the K-distribution and negative exponential distribution can be obtained as the spe-cial cases of the Gamma-Gamma distribution [137]. Recently, a generalized distribution, namely, theM -distribution was proposed. The M -distribution provides the conventional the log-normal, Gamma-Gamma, shadowed-Rician, K-distribution, and negative exponential distributions as the special cases[143]. Moreover, two other statistical models of atmospheric turbulence fading, namely, the doubleGamma-Gamma distribution and the exponentiated-Weibull (EW) distribution were proposed in [144]and [145], respectively. The double Gamma-Gamma distribution is more accurate than the Gamma-232.2. Statistical Model of FSO Channel ImpairmentsGamma distribution in strong and moderate turbulence regimes with spherical wave propagation andplane wave propagation, respectively. On the other hand, the EW distribution is more accurate com-pared to the conventional Gamma-Gamma distribution when aperture averaging is considered. In whatfollows, we first present the essential parameters for atmospheric turbulence fading. Subsequently, wediscuss about statistics of the Gamma-Gamma, K-distribution, and negative exponential distributionssince these distributions are commonly used in the FSO literature.Rytov variance and scintillation index for turbulence fadingRytov variance is an important parameter for characterizing the behavior of atmospheric turbulenceinduced fading. As per [137, eq. (2.12) ], the value of Rytov variance is given byσ2R = 1.23C2nk76L116 (2.10)where C2n is the index of refraction structure parameter, k = 2pi/λ with λ as the wavelength, and Lis the link length. For weak turbulence regime, σ2R < 1 holds, and for moderate-to-strong turbulenceregime, σ2R > 1 holds [137]. In (2.10), C2n is an altitude-dependent parameter, and it attains largervalues at the lower altitudes due to more fluctuation of temperature at the lower altitudes. However,for terrestrial FSO communication between two fixed points, the value of C2n usually remains constant.Typical values of C2n for terrestrial FSO communication was reported from 10−17 m−2/3 to 10−13 m−2/3[7].Scintillation index is another important parameter for quantifying the irradiance fluctuation due toatmospheric turbulence fading. Scintillation index is defined as the normalized irradiance fluctuation,i.e., σ2SI =E[I2](E[I])2 − 1. The value of scintillation index depends on the Rytov variance. From [137, eqs.(2.15), (2.16)], for weak turbulence fading, the value of scintillation index for plane and spherical wavepropagation are given by, respectively,σ2SI ≈ σ2R = 1.23C2nk76L116 , (2.11)andσ2SI = 0.5C2nk76L116 . (2.12)On the other hand, as the values of C2n and/or link distance, L, increase, the irradiance fluctuationenters into moderate-to-strong regime. From [137, eqs. (2.17), (2.18)], for moderate-to-strong turbu-lence fading, the value of scintillation index for plane and spherical wave propagation are given by,respectively,σ2SI = exp 0.54σ2R(1 + 1.22σ12/5R)7/6 + 0.509σ2R(1 + 0.69σ12/5R)5/6− 1 (2.13)andσ2SI = exp 0.17σ2R(1 + 0.167σ12/5R)7/6 + 0.225σ2R(1 + 0.259σ12/5R)5/6− 1. (2.14)242.2. Statistical Model of FSO Channel ImpairmentsGamma-Gamma, K-distributed, and negative exponential modelsAccording to the Gamma-Gamma model, the irradiance fluctuation is described as weak eddiesinduced iradiance fluctuation modulated by strong eddies induced irradiance fluctuation. The weakeddies and strong eddies induced irradiance fluctuations are statistically modeled by Gamma distribu-tion with parameters α and β, respectively. Here, α and β denote the effective number of large andsmall scale eddies, receptively. The probability density function (PDF) of the normalized irradiancefluctuation under Gamma-Gamma model is defined asfIa(Ia) =2Γ(α)Γ(β)(αβ)α+β2 Iα+β2−1a Kα−β(2√αβIa) (2.15)where Γ(·) is the Gamma function [146, eq. (8.310)] and Kα−β(·) is the modified Bessel function ofthe second kind of order α − β [146, eq. (8.432.9)]. The shaping parameters of the Gamma-Gammadistribution, α and β, are related to Rytov variance. Under an assumption of plane wave propagationwith negligible inner scale (which corresponds to long propagation distance and small detector area),from [147, eqs. (2a), (2b)], the values of α and β are determined asα =exp 0.49σ2R(1 + 1.11σ12/5R)7/6 − 1−1(2.16)andβ =exp 0.51σ2R(1 + 0.69σ12/5R)5/6 − 1−1. (2.17)The K-distribution is obtained from the special case of Gamma-Gamma distribution when β = 1.In particular, the K-distribution is used to describe strong atmospheric turbulence fading regime,especially, when the propagation length is 1 Km. The PDF of the normalized irradiance fluctuationwith the K-distribution is given asfIa(Ia) =2Γ(α)(α)α+12 Iα+12−1a Kα−1(2√αIa). (2.18)For the K-distributed turbulence fading, the scintillation index is given as σ2SI = 2/α+ 1. In addition,for the K-distributed turbulence fading, scintillation index is confined by σ2SI ∈ (2, 3). Consequently,the value of α in the K-distributed turbulence fading is obtained as α ∈ (1, 2).The negative exponential distribution is used to describe atmospheric turbulence fading in thesaturation regime, especially when the link length spans over several kilometers. The PDF of thenegative exponential distribution is given asfIa(Ia) = λ exp(−λIa) (2.19)where λ > 0 is the mean of the irradiance fluctuation. When the mean of the irradiance fluctuation isunit, i.e., E[Ia] = 1λ = 1 where E[·] is a statistical expectation operator, the resultant negative expo-252.2. Statistical Model of FSO Channel Impairmentsnential distribution is obtained as fIa(Ia) = exp(−Ia). It can verified that such a negative exponentialdistribution is obtained from the Gamma-Gamma distribution when β = 1 and α → ∞. Thus, thenegative exponential is a special case of the Gamma-Gamma distributed turbulence fading.Spatial correlation of turbulence fadingSpatial correlation of turbulence fading channel is important for the practical system design,especially for diversity transmission/reception and multiplexing systems3. In a diversity transmis-sion/reception system, the required spacing among the receive apertures for uncorrelated fading de-pends on the spatial correlation length. In weak turbulence fading, the minimum required spacingamong the receive apertures for uncorrelated fading is given as, lC =√λL. On the other hand, inthe strong turbulence regime, the required spacing among the receive apertures for uncorrelated fadingis given by lc =λLrowhere ro is the well-know Fried’s parameter [7]. The value of ro depends on theturbulence fading, and for plan wave propagation, it is given as ro = 1.66(C2nk2L)−3/5[151]. Therequired spacing between the receive apertures for the uncorrelated fading increases as the turbulencefading becomes strong and/or the link length increases. In [148], it was shown that for 1 Km link lengthand C2n = 8 × 10−13 m−2/3, the correlation coefficient among the receive apertures become less than0.05 with an inter-aperture spacing 20 centimeter (cm) to 30 cm. Accordingly, spatially uncorrelatedfading in a multi-aperture FSO communication system is practically realizable.2.2.2 Atmospheric Attenuation and Geometric LossThe geometric loss is caused by the divergence of the transmitted optical beam during propagation,and such a geometric loss depends on divergence angle, link distance, and the receiver aperture size [7].On the other hand, both atmospheric absorption and atmospheric scattering result in attenuation ofthe transmitted optical power. In an absorption process, the atmospheric molecules absorb the incidentphoton energy. In contrast, in atmospheric scattering, directional redistribution of energy happens. Asa result, the optical power received at the front end of the receiver can be significantly reduced [151].The atmospheric loss depends on the wavelength of the light. In particular, the rain particles havemuch larger diameter than the wavelength of transmitted optical beam. Consequently, the scatteringloss due to rain does not present significant challenge for FSO links. On the other hand, the fogparticles have diameter similar to the optical wavelength. Thus, significant FSO link attenuation mayhappen in the presence of moderate to dense fog. In the literature, several models were proposed inorder to quantify the geometric loss and atmospheric attenuation in a given FSO link. In what follows,two well-known FSO path loss models are presented.− The path loss factor, ∆L, due to geometric loss and atmospheric attenuation is given as [108, eq.(2)]∆L =[erfc( √pia√2φL)]2× 10−aatmL/10 (2.20)3Conventionally, in an FSO communication system with transmit/receive diversity, the correlation among the diversitybranches degrade the error-rate and outage probability. Recently, it was shown in [149] that the negative correlation amongthe diversity branches improves the outage probability of a wireless commutation system in correlated lognormal fading.However, further investigation is required to verify the existence of negative correlation in the FSO communication system.262.2. Statistical Model of FSO Channel Impairmentswhere erfc(·) is the Gaussian complementary error function, a is the aperture radius, φ is thedivergence angles of the beam, and aatm is the weather dependent path loss coefficient.− The path loss factor, ∆L, due to geometric loss and atmospheric attenuation is given as ∆L =10−Latm/10−Lgeo/10 where Latm and Lgeo are the atmospheric attenuation and geometric loss indB unit [120]. The values of these path loss factors are given asLatm = 4.34(3.91V(λ550)−δ)LLgeo = 10 log(pia2pi (φL/2)2).(2.21)In (2.21), V is the visibility of the considered FSO link, and the value of δ depends on V asfollows: (i) δ = 1.6 for V > 50 Km, (ii) δ = 1.3 for V < 50 Km and for V > 6 Km, and (iii)δ = 0.585V −1/3 for V < 1.6 Km.2.2.3 Statistical Model of Pointing ErrorIn an FSO communication system, the pointing error can arise due to the misalignment betweentransmitter and receiver. Such a misalignment can be caused by the random building sway, error inthe tracking system, and/or mechanical vibrations in the FSO transceivers. The pointing error canseverely degrade the system reliability, especially when the optical beam has a narrow beamwidthand the receiver has a limited field-of-view (FOV). Consequently, it is important to have an accuratestatistical model of the pointing error. In state-of-the-art literature, the statistical distribution of thepointing error for terrestrial FSO communications has been extensively investigated. In particular, theattenuation caused by the pointing error is given by [55, eq. (9)]Ip(r; z) = Ao exp(− 2r2w2zeq)(2.22)where Ao = [erf(v)]2 denotes the fraction of received optical power at the detector center. Here,erf(·) is the Gaussian error function defined as erf(x) = 2√pi∫ x0 exp(−t2) dt, v ,√pi2rwzwith wz as thebeamwidth at distance z, and wzeq is the equivalent beam width given by wzeq = wz( √pierf(v)2v exp(−v2))0.5.Moreover, the beamwidth wz can be approximated as wz = φz. Eq. (2.22) works well when wz/a > 6 issatisfied [55]. Eq. (2.22) represents the irradiance fluctuation caused by the misalignment between thecenters of transmitter and detector. We consider that the pointing error does not corrupt the temporaland spatial coherence between the received optical signal and LO’s output. Such a consideration ismeaningful when the pointing error is small, i.e., effective APT mechanism is employed in the system[150]. Under such a consideration, pointing error appears as a multiplicative attenuation factor for thereceived optical power. As such, the pointing error model given by (2.22) applies to the consideredcoherent FSO communication system. In (2.22), r denotes the radial displacement due to pointing error,and it is defined as r =√x2 + y2 where x and y denote the horizontal displacement and elevation,respectively. Depending on the distribution of x and y, several pointing error models were proposed inthe literature. In what follows, we provide a brief summary of the existing results.272.3. Preliminary of Statistical-QoS Constraint− When both x and y are modeled as zero-mean independent Gaussian RVs with same jitter vari-ance, the radial displacement, r, follows a Rayleigh distribution. By using such a Rayleighdistribution in (2.22), the PDF of the zero boresight pointing error can be obtained. Such aresult was reported in [55, eq. (11)].− When x and y are independent Gaussian RVs with non-zero mean but identical jitter variance,the radial displacement, r, follows a Rice-distribution. Such a pointing error considers non-zerobroesight error. The PDF of the non-zero boresight pointing error was reported in [152, eq. (5)].− In practice, horizontal displacement and elevation can have non-zero mean as well as non-identicaljitter variance. For such a generalized pointing error, the radial displacement, r, follows the Beck-mann distribution. Usually, it is challenging to analyze the performance of a Beckmann distri-bution. The tight upper-bound and lower-bound for the cumulative distribution function (CDF)of the Beckmann distribution (i.e., the outage probability of an FSO system with generalizedpointing error) was presented in [153].− Moreover, horizontal displacement and elevation can have non-zero mean with non-identical jittervariance, and they can be correlated. Such a case represents the correlated building sway in ter-restrial FSO communication system. In order to investigate the impact of the correlated buildingsway, the authors in [154] developed an approximate pointing error PDF by approximating theBeckmann distribution with Rayleigh distribution.In this thesis, we consider zero boresight pointing error for the considered FSO systems. The PDFof the attenuation caused by zero boresight pointing error is given byfIp(Ip) =g2Ag2oIg2−1p , Ip ≤ Ao (2.23)where the parameter g is defined as g =wzeq2σswith σ2s as the jitter variance. The parameter g measuresthe severity of the pointing error. In particular, a small value of g refers to the severe pointing error,and a large value of g refers to the mild pointing error. For the FSO link with perfect alignmentbetween the transmitter and receiver, g approaches infinity.2.3 Preliminary of Statistical-QoS ConstraintStatistical-delay-QoS is employed in the recent literature for performing QoS-aware resource alloca-tions over wireless networks (see [155] and references therein). For delay-sensitive traffic, delay-violationand buffer-overflow at the link layer are the critical QoS parameters. Due to time-varying nature ofthe wireless fading channels, maintaining deterministic delay and buffer-overflow at the link layer ischallenging for wireless fading channels. An alternative strategy is to maintain delay-QoS requirementsprobabilistically over the fading channels. In a statistical-delay-QoS provisioning scheme, the link-layerdelay is maintained less than a certain delay-bound subject to small delay-bound violation probability.Real-time traffic statistically tolerates certain delay-bound violation at the link layer. For example, it isrecommended that the data traffic for real-time voice over internet protocol (VoIP) in LTE-A standard282.3. Preliminary of Statistical-QoS Constraintshould experience maximum 2% probability of having link-layer delay more than 50ms [156]. Similarly,delay-sensitive applications for machine-type communications (MTC) and device-to-device (D2D) com-munications in 5G networks also have delay-bound requirements, and such delay-bound requirementscan be statistically satisfied [157, 158]. Therefore, the analysis of statistical-delay-QoS is importantfor the practical wireless communication systems. In what follows, we briefly review statistical-QoSconstraints for the single-hop and dual-hop fading channels4.2.3.1 Statistical-QoS constraints for single-hop fading channelStatistical-QoS is maintained by satisfying a target buffer-overflow probability at the link layer. Weconsider that the transmitter is equipped with a large buffer. At the time index t, length of the queueis Q[t], a[t] denotes the amount of information bits arrived at the buffer, and R[t] denotes the servicerate of this buffer, i.e., the amount of information bits leaving the buffer in the wireless fading channel.The queue-length of this system satisfies the following Lindley’s equation:Q[t+ 1] = Q[t]−min{Q[t], R[t]}+ a[t]. (2.24)We consider a stable queue, i.e., the queue-length does not grow unboundedly as t → ∞. Therefore,the distribution of Q[t] converges with the distribution of the steady-state queue-length RV, Q[∞]. Forconvenience of the notation, we denote the steady-state queue-length RV as Q. The statistical-QoSconstraint for the considered queuing system is given such that the tail-distribution of the queue-lengthis bounded, and it can be written asPr[Q > Qmax] ≤ Q (2.25)where Qmax is a given queue-length bound (QLB) and Q ∈ [0, 1] is the maximum acceptable QLBviolation probability. The value of Q indicates the strictness of delay-QoS requirements of the trans-mitted traffic. In particular, if Q → 0, the queue-length cannot exceed the given QLB, i.e., Q → 0indicates the stringent delay-QoS requirement. On the other hand, Q → 1 indicates the loose delay-QoS requirement since in this case the queue-length can grow without any restriction. We are interestedto determine the maximum supportable constant arrival rate to buffer, denoted as µ, such that thequeuing-length satisfies (2.25). In order to satisfy (2.25), the tail-distribution of the queue-length isrequired. However, in general, the tail distribution of the queue-length is not available. Towardsthis challenge, we consider a large queue-length regime, i.e., Qmax is large (but finite). Subsequently,the asymptotic-delay analysis, provided in [159], is considered in order to obtain the tractable tail-distribution of the queue-length.For performing the asymptotic delay analysis, we consider that the following assumptions, providedby [159].1. Both a[t] and R[t] are discrete, stationary, and ergodic stochastic processes for t = 1, 2, · · · .2. Both a[t] and R[t] are statistically independent.4In this thesis, we use the terminologies statistical-delay-QoS, statistical-delay, statistical-QoS, and delay-QoS inter-changeably.292.3. Preliminary of Statistical-QoS Constraint3. For all the values 0 ≤ θ <∞, the asymptotic logarithmic moment generating function (LMGF) ofthe arrival and service processes exist. The LMGFs of the arrival and service processes, denotedas Ωa(θ) and Ωs(θ), respectively, are defined as [159]Ωa(θ) = limT→∞1TlogE[exp(θT∑t=1a[t])]Ωs(θ) = limT→∞1TlogE[exp(θT∑t=1R[t])].(2.26)4. Both Ωa(θ) and Ωs(θ) are differentiable.We consider that there exists a unique θ∗ ≥ 0 such that Ωa(θ∗) + Ωs(−θ∗) = 0 is satisfied. Accordingto [159, Theorem 2.1], in such a condition with large value of Qmax, the tail-distribution of the queue-length exponentially decreases. In particular, we obtainθ∗ = − limQmax→∞log (Pr[Q > Qmax])Qmax. (2.27)Hence, the tail-distribution of the queue-length is obtained as Pr[Q > Qmax] = exp (−θ∗Qmax). Al-though the aforementioned tail-distribution of the steady-state queue-length is obtained by consideringlarge queue-length regime, such a tail distribution also applies to real-time traffic with strict QLBviolation probability [160]. By applying such a tail-distribution to (2.25), we obtain θ∗ = − log QQmax .Moreover, for a constant arrival rate, µ, the LMGF of the arrival process is obtained as Ωa(θ∗) = µθ∗.As a result, the maximum supportable constant arrival rate to the buffer subject to (2.25) is obtainedasµ = −Ωs(−θ∗)θ∗. (2.28)Eq. (2.28) provides the maximum constant arrival rate that the considered fading channel can supportsubject to statistical-QoS constraint specified by θ∗, and such an arrival rate is known as EC over fadingchannel [56]. We consider that channel fading is independent and identically distributed (i.i.d.) overtime such that the channel fading co-efficients independently vary across the time index, t, followinga particular distribution. In such a case, the expression of EC given in (2.28), is further simplified as[161, eq. (4)]µ = − 1θ∗logE [exp (−θ∗R)] (2.29)where the time-index is dropped due to the ergodicity of service rate5. Note that, (2.28) and (2.29)consider the constant arrival rate. However, when the arrival rate is stochastic, EC can still be usedin order to determine the maximum supportable average arrival rate [162].5In (2.28) and (2.29), the values of θ (also known as the QoS-exponent) imply the nature of QoS requirements ofthe data traffic. A large value of θ implies strict statistical-QoS requirements, and a small value of θ implies loosestatistical-QoS requirements. For real-time traffic, a stringent statistical-QoS requirement is implied by θ → ∞. Fornon-real time traffic such as data dissemination, statistical-QoS requirement is implied by θ → 0. Some delay-sensitivetraffic, such as interactive web browsing, does not have the stringent QoS requirements similar to the real-time traffic.For such traffic, we have 0 < θ < ∞. In this thesis, we use the terminologies QoS-exponent, statistical-QoS exponent,and statistical-delay-QoS exponent interchangeably.302.3. Preliminary of Statistical-QoS ConstraintRemark I (Justification of i.i.d. block fading): In this work, we consider the i.i.d. block fadingwhere the channel fading co-efficient roughly remains constant for a block of the transmitted symbols,and is statistically independent among the different transmitted blocks. The justification of consideringi.i.d. block fading for FSO communications is following. It was experimentally demonstrated that thescintillation becomes uncorrelated after a duration of 2.1 − 3.6 ms [163]. Accordingly, the channelcoherence time for the FSO communications can be considered on the order of milliseconds [164]. Onthe other hand, as the symbol duration in FSO communications is much smaller, a large number ofsymbol is transmitted in the duration of coherence time. Therefore, it can be considered that all thetransmitted symbols approximately experience similar scintillation (i.e., similar fading co-efficient) ina duration equal to the channel coherence time. Although the i.i.d. block fading model may deviatefrom the actual time-varying channel fading process, such a model is widely used in the contemporaryliterature of FSO communications (see [44, 165, 166]), thanks to its analytical tractability. The mainreason of considering i.i.d. block fading in our system model is explained as follows. Without the i.i.d.block fading assumption, EC depends on the joint statistics of the fading blocks. Such an EC is notonly mathematically involved to analyze but also presents intractability for deriving the optimal ATpolicy. On the other hand, with the i.i.d. block fading assumption, EC depends only on the marginalstatistics of the channel fading, and such an EC has the tractability for analysis and optimization.Remark II (Justification of not transmitting arbitrary long codeword): The considered EC can beachieved without transmitting arbitrary long codewords that span for multiple channel coherence timeslots. Particularly, we consider that the transmitter has accurate knowledge of the instantaneous CSI,and it can adapt the transmit power/rate. As explained in [167], in such a case, the time-varyingfading channel can be reduced to set of parallel non-fading channels. For each of these time-invariantchannels, a capacity achieving encoder/decoder pair can be used in a time multiplexed fashion. As aresult, the transmitted codeword does not need to be arbitrary long in order to experience all possiblechannel fading states.Remark III (Modification of the EC in the correlated fading): In practice, assumption of the inde-pendent block fading does not always hold, and the channel fading can be temporarily correlated.In order to analyze the EC over temporarily correlated fading channel, a finite-state Markov channel(FSMC) based process can be considered. Particularly, for given QoS-exponent, θ, the EC based onFSMC process is given by [161, eq. 30]EC(θ) = −1θlog (ρ (PΦ(θ))) (2.30)where P is the transition probability matrix of the considered FSMC process with N states, ρ(·) denotesthe spectral radius of a matrix, Φ(θ) = diag(e−νnθ)N−1n=0with νn as the number of transmitted bits inthe n-th state. Although (2.30) provides a closed-form expression of the EC over the correlated fadingchannel, such an expression is intractable for developing optimal AT schemes. However, the followingproposition provides an alternative approach to obtain an approximate EC when the channel does notexperience ideal block fading.Proposition 2.3.1: For a given QoS-exponent, θ, ECorg (θ) and ECnew (θ) denote the EC of a fadingchannel with same marginal statistics and channel coherent times, TCorg and TCnew, respectively.312.3. Preliminary of Statistical-QoS ConstraintThen, the following relationship holds:ECnew (θ) ≈ ECorg(TCnewTColdθ). (2.31)Proof: The proof is provided in [161].Eq. (2.31) can be interpreted as follows. Let, TCorg is the given channel coherence time, and itis theoretically assumed that channel fading gain remains constant for a block duration of TCorg, andindependently varies at different blocks. However, in practice, channel fading gain becomes uncorrelatedafter a duration of TCnew where TCnew ≥ TCorg holds. Since, EC is a monotonically decreasingfunction of the QoS-exponent, we can readily show that ECnew (θ) ≤ ECorg (θ) holds. Consequently,EC obtained by the independent block fading assumption can be considered as an (approximate) upperbound for the practical case where the channel fading gain remains correlated for a longer duration.Eq. (2.31) also indicates that the AT schemes, proposed in the thesis, can be applied to such a scenarioby multiplying a factor with the QoS-exponent.Remark IV (Delay-bound violation probability): For stationary and constant traffic arrival rate, thesteady-state queue-length violation probability given by (2.25) also implies a steady-state delay-boundviolation probability at the buffer. We denote D as the link-layer delay and Dmax as the maximumtolerable link-layer delay (i.e., maximum tolerable wait time at the buffer). The value of Dmax can beobtained as Dmax = DE2E −Dc−DT where DE2E is the required end-to-end delay in the network, Dcis the delay associated with the encoding/decoding process, and DT is the transmission delay in thenetwork [168]. We denote µ as the constant arrival rate to the buffer in bits/frame unit and Tf is theduration of each frame. From Little’s formula, at the steady-state, the maximum acceptable QLB canbe written as Qmax = µDmax/Tf . Therefore, at the steady-state, the delay-bound violation probabilityin the buffer is approximated as Pout (Dmax, µ, θ) , Pr [D ≥ Dmax] ≈ exp (−θ∗µDmax/Tf ) [169, eq.(6)]. Such a delay-bound violation probability has the following interpretation. The arrived data isstored in the buffer as frames. Such frames are splitted into bit streams, and such bit streams leave thebuffer at the rate determined by the rate-adaptive transmission schemes. As a result, the wait timeof a frame in the buffer becomes a RV. With a statistical-QoS constraint it is ensured that the waittime of a frame in the buffer is probabilistically bounded. Moreover, the aforementioned delay-boundviolation probability can be used in the following two ways1. For given constant arrival rate and delay-QoS constraint, we can determine the maximum achiev-able throughput as follows. When the queue is in steady state, the average arrival rate is equalto the average departure rate [170]. Accordingly, EC can also be considered as the maximumachievable throughput of communication system subject to the statistical-QoS constraint. Inparticular, for a target delay-bound violation probability, Pr[D ≥ Dmax] ≤ d, the required QoS-exponent should satisfy θ∗ ≥ θo , ln(1/d)µDmax/Tf . Moreover, (2.29) is a monotonically decreasingfunction of θ∗. Therefore, considering the statistical-QoS constraint, the maximum achievablethroughput is obtained as Tmax = min{µ,Ec( − ln(d)µDmax/Tf)}. Obviously, when d → 1, i.e., delay isunconstrained, we obtain Tmax = min {µ,E[R]}. Consequently, the conventional ergodic channelcapacity provides achievable throughput only for the unconstrained link-layer delay.322.3. Preliminary of Statistical-QoS Constraint2. The procedure of calculating the maximum supportable traffic arrival rate in order to maintain agiven delay-bound violation probability is given as follows. We denote µ′ is the maximum support-able arrival rate for maintaining a given maximum acceptable delay-bound violation probabilityδ′. Moreover, the required QoS-exponent is θ′. The values of µ′ and θ′ are jointly determined bysolving µ′ = Ec (θ′) and Pout (Dmax, µ′, θ′) = δ′ where Ec(·) provides the EC, given by, (2.28) and(2.29). In other words, for maintaining the target delay-bound violation probability, the incomingarrival rate should be bounded by µ′.2.3.2 Statistical-QoS constraint for dual-hop fading channelThe dual-hop fading channel with the BA transmitter and relay can be considered as a systemof two concatenated queues. We also assume that both source and relay queues are stable, and thelengths of source and relay queues are Qs and Qr, respectively The statistical-QoS constraint for sucha system is given by Pr[Qs + Qr > Q˜M ] ≤ ζ where Q˜M is a given QLB, and ζ is given maximumacceptable QLB violation probability. In order to satisfy such a constraint, we consider large queue-length regime such that the tail distributions of the queue-lengths exponentially decay. We denote theQoS-exponents (i.e., decaying-rate of the queue-length tail distributions) of the source and relay queuesare θ1 and θ2, respectively. Similar to the single-hop fading channel, we aim to maximize the constantarrival rate to the transmit buffer, µ˜, such that the end-to-end QLB violation probability constraint issatisfied. In [171], the authors developed a numerical approach in order to calculate the values θ1 andθ2 for maximizing the supportable constant arrival rate. However, such a numerical approach is notefficient for developing the AT schemes. The authors in [172, 173] showed that the considered QLBviolation probability attains the lowest value when θ1 = θ2 = θ is satisfied, and the value of θ is givenby θ = − 1Q˜M(1 +W−1(− ζe))where W−1 is the lower branch of the real-valued Lambert W function.On the other hand, for any given θ1 ≥ 0 and θ2 ≥ 0, the source and relay buffers need to satisfythe following conditions [172, eq. (9)].ΩA,s(θ1) + ΩS,s(−θ1) = 0ΩA,r(θ2) + ΩS,r(−θ2) = 0(2.32)where ΩA,s(·) and ΩS,s(·) are the LMGFs of arrival and service processes of the source buffer, respec-tively; and ΩA,r(·) and ΩS,r(·) are the LMGFs of arrival and service processes of the relay buffer,respectively. For the constant arrival rate µ˜, we can write ΩA,s (θ1) = µ˜θ1. The LMGFs for theservice processes from the source and relay buffers are given as ΩS,s(θ1) = logE [exp (θ1Rs(x))] andΩS,r(θ2) = logE [exp (θ2Rr(x))], respectively. Here, R1(x) and R2(x) as the service rates of the sourceand relay queues, respectively, with x as the time varying resource allocation variables. The LMGF ofthe arrival process at the relay buffer is given as [172, eq. (11)]ΩA,r (θ2) ={µ˜θ2, 0 ≤ θ2 ≤ θ1µ˜θ1 + ΩS,s(θ2 − θ1), θ2 > θ1.(2.33)Consequently, the problem of maximizing the constant arrival rate to the source buffer subjectto end-to-end statistical-QoS constraint boils downs to an optimization problem that maximizes the332.4. Chapter Summaryconstant arrival rate to the source buffer such that (2.32) is satisfied with θ1 = θ2 = θ. The maximumconstant arrival rate to the system, denoted as µ˜∗(ζ, Q˜M ), is obtained from the following optimizationproblemµ˜∗(ζ, Q˜M ) = maxµ˜,x∈Xµ˜s.t µ˜θ + ΩS,s(−θ) = 0, µθ + ΩS,r(−θ) = 0.(2.34)In (2.34), X is the feasible region of the considered resource allocation variable x. Eq. (2.34) presentsa key resource allocation problem for maximizing the constant arrival rate to any BA dual-hop systemsubject to the end-to-end statistical-QoS constraint. We utilize (2.34) in Chapter 5 in order to developAT schemes for BA parallel relaying assisted hybrid RF/FSO backhaul network.2.4 Chapter SummaryIn this chapter, we have provided the required background knowledge for the subsequent parts ofthe thesis. At the beginning of this chapter, we have reviewed two well-known detection schemes forterrestrial FSO systems. Subsequently, we have reviewed the existing channel models for the FSOcommunication systems. Finally, we have briefly reviewed the concept of statistical-QoS constraintsover the single-hop and dual-hop wireless fading channels.34Chapter 3Effective Capacity of CoherentPOLMUX OWC Impaired byAtmospheric Turbulence and PointingErrorsThe organization of this chapter is given as follows. The accomplished works and research con-tributions are presented in Section 3.1. The system model and the statistical model of the channelimpairments are discussed in Section 3.2. Section 3.3 provides the EC analysis of the independent andjoint power adaptation schemes in the Gamma-Gamma turbulence fading assuming a perfect align-ment between the transmitter and the receiver. In this section, we consider both perfect and imperfectphase noise compensation schemes. In Section 3.4, we conduct the EC analysis of independent andjoint power adaptation schemes considering both the Gamma-Gamma turbulence fading as well as themisalignment error. Section 3.5 presents the selected numerical results, and Section 3.6 provides someconcluding remarks.3.1 Accomplished Works and Research ContributionsThe contributions of this chapter are summarized as follows. We investigate the EC performanceof an OWC system employing coherent detection and POLMUX over the Gamma-Gamma turbulencechannels considering imperfect alignment between the transmitter and the receiver6. Two differentQoS-aware power adaptation techniques are considered at the transmitter, namely, the independentpower adaptation scheme and the joint power adaptation scheme. The independent power adapta-tion scheme allocates transmit power to a particular channel of the POLMUX system by consideringonly the received SNR (i.e., received CSI) of that particular channel. On the other hand, in the jointpower adaptation scheme, transmit power allocation to a particular channel of the POLMUX systemdepends on the received SNR (i.e., received CSI) of both channels. Closed-form EC expressions aredeveloped for the considered OWC system and the power adaptation schemes. Asymptotic analyses ofthe developed EC expressions reveal the increment of the high SNR EC for 1 dB increase of the averagetransmitted optical power in both non-stringent and stringent statistical-delay constraints. Asymptoticresults also reveal that when the equivalent beamwidth at the receiver is larger than the twice of thejitter standard deviation, the high SNR EC increment for 1 dB increase of the average transmitted6Without loss of generality, in this chapter and in the next chapter, we denote the considered FSO communicationsystem as an OWC system.353.2. System and Channel Modelsoptical power in both non-stringent and stringent statistical-delay constraints becomes independent ofthe pointing error (i.e., the high SNR EC increment in atmospheric turbulence fading with pointingerror becomes same to the high SNR EC increment in atmospheric turbulence fading without pointingerror). Our analysis interestingly shows that the joint power adaptation scheme can support the strin-gent statistical-delay constraints with a much higher throughput compared to the independent poweradaptation scheme when the turbulence fading becomes strong and/or pointing errors become large.However, the performance gap between the joint and independent power adaptation schemes becomessignificantly reduced for the loose statistical-delay constraints and/or weak channel impairments asdepicted from the numerical results. Numerical results also demonstrate the impact of phase noisecompensation error and polarization control error on the achievable EC of the coherent POLMUXOWC systems.3.2 System and Channel Models3.2.1 POLMUX OWC System With Coherent DetectionIn a coherent POLMUX OWC system, the optical signal from a continuous wave laser source issplitted into two orthogonal polarized optical beams by using a polarization beam splitter (PBS).The outputs of PBS are first coherently modulated by the data signals, and then the modulatedoptical beams are passed through adaptive power controllers to adjust the transmit power. Finally, byusing two apertures, the orthogonal polarized beams are transmitted to the atmospheric channel7. Itwas theoretically investigated in [174] and experimentally verified in [175, 176] that the atmosphericturbulence induced fading results in little depolarization effect. As a result, the fluctuation of the stateof polarization (SOP) of the transmitted optical beam is assumed to be in a controllable order and canbe easily adjusted at the receiver [177].At the receiver, two orthogonal polarization filters are employed in order to collect the polarizedoptical beams. In an ideal scenario, the received optical beams are perfectly orthogonal to each other.However, in practice, polarization rotation can happen. In order to recover the orthogonal polarization,a feedback control circuit driven polarization controller (PC) is employed in order to adjust the SOPof the received optical beams [177]. Without loss of generality, we assume that the output of PC hasa residual SOP mismatch (also known as polarization control error) δ, i.e., SOP of both the opticalbeams is rotated δ with respect to their original polarization axis. We denote Ex(t) and Ey(t) as theelectric fields at the output of PC where the subscripts x and y denote the two orthogonal channels(i.e., two orthogonal polarization axises). By using polarization rotation matrix, Ex(t) and Ey(t) are7The transmit power of a coherent modulated optical beam can be varied by varying the amplitude of its electric field,and in practice, such a task can be performed by an electro-optic modulator. In the considered system, two orthogonalpolarized parallel optical beams are transmitted. Such a system configuration can offer certain advantages. We considerthat the spacing between the parallel polarized optical beams is more than the spatial correlation length of the turbulencefading. From the discussion of Section 2.2.1, such a requirement can be realized in practice. Accordingly, the paralleloptical beams experience independent channel fading. Hence, the transmission data rate can be improved by capitalizingAT scheme. Moreover, due to the weak depolarization characteristics of propagation channel, the deleterious impact ofcross-talk in the considered parallel channel system can be overcome. Consequently, the throughput of the system can beimproved by multiplexing data symbols over two parallel optical carriers.363.2. System and Channel Modelswritten as [Ex(t)Ey(t)]=[cos δ − sin δsin δ cos δ][Ex,r(t)Ey,r(t)](3.1)where the values of Ex,r(t) and Ey,r(t) are given by, respectively,Ex,r(t) =√Ps,xej(ωct+φx+φt,c,x)Ey,r(t) =√Ps,yej(ωct+φy+φt,c,y).(3.2)It was explained in [178] that in the coherent POLMUX OWC system, the atmospheric and mis-alignment fading channel induced depolarization is reduced to the rotation of the principle states ofpolarization (PSP). As such, the use of (3.2) is justified for the coherent POLMUX OWC system. In(3.2), Ps,i , AIi is the received optical signal power where A and Ii, respectively, denote the photode-tector area and the channel gain of the i-th orthogonal channel with i ∈ {x, y}; φx and φy are thephase information associated with the modulation order transmitted over x and y orthogonal polarizedchannels, respectively; ωc denotes the carrier frequency; and φt,c,i denotes the accumulated phase noiseintroduced by the atmospheric turbulence and/or lasers for the i-th orthogonal channel with i ∈ {x, y}.From (3.1), it is depicted that due to the polarization rotation, cross-talk (i.e., cross-polarization inter-ference) between two received optical beams occurs. In order to recover the transmitted information, itis required to equalize the interference. For this reason, a post photodetection digital signal processing(DSP) aided coherent receiver, given by [178, Fig. 5], is employed to recover the transmitted symbolsfrom the received electric fields in (3.1). For a fair comparison, the LO power in the considered re-ceiver architecture is equally distributed between two orthogonal polarized modes. In this chapter, weconsider a phase look loop (PLL) aided phase noise compensation mechanism. We assume that thephase noise introduced by the atmospheric turbulence and narrow-linewidth lasers change slowly, andconsequently, they can be compensated by a PLL based phase noise compensation technique. Such anassumption is reasonable since the atmospheric turbulence channel is a slowly varying fading channelwith a channel coherence time on the order of 0.1-10 milliseconds [7], and the narrow-linewidth lasershave linewidth on the order of 10 kHz [43]. Consequently, the accumulated phase noise introducedby the atmospheric turbulence and/or lasers have millisecond variation on the timescales. In orderto compensate such phase noise, the PLL circuits should have a loop bandwidth (also known as theresponse rate of the PLL circuit) on the order of kHz [179]. Note that, a practical PLL circuit canwork successfully up to several MHz [180]. As a result, the accumulated phase noise introduced bythe atmospheric turbulence and/or lasers can be successfully tracked by the practical PLL aided phasenoise compensation mechanism. However, due to the phase estimation error of the PLL circuit, resid-ual phase noise can be present into the input signal of the detector module. Such a residual phasenoise (also known as the phase noise compensation error) can affect the error rate and/or data rateperformance of the system. Following the PLL aided coherent detection technique in [179] and [178,eq. (20)], we express the instantaneous SNR per orthogonal channel asγx =R2PsPLO(cos δ + sin δ)% (∆φx)2qRPLO4f = λxγp% (∆φx) Ixγy =R2PsPLO(cos δ − sin δ)% (∆φy)2qRPLO4f = λyγp% (∆φy) Iy(3.3)373.2. System and Channel Modelswhere γp , R∆L2q4fPt is the normalized average SNR per channel with ∆L as the path loss factor(given in Section 2.2.2) and Pt as the average transmitted optical power; λx = cos δ + sin δ andand λy = cos δ − sin δ; and % (∆φi) = cos2(∆φi) (where i ∈ {x, y}) denotes the SNR penalty factorintroduced by the uncompensated phase noise8,9. Without loss of generality, we assume that theaverage transmitted optical power is equally divided between two optical channels. For a system withfully equalized cross-polarization interference, we have δ = 0◦ or λx = λy = 1. In (3.3), ∆φi (wherei ∈ {x, y}) is the phase noise compensation error given by ∆φi = φt,c,i − φˆt,c,i where φˆt,c,i is theestimation of the accumulated phase noise. ∆φi is an RV, and for a slowly time varying channel, ∆φifollows a Tikhonov distribution, given by [181, eq. (4)]f∆φi(∆φi) =exp (ρ cos(∆φi))2piIo(ρ), |∆φi| ≤ pi (3.4)where ρ = 1σ2∆φ, and σ∆φ is the standard deviation of the phase noise compensation error. Throughoutthe chapter, we make the following assumptions on the system model.A1: We assume that the considered FSO channel experiences an i.i.d. block fading process. Inparticular, the duration of each fading block is roughly same as the channel coherence time such that allthe transmitted symbols in each fading block experiences similar channel fading co-efficient. However,the channel fading co-efficients of different fading blocks are statistically independent. In the Remark Iof Section 2.3.1 it is explained that such an assumption is usually acceptable for FSO communications.A2: We assume that transmitter employs a large buffer in order to store the data packets to betransmitted. Thus, any possible loss of the data packets is prevented. We emphasize that such anassumption is usually made in state-of-the-art statistical-QoS literature in order to facilitate the largequeue-length assumption [161, 171–173]. For the FSO communications, such an assumption can alsobe supported by the fact that the practical FSO transceivers can accommodate large size buffers [110].3.2.2 Statistical Model of Channel ImpairmentsIn an OWC link with misalignment, the transmitted optical signal is subject to both atmosphericturbulence fading and pointing error. The channel gain I can be written as the product of two in-dependen RVs, I = IaIp, where Ia represents the atmospheric turbulence fading induced attenuation,and Ip represents the pointing error induced attenuation. In this work, we consider Gamma-Gammaatmospheric turbulence fading and zero-boresight pointing error. Therefore, the PDFs of Ia and Ipare obtained from (2.15) and (2.23), respectively. The combined PDF of the channel gain impaired byboth atmospheric turbulence and pointing error is given by fI(I) =g2Ag2oIg2−1 ∫∞I/AoI−g2a fIa dIa [55, eq.(14)]. The PDF of the combined channel gain in the Gamma-Gamma turbulence fading is given by8Note that, the SNR expressions given by (3.3) with the uncompensated phase noise is applicable for the transmissionof symbols from one-dimensional constellation, such as, {φx, φy} ∈ {0, pi}. On the other hand, with the assumption offully compensated phase noise, such SNR expressions can be used for the transmission of symbols from two-dimensionalconstellations as well [178].9The electric currents generated from (3.1) by applying photodetection process contains mixture of the transmittedsymbols over both channels. In [178], it is assumed that the considered DSP based detection technique can accuratelyseparate the corresponding symbols for each channel. Therefore, (3.3) provides SNR expression(s) for the best casescenario.383.3. Effective Capacity with Only Atmospheric Turbulence[51, eq. (4)]fI(I) =g2I−1Γ(α)Γ(β)G3,01,3[αβAoI∣∣∣∣∣ g2 + 1g2, α, β](3.5)where Gm,np,q [·] is the Meijer’s G-function [146, eq. (9.301)]. The justification for using (3.5) as an ac-curate model for the channel impairments in coherent POLMUX OWC system is provided as follows.The channel induced depolarization is essentially a rotation of the PSP at the receiver, and the majorstochastic turbulence-induced effect on the POLMUX OWC system comes from the scintillation [178].Moreover, as explained in Section 2.2.3, the pointing error in a coherent OWC system can be modeledas a multiplicative attenuation factor for the received optical power. Accordingly, the composite distri-bution, given in (3.5), provides an accurate statistical model for the channel impairments in coherentPOLMUX OWC system.3.3 Effective Capacity with Only Atmospheric TurbulenceIn this section, we analyze EC of a coherent POLMUX OWC system over an atmospheric turbulencechannel considering both independent and joint power adaptations.3.3.1 Independent Power Adaptation SchemeFrom (2.29), for a given QoS-exponent or decaying-rate of the delay-bound violation probability, θ,the expression of EC for a typical wireless communication system over the fading channel is defined asEC(θ) = −1θlog (E[exp(−θR(θ,γ))]) . (3.6)In this chapter, we interpret the statistical-delay constraints in terms of the values of θ. In (3.6), R(θ,γ)is instantaneous service rate (in bits per frame). For a power adaptive system, instantaneous servicerate is given by R(θ,γ) =TfBc log2 (1 + µ(θ,γ)γ) where γ is the instantaneous SNR, Tf is the frameduration, B is the transmission bandwidth, µ(θ,γ) is the power adaptation factor (also defined as theallocated power to the transmitted symbols normalized by the average transmitted power), c = 2 ifonly real symbols are transmitted, and c = 1 if the complex symbols are transmitted [136]. We assumethat the complete knowledge about the received CSI is available at the transmitter and the transmittercan adapt the power accordingly. The justification of transmit power adaptation is provided as follows.Particularly, due to the randomness of turbulence fading and link attenuation, received optical powerdoes fluctuate. It is mentioned in [64] that “in order to overcome the adverse impacts of weather, lasercommunication system needs to increase the transmit power”. Commercially available FSO transceiver,such as SONAbeamTM 52−M developed by fSONA Inc., also incorporates adaptive power control inresponse to the changing weather conditions leading to the improved link reliability [182]. A recentexperimental work demonstrated that the output power of the laser transmitter can be adaptivelyselected from a given set of pre-defined values, and such an adaptive power control improves the linkreliability [183]. To perform adaptive power control, in this chapter, we consider the average transmitpower constraint which is imposed to ensure the longevity of a laser transmitter and the eye-safety393.3. Effective Capacity with Only Atmospheric Turbulencestandard. State-of-the-art literature on adaptive OWC system have considered average transmit powerconstraint as well [63, 65]. Note that, under an average transmit power constraint, a trivial strategyis to divide the given average transmit power equally between both optical channels and transmitsame power over both optical channels at all times. However, such a trivial transmission strategy willresult in small data rate when either one of optical channels will experience severe turbulence fading,and will lead to a large queueing-delay at the transmitter. Accordingly, for improving delay-QoS overatmospheric turbulence fading channel, transmit power adaptation offers a viable degree of freedomfor an average transmit power constrained OWC system.For the power adaptation purpose, the transmitter can obtain the CSI for the downlink (transmitter-to-receiver link) employing one of the two following schemes. In the first scheme, pilot symbols areinserted at the beginning of each symbol blocks. By observing the pilot symbols, receiver estimatesthe channel fading gain experienced by the pilot symbols. Since atmospheric turbulence channel isa slowly time-varying fading channel, all the data symbols in the symbol block followed by the pilotsymbols will experience the same channel fading. Subsequently, the receiver updates the transmitterabout the estimated channel fading gain through an OWC or a RF feedback channel. It is usuallyassumed that receiver employs a strong error correction code with reliable modulation scheme as suchthe feedback of the estimated CSI will likely be error free. Moreover, due to the slow time-variation ofthe atmospheric turbulence channel, outdated CSI will also be a less likely event for the adaptive OWCsystems. In the second scheme, the transmitter can estimate the CSI by using the signals receivedfrom the receiver, and use such estimated CSI in order to adapt the transmission parameters. Thecommercially available OWC nodes have FD transmission capability, and consequently, bi-directionalOWC system can be realized in practice where the information will be transmitted in both directionssimultaneously. As a result, the transmitter will be able to estimate the CSI from the received signal.However, such an estimated CSI can only be used to adapt the transmission parameters given thechannel reciprocity holds. Recently, it has been theoretically proved and experimentally verified thatatmospheric turbulence induced fading channel exhibits channel reciprocity [187]. Consequently, witha bi-directional OWC system, transmitter can also estimate the CSI for power adaptation withoutrequiring any feedback channel. We also consider that the system employs channel capacity achievingcode such that the Shannon capacity is achieved as the instantaneous service rate10. Note that, theseare the standard assumptions in the existing literature, and such assumptions facilitate us to comparethe systems’ performance and develop insights into the system performance.Following (3.6), the optimal EC of the coherent POLMUX OWC system subject to an averagetransmit power constraint can be written asEoptc,pol = max∫µi(θ,γ)fγ(γ)≤1−1θ logEexp(−θ ∑i∈x,yRi(θ,γ))= max∫µi(θ,γ)fγ(γ)≤1−1θ logE∏i∈x,y(1 + µi(θ,γ)γi)− .(3.7)10The approximate EC with the practical channel coding can be obtained by using (4.3) as the instantaneous servicerate.403.3. Effective Capacity with Only Atmospheric TurbulenceIn (3.7), =θTfBc log 2 , µx(θ,γ) and µy(θ,γ), respectively, denote the power adaptation factors of x andy orthogonal polarized channels. With the independent power adaptation, the total average transmitpower is equally divided between two orthogonal polarized channels. Then the transmit power oneach channel is adapted based only on the SNR of that particular channel under the average transmitpower constraint per channel. Under the consideration of independent power adaptation scheme andindependent fading for both channels, (3.7) boils down toEIndc,pol , max∫µx(θ,γx)fγx (γx)≤1{−1θlog(Eγx[(1 + µx(θ, γx)γx)−])}︸ ︷︷ ︸E(x)c,pol+ max∫µy(θ,γy)fγy (γy)≤1{−1θlog(Eγy[(1 + µy(θ, γy)γy)−])}︸ ︷︷ ︸E(y)c,pol.(3.8)In (3.8), E(x)c,pol and E(y)c,pol are the EC of two orthogonal polarized channels for an independent poweradaptation technique. It can be easily shown that E(x)c,pol and E(y)c,pol will be respectively maximized forµIndx (θ, γx) =[1γ1+1a γ+1x− 1γx]+and µIndy (θ, γy) =[1γ1+1b γ+1y− 1γy]+where [m]+ , max(m, 0) [161].Here γa and γb are the cutoff SNRs for the x and y polarization channels, respectively, and they satisfy∫∞γa(1γ1+1a γ+1x− 1γx)fγx(γx) dγx = 1 and∫∞γb(1γ1+1b γ+1y− 1γy)fγy(γy) dγy = 1. Here, fGGγx (γx) and fGGγy (γy) are respectively the PDFs of the γxand γy considering the perfect phase noise compensation scheme. By using (2.15), (3.3), and [184, eq.(07.34.03.0605.01)], one can obtainfGGγi (γi) =1Γ(α)Γ(β)γ−1i G2,00,2[αβγiλiγp∣∣∣ α, β ] (3.9)where i ∈ x, y. Substituting µIndx (θ, γx) and µIndy (θ, γy) into (3.8) and using [146, eq. (7.811.3) ], weobtainE(x)c,pol =−1θlog(FGGγx (γa) +1Γ(α)Γ(β)×G3,01,3[αβγaλxγp∣∣∣∣∣ η + 1η, α, β])(3.10)andE(y)c,pol =−1θlog(FGGγy (γb) +1Γ(α)Γ(β)×G3,01,3[αβγbλyγp∣∣∣∣∣ η + 1η, α, β])(3.11)where η = +1 is defined as the normalized QoS-exponent. In (3.10) and (3.11), FGGγx (·) and FGGγy (·)are, respectively, the CDFs of γx and γy considering perfect phase noise compensation, and using [146,413.3. Effective Capacity with Only Atmospheric Turbulenceeq. (7.811.2)], they are obtained asFGGγi (γo) =1Γ(α)Γ(β)G2,11,3[αβγoλiγp∣∣∣∣∣ 1α, β, 0](3.12)where i ∈ x, y. When the average SNR is asymptotically high (i.e., γp → ∞), using [184, eq.(07.34.06.0006.01)], G3,01,3[αβγaλxγp∣∣∣∣∣ η + 1η, α, β]in (3.10) can be written asG3,01,3[αβγaλxγp∣∣∣∣∣ η + 1η, α, β]=∏3j=1,j 6=k Γ(b(j)− b(k))Γ(η + 1− b(k))(αβγaλxγp)u(3.13)where {u, k} = {min{η, α, β}, arg min{η, α, β}}, and b = [η, α, β]. Note that, η = +1 ≤ 1, and for theGamma-Gamma turbulence fading usually we have min{α, β} > 1 [43]. As a result, the asymptoticexpression of the Meijer’s G-function at high average SNR in (3.13) is further simplified toG3,01,3[αβγaλxγp∣∣∣∣∣ η + 1η, α, β]= Γ(α− η)Γ(β − η)(αβγaλxγp)η. (3.14)Similarly, we can obtain an asymptotic high SNR expression of G3,01,3[αβγbλyγp∣∣∣∣∣ η + 1η, α, β]in (3.11). In addi-tion, at the asymptotically high average SNR, the outage probability approaches zero, i.e., FGGγx (γa)→ 0and FGGγy (γb) → 0. Therefore, the EC of the coherent POLMUX OWC in high SNR regimes can beapproximated asEInd,asymc,pol = −ηθlog(γaγb)− 2θlog(αηβηΓ(α− η)Γ(β − η)Γ(α)Γ(β))+2ηθlog(R∆L2q∆f)+ηθlog(λxλy) +0.66TfBθTfBlog 2 + 1(10 log10 Pt)(3.15)where we have used γp , R∆L2q4fPt. Eq. (3.15) reveals that for a given finite QoS-exponent (i.e., fornon-stringent statistical-delay constraints) the high SNR EC of the coherent POLMUX OWC withindependent power adaptation scheme increases 0.66θTfBlog 2+1bits/s/Hz as the average transmitted opticalpower increases 1 dB.If the QoS exponent is asymptotically large, i.e., 1, the independent power adaptations aremodified as µIndx (θ, γx) =[1γ1a γx− 1γx]+and µIndy (θ, γy) =[1γ1b γx− 1γy]+. Substituting the modifiedpower adaptations into (3.8), we obtainE(x)c,pol = −1θlog(FGGγx (γa) + γa(1− FGGγx (γa)))(3.16)andE(y)c,pol = −1θlog(FGGγy (γb) + γa(1− FGGγy (γb))). (3.17)423.3. Effective Capacity with Only Atmospheric TurbulenceHere the cutoff SNRs, γa and γb, respectively satisfy γa =(1 + 1Eγa [γ−1x ])−and γb =(1 + 1Eγb [γ−1y ])−with Eγo [γ−1i ] =∫∞γoγ−1i fγi(γi) dγi for i ∈ x, y. We can readily show that for the stringent statistical-delay constraints, i.e., θ → ∞, the value of the cutoff SNR approaches zero, and consequently, theoutage probability of the system approaches zero (i.e., the system will never be in outage) [161].Consequently, for the stringent statistical-delay constraints, the EC of the coherent POLMUX OWCwith independent power adaptation scheme in the Gamma-Gamma turbulence fading is obtained aslimθ→∞EIndc,pol = TfB log2(1 +1E0[γ−1x ])+ TfB log2(1 +1E0[γ−1y ])= TfB log2(1 +(α− 1)(β − 1)αβλxγp)+ TfB log2(1 +(α− 1)(β − 1)αβλyγp) (3.18)where the first negative integer moments, E0[γ−1x ] and E0[γ−1y ], are obtained using [146, eq. (7.811.4)].It can be easily shown that for the stringent statistical-delay constraints, the high SNR EC of thecoherent POLMUX OWC with an independent power adaptation scheme increases 0.66 bits/s/Hzas the average transmitted optical power increases 1 dB. In this subsection, we assume that phasenoise is perfectly compensated. In Appendix A, we provide the analysis of EC of the independentpower adaptation without considering perfect phase noise compensation scheme over the atmosphericturbulence channels.3.3.2 Joint Power Adaptation SchemeIn case of a joint power adaptation scheme, the transmit power allocated in each channel of thecoherent POLMUX OWC depends on the channel conditions of both channels. The motivation of jointpower allocation is provided as follows. In the previous section, it is explained that the transmit poweradaptation over the parallel optical channels improves the delay-QoS of the system. Specifically, in theprevious section, we have considered per-aperture average transmit power constraint. Instead, in thissection, we consider the total and/or sum average transmit power constraint for both apertures. Weemphasize that such a constraint enables us to jointly optimize transmit power of both parallel opticalchannels. Particularly, if one optical channel experiences severe turbulence fading, more transmit powerwill be allocated to the other optical channel, and the overall throughput will be improved. Therefore,the joint power allocation is indeed beneficial for the considered dual-channel OWC system.A generalized joint power adaptation approach in order to maximize the EC of a wireless multi-channel system was discussed in [188]. With a similar approach, we can also formulate a joint poweradaptation scheme in order to maximize the EC of the coherent POLMUX OWC. The key steps of thejoint power adaptation scheme can be summarized as follows.− If both channels of the coherent POLMUX have an instantaneous SNR larger than the cutoffvalue γφ, then the transmit power in both channels will be allocated according toµ(1)i (θ, γx, γy) = 1γ1e+1φ (γxγy)e2(e+1)− 1γi+ (3.19)433.3. Effective Capacity with Only Atmospheric TurbulenceEjointc,pol(θ) =−1θlog∫ ∞γφ∫ ∞γφfγx,γy(γx, γy) dγx dγy︸ ︷︷ ︸I1+∫ ∞γφ∫ ∞γφ∏i∈x,y(1 + µ(1)i (θ, γx, γy)γi)− e2fγx,γy(γx, γy) dγx dγy︸ ︷︷ ︸I2+∫ ∞γφ∫ γφ0(1 + µ(2)x (θ, γx, γy)γx)− e2fγx,γy(γx, γy) dγx dγy︸ ︷︷ ︸I3+∫ γφ0∫ ∞γφ(1 + µ(2)y (θ, γx, γy)γy)− e2fγx,γy(γx, γy) dγx dγy︸ ︷︷ ︸I4 .(3.22)where i ∈ x, y and e = 2θTfBc log 2 .− If only one particular channel has an instantaneous SNR larger than the cutoff value γφ, then thetransmit power will be allocated to that particular channel according toµ(2)i (θ, γx, γy) = 1γ2e+2φ γee+2i− 1γi+ , i ∈ x, y (3.20)and the transmit power on other channel will be set to zero. If both of the channels have aninstantaneous SNR smaller than the cutoff value γφ, then transmit powers on both channels setto zero and consequently, the system experiences an outage.− Under an average transmit power constraint, the cutoff SNR γφ will satisfy [188, eq. (27)], givenas ∫ ∞γx=γφ∫ ∞γy=γφ[µ(1)x (θ, γx, γy) + µ(1)y (θ, γx, γy)]fγx,γy(γx, γy) dγx dγy+∫ ∞γx=γφ∫ γφγy=0µ(2)x (θ, γx, γy)fγx,γy(γx, γy) dγx dγy+∫ ∞γy=γφ∫ γφγx=0µ(2)y (θ, γx, γy)fγx,γy(γx, γy) dγx dγy = 2.(3.21)For a given set of channel parameters, QoS-exponent, and average SNR and/or transmit power, thevalue of the cutoff SNR is numerically calculated by using (3.21). With such a joint power adaptationscheme, the EC of the coherent POLMUX OWC over the atmospheric turbulence channel is obtained as(3.22) at the top of next page. Assuming independent Gamma-Gamma turbulence fading per channel,443.3. Effective Capacity with Only Atmospheric Turbulencei.e., fγx,γy(γx, γy) = fγx(γx)fγy(γy), we can evaluate I1, I2, I3, and I4 in (3.22) asI1 = FGGγx (γφ)FGGγy (γφ), (3.23)I2 =1Γ(α)Γ(β)G3,01,3[αβγφλxγp∣∣∣∣∣ e2(e+1) + 1e2(e+1) , α, β]× 1Γ(α)Γ(β)G3,01,3[αβγφλyγp∣∣∣∣∣ e2(e+1) + 1e2(e+1) , α, β],(3.24)I3 = FGGγy (γφ)1Γ(α)Γ(β)G3,01,3[αβγφλxγp∣∣∣∣∣ ee+2 + 1ee+2 , α, β], (3.25)andI4 = FGGγx (γφ)1Γ(α)Γ(β)G3,01,3[αβγφλyγp∣∣∣∣∣ ee+2 + 1ee+2 , α, β]. (3.26)In obtaining (3.24)-(3.26), we have used [146, eq. (7.811.3)]. When the average SNR is asymptoticallyhigh, the outage probability approaches zero, and consequently, (3.23), (3.25), and (3.26) also approachzero. Following a similar method to derive (3.14), we can also obtain the asymptotic high SNR expres-sions of G3,01,3[αβγφλiγp∣∣∣∣∣ e2(e+1) + 1e2(e+1) , α, β]in (3.24) for i ∈ x, y. Therefore, the asymptotic high SNR EC canbe written asEjoint,asymc,pol (θ) = −2θlog(αη1βη1Γ(α− η1)Γ(β − η1)Γ(α)Γ(β))+η1θlog(R∆L√λxλy2q∆fγφ)2+0.66TfB2θTfBlog 2 + 1(10 log10 Pt)(3.27)where η1 =e2(e+1) =+12+1η. From (3.27), for the non-stringent statistical-delay constraints, the highSNR EC of the coherent POLMUX with the considered joint power adaptation increases 0.662θTfBlog 2+1bits/s/Hz as the average transmitted optical power increases 1 dB.When the QoS-exponent is asymptotically large, (i.e., e , 2θTfBlog 2 2), after some algebraic manip-ulations, (3.21) can be written as2γ− 1eφ Eγφ[γ−1/2x]Eγφ[γ−1/2y]− Eγφ[γ−1x]− Eγφ [γ−1y ]+ γ− 2eφ(Fγy(γφ)Eγφ[γ−1x]+ Fγx(γφ)Eγφ[γ−1y])= 2.(3.28)Using some algebraic manipulations, EC of the coherent POLMUX with joint power adaptation forthe asymptotically large QoS-exponents can be written asEjointc,pol(θ) = −1θlog[γφ + (1− γφ)Fγx(γφ)Fγy(γφ)]. (3.29)Applying (3.28) into (3.29), and using the fact that for the stringent statistical-delay constraints (i.e.,453.3. Effective Capacity with Only Atmospheric Turbulenceθ →∞), γφ → 0 and Fγi(γφ)→ 0 for i ∈ x, y [188], we can write (3.29) aslimθ→∞Ejointc,pol(θ) = 2TfB log22 + E0 [γ−1x ]+ E0 [γ−1y ]2E0[γ−1/2x]E0[γ−1/2y] . (3.30)Finally, using [146, eq. 7.811(4)] we can write (3.30) aslimθ→∞Ejointc,pol(θ) =2TfB log2(Γ2(α)Γ2(β)√λxλyγpΓ2(α− 1/2)Γ2(β − 1/2)αβ+12Γ(α− 1)Γ(β − 1)Γ(α)Γ(β)√λx/λyΓ2(α− 1/2)Γ2(β − 1/2)+12Γ(α− 1)Γ(β − 1)Γ(α)Γ(β)√λy/λxΓ2(α− 1/2)Γ2(β − 1/2)).(3.31)Eq. (3.31) facilitates us to evaluate the EC of the coherent POLMUX OWC in the stringent statistical-delay constraints case with a joint power adaptation for different channel parameters, average SNRs,and/or polarization control errors. In asymptotic high SNR regime, the performance gap (in dB)between the joint and independent power adaption techniques is defined asSNRGGdiff , γpInd,req(dB)− γpJoint,req(dB) ≈ 10 log10(limθ→∞,γp→∞Ejointc,pol(θ)limθ→∞,γp→∞ EIndc,pol)(3.32)where γpInd,req and γpJoint,req denote the required SNRs (in dB) in order to achieve a given EC in thestrict delay constraints and high SNR regime over the Gamma-Gamma turbulence fading channel withindependent and joint power adaptation techniques, respectively. By comparing (3.18) and (3.31) inthe asymptotic high SNR regime, we obtainSNRGGdiff ≈ 10 log10(Γ2(α− 1)Γ2(β − 1)(α− 1)(β − 1)Γ2(α− 1/2)Γ2(β − 1/2)). (3.33)Eq. (3.33) provides the difference of the required SNR (in dB) between the independent and jointpower adaptation techniques in order to support the stringent statistical-delay constraint services witha given throughput over the Gamma-Gamma turbulence fading channels. Such a SNR difference factorincreases as the values of α and/or β decrease. Therefore, for a coherent POLMUX OWC system,joint power adaptation scheme outperforms the independent power adaptation scheme, especially inthe strong turbulence fading. However, joint power adaptation has a relatively higher implementationcomplexity compared to an independent power adaptation scheme. We can also show that in the highSNR regimes, stringent statistical-delay constraints limited capacity of the coherent POLMUX withjoint power adaptation increases 0.66 bits/s/Hz for 1 dB increase in the average transmitted opticalpower. In Appendix B, we provide the analysis of the EC of joint power adaptation over atmosphericturbulence channels considering the impact of the uncompensated phase noise.463.4. Effective Capacity with Atmospheric Turbulence and Misalignment Fading3.4 Effective Capacity with Atmospheric Turbulence andMisalignment Fading3.4.1 Independent Power Adaptation SchemeAssuming perfect phase noise compensation, and using (3.3) and (3.5), the PDF and CDF of theSNRs of coherent POLMUX OWC in the presence of Gamma-Gamma turbulence fading and pointingerror are respectively obtained asfγi(γi) =g2γ−1iΓ(α)Γ(β)G3,01,3[αβAoλiγpγi∣∣∣∣∣ g2 + 1g2, α, β](3.34)andFGG,pγi (γo) =g2Γ(α)Γ(β)G3,12,4[αβγoAoλiγp∣∣∣∣∣ 1, g2 + 1g2, α, β, 0](3.35)where i ∈ x, y, and we have used [146, eq. (7.811.2)] to obtain (3.35) from (3.34). Substituting (3.34)into (3.8) and using [146, eq. (7.811.3)], we obtain E(x)c,pol and E(y)c,pol respectively as11E(x)c,pol =−1θlog[FGG,pγx (γν,1) +g2Γ(α)Γ(β)×G4,02,4[αβγν,1Aoλxγp∣∣∣∣∣ g2 + 1, η + 1η, g2, α, β]](3.36)andE(y)c,pol =−1θlog[FGG,pγy (γν,2) +g2Γ(α)Γ(β)×G4,02,4[αβγν,2Aoλyγp∣∣∣∣∣ g2 + 1, η + 1η, g2, α, β]]. (3.37)where γν,1 and γν,2 are, respectively, the cutoff SNRs of x and y polarized channels over the Gamma-Gamma turbulence-misalignment fading channels. When the average SNR is asymptotically high (i.e.,γp →∞), using [184, eq. (07.34.06.0006.01)], G4,02,4[αβγν,1Aoλxγp∣∣∣∣∣ g2 + 1, η + 1η, g2, α, β]in (3.36) can be written asG2,44,0[αβγν,1Aoλxγp∣∣∣∣∣ g2 + 1, η + 1η, g2, α, β]=∏4j=1,j 6=i Γ(B(j)−B(i))∏2j=1 Γ(A(j)−B(i))(αβγν,1Aoλxγp)u(3.38)where {u, i} = {min{η, g2, α, β}, arg min{η, g2, α, β}}, A = [g2+1, η+1], andB = [η, g2, α, β]. Similarly,we can obtain an asymptotic high SNR expression of G4,02,4[αβγν,2Aoλyγp∣∣∣∣∣ g2 + 1, η + 1η, g2, α, β]in (3.37). Finally,the asymptotic high SNR EC of coherent POLMUX OWC with independent power adaptation scheme11The power adaptation in the misalignment fading channel requires estimation of the pointing error parameters. In[185], the authors developed a maximum likelihood estimation scheme in order to estimate the jitter standard deviation,σs, of the pointing error. In addition, assuming a Gaussian beam propagating in atmospheric turbulence, the beamwidth,wz, can be determined from [55].473.4. Effective Capacity with Atmospheric Turbulence and Misalignment Fadingcan be obtained asEind,asymc,pol = −2θlog[g2∏4j=1,j 6=i Γ(B(j)−B(i))Γ(α)Γ(β)∏2j=1 Γ(A(j)−B(i))]− uθlog(α2β2γν,1γν,2A2oλxλy)+2uθlog(R∆L2q∆f)+0.2ulog10 exp(θ)(10 log10 Pt).(3.39)Therefore, for a finite QoS-exponent (i.e., non-stringent statistical-delay constraints), the high SNR ECof coherent POLMUX with independent power adaptation scheme over the Gamma-Gamma turbulence-misalignment fading channels increases 0.2ulog10 exp(θ)TfBbits/s/Hz for 1 dB increase in the average trans-mitted optical power. In what follows we show when g2 > η is satisfied, we get similar EC incrementwith and without pointing error. Since min{α, β} > η, we have u , min{η, g2, α, β} = η when g2 > η.Under this condition, the high SNR EC increment in the non-stringent statistical-delay constraints for1 dB increase of the average transmitted optical power becomes 0.66θTfBlog 2+1bits/s/Hz. Such a high SNREC increment is identical to the high SNR EC increment in the case of having no pointing error, asshown in the Section 3.3.1. Note that g2 > η can be satisfied by setting the minimum required equiv-alent beamwidth at the receiver as wzeq > 2σs since g =wzeq2σsand η ≤ 1. In addition, note that, theaforementioned observation on the high SNR EC increment is analogous to the observations made in[137] that the diversity order of an OWC system is independent of the pointing error when wzeq > 2σsis satisfied. Following this condition and applying [146, eq. (7.811.4)] to (3.18), EC of the independentpower adaptations in the stringent statistical-delay constraints is obtained aslimθ→∞EIndc,pol= TfB log2(1 +(α− 1)(β − 1)(g2 − 1)g2αβAoλxγp)+ TfB log2(1 +(α− 1)(β − 1)(g2 − 1)g2αβAoλyγp).(3.40)Eq. (3.40) reveals that in the stringent statistical-delay constraints, wzeq > 2σs also results in thesimilar high SNR EC increment (0.66 bits/s/Hz) in both the absence and presence of pointing errorfor the independent power adaptation scheme over the Gamma-Gamma turbulence fading channel.3.4.2 Joint Power Adaptation SchemeUsing (3.34) and [146, eq. (7.811.3)] into (3.22), we obtainI1 = FGG,pγx (γψ)FGG,pγy (γψ) (3.41)I2 = γee+1ψ(g2γ−η1ψΓ(α)Γ(β)G4,02,4[αβγψAoλxγp∣∣∣∣∣ g2 + 1, η1 + 1η1, g2, α, β]× g2γ−η1ψΓ(α)Γ(β)G4,02,4[αβγψAoλyγp∣∣∣∣∣ g2 + 1, η1 + 1η1, g2, α, β])(3.42)483.4. Effective Capacity with Atmospheric Turbulence and Misalignment FadingI3 = FGG,pγy (γψ)g2Γ(α)Γ(β)G4,02,4[αβγψAoλxγp∣∣∣∣∣ g2 + 1, ee+2 + 1ee+2 , g2, α, β](3.43)andI4 = FGG,pγx (γψ)g2Γ(α)Γ(β)G4,02,4[αβγψAoλyγp∣∣∣∣∣ g2 + 1, ee+2 + 1ee+2 , g2, α, β](3.44)where γψ is the cutoff SNR for the joint power adaptation over the Gamma-Gamma turbulence fadingchannels with pointing error. By using a similar method to derive (3.38) and (3.39), the asymptotichigh SNR EC for the joint power adaptation over the Gamma-Gamma turbulence and misalignmentfading channels is obtained asEjoint,asymc,pol = −2θlog[g2∏4j=1,j 6=k Γ(Ω(j)−Ω(k))Γ(α)Γ(β)∏2j=1 Γ(Π(j)−Ω(k))]− κθlog(α2β2γ2φA2oλxλy)+2κθlog(R∆L2q∆f)+0.2κlog10 exp(θ)(10 log10 Pt)(3.45)where {κ, k} = {min{η1, g2, α, β}, arg min{η1, g2, α, β}}, Π = [g2 + 1, η1 + 1], and Ω = [η1, g2, α, β].Eq. (3.45) reveals that for a non-stringent statistical-delay constraint, high SNR EC of joint poweradaptation over a Gamma-Gamma turbulence-misalignment fading channel increases 0.2κlog10 exp(θ)TfBbits/s/Hz as the average transmitted optical power increases 1 dB. Under the condition of wzeq > 2σs,κ = min{η1, g2, α, β} = η1, and the increment of the high SNR EC of joint power adaptation inthe non-stringent statistical-delay constraints becomes independent of the pointing error. Assumingwzeq > 2σs and applying [146, eq. (7.811.4)] to (3.30), the stringent statistical-delay constraint limitedEC is evaluated aslimθ→∞Ejointc,pol(θ)= 2TfB log2[Γ2(α)Γ2(β)(g2 − 1/2)2Ao√λxλyγpg4Γ2(α− 1/2)Γ2(β − 1/2)αβ +12(g2 − 1/2)2Γ(α− 1)Γ(β − 1)Γ(α)Γ(β)√λx/λyg2Γ(g2)(g2 − 1)Γ2(α− 1/2)Γ2(β − 1/2)+12(g2 − 1/2)2Γ(α− 1)Γ(β − 1)Γ(α)Γ(β)√λy/λxg2Γ(g2)(g2 − 1)Γ2(α− 1/2)Γ2(β − 1/2)].(3.46)Eq. (3.46) facilitates us to evaluate the stringent statistical-delay constraints limited EC of the coherentPOLMUX OWC with joint power adaptation for different atmospheric turbulence channel parameters,pointing error parameters, and/or, polarization control errors. In the asymptotic high SNR regime,the performance gap (in dB) between the joint and independent power adaption techniques in theGamma-Gamma turbulence and misalignment fading is defined asSNRGG,pointingdiff , γp,1Ind,req(dB)− γp,1Joint,req(dB) (3.47)493.5. Numerical Resultswhere γp,1Ind,req and γp,2Joint,req denote the required SNRs (in dB) in order to achieve a given EC in thestrict delay constraints and high SNR regime over Gamma-Gamma turbulence and misalignment fadingchannel with independent and joint power adaptation techniques, respectively. Comparing (3.46) and(3.40) in the asymptotic high SNR regime, the performance gap (in dB) between the independent andjoint power adaptation schemes in the Gamma-Gamma turbulence and misalignment fading is obtainedasSNRGG,pointingdiff ≈ 10 log10(Γ2(α− 1)Γ2(β − 1)(α− 1)(β − 1)(g2 − 1/2)2g2Γ2(α− 1/2)Γ2(β − 1/2)(g2 − 1)). (3.48)We can show from (3.48) that the performance gap between (3.46) and (3.40) increases for the decreasingvalues of g, α, and/or β. Consequently, for a coherent POLMUX OWC system, joint power adaptationscheme is more efficient in order to support stringent the statistical-delay constraints compared toan independent power adaptation scheme when the turbulence fading becomes strong and/or jittervariance of the pointing error increases.3.5 Numerical ResultsIn this section, we validate our developed EC expressions with the exact EC of both independentand joint power adaptation schemes obtained from numerical integrations. We consider a light fogoptical channel with 11.5 dB/Km path loss in strong Gamma-Gamma turbulence with α = 2.04,β = 1.10, and in weak Gamma-Gamma turbulence with α = 4.43, β = 4.39. We make the followingassumptions on the system parameters: R = 0.75 Amp/W, Tf = 10−6s, and B = 108 Hz. Moreover,we consider that the diameters of both apertures at the transmitter and receiver are 8 cm, the spatialseparation between two apertures is 30 cm, the divergence angle of the transmitted optical beam is 0.1milli-radian, and the link range is 500 meter to 4 Km.Figure 3.1 presents EC (normalized by TfB) of the coherent POLMUX OWC systems with in-dependent and joint power adaptation schemes over a Gamma-Gamma turbulence fading channel byconsidering accurate alignment between the transmitter and receiver, α = 4.43, β = 4.39, γp = 30 dB,and δ = 0o. Figure 3.1 depicts an excellent agreement between the developed EC expressions with theexact EC for all the considered cases. From this figure we observe that when the QoS-exponent is small(i.e., the statistical-delay constraint is loose), both independent and joint power adaptation schemesachieve similar EC performance. Such a result is expected because as the QoS-exponents becomesmall, the considered system can tolerate long delay, and consequently, both independent and jointpower adaptation schemes can achieve the maximum traffic arrival rate. On the other hand, both inde-pendent and joint power adaptation schemes respectively approach a constant channel capacity givenby (3.18) and (3.31) as the QoS-exponent increases. Figure 3.1 shows that the joint power adaptationscheme outperforms the independent power adaptation scheme in the large QoS-exponents. Therefore,joint power adaptation technique is more efficient compared to the independent power adaptation tech-nique in order to support the large QoS-exponents (i.e., stringent statistical-delay constraints) over thefading channels. For the completeness of comparison, EC of a conventional water-filling (WF) powerallocation is also presented in Figure 3.1. The WF power allocation offers an opportunity to take theadvantage of the randomness of the channel and it is conventionally used in order to maximize the503.5. Numerical Results10−5 10−4 10−3 10−2 10−11717.51818.51919.5θNormalized Effective Capacity (bits/s/Hz) Exact,Joint Power AdaptationApprox,Joint Power AdaptationExact,Independent Power AdaptationApprox,Independent Power AdaptationWF Power AllocationStringent Delay Limited Effective CapacityQoS-exponent, Figure 3.1: EC comparison between the coherent POLMUX with joint and independent power adap-tation schemes over a Gamma-Gamma turbulence channel without pointing error (α = 4.43, β = 4.39)and with γp = 30 dB, 0o polarization control error, and perfect phase noise compensation.10-5 10-4 10-3 10-2QoS-exponent, θ1515.51616.51717.51818.51919.5Normalized Effective Capacity (bits/s/Hz)With ideal phase noise compensationNon-ideal phase noise compensation with σ∆φ=100Non-ideal phase noise compensation with σ∆φ=200Non-ideal phase noise compensation with σ∆φ=300Figure 3.2: EC of coherent POLMUX with independent power adaptation scheme over a Gamma-Gamma turbulence channel (α = 4.43, β = 4.39) with γp = 30 dB, 0o polarization control error, andimperfect phase noise compensation.513.5. Numerical Results10-5 10-4 10-3 10-2QoS-exponent, θ17.417.617.81818.218.418.618.81919.219.4Normalized Effective Capacity (bits/s/Hz)With ideal phase noise compensationNon-ideal phase noise compensation with σ∆φ=100Non-ideal phase noise compensation with σ∆φ=200Non-ideal phase noise compensation with σ∆φ=300Figure 3.3: EC of coherent POLMUX with joint power adaptation scheme over a Gamma-Gammaturbulence channel (α = 4.43, β = 4.39) with γp = 30 dB, 0o polarization control error, and imperfectphase noise compensation.-12 -10 -8 -6 -4 -2 0 2 4Average Transmitted Optical Power, Pt (dbm)51015202530Normalized Effective Capacity (bits/s/Hz)Coherent POLMUX with Joint Power AdaptationCoherent POLMUX with Independent Power Adaptationα=2.04,β=1.10α=4.43,β=4.39δ=30oδ=0o & 10oδ=30oδ=0o & 30oδ=0o & 10oδ=30oFigure 3.4: Stringent statistical-delay constrained EC comparison between the coherent POLMUXwith joint and independent power optimizations in Gamma-Gamma turbulence without pointing errorand with perfect phase noise compensation.523.5. Numerical Results-12 -10 -8 -6 -4 -2 0 2 4Average Transmitted Optical Power, Pt (dbm)10121416182022242628Normalized Effective Capacity (bits/s/Hz)Coherent POLMUX with Joint Power OptimizationCoherent POLMUX with Independent Power Optimizationα=4.43,β=4.39,g=1.095α=4.43,β=4.39,g=6Figure 3.5: Stringent statistical-delay constrained EC comparison between the coherent POLMUXwith joint and independent power optimizations in misalignment-weak turbulence fading channel withδ = 0o, Ao = 0.75, and perfect phase noise compensation.−12 −10 −8 −6 −4 −2 0 2 4101520253035Average Transmitted Optical Power, Pt (dbm)Normalized Effective Capacity (bits/s/Hz) Coherent POLMUX with Joint Power OptimizationCoherent POLMUX with Independent Power Optimizationα=2.04,β=1.10,g=1.095α=2.04,β=1.10,g=6Figure 3.6: Stringent statistical-delay constrained EC comparison between the coherent POLMUXwith joint and independent power optimizations in misalignment-strong turbulence fading channelwith δ = 0o, Ao = 0.75, and perfect phase noise compensation.533.5. Numerical Results-8 -6 -4 -2 0 2 4 6 8 10Average Transmitted Optical Power, Pt (dbm)51015202530Normalized Effective Capacity (bits/s/Hz)With ideal phase noise compensationNon-ideal phase noise compensation with σ∆φ=100Non-ideal phase noise compensation with σ∆φ=200Non-ideal phase noise compensation with σ∆φ=300Joint power adaptationIndependent power adaptationFigure 3.7: Stringent statistical-delay constrained EC comparison between the coherent POLMUX withjoint and independent power optimizations in strong Gamma-Gamma turbulence with 0o polarizationcontrol error and imperfect phase noise compensation.6 7 8 9 10 11 12 13 14 150123456789Normalized Beam Width, wz/rPower Penalty in dBm α=2.04,β=1.10,Required effctive capacity=10 bits/s/Hzα=2.04,β=1.10,Required effctive capacity=20 bits/s/Hzα=4.43,β=4.39,Required effctive capacity=10 bits/s/Hzα=4.43,β=4.39,Required effctive capacity=20 bits/s/HzFigure 3.8: Power penalty factor (in dBm) of the independent power adaptation scheme with respect tothe joint power adaptation scheme in the stringent statistical-delay constraints with σs/r = 1, δ = 0o,and perfect phase noise compensation.543.5. Numerical Results0.5 1 1.5 2 2.5 3 3.5 4Link distance (in Km)0510152025303540Normalized Effective Capacity (bits/s/Hz)Joint power adaptation with 0o polarization control errorJoint power adaptation with 10o polarization control errorJoint power adaptation with 30o polarization control errorIndependet power adaptation with 0o polarization control errorIndependet power adaptation with 10o polarization control errorIndependet power adaptation with 30o polarization control errorα=2.04,β=1.10α=4.43, β=4.39Figure 3.9: Stringent statistical-delay constrained EC comparison between the coherent POLMUXwith joint and independent power optimizations in Gamma-Gamma turbulence with 0o polarizationcontrol error and perfect phase noise compensation for different link distances.Shannon capacity over the fading channels. In particular, WF power allocation allocates more transmitpower when the channel condition is good, reduces transmit power when the channel condition is poor,and suspends the transmission when the received SNR falls below a certain threshold. It is obviousfrom Figure 3.1 that the EC of a coherent POLMUX OWC with a WF power allocation drasticallyreduces at large QoS-exponents. Consequently, the conventional WF power allocation is not suitablefor the coherent POLMUX OWC in order to support stringent statistical-delay constraints over thefading channels.Figures 3.2 and 3.3 illustrate EC (normalized by TfB) of the coherent POLMUX OWC systemswith independent and joint power adaptation schemes, respectively, over a weak Gamma-Gammaturbulence fading channel considering the perfect alignment between the transmitter and receiver, andnon-ideal phase noise compensation mechanism. From both figures we observe that EC of coherentPOLMUX system deteriorates due to a non-ideal phase noise compensation scheme. In particular, theperformance degradation is more noticeable for large QoS exponents when the standard deviation ofuncompensated phase noise is large. This is because in order to support the large QoS exponents (i.e.,the tight statistical-delay constraints), constant service rate is required. However, the uncompensatedphase noise with large standard deviation results in more fluctuation (i.e., larger variance) of the servicerate. It is known that a service process with larger variance can support less strict statistical-delayconstraints. As a result, the uncompensated phase noise with large standard deviation makes thesystem support strict statistical-delay constraints with (relatively) poor EC. This result suggests theimportance of having a proper phase noise compensation mechanism in order to support the strictstatistical-delay constraints in a coherent POLMUX OWC system. Also, both figures 3.2 and 3.3553.5. Numerical Resultsillustrate when the uncompensated phase noise standard deviation is less than 10o, there is little effectof the phase noise on the EC performance of both power adaptation schemes. With the followingsteps, one can determine the tolerable standard deviation of the phase noise compensation error forcertain delay-QoS guarantee. Specifically, figures 3.2 and 3.3 provide the achievable EC with respectto the QoS-exponent, θ, for the given value of σ∆φ. By using such EC, one can obtain a plot of thedelay-bound violation probability versus QoS-exponent, θ, for the given value of σ∆φ. In this way,one can obtain multiple (parallel) delay-bound violation probability versus QoS-exponent plots, andeach plot corresponds to a certain value of σ∆φ. Subsequently, from these (parallel) plots, one canselect the maximum value of σ∆φ that would give the desired delay-bound violation probability. Sucha maximum σ∆φ will be the tolerable standard deviation of the phase noise compensation error for therequired delay-QoS constraint.Figure 3.4 compares the stringent statistical-delay constrained EC (normalized by TfB) of thecoherent POLMUX OWC with joint and independent power adaptation schemes over a 2 Km Gamma-Gamma turbulence fading channel with channel parameters α = 2.04, β = 1.10, and α = 4.43, β =4.39, assuming a perfect alignment between the transmitter and the receiver. Figure 3.4 illustratesthat in the stringent statistical-delay constraints case, coherent POLMUX OWC with joint poweradaptation scheme outperforms coherent POLMUX OWC with independent power adaptation scheme.For instance when α = 2.04, and β = 1.10, at −4 dBm average transmitted optical power coherentPOLMUX OWC with joint power adaptation scheme supports the stringent statistical-delay constraintswith 20 bits/s/Hz service rate. On the other hand, at the same average transmitted optical power,coherent POLMUX OWC with independent power adaptation scheme supports the stringent statistical-delay constraints with 15 bits/s/Hz service rate. However, the EC performance gap between the jointand independent power adaptation schemes is significantly reduced in the weak turbulence fading. Forinstance in a weak Gamma-Gamma turbulence fading with α = 4.43, β = 4.39, at −4 dBm averagetransmitted optical power, coherent POLMUX with joint and independent power adaptation schemessupport the stringent statistical-delay constraints with 23.12 bits/s/Hz and 22.5 bits/s/Hz service rate,respectively. In addition, we observe that for a given fading channel, the performance gap betweenthe coherent POLMUX with joint and independent power adaptation schemes remains constant as theaverage transmitted power increases. This result is expected because we have analytically shown that inthe stringent statistical-delay constraints, both coherent POLMUX with joint and independent poweradaptations gain 0.66 bits/s/Hz as the average transmitted optical power increases 1 dB. Finally, weobserve from figure 3.4 that the stringent statistical-delay constrained EC of the coherent POLMUXis not significantly affected by a polarization control error within 10o.Figures 3.5 and 3.6 illustrate the stringent statistical-delay constraint limited EC performance of thejoint and independent power adaptation schemes in different Gamma-Gamma turbulence fading andpointing error scenarios for 2 Km link. In both figures 3.5 and 3.6 we have used g > 1 or wzeq > 2σs,and we observe that the ECs in figures 3.4, 3.5, and 3.6 have identical increment for 1 dB increase of theaverage transmitted optical power. Such an observation depicts that an equivalent beamwidth at thereceiver larger than 2σs makes the EC increment independent of the pointing error, as observed fromour asymptotic analysis. Note that, without violating the eye-safety standard, the average transmitpower budget of a practical OWC system can be increased by choosing specific wavelength and laser563.5. Numerical Resultsclass (see [33, Table 1.6]). However, from both figures 3.5 and 3.6 it is obvious that for a giventurbulence and pointing error parameters, the performance gap between the joint and independentpower adaptation schemes can not be reduced by increasing the average transmitted power. Thisis because in the stringent statistical-delay constraints, both power adaptation techniques over theturbulence-misalignment fading channels achieve 0.66 bits/s/Hz EC increment for 1 dB increase ofthe average transmitted optical power, as depicted from our asymptotic analysis. We also observethat the performance gap between the joint and independent power adaptation schemes increases asthe turbulence fading becomes strong and/or pointing error becomes severe, as expected from ourasymptotic analysis. For example, the largest performance gap (around 10 dBm) is observed whenα = 2.04, β = 1.10, and g = 1.095, and the smallest performance gap (around 1 dBm) is observedwhen α = 4.43, β = 4.39, and g = 6.Figure 3.7 compares the stringent statistical-delay constrained EC (normalized by TfB) of thecoherent POLMUX OWC with joint and independent power adaptation schemes over a 2 Km strongGamma-Gamma turbulence fading channel assuming a perfect alignment between the transmitter andthe receiver, and non-ideal phase noise compensation mechanism. From this figure we observe thatthe uncompensated phase noise reduces EC of both joint and independent power adaptation schemes.However, in the stringent statistical-delay constraints, joint power adaptation scheme outperformsindependent power adaptation scheme even in the presence of uncompensated phase noise. Moreover,independent power adaptation scheme is more vulnerable to the large uncompensated phase noisecompared to the joint power adaptation scheme. Figure 3.7 also depicts that a uncompensated phasenoise with a standard deviation less than 10o does not have a significant impact on the EC of bothpower adaptation schemes. Finally we observe that in the stringent statistical-delay constraints, EC ofboth power adaptation schemes offers the same increment for per dB increase of the average transmittedoptical power regardless of the phase noise. This is because phase noise related terms in both (A.8)and (B.7) do not depend on the average transmitted optical power.Figure 3.8 illustrates the power penalty factor of the independent power adaptation scheme withrespect to the joint power adaptation scheme in order to maintain a target stringent statistical-delayconstrained EC for different values of normalized beamwidth. From this figure we observe that fora given beamwidth (and/or given jitter variance), the power penalty factor increases when the at-mospheric turbulence fading is strong. This result is expected since in figures 3.5 and 3.6 we havedemonstrated that for a given value of g as the atmospheric turbulence becomes strong, the perfor-mance gap between joint and independent power adaptation schemes becomes large. Figure 3.8 alsodepicts that for a given turbulence fading the power penalty factor of the independent power adap-tation scheme decreases as the beamwidth increases. Such an observation is also expected since for agiven jitter variance, the value of g increases as the beamwidth increases. Figures 3.5 and 3.6 illustratethat for the given atmospheric turbulence parameters, the performance gap between the independentand joint power adaptation schemes gets reduced as the value of g increases. However, it is obviousfrom figure 3.8 that the power penalty factor of the independent power adaptation scheme from thejoint power adaptation scheme for a given turbulence fading can not be further reduced by increasingbeamwidth after a certain value. Such an observation can be explained by the following argument. Thelarge beamwidth mitigates the pointing error, and eventually, in large beamwidth, the performance gap573.6. Chapter Summarybetween the joint and independent power adaptation schemes is mainly contributed by the atmosphericturbulence fading. Consequently, such a performance gap can not be reduced by further increasing thebeamwidth.Figure 3.9 illustrates stringent statistical-delay constraint limited EC of the independent and jointpower adaptation schemes over a strong Gamma-Gamma turbulence fading channel for different linklengths. Without loss of generality, in this numerical result we have selected the average transmitpower, P t = 4 dBm12. Figure 3.9 depicts that EC of both power adaptation schemes reduces as thelink length increases which is expected. We also observe from this figure that the joint power adaptationscheme outperforms the independent power adaptation scheme for all link lengths, especially in thestrong turbulence fading regime. Figure 3.9 illustrates that for a given polarization control error, ECdecreases almost linearly with respect to the link length. This result suggests that increasing link lengthhas a little impact on the polarization de-multiplexing. Such an observation can be supported by thefollowing argument. For an atmospheric turbulence channel, the root mean square of depolarizationis given by σδ =√C2nλ7/6L2/32√2pi3/4l3/2where C2n, λ, L, and l are index of refraction structure parameter,wavelength of transmitted optical signal, link length, and correlation length [176, eq. 6]. Typicalvalues of C2n, λ, and l are 2 × 10−14m−2/3, 1550 nm, and 10 cm, respectively. By using such values,we obtain σδ = 7.0384 × 10−12 rad for L = 0.5 Km and σδ = 2.8154 × 10−11 radian for L = 4 Km.Consequently, increasing link length has a negligible impact on the depolarization. In other words,polarization de-multiplexing is not significantly affected by increasing the link length.The EC displayed in the aforementioned numerical results is obtained by considering that thesystem experiences i.i.d. block fading (see the assumption A1 of Section 3.3.1). If such a condition isnot satisfied, it can be concluded from (2.31) that the EC will be reduced. Therefore, for the scenariowhere the aforementioned condition does not hold, the numerical results of this chapter will be theupper bound of the EC achieved by the independent and joint power adaptation techniques.3.6 Chapter SummaryIn this chapter, the EC of a coherent OWC system employing POLMUX and transmit poweradaptation has been investigated. Closed-form expressions of achievable EC have been developedby considering Gamma-Gamma turbulence fading and zero-boresight pointing error. Our numericalresults have showed that when the polarization control error and/or the variance of phase noise areless than 10◦, the resultant degradation of EC is small. In addition, some insights have been revealedby performing the asymptotic analysis.12In this numerical result, we select the maximum link length as 4 Km. This is because with the given transmit powerand path loss exponent, the average SNR becomes very small for a link length beyond 4 Km.58Chapter 4Delay-QoS Aware Joint AdaptiveModulation and Power Allocation forMultichannel Coherent OWC SystemIn Chapter 3, we analyzed the achievable throughput of a dual-channel coherent OWC by con-sidering statistical-delay-constraint. However, we did not consider any restriction on the transmittedconstellations over the OWC channels. For practical scenario, discrete rate adaptation is preferred.As a result, in this chapter, we extend the previous chapter’s analysis by considering the practicalmodulation schemes. In particular, we develop AM and power allocation for a coherent OWC systememploying multiple parallel optical beams. The organization of this chapter is given as follows. InSection 4.1, we provide the accomplished works and research contributions. In Section 4.2, we providethe description of the system model along with the considered assumptions. In Section 4.3, we discussthe development of QoS-aware AM and power allocation for dual-channel coherent OWC subject to theaverage transmit power constraint. In Section 4.4, we develop AT schemes for multichannel coherentOWC with peak transmit power constraint. Section 4.5 provides some illustrative numerical results,and Section 4.6 provides some concluding remarks.4.1 Accomplished Works and Research ContributionsThe contributions of this chapter are summarized as follows.1. In the first part of this chapter, we propose statistical-delay-QoS aware AM and power allocationfor a dual-channel coherent OWC system over the Gamma-Gamma turbulence channels. Differentpractical coherent OWC systems, such as coherent POLMUX and 2× 2 coherent multiple-inputmultiple-output OWC, can be modeled as the dual-channel coherent OWC systems. For givenstatistical-delay constraints and target BER requirements, we formulate the proposed AM andpower allocation as an optimization problem of maximizing effective spectral efficiency (ESE)subject to transmit power constraints. Although the sources of energy for OWC systems arenot limited, due to the practical operation of laser transmitter and eye safety standards foroutdoor OWC communications, the transmission power of an OWC system is not unbounded[98, 189]. Consequently, average and/or peak transmit power constraints are employed for theoutdoor OWC communications [65]. Unlike RF communications, the goal of our power allocationscheme is not to reduce energy consumption at the transmitter by minimizing the transmit power.Our objective is to efficiently allocate the total available output power of a laser transmitterbetween two optical channels, based on the channel fading gains and delay-QoS requirements594.1. Accomplished Works and Research Contributionsof the transmitted traffic, so that the considered OWC system can achieve an improved ESEover the atmospheric turbulence channel. Towards this objective, we present independent andjoint channel optimizations by considering average transmit power constraint. In an ICO scheme,modulation order and transmit power of each channel are adapted based on the CSI of theindividual optical channel. In a JCO scheme, modulation order and transmit power of bothoptical channels are proposed to adapt jointly if both optical channels have instantaneous SNRslarger than a certain threshold. We develop closed-form ESE expressions for both ICO and JCObased AT schemes subject to the average transmit power constraints. Our analysis reveals thefollowing insights: (i) at the loose statistical-delay constraint, both ICO and JCO achieve ESEsimilar to the average spectral efficiency (ASE) of the conventional variable-power variable-rate(VPVR) AT scheme and (ii) at the stringent statistical-delay constraint, ICO approaches a fixed-rate channel inversion scheme. In addition, we explain the required computational complexityof our proposed AT schemes. Numerical results demonstrate that our proposed AM and powerallocation achieve significant larger ESE compared to the conventional AT schemes in the strictstatistical-delay constraints. Numerical results also confirm that the proposed JCO achieveslarger ESE in strong turbulence fading and strict statistical-delay constraints. However, theperformance gap between ICO and JCO based AT schemes is reduced as turbulence fadingbecomes weak and/or statistical-delay constraint becomes loose.2. In the second part of this chapter, we investigate discrete-rate AT schemes for improving ESE ofthe coherent OWC system equipped with multiple parallel optical beams subject to peak transmitpower constraint13. We investigate the following techniques, namely, ICO, JCO, and ICO/BS inorder to perform AT over the multiple parallel optical beams. Our analysis and simulation resultsreveal the following three insights: (i) activating only suitable optical beams and adapting theirtransmission parameters significantly improve ESE in the strict statistical-delay constraint; (ii)at both loose and strict statistical-delay constraints, equal power allocation among the suitableoptical beams provides near optimal ESE in high SNR regimes; and (iii) allocating all the powerto the strongest optical beam provides near optimal ESE at the strict statistical-delay constraintand low SNR regimes. We also provide the required computational complexity of the AT schemeswith peak transmit power constraint.Remark on transmit power allocation: In this work, we consider the sum average and the sum peak(i.e., instantaneous) transmit power constraints. An explanation of considering a sum average transmitpower constraint for the dual-channel OWC system is provided in Section 3.3.2. In what follows, weexplain the use of the sum peak transmit power constraint for an OWC system with multiple paralleloptical beams. For the purpose of clarification, we consider two different scenarios.− As depicted from the assumption A3 of the next section, multiple parallel optical beams canbe generated from the physically separated multiple apertures. We first consider a hypothetical13Compared to the average transmit power constraint, peak or instantaneous transmit power constraint is more usefulfor maintaining the prescribed safety standard. In particular, when power adaptation subject to average power constraintis performed, transmit power can (significantly) increase in order to combat the deep fading. However, such a hightransmit power may violate the safety standard. By using peak transmit power constraint, such an incident can beavoided.604.2. System Model and Assumptionsscenario where no power limitation is imposed due to eye-safety, i.e., arbitrary large power canbe transmitted from each aperture. However, even in such a hypothetical scenario, the totaltransmit power can not be extremely large. From [190] it is evident that for an OWC laser,such as a distributed feed back (DFB) laser which is used for 1550 nm wavelength, high drivingcurrent is required in order to generate high output laser power. Nevertheless, a certain value ofhigh driving current for a certain period of time results in large thermal power dissipation andincreased heating which eventually affects life time of the lasers. Therefore, extreme high outputpower of a laser impacts the life time of the laser. On the other hand, when the optical beamfrom each aperture experiences independent fading, some optical beams can suffer from severeturbulence fading. In such a case, allocating transmit power only to the suitable optical beamssubject to the sum power constraint can improve the instantaneous throughput. Therefore, evenwhen eye-safety is not an issue, transmit power allocation subject to the sum power constraint isstill advantageous for efficiently exploiting the scintillation over the parallel optical beams.− We now consider a more realistic scenario where eye-safety issue exists, the transmitter hasmultiple apertures, and the parallel optical beams from each aperture experience independentchannel fading. If the total output power of the laser transmitter is less than or equal to thestandard eye-safety limit, the sum power constraint is meaningful in order to efficiently allocatethe available transmit power among the parallel optical beams. For example, the eye-safety limitof the class 3B laser is 500 mW [33]. Accordingly, when the total output power of the lasertransmitter is less than or equal to 500 mW, transmit power allocation among the parallel opticalbeams subject to the sum power constraint is beneficial. Moreover, the sum transmit powerconstraint is usually imposed for conducting fair performance comparison among the systemswith different number of apertures. Accordingly, the sum transmit power constraint has practicalutilizations, indeed.4.2 System Model and AssumptionsFigure 4.1 shows the block diagram of the considered system model. From a given data source, thetraffic arrives in the transmitter at a constant arrival rate. Such traffic is grouped into multiple framesat the data link layer and stored at a transmit buffer. Each frame is decomposed into multiple parallelbit streams that are transmitted over the parallel optical channels. At a given transmission slot (TS),AMs are applied to the parallel bit streams. The modulated symbols drive an optical modulator inorder to yield coherent modulated parallel optical carriers. Finally, adaptive power control is appliedin order to adjust the transmit power of the modulated optical carriers. At the receiver, coherentdetection and demodulation are applied on each optical carrier. Following this stage, the detectedinformation bits are stored in a receive buffer and data sink. The modulation order and the transmitpower for each optical carrier are adapted at each TS based on the statistical-delay-QoS requirementsof the transmitted traffic, target BER requirements, and CSI obtained from the receiver. In the systemmodel, we consider that the duration of a typical TS is roughly same as the channel coherence time (onthe order of ms). Consequently, the channel gains remain constant over a given TS, and independentlyvary from one TS to another TS. We denote the total average transmit power of the considered system614.2. System Model and AssumptionsFigure 4.1: System block diagram.as P t, and without loss of generality, we assume that the average transmit power is equally dividedbetween both channels. Following [138], the instantaneous SNR (per symbol) of the i-th optical channelat the t-th TS is written asγi , γi[t] = γcIi[t], ∀i ∈ {1, 2} (4.1)where γc is the average SNR defined as γc =R∆L2qB P t. Here, Ii[t] is the atmospheric turbulence fadingcoefficient of the i-th channel at the t-th TS, and the other symbols are defined in Chapter 2 of thisthesis. In an OWC system, the duration of a typical frame in data link layer is on the order of microseconds (µs) [70]. Consequently, a given TS contains a large number of frames, and similar modulationorder and transmit power are selected for all the frames. Therefore, all the frames in a given TS aretransmitted by using the same transmission rate. However, the transmission rate independently variesfor different TSs. Based on [191, eq. 14], we consider the following conditional BER expression forM -ary modulation over the i-th optical channel, ∀i ∈ {1, 2}.BERt ≈ c1 exp(− c2γiµi (θ,γ)M c3i (θ,γ)− 1). (4.2)In (4.2), θ is QoS-exponent; BERt is the target BER; µi (θ,γ) is the statistical-delay-QoS aware trans-mit power adaptation factor (ratio of the allocated power to average transmit power) for the i-thoptical channel; Mi(θ,γ) is the selected modulation order based on instantaneous SNR and statistical-624.2. System Model and Assumptionsdelay-QoS requirements for the i-th optical channel; and c1, c2, and c3 are the modulation dependentparameters. In particular, we have (c1, c2, c3) = (0.2, 1.6, 1) [191, eq. 9], (c1, c2, c3) = (0.05, 6, 1.9) [191,eq. 11], (c1, c2, c3) = (0.2, 1.85, 2.19) [63, eq. 7] forM -ary quadrature amplitude modulation (M -QAM),M -ary phase shift keying (M -PSK), and M -ary pulse amplitude modulation (M -PAM), respectively.Eq. (4.2) provides approximate BER expression. Nevertheless, such a BER expression is invertible, andis useful for designing delay-QoS aware AM and power allocation. Moreover, such a BER expression ishighly accurate for BER smaller than 10−3. Therefore, we consider BERt < 10−3 in our system model.From (4.2), M c3i (θ,γ) = 1 + Kµi (θ,γ) γi where the factor K is given by K = − c2log(BERt/c1) . At thet-th TS, the transmission rate of a frame (in bits/frame unit) of the i-th OWC channel by consideringcontinuous rate adaptation and BER constraint is obtained as [161, eq. 16]Ri[t] =TfBc3log2 (1 +Kµi (θ,γ) γi) , ∀i ∈ {1, 2} (4.3)where Tf is the frame duration. Due to discrete rate adaptation in practice, (4.3) provides an upperbound of the practical transmission rate. We will use (4.3) in order to develop JCO based AM andpower allocation in Section 4.3. We consider the following assumptions:A1: The data traffic has a constant arrival rate at the transmitter. The constant arrival rate ofthe data at the transmitter is a standard assumption for the statistical-QoS provision over the fadingchannels [161, 171–173]. The assumption of the constant data arrival rate can be justified in thepractical applications. For example, the channel coherence time of OWC communications is on theorder of ms, and the typical timescale of a video source rate adaptation is on the order of seconds[192]. Hence, the traffic arrival rate remains constant over a large number of independent channelfading realizations. We also emphasize that in many practical applications, data arrives to the OWCsystem from the optical fiber based backhaul network. As such, it is possible to maintain a constantdata arrival rate to the OWC transmitter.A2: The accumulated phase noise introduced by the atmospheric turbulence and/or lasers can betracked and corrected almost perfectly following the photodetection. In particular, carrier phase error(CPE) is present during the detection of transmitted symbols with imperfect phase noise compensation.CPE results in mathematically involved BER expressions for higher order two-dimensional coherentmodulations [193]. Due to such involved BER expressions, it is challenging to develop statistical-delay-QoS aware joint AM and power allocation with imperfect phase noise compensation at the re-ceiver. Consequently, we assume the perfect phase noise compensation which ensures the mathematicaltractability of the ensuing AM and power allocation analysis. We emphasize that the assumption ofperfect phase noise compensation can be satisfied in the practical coherent OWC systems with thePLL based phase noise compensation scheme, as explained in Section 3.2.1 of this thesis. Moreover,the assumption of accurate phase noise compensation for coherent OWC system was experimentallyverified in [178] as well.A3: In each TS, the parallel optical channels experience independent channel fading co-efficients.Such an assumption is made for performing AT, and it can be satisfied in practice. Particularly, theparallel optical beams can be generated by using multiple apertures, and uncorrelated fading amongthese optical beams can be ensured with an inter-aperture spacing of 20 cm to 30 cm [148]. In addition,the complete knowledge of the channel statistics and instantaneous CSI is available at the transmitter634.3. QoS-Aware AM and Power Allocation for Dual-Channel System with Average Power Constraintso that the transmitter can adapt the transmission parameters. As explained in Section 3.3.1, such anassumption can also be satisfied for the practical OWC systems.4.3 QoS-Aware AM and Power Allocation for Dual-ChannelSystem with Average Power ConstraintFor a given steady-state QLB violation probability constraint, our objective is to maximize thesupportable arrival rate to the transmit buffer of the figure 4.1 by performing discrete-rate AT overboth parallel optical beams. Towards this objective, in what follows we present ICO and JCO thatmaximize the achievable ESE for a given statistical-QoS constraint.4.3.1 ICO with Average Transmit Power ConstraintIn ICO, the transmission parameters of each channel of a dual-channel coherent OWC system areindependently adapted subject to the average transmit power per channel constraint. In this section,we develop AM and power allocation for a dual-channel coherent OWC system by employing an ICOapproach. We assume that for each optical channel, total N number of constellations are available, andwe denote Mi(θ,γ) as the assigned constellation for the i-th channel. We divide the range of receivedSNR for each channel into N non-overlapping regions, and we associate each region with a uniqueconstellation. For a given target BER, the constellation selection and transmit power adaptation ruleis given as14select Mi(θ,γ) = 2n and µi(θ,γ) =2nc3 − 1Kγiif γi,n ≤ γi < γi,n+1, n = 1, 2, ·, ·, N, ∀i ∈ {1, 2}.(4.4)In (4.4), {γi,n} are the region boundaries. We also select γi,N+1 = ∞, and µi(θ,γ) = 0 if γi < γi,1,∀i ∈ {1, 2}. The region boundaries for each channel are determined by maximizing ESE of the channelsubject to average transmit power per channel constraint. The region boundary selection problem forthe i-th channel is given bymin{γi,n}N∑n=0∫ γi,n+1γi,nexp(−θTfBn)fγi(γ) dγs.t.N∑n=1∫ γi,n+1γi,n2nc3 − 1kγfγi(γ) dγ = 1γi,0 < γi,1 < γi,2 < ·· < γi,N <∞(4.5)14In (4.4), we consider discrete rate adaptation. In this case, the transmission rate of a frame over the i-th opticalchannel is given by Ri = TfBni where ni ∈ {1, 2, ·, ·, N}. In order to satisfy the target BER constraint for discrete rateadaptation, we consider µi(θ,γ) =2nic3−1Kγi, ∀i ∈ {1, 2}. Note that, {µi(θ,γ)} depends on the selected constellations.However, selection of a constellation is determined by jointly considering (4.4) and (4.7). Consequently, the value ofQoS-exponent, θ, influences the selection of constellation and the transmit power adaptation factor.644.3. QoS-Aware AM and Power Allocation for Dual-Channel System with Average Power Constraintwhere γi,0 = 0 and fγi(γ) is the PDF of the instantaneous SNR of the i-th channel. The Lagrangianfunction of (4.5) is given asL =∫ γi,10fγi(γ) dγ +N∑n=1∫ γi,n+1γi,nexp(−θTfBn)fγi(γ) dγ+ λi(N∑n=1∫ γi,n+1γi,n2nc3 − 1kγfγi(γ) dγ − 1)+N−1∑n=1νn (γi,n+1 − γi,n)− γi,1(4.6)where λi, {νn}, and are the Lagrangian multipliers. By using the complementary slackness of theKarush-Khun-Tucker (KKT) condition, we can show that = 0 and {νn} = 0. The local minimizer of(4.5) can be obtained by the following KKT condition:∂L∂γi,n= 0=⇒ γi,n =λi(2nc3 − 2(n−1)c3)K(2−η(n−1) − 2−ηn) , n = 1, 2, · · · , N(4.7)where η =θTfBc3 ln 2. The value of λi is obtained by satisfying the average transmit power per channelconstraint which is given asN∑n=12nc3 − 1K(Eγi,n [γ−1]−Eγi,n+1 [γ−1])= 1 (4.8)where Eγo[γ−1]=∫∞γo1γ fγi(γ) dγi. By using (4.1), (2.15), [184, eq. 07.34.03.0605.01], and [146, eq.7.811.4], we can write (4.8) asN−1∑n=12nc3 − 1KΓ(α)Γ(β)(Λ(α, β, γi,n)− Λ(α, β, γi,n+1))+2Nc3 − 1KΓ(α)Γ(β)Λ(α, β, γi,N ) = 1(4.9)where Λ(α, β, γi,n) =1γi,nG3,00,3[αβγi,nγc∣∣∣∣∣ 21, α, β], and where Gm,np,q [·] is the Meijer’s G-function [146,eq. (9.301)]. Eq. (4.9) is numerically solved in order to obtain the value of {λi}, ∀i ∈ {1, 2}. Fordiscrete-rate adaptation, ESE provides maximum achievable spectral efficiency (i.e., maximum achiev-able bits/s/Hz with practical modulation schemes) subject to certain statistical-delay-QoS constraintspecified by θ. We evaluate ESE with respect to the QoS-exponent as a performance metric for our pro-posed AM and power allocation schemes. Evaluation of the ESE against the QoS-exponent illustratesthe change of achievable spectral efficiency of our proposed AT scheme as the statistical-delay-QoSrequirements of the transmitted traffic change. Therefore, for AM and power allocation over fadingchannels, ESE is a more generalized performance metric compared to ASE. Since an OWC system654.3. QoS-Aware AM and Power Allocation for Dual-Channel System with Average Power Constraintsupports different class of traffic with different link-layer delay requirements, it is practically importantto evaluate ESE against the QoS-exponents for the OWC systems. We obtain ESE (in bits/s/Hz unit)of a dual-channel coherent OWC with an ICO based AM and transmit power allocation scheme asEIndSE (θ) =∑i∈{1,2}EIndSE,i(θ) (4.10)where EIndSE,i(θ) is the ESE of the i-th channel, and it is given asEIndSE,i(θ)= − 1θTfBlog(Fγi(γi,1) +N−1∑n=1exp(−θTfBn) (Fγi(γi,n+1)− Fγi(γi,n)) + exp(−θTfBN)(1− Fγi(γi,N ))).(4.11)In (4.11), Fγi(·) is the cumulative distribution function (CDF) of the received SNR of the i-th channel.By using (4.1), (2.15), [184, eq. 07.34.03.0605.01], and [146, eq. 7.811.2], we obtainFγi(γo) =1Γ(α)Γ(β)G2,11,3[αβγoγc∣∣∣∣∣ 1α, β, 0]. (4.12)Note that if γc → ∞, Fγi(γo) → 0. Therefore, for 0 < θ < ∞, ESE of a dual-channel coherent OWCapproaches 2N bits/s/Hz at asymptotically high average SNR. From (4.7), we can show that for agiven average SNR, the region boundaries for selecting higher order modulations increase with θ. Asa result, with the increase of θ (or with the decrease of required delay-bound violation probability),the transmitter tends to pick lower order modulations. Consequently, ESE of the considered systemreduces as the statistical-delay constraint becomes strict.Special Case I: We first consider the loose statistical-delay constraint, i.e., θ → 0. ESE of the i-thchannel (in the unit of bits/s/Hz) at loose statistical-delay constraint is obtained aslimθ→0EIndSE,i(θ)= limθ→0log(Fγi(γ˜i,1) +∑N−1n=1 exp(−θTfBn) (Fγi(γ˜i,n+1)− Fγi(γ˜i,n)) + exp(−θTfBN)(1− Fγi(γ˜i,N )))−θTfB= limθ→0∑N−1n=1 n exp(−θTfBn) (Fγi(γ˜i,n+1)− Fγi(γ˜i,n)) +N exp(−θTfBN)(1− Fγi(γ˜i,N ))Fγi(γ˜i,1) +∑Nn=1 exp(−θTfBn) (Fγi(γ˜i,n+1)− Fγi(γ˜i,n)) + exp(−θTfBN)(1− Fγi(γ˜i,N ))=N∑n=1n (Fγi(γ˜i,n+1)− Fγi(γ˜i,n)) = N −N∑n=1Fγi(γ˜i,n).(4.13)In (4.13), {γ˜i,n} are the region boundaries at the loose statistical-delay constraint, and {γ˜i,n} are664.3. QoS-Aware AM and Power Allocation for Dual-Channel System with Average Power Constraintobtained asγ˜i,n = limθ→0γi,n =λ′(2nc3 − 2(n−1)c3)K,n = 1, 2, ··, Nγ˜i,N+1 =∞(4.14)where λ′ is obtained by applying (4.14) to (4.9). The total ESE of a dual channel coherent OWC inthe loose statistical-delay constraint is obtained as limθ→0EIndSE (θ) = 2N − 2∑Nn=1 Fγi(γ˜i,n) bits/s/Hz.Consequently, at loose statistical-delay constraints, an ICO achieves ESE similar to the ASE of aconventional VPVR AT scheme [191]. Such a result is expected because VPVR adaptive transmissionscheme does not consider any delay constraint. When the region boundaries given by (4.14) are usedfor AM and transmit power allocation with any arbitrary QoS exponent, the resultant ESE is obtainedasEVPVRSE (θ) =∑i∈{1,2}− 1θTfBlog(Fγi(γ˜i,1) +N−1∑n=1exp(−θTfBn) (Fγi(γ˜i,n+1)− Fγi(γ˜i,n))+ exp(−θTfBN)(1− Fγi(γ˜i,N ))) .(4.15)Special Case II: We now consider the stringent statistical-delay constraint, i.e., θ →∞. For the strin-gent statistical-delay constraint and continuous rate adaptation, transmit power allocation approachesa fixed-rate channel inversion scheme, i.e., limθ→∞ µi(θ,γ) = σKγi where σ is a constant [161]. Weassume that there is a modulation order, Mnd = 2nd , such that Mnd ≤ 1 + σ < Mnd+1. Conse-quently, at stringent statistical-delay constraint, Mnd-ary modulation is selected with a transmit powerµi(θ,γ) =2ndc3−1Kγi, ∀i ∈ {1, 2}. The value of Mnd is selected from the average transmit power perchannel constraint, i.e., Eγi[2ndc3−1Kγi]≤ 1. Consequently, at stringent delay constraint, nd number ofbits will be transmitted over each channel where nd = min{⌊1c3log2(1 + KE[γ−1])⌋, N}.For performance comparison, we also consider two conventional ICO based transmission technolo-gies, namely, CPVR and constant-power fixed-rate (CPFR) transmission schemes. In a CPVR trans-mission scheme, the transmit power over each channel is kept constant (i.e., P s/2), and we haveµi(θ,γ) = 1, ∀i ∈ {1, 2}. The modulation orders are selected based on the following rule:select Mi(θ,γ) = 2n if γ̂i,n ≤ γi < γ̂i,n+1n = 1, 2, ·, ·, N, ∀i ∈ {1, 2}.(4.16)In (4.16), γ̂i,1 = 0.5(Q−1(BERt))2with Q−1(·) is the inverse of the Gaussian Q-function [60], γ̂i,n =2nc3−1K , for n = 2, 3, ·, ·, N , and γ̂i,N+1 = ∞. The resultant ESE of a CPVR transmission scheme isobtained asECPVRSE (θ) =∑i∈{1,2}− 1θTfBlog(Fγi(γ̂i,1) +N−1∑n=1exp(−θTfBn)(Fγi(γ̂i,n+1)− Fγi(γ̂i,n))+ exp(−θTfBN)(1− Fγi(γ̂i,N ))) .(4.17)In a CPFR scheme, we also have µi(θ,γ) = 1, ∀i ∈ {1, 2}. For the i-th (i ∈ {1, 2}) channel, Mnφ = 2nφ674.3. QoS-Aware AM and Power Allocation for Dual-Channel System with Average Power Constraint(where nφ ∈ {1, 2, ·, ·, N}) order modulation is selected if γi ≥ γφ , 2nφc3−1K , and transmission issuspended if γi < γφ. The ESE of a CPFR transmission scheme is obtained asECPFRSE (θ) =∑i∈{1,2}− 1θTfBlog (Fγi(γφ) + exp(−θTfBnφ)(1− Fγi(γφ))) . (4.18)4.3.2 JCO with Average Transmit Power ConstraintContinuous Rate Adaptation and Power AllocationWe first summarize the transmit power allocation assuming continuous rate adaptation in a dual-channel coherent OWC system [71]. Based on such results, we will derive modulation selection andpower adaptation rules for discrete constellations. By using (4.3), the EC maximization problem for adual-channel coherent OWC system subject to JCO and average transmit power constraint is given bymax{µi(θ,γ)}−1θlogE ∏i∈{1,2}(1 +Kµi (θ,γ) γi)−ηs.t. E ∑i∈{1,2}µi (θ,γ) = 2.(4.19)We denote γφ as the cutoff SNR. Following [71], the power adaptation rules are summarized as follows.− Both channels are active (min(γ1, γ2) > γφ):µi (θ,γ) = 1γ11+2ηφ K2η1+2η (γ1γ2)η1+2η− 1Kγi+ (4.20)where i ∈ {1, 2} and [x]+ = max(x, 0).− Only one channel is active (min(γ1, γ2) < γφ ≤ max(γ1, γ2)):µi (θ,γ) =1γ11+ηφ (Kγi)η1+η− 1Kγi,µj (θ,γ) = 0(4.21)where (i, j) ∈ {1, 2}, i 6= j, and γi > γj .− No channel is active: max(γ1, γ2) < γφ and µi (θ,γ) = 0, ∀i ∈ {1, 2}.In the case of continuous rate adaptation, the value of γφ is obtained by applying (4.20) and (4.21) tothe average transmit power constraint given by [71, eq. 23].AM and Transmit Power AllocationWe consider the following scenarios: (i) both channels are active and modulation orders are jointlyselected, (ii) only the channel with maximum instantaneous SNR is active, and (iii) no channel is active.684.3. QoS-Aware AM and Power Allocation for Dual-Channel System with Average Power ConstraintBoth channels are active and modulation orders are jointly selected: By using (4.20), the relationsbetween the assigned constellation sizes and instantaneous SNRs in a JCO approach are obtained asM c31 (θ,γ) =Kγ1γ11+2ηφ K2η1+2η (γ1γ2)η1+2η,M c32 (θ,γ) =Kγ2γ11+2ηφ K2η1+2η (γ1γ2)η1+2η.(4.22)From (4.22), we obtainγ1 =(γφK)M c31 (θ,γ) (M1 (θ,γ)M2 (θ,γ))ηc3 ,γ2 =(γφK)M c32 (θ,γ) (M1 (θ,γ)M2 (θ,γ))ηc3 .(4.23)We denote Mni = 2ni as the modulation order selected for the i-th channel where ni ∈ {1, 2, ·, ·, ·, N}and i ∈ {1, 2}. We use (4.23) for developing the modulation order selection rule in a JCO approach.Mn1-ary and Mn2-ary modulations will be jointly selected for the first and second channels, respectively,if γ1 and γ2 jointly satisfy the following conditions:Γ(1)n1,n2 ≤ γ1 < Γ(1)n1+1,n2and Γ(1)n2,n1 ≤ γ2 < Γ(1)n2+1,n1(4.24)where Γ(1)n,m =(γφK)2ηc3(n+m)+nc3 and Γ(1)N+1,m = ∞, ∀{n,m} ∈ {1, 2, ·, ·, ·, N}. In order to satisfythe target BER requirements, the corresponding transmit power adaptation factors over the first andsecond channels are respectively determined asµ(1)1 (θ,γ) =2n1c3 − 1Kγ1and µ(1)2 (θ,γ) =2n2c3 − 1Kγ2. (4.25)Note that when both channels are active, each channel will be able to transmit at least the binary con-stellation. Therefore, both channels will be active when min(γ1, γ2) ≥(γφK)2(2η+1)c3 . The probabilityof jointly transmitting n1 and n2 bits over the first and second channels, respectively, is given asF (n1, n2) =(Fγ1(Γ(1)n1+1,n2)− Fγ1(Γ(1)n1,n2))×(Fγ2(Γ(1)n2+1,n1)− Fγ2(Γ(1)n2,n1)).(4.26)Only the channel with maximum instantaneous SNR is active: If min(γ1, γ2) <(γφK)2(2η+1)c3 , onlythe channel with maximum instantaneous SNR can remain active. We need to consider the twofollowing cases: (I) γm , max(γ1, γ2) ≥(γφK)2(2η+1)c3 and (II)(γφK)2(η+1)c3 ≤ γm <(γφK)2(2η+1)c3where m = arg max(γ1, γ2).We first consider γm ≥(γφK)2(2η+1)c3 . By using (4.21), we obtain the relation between the assignedconstellation size and maximum instantaneous channel SNR asM c3m (θ,γ) =(Kγmγφ) 11+η. (4.27)694.3. QoS-Aware AM and Power Allocation for Dual-Channel System with Average Power ConstraintBy using (4.27), we obtain the modulation order selection and power adaptation rule for the channelwith maximum SNR asselect Mm(θ,γ) = 2n and µ(2)m (θ,γ) =2nc3 − 1Kγmif Γ(2)n ≤ γm < Γ(2)n+1, n = 1, 2, ·, ·, ·, N.(4.28)In (4.28), Γ(2)1 =(γφK)2(2η+1)c3 , Γ(2)n =(γφK)2nc3(η+1) for n = 2, 3, ·, ·, ·, N , and Γ(2)N+1 =∞.We now consider that the maximum instantaneous channel SNR satisfies the following condition:(γφK)2(η+1)c3 ≤ γm <(γφK)2(2η+1)c3 . (4.29)If (4.29) is satisfied, only binary constellation will be transmitted over the channel having maximuminstantaneous SNR with a transmit power adaptation factor µ(2)m (θ,γ) =2c3−1Kγm. The following twocases can happen: (i) {γ1, γ2} ∈[(γφK)2c3(η+1),(γφK)2c3(2η+1))and (ii) γi ∈[0,(γφK)2c3(η+1)), γj ∈[(γφK)2c3(η+1),(γφK)2c3(2η+1)), ∀(i, j) ∈ {1, 2}, and i 6= j. We obtain the probability of transmittingbinary constellation over the channel having maximum instantenous SNR asP =∫ ( γφK)2c3(2η+1)γ2=(γφK)2c3(η+1)∫ γ2γ1=(γφK)2c3(η+1)fγ1,γ2(γ1, γ2) dγ1dγ2+∫ ( γφK)2c3(2η+1)γ1=(γφK)2c3(η+1)∫ γ1γ2=(γφK)2c3(η+1)fγ1,γ2(γ1, γ2) dγ1dγ2+∫ ( γφK)2c3(η+1)γ1=0∫ ( γφK)2c3(2η+1)γ2=(γφK)2c3(η+1)fγ1,γ2(γ1, γ2) dγ1dγ2+∫ ( γφK)2c3(η+1)γ2=0∫ ( γφK)2c3(2η+1)γ1=(γφK)2c3(η+1)fγ1,γ2(γ1, γ2) dγ1dγ2.(4.30)In (4.30), fγ1,γ2(γ1, γ2) is the joint PDF of γ1 and γ2. We assume that γ1 and γ2 are i.i.d. RVs. There-fore, we have fγ1,γ2(γ1, γ2) = fγ1(γ1)fγ2(γ2), and Fγ1(r) = Fγ2(r) , Fγ(r) for any r > 0. Consequently,when (4.29) is satisfied, we obtain the probability of transmitting binary constellation over the channelhaving maximum instantenous SNR asP =(Fγ((γφK)2(2η+1)c3))2 − (Fγ ((γφK)2(η+1)c3))2. (4.31)No channel is active: When max(γ1, γ2) <(γφK)2(η+1)c3 , transmission over both channel is sus-pended, i.e., µi(θ,γ) = 0, ∀i ∈ 1, 2.Considering the aforementioned scenarios, we obtain the average transmit power constraint in JCO704.3. QoS-Aware AM and Power Allocation for Dual-Channel System with Average Power Constraintbased AM and power allocation asN∑n1=1N∑n2=1(Fγ2(Γ(1)n2+1,n1)− Fγ2(Γ(1)n2,n1))An1(Γ(1)n1,n2 ,Γ(1)n1+1,n2)+N∑n1=1N∑n2=1(Fγ1(Γ(1)n1+1,n2)− Fγ1(Γ(1)n1,n2))An2(Γ(1)n2,n1 ,Γ(1)n2+1,n1)+∑i∈{1,2}Fγj 6=i((γφK)2c3(η+1)) N∑ni=1Ani(Γ(2)ni ,Γ(2)ni+1)+∑i∈{1,2}Gi((γφK)2c3(η+1),(γφK)2c3(2η+1))= 2.(4.32)In (4.32), An (γa, γb) and Gi(γa, γb) are respectively defined asAn (γa, γb) =M c3n − 1KΓ(α)Γ(β)×G3,00,3[[αβγaγc∣∣∣∣∣ 21, α, β]−G3,00,3[αβγbγc∣∣∣∣∣ 21, α, β]] (4.33)andGi(γa, γb) =∫ γbγa2c3 − 1KγiFγj (γi)fγi(γi) dγi (4.34)where i, j ∈ {1, 2}, i 6= j. Eq. (4.32) is numerically solved in order to obtain the value of γφ used in(4.24)-(4.31). The closed-form ESE (in bits/s/Hz unit) of a JCO approach is obtained asEJointSE (θ) = −1θTfBlog[N∑n1=1N∑n2=1F (n1, n2) exp (−θTfB(n1 + n2))+2Fγ((γφK)2c3(2η+1)) N∑n=1(Fγ(Γ(2)n+1)− Fγ(Γ(2)n))exp (−θTfBn)+((Fγ((γφK)2(2η+1)c3))2 − (Fγ ((γφK)2(η+1)c3))2)exp (−θTfB) +(Fγ((γφK)2(2η+1)c3))2].(4.35)We can show that n , limθ→0 Γ(1)n,m = limθ→0 Γ(2)n =(γφK)2nc3 . Consequently, at the loosestatistical-delay constraint, the region boundaries associated with given a channel depend only onthe modulation order selected for that particular channel. After some algebraic manipulations, weobtain ESE of the JCO approach in the loose statistical-delay constraint aslimθ→0EJointSE (θ) =2(N −∑Nn=1 Fγ (n)) (1− Fγ (1)) + 2Fγ (1)(N −∑Nn=1 Fγ (n))(1− Fγ (1))2 + 2Fγ (1) (1− Fγ (1)) + F 2γ (1)= 2N − 2N∑n=1Fγ (n) bits/s/Hz.(4.36)714.4. QoS-Aware AM and Power Allocation for Multi-beam System with Peak Transmit Power ConstraintFrom (4.36), it is evident that both ICO and JCO achieve similar ESE at the loose statistical-delayconstraint. Such an observation is also depicted from our numerical results.4.3.3 Computational Complexity of ICO and JCOComplexity of ICO: To analyze the complexity of an AT scheme, we need to determine the complex-ity of calculating the region boundaries, and the complexity of performing AM and power allocation forgiven region boundaries. The region boundaries of ICO based AM and power allocation are obtainedby jointly solving (4.7) and (4.9). We emphasize that (4.9) depends only on the channel statistics andstatistical-delay-QoS requirements of the traffic. Hence, (4.9) can be solved off-line. Consequently, inICO based AM and power allocation scheme, the region boundaries are calculated off-line and suchregion boundaries are stored at the transmitter. Therefore, the required complexity for calculating theregion boundaries can be affordable. In an online operation, ICO independently selects the modulationorder and corresponding power adaptation factor for each optical channel by using the stored regionboundaries in (4.4). We can show that our proposed ICO based AM and power allocation require asimple mapping in online operation. In particular, the maximum complexity of such a mapping isO(N). Note that, a mapping of similar complexity is also required in the conventional adaptive OWCsystems [59, 60].Complexity of JCO: The region boundaries for JCO based AM and power allocation depend on thethe value of γφ and delay-QoS requirements of the transmitted traffic. The value of γφ is obtained bynumerically solving (4.32). Depending on the size of available constellations, the numerical evaluation of(4.32) can be computationally extensive. However, (4.32) can be numerically solved off-line since (4.32)depends only on the channel statistics and statistical-delay-QoS requirements of the traffic. As a result,the region boundaries of JCO based AM and power allocation are calculated off-line at the transmitterwith affordable complexity. Moreover, such region boundaries are stored at the transmitter for onlineoperation. In an online operation, JCO needs to find a suitable condition, from (4.24), (4.28), and(4.29), that is satisfied for a given set of instantaneous SNRs. We can show that the online operation ofJCO requires maximum O(N2) iterations in order to select the suitable modulation orders and poweradaptation factors for both optical channels. Since atmospheric turbulence fading has a (relatively)large channel coherence time, such a computation can be expected to be affordable within the channelcoherence time.4.4 QoS-Aware AM and Power Allocation for Multi-beam Systemwith Peak Transmit Power Constraint4.4.1 System Model and Problem FormulationFor the benefit of the readership, we briefly describe the considered system model and problemformulation. A coherent OWC is considered with L orthogonal parallel optical beams between thetransmitter and receiver. Similar to Section 4.3, we assume that the data traffic arrives in the trans-mitter at a constant rate. The assumption of constant traffic arrival rate is justified when the rate ofchannel variation is much faster than the source rate variation. Moreover, such traffic are grouped into724.4. QoS-Aware AM and Power Allocation for Multi-beam System with Peak Transmit Power Constraintmultiple frames and stored at a transmit buffer. Each frame is decomposed into multiple parallel bitstreams that are multiplexed over parallel optical beams. We also assume that the channel statisticsand accurate CSI are available at the transmitter. Based on statistical-delay-QoS requirements of thetransmitted traffic, target BER, and CSI, AM and power allocation are determined for the opticalbeams at the guard interval of each TS. The duration of a typical TS is considered to be approximatelysame as the channel coherence time. Consequently, the channel gains remain constant during each TS,and independently vary from one TS to another TS. Finally, similar to Section 4.3, we consider idealphase noise compensation along with independent channel fading for the parallel optical beams.The transmitter employs adaptive M -ary QAM. We denote the total available transmit power as Pt.The transmit power of the i-th optical beam is denoted as Pi(θ,γ) = µi(θ,γ)Pt where µi(θ,γ) ∈ [0, 1]is the transmit power allocation factor. By using (4.2) as the conditional BER of M -QAM for targetBER < 10−3, the transmission rate (in bits/frame unit) over the i-th optical beam is obtained asRi = TfB log2 (1 +Kµi(θ,γ)γi). Here, γi is the instantaneous received SNR per symbol (normalizedby the power allocation factor) of the i-th optical beam; γi is given as γi =R∆LPtq∆fIi; and Ii is theatmospheric turbulence fading coefficient of the i-th optical beam. Without loss of generality, we denotethe maximum supportable arrival rate to the transmitter as EpeakSE (in bits/s/Hz) for an acceptabledelay-bound violation probability, δ, and the required QoS-exponent is θ. Therefore, in order tosupport the traffic arrival rate EpeakSE while satisfying the required delay-bound violation probability,the transmission parameters of the (active) optical beams need to be adapted based on θ. On the otherhand, for given transmit power budget, the AM and power allocation over multiple optical beamscan be determined by an exhaustive search. However, the complexity of such an exhaustive searchincreases exponentially with the increase of number parallel optical beams. Therefore, in order todevelop discrete-rate AT scheme(s) with the reasonable complexity, we formulate the following problemto maximize ESE subject to transmit power constraint:EpeakSE = max{µi(θ,γ)}− 1θTfBlogE[L∏i=1(1 +Kµi (θ,γ) γi)−η]s.t.L∑i=1µi(θ,γ) = 1, µi(θ,γ) ∈ [0, 1], ∀i ∈ {1, 2, · · · , L}.(4.37)In (4.37), η =θTfBlog 2 . Eq. (4.37) is formulated by considering continuous rate adaptation. The solutionto this problem will be used to develop statistical-QoS aware discrete-rate AT schemes in the subsequentanalysis.4.4.2 Independent Channel OptimizationWe consider that N different QAM modulations are available for each optical beam. In an ICOscheme, all the optical beams are active, and the sum of the individual ESE of the optical beams is734.4. QoS-Aware AM and Power Allocation for Multi-beam System with Peak Transmit Power Constraintmaximized. Considering ICO and solving (4.37), the transmit power allocation factors are obtained asµ(L),Ii (θ,γ) =(γ(L)o)− 1η+1(Kγi)ηη+1− 1Kγi+, ∀i ∈ {1, 2, · · · , L} (4.38)where γ(L)o = 1+∑Li=1 1Kγi∑Li=1(1Kγi) ηη+1−(η+1), and [x]+ = max(x, 0). We denote Mi(θ,γ) as the order ofQAM modulation selected for the i-th optical beam. AM and transmit power allocation for the i-th(i ∈ {1, 2, · · · , L}) optical beam are performed according to the following rule15:select Mi(θ,γ) = 2ni and Pi(θ,γ) = µ(L),Ii (θ,γ)Ptif ν(L)ni ≤ γi < ν(L)ni+1, ni = 1, 2, ·, ·, N(4.39)where ν(L)ni =(γ(L)oK)2ni(η+1), ν(L)N+1 =∞, and transmission over the i-th optical beam is suspended ifγi < ν(L)1 . We provide the following remarks:Remark on θ →∞ at high SNR: We denote γmin = mini∈{1,2,··· ,L} γi, and γmin 2nLK where n ∈{1, 2, · · · , N}. In this case 0 < ν(L)n ≤ 1K(2nLKγmin)η+1, and limθ→∞ ν(L)n = 0. If γmin 2nLK is satisfiedat the stringent statistical-delay constraint, all the optical beams can transmit at least 2n-ary QAM.Moreover, limθ→∞ µ(L),Ii (θ,γ) =1Kγi∑Li=11Kγi→ 1L , as γi → ∞, ∀i, i.e., in asymptotic high-SNR regimetransmit power is equally allocated among all the optical beams.Remark on θ →∞ at low SNR: At low SNR, ∑Li=1 1Kγi 1. We can show that in this case ν(L)1 =2η+1K , and limθ→∞ ν(L)1 =∞. Consequently, the optical beams will not be able to transmit the smallestmodulation order. Hence, ICO does not support the stringent statistical-delay constraint at low SNR.Remark on Complexity: At each TS, ICO requires the following online computations: (1) L andN number of computations for calculating power allocation factors and region boundaries, respec-tively, and (2) maximum N + 1 searches for selecting suitable modulation order for each optical beam.Therefore, the total computational complexity of ICO is O (L+N + L(N + 1)) ≈ O (LN).4.4.3 Joint Channel OptimizationIn a given TS, JCO activates only the suitable optical beams. We denote γ(1) > γ(2) > · · · > γ(L)where γ(m) is the SNR of the m-th best optical beam. We consider the following cases:Case I: The m best optical beams are considered for performing AT where 2 ≤ m ≤ L. By solving(4.37), the transmit power allocation factor for the i-th best optical beam, i ∈ {1, 2, · · · ,m}, is obtained15The transmission rate over the i-th parallel optical beam is given as Ri = TfBni when 2ni -ary QAM is selectedfor the i-th optical beam. The ESE of the considered discrete-rate AT schemes, in bits/s/Hz unit, is expressed asEpeakSE = − 1θTfB logE[exp(−θ∑Li=1 Ri)].744.4. QoS-Aware AM and Power Allocation for Multi-beam System with Peak Transmit Power Constraintasµ(m),Ji (θ,γ) =(γ(m)φ)− 11+mη(∏mi=1Kγ(i)) η1+mη− 1Kγ(i)+(4.40)where γ(m)φ =(1+∑mi=11Kγ(i)m(∏mi=1Kγ(i))− η1+mη)−(1+mη). For continuous rate adaptation, the relation betweenmodulation order and power allocation factor is given by, Mi(θ,γ) = 1+Kµ(m),Ji (θ,γ)γ(i), ∀i. Plugging(4.40) to this relation, the adaptive transmission rule for the i-th best optical beam is obtained asfollows.select Mi(θ,γ) = 2ni and Pi(θ,γ) = µ(m),Ji (θ,γ)Ptif Γ(m)ni ≤ γ(i) < Γ(m)ni+1, ni = 1, 2, · · · , N, ∀i ∈ {1, 2, · · · ,m}.(4.41)In (4.41), Γ(m)ni =2niK(1m+ 1H(m)) , Γ(m)N+1 = ∞, and H(m) is the harmonic mean of {Kγ(1), · · · ,Kγ(m)}.Note that, them best optical beams will be simultaneously active if γ(m) ≥ 2K(1m+ 1H(m)) and µ(m),Ji (θ,γ) >0, ∀i ∈ {1, 2, · · · ,m}.Case II: All the transmit power is allocated to the strongest optical beam. The modulation orderfor the strongest optical beam is selected according to the following rule:select M1(θ,γ) = 2n1 if 2n1 ≤ 1 +Kγ(1) < 2n1+1. (4.42)Case III: If the strongest optical beam can not carry binary constellation, then the transmission issuspended.Algorithm 1 JCO based AT scheme1: Sort optical beams according to descending SNRs.2: Find the largest m ∈ {L,L − 1, · · · , 2} such that γ(m) ≥ 2K(1m+ 1H(m)) , and µ(m),Ji (θ,γ) > 0,∀i ∈ {1, 2, · · · ,m}.3: if m ≥ 2 then4: Activate the m best optical beams with transmission parameters according to (4.41).5: else if γ(1) ≥ 1/K then6: Activate only the strongest optical beam with P1(θ,γ) = Pt. Select modulation order for thestrongest optical beam according to (4.42).7: else Suspend the transmission.8: end ifAlgorithm 1 activates the suitable optical beams, and determines corresponding modulation orderand transmit power assignments. We provide the following remarks:Remark on θ → 0: We can show that limθ→0 ν(L)n = Γ(L)n , ∀n. Consequently, both ICO and JCOachieve similar ESE at the loose statistical-delay constraint. For γmin 2nLK , limθ→0 µ(L),Ii (θ,γ) =limθ→0 µ(L),Ji (θ,γ) =1L . When γmin 2nLK is satisfied, all the optical beams are active in both ICO754.4. QoS-Aware AM and Power Allocation for Multi-beam System with Peak Transmit Power Constraintand JCO, and transmit power is equally allocated among all the optical beams.Remark on θ →∞ at high SNR: We assume that the m best optical beams are active, and γ(m) 2nmK . We can show that limθ→∞ µ(m),Ji (θ,γ) =1m , and γ(i) ≥ Γ(m)n , ∀i ∈ {1, · · · ,m}. Consequently,when γ(m) 2nmK is satisfied at the stringent statistical-delay constraint, transmit power is equallyallocated among the m active optical beams, and each optical beam can transmit at least 2n-ary QAM.We observe that the transmit power is equally allocated among the active optical beams at boththe loose and stringent statistical-delay constraints in the high SNR regimes. Hence, JCO convergesto a simple equal-power allocation with beam selection (EPA/BS) based AT scheme in the high SNRregimes. For the completeness of the work, we briefly describe EPA/BS based AT scheme. In EPA/BS,transmitter selects the largest m ∈ {L,L − 1, · · · , 1} optical beams such that γ(m) ≥ mK is satisfied.Transmitter equally allocates the power among the selected beams. Assuming the m best optical beamsare selected, modulation order for the i-th best optical beam, i ∈ {1, 2, · · · ,m}, is determined asselect Mi(θ,γ) = 2ni ifm(2ni − 1)K≤ γ(i) < m(2ni+1 − 1)K. (4.43)Our simulation result depicts that EPA/BS provides near optimal ESE.Remark on θ →∞ at low SNR: We consider the m best optical beams for performing AT where1 +∑mi=11Kγ(i)≈ ∑mi=1 1Kγ(i) , ∀m ∈ {L,L − 1, · · · , l}. We first assume l > 2. In this case, the m ≥ lbest optical beams will be simultaneously active, if γ(m)H(m)≥ 2K is satisfied. However, γ(m)H(m)≤ 1K alwaysholds. Accordingly, in this case, only the m < l best optical beams can be simultaneously active. Inthe worst-case scenario, when 1 +∑mi=11Kγ(i)≈ ∑mi=1 1Kγ(i) , ∀m ≥ 2, JCO allocates all the power tothe strongest optical beam, and selects the modulation order according to (4.42). Therefore, JCO cansupport the stringent statistical-delay constraint in the low SNR regimes. Our simulation result showsthat the strongest beam selection scheme (where all the transmit power is always allocated to thestrongest optical beam) achieves almost similar ESE to JCO for the strict statistical-delay constraintand small received SNR.Remark on complexity: For 2 ≤ l ≤ L active optical beams, JCO requires maximum ∑Lm=l(m +1) + (l + 1)N + l number of computations. Therefore, at each TS, the worst-case complexity of JCOis O (max(L2 + 3N,LN)).4.4.4 Independent Channel Optimization with Beam SelectionFor performance comparison, we consider ICO/BS technique. ICO/BS technique activates only thesuitable optical beams at each TS, and independently optimizes the transmission parameters of theactive optical beams. Similar to Section 4.4.3., we consider γ(1) > γ(2) > · · · > γ(L) where γ(m) is theSNR of the m-th best optical beam. The transmit power allocation factors for the 2 ≤ m ≤ L bestoptical beams, {µ(m),Ii (θ,γ)}, are obtained by substituting L with m and {γi} with {γ(i)} in (4.38).Transmission parameters of these beams are adapted asselect Mi(θ,γ) = 2ni and Pi(θ,γ) = µ(m),Ii (θ,γ)Ptif ν(m)ni ≤ γ(i) < ν(m)ni+1, ni = 1, 2, · · · , N, ∀i ∈ {1, 2, · · · ,m}(4.44)764.5. Numerical Results10-5 10-4 10-3 10-2 10-1QoS-exponent0123456789Effective Spectral Efficiency (bits/s/Hz)Monte Carlo SimulationAdaptive M-QAM, weak turbulenceAdaptive M-PSK, weak turbulenceAdaptive M-PAM, weak turbulenceAdaptive M-QAM, strong turbulenceAdaptive M-PSK, strong turbulenceAdaptive M-PAM, strong turbulenceFigure 4.2: ESE comparison among different M -ary modulations with ICO, average transmit powerconstraint, γc = 30 dB, and BERt = 10−6.where ν(m)ni =(γ(m)oK)2ni(η+1), and ν(m)N+1 =∞. At a given TS, the m best optical beams will be activeif γ(m) ≥ ν(m)1 , and µ(m),Ii (θ,γ) > 0, ∀i ∈ {1, 2, · · · ,m}. If γ(2) < ν(2)1 , ICO/BS allocates all the powerto the strongest optical beam, and selects modulation order according to (4.42). ICO/BS requires amethod similar to Algorithm 1. Therefore, at a given TS, the required complexity of ICO/BS is alsoO (max(L2 + 3N,LN)).Remark on θ →∞ at low SNR: At the low SNR regime, when ∑mi=1 1Kγ(i) 1, ∀m ≥ 2 conditionoccurs, we can show that limθ→∞ ν(m)1 = ∞, ∀m ∈ {L,L − 1, · · · , 2}. Consequently, at the stringentstatistical-delay constraint and low SNR regimes, ICO/BS activates only the strongest optical beam.4.5 Numerical Results4.5.1 AT For Dual-Channel System With Average Power ConstraintIn this section, we present the selected numerical results in order to demonstrate the performanceof the proposed ICO and JCO based AT schemes of Section 4.3. We consider strong Gamma-Gammaturbulence fading with α = 2.04, β = 1.10, weak Gamma-Gamma turbulence fading with α = 4.43,β = 4.39, and K-turbulence fading fading with α = 1.99 and α = 1.11. In all the numerical results,we consider that N = 4 constellations are available for each channel. We assume the following systemparameters: R = 0.75 Amp/Watt, Tf = 10−6 second, and B = 108 Hz. Similar to the Chapter 3,we consider that the diameters of both apertures at the transmitter and receiver are 8 cm, the spatialseparation between two apertures is 30 cm, and the divergence angle of the transmitted optical beamis 0.1 milli-radian.774.5. Numerical Results10-5 10-4 10-3 10-2 10-1QoS-exponent0123456789Effective Spectral Efficiency (bits/s/Hz)JCO, Eq. (40)ICO, Eq. (15)VPVR, Eq. (20)CPVR, Eq. (22)16-QAM CPFR, Eq. (23)Weak TurbulenceStrong TurbulenceWeak TurbulenceStrong TurbulenceFigure 4.3: ESE comparison among different M -QAM based adaptive transmissions in Gamma-Gammaturbulence fading with average transmit power constraint, γc = 30 dB, and BERt = 10−6.10-5 10-4 10-3 10-2 10-1QoS-exponent01234567Effective Spectral Efficiency (bits/s/Hz)JCO, =1.99, Eq. (40)JCO, =1.11, Eq. (40)ICO, =1.99, Eq. (15)ICO, =1.11, Eq. (15)VPVR, Eq. (20)CPVR, Eq. (22)16-QAM CPFR, Eq. (23)=1.99=1.99=1.11=1.11Figure 4.4: ESE comparison among different M -QAM based adaptive transmissions in K-turbulencefading with average transmit power constraint, γc = 30 dB, and BERt = 10−8.784.5. Numerical Results10-5 10-4 10-3 10-2 10-1 QoS-exponent0.511.522.533.5Effective Spectral Efficiency (bits/s/Hz)ICO, Without Phase NoiseICO, With Phase Noise =200ICO, With Phase Noise =300JCO, Without Phase NoiseJCO, With Phase Noise =200JCO, With Phase Noise =300Figure 4.5: ESE comparison between coherent M -PAM based ICO and JCO in K-turbulence fading(α = 1.99) with average transmit power constraint, imperfect phase noise compensation, γc = 30 dB,and target BER = 10−8.10-5 10-4 10-3 10-2 10-1QoS-exponent10-1410-1210-1010-810-610-410-2100Delay-bound violation probability, Pr[D>Dmax]JCO, =2.04, =1.10, Target BER=10-6ICO, =2.04, =1.10, Target BER=10-6JCO, =1.11, =1.00, Target BER=10-8ICO, =1.11, =1.10, Target BER=10-8Figure 4.6: Delay-bound violation probability of M -QAM based ICO and JCO subject to averagetransmit power constraint.794.5. Numerical ResultsFigure 4.2 compares ESE of different AMs by considering ICO and average transmit power con-straint over the Gamma-Gamma turbulence channels. Figure 4.2 shows that the ESE obtained fromour developed expression matches well with the ESE obtained from Monte-Carlo simulations. Figure4.2 depicts that ESE of a given M -ary modulation reduces as the value of θ increases. In other words,for an OWC system, maximum spectral efficiency is achieved at loose delay constraints, and the achiev-able spectral efficiency gradually decreases as the delay-constraint becomes strict. Such an observationis consistent with our analysis in Section 4.3.1. Consequently, delay-QoS requirements of the trans-mitted traffic indeed influence the achievable spectral efficiency of an OWC system. For the OWCsystems supporting delay-sensitive traffic, delay-QoS requirements need to be considered for evaluatingachievable spectral efficiency of such OWC systems. Figure 4.2 also depicts the superiority of adaptiveM -QAM over adaptive M -PSK and M -PAM in both weak and strong turbulence fading channels. Theregion boundaries in an adaptive M -QAM are smaller compared to the region boundaries in adaptiveM -PSK and M -PAM. Consequently, the considered coherent OWC transmitter tends to select higherorder modulation without sacrificing the target BER requirements when adaptive M -QAM based ICOis employed. As a result, an adaptive M -QAM based ICO provides larger ESE compared to the adap-tive M -PSK and M -PAM based ICO techniques. Due to the superior ESE performance over the fadingchannels, we consider adaptive M -QAM in the subsequent numerical results.Figure 4.3 compares ESE of ICO and JCO over the Gamma-Gamma turbulence fading channelconsidering average transmit power constraint. Here, ESE of ICO and JCO are obtained by evaluating(4.10) and (4.35), respectively. Figure 4.3 depicts that both ICO and JCO achieve similar ESE forsmall values of θ (i.e., in the loose statistical-delay constraints). Such a result is expected since wehave analytically showed that ESE of ICO and JCO converges at loose statistical-delay constraints.However, JCO outperforms ICO as θ becomes large, i.e., statistical-delay constraints become strict.Such a performance gap is more pronounced in the strong turbulence fading. Figure 4.3 shows that atθ = 10−1, JCO achieves 8.5% and 38.4% higher ESE compared to ICO in weak and strong Gamma-Gamma turbulence fading, respectively. Figure 4.3 also depicts that ESE of VPVR scheme converges tothe ESE of ICO and JCO at the loose statistical-delay constraints which is consistent with our analysis.However, ESE of VPVR scheme significantly reduces at the strict statistical-delay constraints. Atθ = 10−1, JCO achieves 3.5 and 4.7 times larger ESE compared to VPVR scheme in weak and strongGamma-Gamma turbulence fading, respectively. ESE of constant transmit power based schemes,such as CPVR and 16-QAM based CPFR, are also plotted in figure 4.3. It is evident from figure4.3, that the proposed ICO and JCO significantly outperform both CPVR and 16-QAM based CPFRtransmission schemes, especially in the strict statistical-delay constraints. As explained in Section 4.3.3,our proposed ICO and JCO based adaptive transmissions have reasonable complexity. Therefore, ourproposed AM and transmit power allocation provide large delay-QoS aware throughput gain withoutrequiring significant computational complexity. Such an observation motivates using the proposed AMand power allocation for the delay-QoS constrained OWC systems instead of the constant transmitpower based schemes.Figure 4.4 compares ESE of ICO and JCO over the K-turbulence fading channels consideringaverage transmit power constraint. Comparing figures 4.3 and 4.4, we observe that the ESE gain ofJCO in strict statistical-delay constraint becomes more prominent as the turbulence fading becomes804.5. Numerical Resultsstronger. In figure 4.4, JCO improves ESE of ICO by 36.8% at θ = 10−1 and α = 1.99. However, JCOachieves almost 2.05 times larger ESE compared to ICO for the same value of θ when α = 1.11. Hence,our proposed JCO efficiently supports strict delay constraints over strong turbulence fading channels.Figure 4.4 also depicts ESE of the conventional VPVR, CPVR, and 16-QAM based CPFR over the K-turbulence channels. Our proposed AT schemes significantly outperform the conventional AT schemesin the strict statistical-delay constraints, especially when α becomes small (i.e., when severity of theK-turbulence fading increases). From figures 4.3 and 4.4, we obtain the following insights on the AMand power allocation for OWC systems: (i) only channel aware AT schemes, such as VPVR and CPVR,do not support strict delay-QoS constraints, and (ii) in order to achieve suitable spectral efficiency instrict delay-QoS requirements, AM and power allocation for an OWC system should jointly consider thevariation of optical transmission link as well as statistical-delay-QoS requirements of the transmitteddata.Note that, due to the intractability of the BER expressions, it is challenging to investigate impactof the uncompensated phase noise on the proposed AT schemes with M -PSK and M -QAM. However,such an intractability is not present when M -PAM is used. Due to repetitive nature of analysis, weomit the detailed analysis of the ESE of M -PAM based ICO and JCO with uncompensated phasenoise. In figure 4.5, we compare ESE of ICO and JCO employing adaptive M -PAM over the K-turbulence fading in the presence of uncompensated phase noise. We consider that the transmitterhas perfect knowledge about the instantaneous channel gains and channel statistics. On the otherhand, the transmitter does not have knowledge about the phase noise at the receiver. Consequently,the transmitter adapts modulation orders and transmit powers without considering phase noise at thereceiver. Figure 4.5 depicts that both ICO and JCO based adaptive transmission schemes experienceESE degradation as the standard deviation of the uncompensated phase noise increases. Figure 4.5also depicts that JCO outperforms ICO even in the presence of uncompensated phase noise, especiallyin the strict statistical-delay constraints (i.e., for the large values of the QoS-exponents).Figure 4.6 illustrates the change of delay-bound violation probability of a data frame in the buffer(i.e, the probability that the wait time of the arrived data frame in the buffer will exceed beyond Dmax)with respect to the change of QoS-exponents. We consider Dmax = 10−6 second16. Figure 4.6 illustratesthat both JCO and ICO achieve same delay-bound violation probability for small values of θ. Suchan observation is expected since ESE of both JCO and ICO converges for small values of θ. However,delay-bound violation probability of both ICO and JCO decreases as θ increases. For larger valuesof θ, we have the following two observations: (i) For a given set of physical system parameters (i.e.,turbulence fading and target BER), JCO achieves smaller delay-bound violation probability comparedto ICO, and (ii) compared to ICO, JCO experiences less degradation of the achievable delay-boundviolation probability as the turbulence fading gets strong and/or target BER requirement becomesmore strict. Both observations can be explained by the following arguments. In our previous numericalresults, we have demonstrated that JCO achieves larger ESE compared to ICO in large QoS-exponents.Moreover, in large QoS-exponents, the ESE performance gap between JCO and ICO increases as theturbulence fading gets strong and/or target BER requirement becomes more strict. Due to larger ESE,16In FSO communications, the duration of a typical TS is 1 ms, and 1000 of data-frames are transmitted in a typicalTS [70]. Consequently, we are interested to calculate the probability that arrived data-frame will wait more than 10−6second.814.5. Numerical ResultsJCO has better probability of satisfying the delay-bound even for strong turbulence fading and/orstrict target BER requirements. The larger ESE of JCO compared to ICO in the large QoS-exponentscan be explained by the following arguments. In ICO, transmit power of each channel is independentlyoptimized subject to individual average transmit power-per-channel constraint. On the other hand, inJCO, transmit power of both channels are jointly optimized subject to total average transmit powerconstraint. As a result, JCO provides more efficient allocation of the available transmit power betweentwo channels. Due to such an efficient transmit power allocation, JCO provides larger ESE and im-proved delay-bound violation probability compared to ICO, even when turbulence fading gets strongand/or target BER requirements become strict. Accordingly, for a delay-constrained dual-channelOWC system, it is beneficial to jointly adapt the transmit parameters of both optical channels.Note that, figures 4.2 to 4.4 illustrate ESE of the proposed and conventional AT schemes by assumingthat both optical channels experience independent channel gains, and the receiver can accuratelycompensate the phase noise (see the assumptions A2 and A3 of Section 4.2). For the scenario wherethe aforementioned assumptions do not hold, figures 4.2 to 4.4 will be the upper bound of the ESEachieved by the considered discrete-rate AT schemes. Similarly, in such a case, figure 4.6 will be thelower bound of the achievable delay-bound violation probability for the proposed ICO and JCO basedAT schemes.4.5.2 AT For Multi-Channel System With Peak Power ConstraintFor simulations, we consider the following parameters: L = 4, N = 5, BERt = 10−6, Tf = 10−6s,B = 108 Hz, R = 0.75 A/W, strong and weak Gamma-Gamma turbulence fading with α = 2.04,β = 1.10 and α = 4.43, β = 4.39, respectively (α and β are channel parameters), 11.5 dB/Kmpath loss exponent, and 28.3 dB geometric loss factor [138]. Moreover, we consider that the spatialseparation between the apertures at both transmitter and receiver is 30 cm, the divergence angle of thetransmitted optical beam is 0.1 milli-radian, and two different link ranges, such as, 500 meter and 650meter so that the parallel optical beams do not overlap and experience independent channel fading.Figure 4.7 compares ESE of JCO (proposed in Section 4.4.3), EPA/BS, CPVR, and CPFR trans-mission schemes. In both CPVR and CPFR, transmit power is equally allocated among all the opticalbeams. In CPFR, an optical beam is active when it can transmit a predefined modulation order. InCPVR, modulation orders of each optical beam are adaptively selected. Figure 4.7 depicts that CPVRachieves near optimal ESE only for the small QoS-exponents. At the large QoS-exponents, ESE ofCPVR, 32-QAM CPFR, and 8-QAM CPFR approaches zero even when high transmit power (0.5W)is used. However, JCO achieves significant higher ESE in the large QoS-exponents compared to bothCPVR and CPFR transmission schemes. Figure 4.7 also depicts that EPA/BS provides almost similarESE to JCO, as expected from our analysis in Section 4.4.3. Therefore, at both the loose and strictstatistical-delay constraints, near optimal ESE can be achieved by performing equal power allocationand AM only for the suitable optical beams. Such an observation is important for the implementationsimplicity of AT schemes in the practical systems.Figures 4.8 and 4.9 compare ESE of different QoS-aware AT schemes in weak and strong turbulencefading, respectively. We observe that ICO (proposed in Section 4.4.2) is only efficient at small QoS-exponents and/or weak turbulence fading. For strong turbulence fading and large QoS-exponents, ESE824.5. Numerical Results10-5 10-4 10-3 10-2 10-1 100QoS-exponent, 024681012141618Effective Spectral Efficiency (bits/s/Hz)JCO, Pt=0.5WEPA/BS, Pt=0.5WCPVR, Pt=0.5WJCO, Pt=0.16WEPA/BS, Pt=0.16WCPVR, Pt=0.16W32-QAM CPFR, Pt=0.5W8-QAM CPFR,Pt=0.5WPt=0.5 WPt=0.16 WFigure 4.7: ESE comparison among different AT schemes subject to peak transmit power constraint instrong turbulence fading and 650m long link.10-5 10-4 10-3 10-2 10-1QoS-exponent, 246810121416182022Effective Spectral Efficiency (bits/s/Hz)JCO, 500m LinkICO/BS, 500m LinkICO 500m LinkStrongest beam selection, 500m LinkJCO, 650m LinkICO/BS, 650m LinkICO, 650m LinkStrongest beam selection, 650m Link500m Link 650m LinkFigure 4.8: ESE comparison among QoS-aware AT schemes (proposed in Sections 4.4.2-4.4.4) forPt = 0.16W in weak turbulence fading.834.6. Chapter Summary10-5 10-4 10-3 10-2 10-1 100QoS-exponent, 05101520253035Effective Spectral Efficiency (bits/s/Hz)JCO, 500m LinkICO/BS, 500m LinkICO, 500m LinkStrongest beam selection, 500m LinkJCO, 650m LinkICO/BS, 650m LinkICO, 650m LinkStrongest beam selection, 650m Link500m Link650m LinkFigure 4.9: ESE comparison among QoS-aware AT schemes (proposed in Sections 4.4.2-4.4.4) forPt = 0.16W in strong turbulence fading.of ICO approaches zero. ICO/BS (proposed in Section 4.4.4) outperforms ICO in strong turbulencefading. Moreover, JCO (proposed in Section 4.4.3) achieves improved ESE in the large QoS-exponentscompared to both ICO and ICO/BS schemes. For example, at θ = 10−0.5 in weak turbulence fadingand 650 meter long link, JCO, ICO/BS, and ICO achieve 8.39 bits/s/Hz, 4.29 bits/s/Hz, and 3.44bits/s/Hz ESE, respectively. JCO also outperforms the strongest beam selection scheme in weakturbulence fading. However, for strong turbulence fading and 650 meter long link, ESE of both JCOand the strongest beam selection scheme converges at the large QoS-exponents. Therefore, the strongestbeam selection scheme provides near optimal ESE for the small received SNR and strict statistical-delayconstraint.Note that, in figures 4.7 to 4.9, it is considered that all the parallel optical beams experienceindependent channel fading and the receiver can accurately compensate the phase noise (see the as-sumptions A2 and A3 of Section 4.2). For the scenario where the aforementioned assumptions do nothold, figures 4.7 to 4.9 will be the upper bound of the ESE achieved by the considered discrete-rate ATschemes.4.6 Chapter SummaryIn this chapter, we have investigated discrete-rate AT schemes for a coherent OWC system equippedwith multiple parallel optical beams by considering statistical-delay constraints of the transmittedtraffic. We have considered both average and peak transmit power constraints. Our simulation resultshave illustrated that for both average and peak transmit power constraints, JCO based AT schemenotably improves achievable ESE in the strong turbulence fading and strict statistical-delay constraints.84Chapter 5Hybrid RF/FSO Backhaul Networkwith Statistical-QoS AwareBuffer-aided Parallel RelayingIn Chapters 3 and 4, we investigated AT schemes in order to maximize the supportable trafficarrival rate, subject to given link-layer delay-constraint, for a point-to-point FSO communication sys-tem with multiple parallel optical beams. The reliability of such FSO communication systems can befurther improved by incorporating relay assisted hybrid RF/FSO system. To this end, in this chapter,we investigate statistical QoS-aware AT schemes for hybrid RF/FSO based backhaul network withBA parallel relaying. The organization of this chapter is as follows. In Section 5.1, we summarizethe accomplished works and research contributions of this chapter. The considered system model ispresented in Section 5.2. Sections 5.3 and 5.4 provide the required problem formulations and corre-sponding optimal solutions for two different hybrid RF/FSO systems. Illustrative simulation resultsare provided in Section 5.5. Finally, Section 5.6 provides the concluding remarks.5.1 Accomplished Works and Research ContributionsThe motivation of this work is to develop optimal AT schemes for connecting a MBS with a SBSby using BA parallel relaying assisted hybrid RF/FSO backhaul network. In order to efficiently utilizethe available RF and FSO bandwidths, two simultaneous data streams are supported over RF andFSO links. We aim to improve the end-to-end throughput of the network by maximizing the constantarrival rate at the MBS, and ensuring that the total queue occupancy in the network is bounded withcertain acceptable QLB violation probability. Specific contributions of this work are summarized asfollows.1. We present AT schemes for single-carrier (SC) and multi-carrier (MC) hybrid RF/FSO systems.In the SC hybrid RF/FSO system, all the parallel relaying links operate by using the same RFbandwidth, and both hops of each relaying link have one transmit and one receive apertures forFSO communications. In RF domain, the MBS broadcasts same information to all the relaynodes (RNs), and only one RN is selected to simultaneously transmit to SBS. However, multipleRNs can simultaneously transmit and receive in FSO domain. In the MC hybrid RF/FSOsystem, multiple orthogonal RF sub-channels exist under an OFDMA setup, and both hopsof each relaying link have multiple FSO transmit-receive apertures. Note that, in order to avoidSI and/or IRI, half-duplex (HD) RF relaying was considered in [106–108]. However, HD RFrelaying does not efficiently utilize the available RF bandwidth during severe channel fading855.2. System Modelover FSO links. Compared to the relay selection and RF transmission scheduling, provided in[108] and [106], respectively, our proposed schemes ensure QoS guarantee with a generalizedutilization of the available system resources. Moreover, BA FSO relaying in [110] considered onlysingle optical beam in each hop with the fixed transmission parameters. Due to the presence ofmultiple parallel optical beams in a given FSO link and statistical-QoS aware adaptation of thetransmission parameters, our considered BA FSO relaying is different compared to [110].2. Our developed AT scheme for the SC hybrid RF/FSO system performs the following two tasks:(i) it determines the optimal broadcasting power of the MBS, active RN in the second hop, andtransmit power of the active RN by considering end-to-end statistical-QoS constraint, practicalself-interference-cancellation (SIC), and IRI in FD RF relaying, and (ii) it optimally allocates theoptical transmit power of the MBS towards different parallel RNs. We show that the optimalbroadcasting power of the MBS and transmit power of the active RN for RF transmission canbe obtained in closed-form at the loose statistical-delay constraint. We reveal the followingtwo insights: (i) for asymptotically large SI at the RNs, the proposed adaptive RF transmissionconverges to statistical-QoS aware adaptive link scheduling (ALS), and (ii) all-active and selectiveFSO relaying are obtained as special cases of the proposed optical transmit power allocation inthe high and low SNR regimes, respectively.3. Our developed AT scheme for the MC hybrid RF/FSO system performs the following two tasks:(i) it determines adaptive power allocation and RF sub-channel assignment among all the relay-ing links for RF transmission, and (ii) it adaptively selects an optimal spatial transmission mode(STM) and allocates available transmit power among the (transmit) apertures for FSO commu-nications in both hops of each relaying link. We reveal insights by considering different specialcases of the statistical-QoS constraint, channel fading, and number of FSO transmit apertures.In the proposed solutions, significant computations demanding Lagrangian multipliers can becalculated offline, and consequently, the proposed AT schemes have reasonable online complexity.4. By simulation, we illustrate the superiority of our proposed AT schemes for maximizing thesupportable arrival rate. For performance comparison, we consider the conventional NBA all-active/selective relaying and BA relaying with fixed transmission parameters. We evaluate theimpact of the non-ideal RF SIC, statistical QoS-constraint, and weather-induced attenuation inthe FSO link on the maximum supportable arrival rate in hybrid RF/FSO backhaul network.5.2 System Model5.2.1 Overview of the Considered System ConfigurationsFigure 5.1(a) depicts the hybrid RF/FSO communication system with BA parallel DF relaying, andfigure 5.1(b) shows an example of relay-assisted hybrid RF/FSO backhaul network. At the MBS, ascheduler divides the incoming data streams into two parallel data streams according to the supportedarrival rates over RF and FSO links, and these two streams are simultaneously transmitted over RFand FSO links [94, 98]. As per the standard assumption in BA parallel relaying [103], SBS can correctlyorder the received packets over RF and FSO links and recover the original information. Both MBS and865.2. System Model(a) Hybrid RF/FSO with BA parallel DF relaying. (b) Hybrid RF/FSO downlink backhaul network ex-ample.Figure 5.1: Hybrid RF/FSO communication system with BA parallel RN(s).RNs maintain two separate buffers for RF and FSO transmission. In a given node, the RF and FSOqueues are evolved independently, and consequently, we decouple RF and FSO link adaptation. Such adecoupling is motivated by the fact that a given end-to-end hybrid RF/FSO link can be decomposed intotwo FD and non-interfering parallel relaying links where each parallel relaying link can be independentlyoptimized. For analytical tractability, we make the following assumptions on the system model: (i)the buffer size is large such that there is no packet loss in a buffer; (ii) buffers are non-empty andthey always attempt to transmit; and (iii) data arrives at a constant rate to MBS. Such assumptionsare usually made in the existing statistical-QoS provisioning literature [171, 173], and the resultantAT scheme provides an upper bound of the achievable link-layer throughput. We also assume thatthe MBS and the SBS do not have direct link. Both MBS and SBS have multiple FSO transceiverswhere each transceiver is pointed to a unique RN. Each RN has FSO transmitter and receiver pointedto the SBS and MBS, respectively. Coherent detection for the FSO links is employed with accuratecompensation of phase noise at the receiver. In order to enable hybrid RF/FSO transmission, MBS,RN(s), and SBS are equipped with single antenna RF transmitter and receiver. We consider practical(i.e, non-ideal) SIC scheme at the RNs for FD RF relaying, and consequently, a non-zero residual SIis present during the decoding of the received symbols at the RNs. Similar to [173, 194], the non-zeroresidual SI is modeled as zero mean and additive Gaussian random variable with variance proportionalto the relay transmit power17.SC hybrid RF/FSO system: Same bandwidth-time resource blocks are employed for the RF linksover all the parallel relaying links. For FSO communication, in both hops of a given relaying link,17The considered hybrid RF/FSO system in figure 5.1(b) can be used for the backhaul link of a two-tier HetNet withthe following deployment scenario. In particular, the total RF bandwidth, available for backhauling, is divided amongthe small cells such that each small cell is allocated non-overlapping RF backhaul bandwidth. Moreover, the dedicatedRN(s) are deployed for providing RF and FSO backhaul connectivity from the MBS to the SBS. Therefore, the deployedbackhaul network for each SBS (or small cell) in the considered two-tier HetNet will have the similar structure of figure5.1(b). In such a case, the AT scheme for each SBS’s backhaul network can be independently optimized.875.2. System Modelone transmit aperture and one receive aperture are available, and thus, only single optical beam issupported. Over RF link, at each transmission slot (TS), the MBS broadcasts same information to allthe RNs, and only one RN is selected to transmit to SBS. Such an RF transmission strategy avoidsmulti-user decoding at SBS, reduces IRI, and provides diversity through selection of the transmittingRN. We emphasize that our proposed transmitting relay selection (RS) takes QoS constraint, SI, andIRI into account, and such an RS is different than the existing BA FD RS protocols [105]. Due to thespatial separation, the FSO links between the MBS and parallel RNs do not interfere with each other.At each TS, the MBS simultaneously transmits to all the RNs via spatial multiplexing (SM) over FSOlinks. Multiple RNs also simultaneously transmit to the SBS over the FSO links, and informationreceived from each RN over the FSO link is independently decoded at the SBS.MC hybrid RF/FSO system: The system has multiple RF sub-channels. Orthogonal RF sub-channels are allocated in both hops of the parallel relaying links. Consequently, the parallel RNssimultaneously transmit and receive over RF links without introducing SI and IRI. Due to adaptiveallocation of the RF sub-channels and RF power among the BA parallel relaying link, the overallthroughput for RF transmission is improved. All the parallel RNs simultaneously transmit and receiveover FSO links as well. The FSO transmitter and receiver in both hops of a given relaying link havemultiple transmit and receive apertures, respectively. Thus, each relaying link supports multiple par-allel optical beams. In the FSO link of each hop, a suitable STM, from SM, spatial diversity (SD), andhybrid transmission (HT), is adaptively selected along with the power allocation among the transmitapertures. In SM, independent symbols are transmitted over each optical beam. In SD, same symbolis transmitted over all the optical beams, and the signals from all the receive apertures are optimallycombined before decoding. In each hop, HT supports transmitting multiple symbols over the paralleloptical beams by integrating both SM and SD [195].Remark I: The hardware complexity and the computational load requirements at the RNs arebriefly described as follows. Each RN requires a coherent FSO receiver and a coherent FSO transmitterwhich are pointed to the MBS and SBS, respectively. Moreover, for the MC system, the coherent FSOtransceivers at each RN are also equipped with multiple apertures, and it is assumed that the apertureshave the sufficient spacing so that the optical channels from the the apertures experience independentchannel fading. Each RN coherently decodes the received signal over the FSO links from the MBS,stores the decoded data in the buffer, and coherently encodes the output of the buffer over the FSOlinks to the SBS. We emphasize that the aforementioned hardware and computational load requirementsincrease the implementation complexity, and such implementation complexity might be challenging forthe simple airborne FSO RNs. However, the terrestrial FSO RNs are static and primarily installed onthe rooftop of the buildings. As such, the required hardware and computational load requirements canbe accommodated in the terrestrial FSO RNs. Note that, state-of-the-art literature on BA FSO relays,such as [108, 110], also have considered that the FSO RNs are equipped with the transmitter andreceiver pointed to the destination and source, respectively, and the FSO RNs have both the decodingas well as buffering capability.885.3. Optimal AT for Single-Carrier Hybrid RF/FSO System(a) Equivalent relay RF queue. (b) Equivalent relay FSO queue.Figure 5.2: Equivalent queue model for parallel relay network.5.2.2 Channel Model and CSI RequirementsFor both RF and FSO links, we consider block fading process where the channel fading remainsconstant at each TS (with a duration on the order of milliseconds), and independently varies from oneTS to another TS. Moreover, the RF and FSO links in both hops experience mutually independentchannel fading. We consider the Gamma-Gamma turbulence fading and Rician fading for the FSOand RF links, respectively. The path loss exponents over RF and FSO links are obtained from [108].However, our proposed AT schemes are valid for any channel model. Without loss of generality, theproposed optimization is implemented at the MBS. It is assumed that the MBS knows the instantaneousand statistical CSI of all the parallel relaying links of the system. In addition, for decoding the receivedinformation, the instantaneous CSI of the link between the MBS and an RN is available at the RN,and instantaneous CSI of all the RN-to-SBS links is available at the SBS. Because of the (relatively)large channel coherence time of hybrid RF/FSO system, the availability of instantaneous CSI throughchannel estimation and feedback is usually afforded [108]. Finally, we consider that for both RF andFSO links, rate-adaptive modulation/coding is applied at the transmitter(s) of each hop based oninstantaneous CSI, and instantaneous channel capacity is achieved at each hop18.5.3 Optimal AT for Single-Carrier Hybrid RF/FSO SystemWe consider that the system has L BA parallel RNs. We introduce the following symbols for RFtransmission: h˜(i,m)RF is the equivalent RF channel gain considering fading and path loss for the i-thhop of the m-th parallel relaying link; ĥ(m,n)RF is the equivalent RF channel gain considering fading andpath loss in the link between the m-th and the n-th RNs; β(m)SI is the SIC factor at the m-th RN; Ps isthe RF broadcasting power of MBS; P(m)R is the transmit power of the m-th RN; and xm is a binaryvariable such that xm = 1 if the m-th RN is selected to be active in the second hop, and xm = 0,otherwise. We introduce the following symbols for FSO transmission: g˜(i,m)FSO is the equivalent FSOchannel gain considering fading and path loss for the i-th hop of the m-th parallel relaying link; P(s)FSOand P(R)FSO are the optical transmit power budgets of MBS and RN(s), respectively; and am ∈ [0, 1]is the optical transmit power allocation factor in the link between MBS and the m-th RN. WRF andWFSO denote the bandwidth of RF and FSO links, respectively, and TRFf and TFSOf denote duration18In hybrid RF/FSO system, channel capacity of RF and FSO links can be achieved by using the hybrid channel code,proposed in [196].895.3. Optimal AT for Single-Carrier Hybrid RF/FSO Systemof the transmitted data frames over RF and FSO links, respectively. Finally, σ2RF and σ2FSO denote thenoise variance in RF and FSO receivers, respectively, and φRF and φFSO denote the SNR gaps betweenideal channel capacity and practical modulation/coding scheme for RF and FSO links, respectively.Remark II: Due to the broadcasting and selective relaying over RF links in the first and second hops,respectively, SBS may receive multiple replicas of the previously received/decoded data packets overRF links. In order to alleviate such issue, at each TS, SBS broadcasts information of the successfullydecoded data packets to all the RNs, and RNs drop those packets from their RF queues. Owing toSM over MBS-to-parallel RN links, FSO queue of each RN receives (and transmits) non-identical datapackets. Thus, a similar queue adjustment is not required for the FSO links.5.3.1 AT over RF Links: Optimal Problem Formulation and SolutionWe define the statistical-QoS constraint as Pr[Q(s)RF +∑Lm=1Q(m)RF,R > Q(1)max] ≤ ζ1 where Q(s)RF andQ(m)RF,R are the lengths of RF queues at MBS and the m-th RN, respectively; Q(1)max is a given QLB; andζ1 is a given maximum acceptable QLB violation probability. Such a constraint ensures that the end-to-end queuing-length (and queuing-delay) of each parallel relaying link is bounded with certain QLBviolation probability. Moreover, ζ1 → 0 and ζ → 1 provide the strict and loose delay-QoS constraints,respectively. Inspired by [103], we represent the input-output dynamics of RF queues of the L parallelRNs by a single RF queue, depicted as equivalent relay RF (ER-RF) queue, in figure 5.2(a). The ER-RF queue has L input and output switch pairs, and L concatenated blocks where each block representsthe RF queue of an RN. In the ER-RF queue, the l-th input-output switch pair is connected with thel-th block. Because of broadcasting in the first hop, similar information bits are sent from MBS’s RFqueue to all input switches of the ER-RF queue. If xm = 1, the m-th output switch is connected withSBS’s RF queue, and the information bits stored at the m-th block are extracted. In a given TS, thesuccessfully transmitted information bits from a given block are also dropped from all other blocks.Consequently, ∀m ∈ {1, 2, · · · , L}, the m-th block in the ER-RF queue is filled and emptied similarly tothe m-th RN’s RF queue in figure 7.2(a). In the steady state, the length of ER-RF queue provides thetotal length of all the relay RF queues in the network [103]. Accordingly, the considered statistical-QoSconstraint is equivalently written as Pr[Q(s)RF +QE−RF > Q(1)max] ≤ ζ1 where QE−RF is the steady statelength of ER-RF queue. For such an equivalence, the transmission rate of the MBS and the receivedrate of the SBS in the equivalent queue model and in the original parallel relay network need to besame19. The service rates of RF queue of the MBS and the ER-RF queue, denoted as R(RF )s andRE−RF , respectively, are expressed asR(RF )s = TRFf WRF log2(1 + minm∈{1,··· ,L}{Psh˜(1,m)RF /φRF∑Ll=1 xlb(m)l P(l)R + σ2RF}), (5.1a)RE−RF = TRFf WRFL∑m=1xm log2(1 +P(m)R h˜(2,m)RF /φRFσ2RF). (5.1b)19Note that, the total queue occupancy distribution in a parallel queuing network remains unchanged if the parallelqueues are replaced by an equivalent queue with the arrival rate equal to sum of individual arrival rates to the parallelqueues [197].905.3. Optimal AT for Single-Carrier Hybrid RF/FSO SystemIn (5.1a), b(m)l = β(m)SI if l = m and b(m)l = ĥ(m,l)RF , otherwise. Consequently, we obtain a concatenateddual-queuing system for RF transmission with service rates defined in (5.1a) and (5.1b). In orderto satisfy the maximum acceptable QLB violation probability constraint, both RF queue of MBS andER-RF queue should achieve statistical-QoS exponent θ(1)TAR = − 1Q(1)max(1 +W−1(− ζ1e)). Accordingly,by using (2.34), the maximum supportable arrival rate to the RF queue of MBS, µ∗RF,SC(ζ1, Q(1)max),is obtained from the following optimization problem:P1 : µ∗RF,SC(ζ1, Q(1)max)= maxµ≥0,Ps≥0,P (m)R ≥0,xm∈{0,1}µs.t. C1: µθ(1)TAR + logE[exp(−θ(1)TARR(RF )s)]= 0, µθ(1)TAR + logE[exp(−θ(1)TARRE−RF)]= 0C2: Ps +L∑m=1xmP(m)R ≤ Pmax, C3:L∑m=1xm = 1.(5.2)In P1, C1 ensures statistical-QoS constraint, C2 is RF power allocation constraint with Pmax as theavailable RF transmit power budget, and C3 is the transmitting RN selection constraint.Proposition 5.3.1: In a given TS, the optimal selection of the transmitting RN is given asxm ={1, if m = arg minmˆ∈{1,2,··· ,L} V (mˆ)0, otherwise.(5.3)Here, V (mˆ) is defined asV (mˆ) = (1− ∗)(1 + P (mˆ)s × minm∈{1,2,··· ,L}{h˜(1,m)RF /φRFb(m)mˆ P(mˆ)R + σ2RF})−η(1)T+ ∗(1 +P(mˆ)R h˜(2,mˆ)RFφRFσ2RF)−η(1)T.(5.4)In (5.4), η(1)T =θ(1)TARTRFf WRFlog 2 , ∗ is the optimal Lagrangian multiplier, and the values of P (mˆ)s and P(mˆ)Rare obtained as(P (mˆ)s , Pˆ(m)R)=(P, Pmax − P ) , ∃P ∈ (0, Pmax) and G(mˆ) (∗, P ) = 0(Pmax, 0) , elseif G(mˆ)1 (∗) < G(mˆ)2 (∗)(0, Pmax) , elseif G(mˆ)1 (∗) > G(mˆ)2 (∗) .(5.5)In (5.5), G(mˆ) (∗, P ), G(mˆ)1 (∗), and G(mˆ)2 (∗) are defined as, respectively,G(mˆ) (∗, P ) = Bmˆ(1 +(Pmax − P ) h˜(2,mˆ)RFφRFσ2RF)−(η(1)T +1)−Amˆ(Pmax + P(h(1,mˆ)eq − 1))−(η(1)T +1)(Pmax − P )−(η(1)T −1), (5.6)G(mˆ)1 (∗) = (1− ∗)(1 +PmaxφRFσ2RFh˜(min,1)RF)−η(1)T+ ∗, (5.7)915.3. Optimal AT for Single-Carrier Hybrid RF/FSO SystemG(mˆ)2 (∗) = ∗(1 +PmaxφRFσ2RFh˜(2,mˆ)RF)−η(1)T+ (1− ∗) . (5.8)In (5.6)-(5.8), h(1,mˆ)eq = min{h˜(1,1)RFĥ(1,mˆ)RF, · · · , h˜(1,mˆ)RFβ(mˆ)SI, · · · , h˜(1,L)RFĥ(L,mˆ)RF}, h˜(min,1)RF = minm∈{1,2,··· ,L} h˜(1,m)RF , Amˆ =η(1)T (1− ∗)h(1,mˆ)eq Pmax, and Bmˆ =η(1)T ∗h˜(2,m̂)RFφRF σ2RF. The optimal RF broadcasting power of the MBS and theoptimal transmit power of the active RN are obtained as P ∗s = P(m∗)s and P ∗R = P(m∗)R , respectively,where m∗ = arg minmˆ∈{1,2,··· ,L} V (mˆ). The maximum supportable arrival rate (in bits/second unit) tothe RF queue of MBS is expressed asµ∗RF,SC(ζ1, Q(1)max)= − 1θ(1)TARTRFflogE(1 + minm∈{1,2,··· ,L}{P ∗s h˜(1,m)RF /φRFb(m)m∗ P∗R + σ2RF})−η(1)T . (5.9)Proof (Outline): The optimal solution to P1 is obtained by solving the corresponding Lagrangiandual problem per channel fading state [198]. The key steps of the proof are following. We first formulatethe Lagrangian problem to P1 per channel fading state. For a given selection of the transmitting RN, theC3 constraint of P1 has to be satisfied with equality. By using such a fact to the formulated Lagrangianproblem and applying the first order optimality condition, we obtain optimal power allocation(s) andcost metrics given by (5.5) and (5.4), respectively. Finally, we select the active RN in the second hopand power allocations in both hops correspond to the lowest cost metric. The detailed derivation isomitted for brevity.Calculation of ∗: If = 0 or ≥ 1, regardless of the statistical-QoS constraint, always same solutionto P1 is obtained, which is (intuitively) non-optimal. Consequently, ∗ ∈ (0, 1). The value of ∗ willsatisfy E[exp(−θ(1)TARR(RF )s)]= E[exp(−θ(1)TARRE−RF)]for the power allocation and relay selectionobtained from Proposition 5.3.1. Moreover, ∗ depends on the statistics of RF channels, SIC factor atthe RNs, and statistical-QoS exponent. Consequently, an offline one-dimensional binary search overthe (0, 1) interval is performed in order to obtain the value of ∗.Special case of loose statistical-delay constraint: For delay-tolerant traffic, we obtain θ(1)TAR → 0 (i.e.,ζ1 → 1). In this case, the optimal selection of the transmitting RN in the second hop is given by xm˜ = 1and xm˜6=m∗ = 0 where m˜ = arg maxmˆ∈{1,2,··· ,L}(max{G˜(P˜(mˆ)1 ), G˜(P˜(mˆ)2 )}), and where G˜(P˜(mˆ)i ) withi = 1, 2 is defined asG˜(P˜(mˆ)i ) = (1− ̂) log21 + minm∈{1,2,··· ,L} P˜(mˆ)i h˜(1,m)RF /φRFb(m)mˆ(Pmax − P˜ (mˆ)i)+ σ2RF+ ˜ log21 +(Pmax − P˜ (mˆ)i)h˜(2,mˆ)RFφRFσ2RF .(5.10)In (5.10), the value of ̂ ∈ (0, 1) is determined in offline such that the average arrival and departure925.3. Optimal AT for Single-Carrier Hybrid RF/FSO Systemrates of E-RF queue are equal. The values of P˜(mˆ)1 and P˜(mˆ)2 are obtained asP˜(mˆ)1 =ν(mˆ)2 +√((ν(mˆ)2)2 − 4ν(mˆ)1 ν(mˆ)3 )+ 12ν(mˆ)1Pmax0,P˜(mˆ)2 =ν(mˆ)2 −√((ν(mˆ)2)2 − 4ν(mˆ)1 ν(mˆ)3 )+ 12ν(mˆ)1Pmax0.(5.11)Here, [c]+ = max(c, 0), ν(mˆ)1 = h(1,mˆ)eq /φRF −1, ν(mˆ)2 =(h(1,mˆ)eq /φRF − 1)Pmax−Pmax+ (1−̂)Pmaxh(1,mˆ)eq̂ ,and ν(mˆ)3 =(1−̂)Pmaxh(1,mˆ)eq̂(1 +h˜(2,mˆ)RFφRF σ2RF)Pmax − P 2max. The optimal broadcasting power of the MBS,P ∗s , and the transmit power of the active RN in the second hop, P ∗R, are obtained as(P ∗s , P∗R) =(P˜(m˜)1 , Pmax − P˜ (m˜)1), if G˜(P˜(m˜)1 ) > G˜(P˜(m˜)2 )(P˜(m˜)2 , Pmax − P˜ (m˜)2), if G˜(P˜(m˜)1 ) < G˜(P˜(m˜)2 ).(5.12)Therefore, for the loose statistical-delay constraint over RF links, the optimal broadcasting power ofthe MBS and the transmit power of the active RN in the second hop are obtained in closed-forms.Special case of large residual SI: When β(m)SI → ∞, ∀m, FD RF relaying is no longer possible. Insuch a case, either only MBS broadcasts to all the RNs by using maximum transmit power or only theRN having maximum channel gain in the second hop transmits to the SBS with maximum transmitpower. In particular, when the minimum channel gains in the first hop satisfies h(min,1)RF > ∆, we obtainP ∗s = Pmax and P(m)R = 0, ∀m. Otherwise, we obtain P (m∗)R = Pmax, P(m)R = 0, ∀m 6= m∗, P ∗s = 0, andm∗ = arg maxm h˜(2,m)RF . The value of ∆ is given by ∆ =(1−′)1η(1)T σ2RFφRFPmax(1−2′)+′(1+Pmaxh˜(max,2)RFφRF σ2RF)−η(1)T1/η(1)T−σ2RFφRFPmaxwhere h˜(max,2)RF = maxm h˜(2,m)RF . For large value of {β(m)SI }, the proposed adaptive RF transmis-sion converges to BA ALS. Compared to the conventional ALS, the link switching threshold dependson the QoS-constraint and maximum channel gain of the second hop. Here, ′ ∈ (0, 1) is numericallyobtained such that E[exp(−θ(1)TARR(RF )s)]= E[exp(−θ(1)TARRE−RF)]is satisfied for the QoS-awareALS.5.3.2 AT over FSO Link: Optimal Optical Transmit Power Allocation at MBSThe total queue occupancy constraint for FSO link is given by Pr[Q(s)FSO +∑Lm=1Q(m)FSO,R >Q(2)max] ≤ ζ2 where Q(s)FSO and Q(m)FSO,R are the lengths of FSO queues at the MBS and the m-thRN, respectively; Q(2)max and ζ2 are the given QLB and maximum acceptable QLB violation prob-ability, respectively. For satisfying such a constraint, we adopt an equivalent queue approach byreplacing the FSO queues of L parallel RNs with an equivalent relay FSO (ER-FSO) queue of fig-ure 5.2(b). We can justify that the relay FSO queues in figure 5.1(a) and the blocks of ER-FSOqueue in figure 5.2(b) are similarly filled and emptied. Accordingly, the total FSO queue occupancyconstraint is satisfied when both FSO queue of the MBS and the ER-FSO queue achieve statistical-935.3. Optimal AT for Single-Carrier Hybrid RF/FSO SystemQoS exponent θ(2)TAR = − 1Q(2)max(1 +W−1(− ζ2e)). The service rates of FSO queue of the MBS andthe ER-FSO queue are given as, respectively, R(FSO)s = TFSOf WFSO∑Lm=1 log2(1 + amγFSOm)andRE−FSO = TFSOf WFSO∑Lm=1 log2(1 +RP(R)FSO g˜(2,m)FSOφFSOσ2FSO). Here, γFSOm =RP(s)FSO g˜(1,m)FSOφFSOσ2FSOdenotes the av-erage received SNR over FSO link at the m-th RN. By using adaptive power allocation for theFSO transmitter at the MBS, the maximum supportable arrival rate to the FSO queue of the MBS,µ∗FSO,SC(ζ2, Q(2)max), is obtained asP2 : µ∗FSO,SC(ζ2, Q(2)max)= maxµ≥0,am∈[0,1]µs.t. C4: µθ(2)TAR + logE[exp(−θ(2)TARR(FSO)s)]= 0,C5: µθ(2)TAR + logE[exp(−θ(2)TARRE−FSO)]= 0, C6:L∑m=1am = 1.(5.13)Proposition 5.3.2: Without loss of generality, we assume γFSO1 > γFSO2 > · · · > γFSOL holds. Ifthere exists a maximum value of L′ such that 2 ≤ L′ ≤ L, and γFSOL′ ≥ Σ1L′η(2)T+1×∏L′m=1 (γFSOm ) η(2)TL′η(2)T+1 ,where η(2)T =θ(2)TARTFSOf WFSOlog 2 , then, for given channel fading state, the optimal optical transmit powerallocation at the MBS towards the parallel RNs is obtained asa∗m =1Λ 1Σ1L′η(2)T+1 ∏L′m=1(γFSOm )η(2)TL′η(2)T+1− 1γFSOm , m = 1, 2, · · · , L′.0, m = L′ + 1, · · · , L.(5.14)Otherwise, the optimal optical transmit power allocation at the MBS is obtained as a∗m = 1 and a∗m = 0for m = 1 and m = 2, 3, · · · , L, respectively. In (5.14), Σ > 0 is a constant that is determined offlinefrom the solution of E[exp(−θ(2)TARR(FSO)s)]−E[exp(−θ(2)TARRE−FSO)]= 0, and Λ is a normalizingfactor such that∑Lm=1 a∗m = 1 is satisfied. The maximum supportable arrival rate (in bits/secondunit) to the FSO queue of MBS is expressed asµ∗FSO,SC(ζ2, Q(2)max)= − 1θ(2)TARTFSOflogE[L∏m=1(1 + a∗mγFSOm)−η(2)T ] . (5.15)Proof : The proof is straightforward, and it is omitted for brevity.Special case of asymptotically high SNR: Let, θ(2)TAR → 0 and γFSOm → ∞, ∀m. We first assumethat non-zero optical power is allocated only to the best L′ RNs. Consequently, we obtain a∗m =1Λ(1Σ − 1γFSOm), m = 1, 2, · · · , L′, and a∗m = 0, m = L′+ 1, · · · , L. Since γFSOm →∞, 1Σ 1/γFSOm , and∑Lm=1 a∗m = 1 are satisfied, we obtain a∗m ≈ 1L′ , m = 1, 2, · · · , L′. Moreover, since γFSOm → ∞, ∀m,it can be justified that a∗m =1L , ∀m will provide better throughput than a∗m = 1L′ , m = 1, 2, · · · , L′and a∗m = 0, m = L′ + 1, · · · , L. Consequently, transmit power of the FSO transmitter at the MBSwill be equally allocated among all the parallel RNs. We can also show that when θ(2)TAR is large and945.3. Optimal AT for Single-Carrier Hybrid RF/FSO SystemγFSOm →∞, ∀m, optical transmit power of the MBS is equally allocated among all the RNs. Therefore,in the asymptotic high SNR regime, the proposed optical transmit power allocation converges to theall-active FSO relaying with equal-power allocation.Special case of low SNR: Regardless of the statistical-QoS exponent, MBS allocates all the availableoptical transmit power to the strongest RN in the first hop at low SNR regime. Consequently, in thepresence of severe channel fading and/or attenuation, the proposed optical transmit power allocationconverges to a selective relaying scheme. Depending on the FSO link condition, the proposed ATscheme switches between all-active and selective FSO relaying schemes.5.3.3 Maximum Supportable Arrival RateWith the help of Proposition 5.3.1 and Proposition 5.3.2, the net optimal arrival rate to MBS (inbits/second unit) is obtained as µ∗SC(ζ1, ζ2, Q(1)max, Q(2)max) = µ∗RF,SC(ζ1, Q(1)max)+µ∗FSO,SC(ζ2, Q(2)max).For given values of ∗ and Σ, Proposition 5.3.1 and Proposition 5.3.2 require maximum O(L) com-putations. Therefore, the proposed AT schemes for the RF and FSO links have reasonable onlinecomplexity. For performance comparison, we consider conventional FD NBA selective and all-activerelaying schemes with statistical-QoS constraint.NBA Selective relaying: In NBA parallel relaying, statistical-QoS constraint needs to be satisfiedonly for the RF and FSO queues at the MBS. In both RF and FSO links, the best RN is selected fortransmission and reception. The maximum supportable arrival rate to the MBS (in bits/second unit)is given asµSR−NBA = − 1θ˜1TRFflogE[exp(−θ˜1TRFf WRFCe2e,1RF)]− 1θ˜2TFSOflogE[exp(−θ˜2TFSOf WFSOCe2e,1FSO)] (5.16)where θ˜i = − ln ζiQ(i)maxwith i = 1, 2. In (5.16), the available RF transmit power is equally allocated betweentwo hops. Hence, Ce2e,1RF = maxm∈{1,2,··· ,L} log2(1 + min{Pmax/2×h˜(1,m)RFφRF β(m)SI Pmax/2+φRF σ2RF,Pmax/2×h˜(2,m)RFφRF σ2RF}),and Ce2e,1FSO = maxm∈{1,2,··· ,L} log2(1 + min{RP(s)FSO g˜(1,m)FSOφFSOσ2FSO,RP(R)FSO g˜(2,m)FSOφFSOσ2FSO}).NBA All-active relaying: The MBS does not have instantaneous CSI and it transmits to all theRNs such that each RN can successfully decode the received signal. The RNs cooperatively transmitto the SBS. The maximum supportable arrival rate to the MBS (in bits/second unit) is given asµAAR−NBA = − 1θ˜1TRFflogE[exp(−θ˜1TRFf WRF ×min{rRF1 , rRF2})]− 1θ˜2TFSOflogE[exp(−θ˜2TFSOf WFSO ×min{rFSO1 , rFSO2})] (5.17)where rRF1 = log2(1 + minmPmax/2×h˜(1,m)RF /φRF∑Ll=1 b(m)l Pmax/2L+σ2RF), rFSO1 = log2(1 +RP(S)FSOLφFSOσ2FSOminm g˜(1,m)FSO), rRF2 =log2(1 + Pmax/2LφRF σ2RF(∑Lm=1√h˜(2,m)RF)2), and rFSO2 = log2(1 +RP(R)FSOφFSOσ2FSO∑Lm=1 g˜(2,m)FSO).955.4. Optimal AT for Multi-Carrier Hybrid RF/FSO System5.4 Optimal AT for Multi-Carrier Hybrid RF/FSO SystemStatistical-QoS constraints for transmission over the RF and FSO links in the MC system arerespectively given by Pr[Q(s)RF +∑Lm=1Q(m)RF,R > Q(3)max] ≤ ζ3 and Pr[Q(s)FSO +∑Lm=1Q(m)FSO,R > Q(4)max] ≤ζ4. Here, {Q(3)max, Q(4)max} and {ζ3, ζ4} are the given QLB and the maximum acceptable QLB violationprobability, respectively. We adopt an equivalent queue approach for satisfying these constraints. Forequivalence of the total queue occupancy constraints over the RF(FSO) links in the network with Lparallel RF(FSO) relay queues and in the network with ER-RF (ER-FSO) queue, the transmissiondata rate of the MBS and the received data rate of the SBS need to be same in both networks.5.4.1 Optimal Power Allocation and Sub-channel Assignment for RFTransmissionWe denote that Nsc is the total number of orthogonal RF sub-channels and Nsc is the set of RFsub-channels; W˜RF is the bandwidth per sub-channel; T˜fRFis the duration of transmitted frame persub-channel; h˜(m,n)RF,i is the equivalent RF channel gain of the n-th RF sub-channel in the i-th hop of them-th relaying link; P(m,n)RF,s is the transmit power of MBS in the n-th RF sub-channel assigned to them-th RN; and P(m,n)RF,R is the transmit power of the m-th RN in the n-th RF sub-channel. We introducetwo binary variables, α(m,n)RF,1 and α(m,n)RF,2 , where α(m,n)RF,i = 1 if the n-the RF sub-channel is assigned inthe i-th hop of the m-th relaying link, and α(m,n)RF,i = 0, otherwise. The service rates of the RF queue ofthe MBS and the ER-RF queue are written as, respectively,R(RF )s,MC = T˜fRFW˜RFL∑m=1Nsc∑n=1α(m,n)RF,1 log21 + P (m,n)RF,s h˜(m,n)RF,1φRFσ2RF , (5.18a)RE−RF,MC = T˜fRFW˜RFL∑m=1Nsc∑n=1α(m,n)RF,2 log21 + P (m,n)RF,R h˜(m,n)RF,2φRFσ2RF . (5.18b)The maximum arrival rate to the RF queue of MBS, µ∗RF,MC(ζ3, Q(3)max), QoS-aware RF power allo-cation and sub-channel assignment are obtained from the following optimization problem.P3 : µ∗RF,MC(ζ3, Q(3)max)= maxµ≥0,{P (m,n)RF,s ,P(m,n)RF,R }≥0,{α(m,n)RF,1 ,α(m,n)RF,2 }∈{0,1}µs.t. C7: µθ(3)TAR + logE[exp(−θ(3)TARR(RF )s,MC)]= 0, µθ(2)TAR + logE[exp(−θ(2)TARRE−RF,MC)]= 0C8:L∑m=1Nsc∑n=1α(m,n)RF,1 P(m,n)RF,s +L∑m=1Nsc∑n=1α(m,n)RF,2 P(m,n)RF,R ≤ Pmax, C9:L∑m=1α(m,n)RF,1 + α(m,n)RF,2 = 1,∀n ∈ Nsc.(5.19)In P3, θ(3)TAR = − 1Q(3)max(1 +W−1(− ζ3e)), C7 ensures the required statistical-QoS constraint, C8 pro-vides total RF transmit power constraint with Pmax as the total power budget, and C9 provides RFsub-channel assignment in order to avoid SI and IRI. The justification of using total power constraintin C10 is following. First of all, such a constraint allows to optimize both transmit power along with965.4. Optimal AT for Multi-Carrier Hybrid RF/FSO SystemRF sub-channel assignment in both hops of the parallel relaying links. The complexity for computingdual variables, compared to the case with individual power constraint, is also reduced. Finally, thetotal power constraint also limits the RF interference generation to the external cellular network.Proposition 5.4.1: At each TS, the optimal RF transmit power allocations are obtained asP(m,n),∗RF,s =[Λ∗RF,1 − φRF σ2RFh˜(m,n)RF,1]+,∀m ∈ {1, 2, · · · , L}, n ∈ N (m,∗)sc,10,∀m ∈ {1, 2, · · · , L}, n /∈ N (m,∗)sc,1 .(5.20a)P(m,n),∗RF,R =[Λ∗RF,2 − φRF σ2RFh˜(m,n)RF,2]+,∀m ∈ {1, 2, · · · , L}, n ∈ N (m,∗)sc,20,∀m ∈ {1, 2, · · · , L}, n /∈ N (m,∗)sc,2 .(5.20b)In (5.20a) and (5.20b), N (m,∗)sc,1 and N (m,∗)sc,2 are the optimal set of RF sub-channels having non-zerotransmission rate in first and second hops of the m-th relaying link, respectively, and Λ∗RF,i, wherei = 1, 2, is defined asΛ∗RF,i =((1− ω∗1)η(3)Tω∗2) 11+η(3)T∑Lm1=1∑n1∈N(m1,∗)sc,iα(m1,n1),∗RF,i×L∏m1=1∏n1∈Nm1,∗sc,i h˜(m,n)RF,iφRFσ2RF−η(3)Tα(m1,n1),∗RF,i1+η(3)T∑Lm1=1∑n1∈N(m1,∗)sc,iα(m1,n1),∗RF,i.(5.21)In (5.21), η(3)T =θ(3)TART˜fRFW˜RFlog 2 , ω∗1 ∈ (0, 1) and ω∗2 > 0 are the constants corresponding to the optimalLagrangian multipliers. The optimal RF sub-channel assignment rules are obtained asα(m,n),∗RF,1 ={1,m = arg minm̂∈{1,··· ,L}∆(1)m̂,n and ∆(1)m,n < minm̂∈{1,··· ,L}∆(2)m̂,n,0, otherwise(5.22a)α(m,n),∗RF,2 ={1,m = arg minmˆ∈{1,··· ,L}∆(2)m̂,n and ∆(2)m,n < minm̂∈{1,··· ,L}∆(1)m̂,n,0, otherwise(5.22b)where∆(i)m,n = ω∗2(Λ∗RF,i(1− ln(Λ∗RF,ih˜(m,n)RF,iφRF σ2RF))− φRF σ2RFh˜(m,n)RF,i),∀m ∈ {1, 2, · · · , L}, n ∈ N (m,∗)sc,i0,∀m ∈ {1, 2, · · · , L}, n /∈ N (m,∗)sc,i .(5.23)In (5.22a) and (5.22b), ∆(i)m,n provides the RF sub-channel assignment metric in the i-th hop of them-th relaying link. The maximum supportable arrival rate to the MBS’s RF queue is expressed asµ∗RF,MC(ζ3, Q(3)max)= − 1θ(3)TART˜fRFlogEexp−η(3)T L∑m=1Nsc∑n=1α(m,n),∗RF,1 ln1 + P (m,n),∗RF,s h˜(m,n)RF,1φRFσ2RF .(5.24)975.4. Optimal AT for Multi-Carrier Hybrid RF/FSO SystemProof (Outline): Proof of Proposition 5.4.1 has the following outline. Following a time-sharingrelaxation technique, we convert (P3) to a convex optimization optimization problem by relaxing theinteger variables as α(m,n)RF,1 ∈ [0, 1], and introducing two auxiliary variable Q(m,n)RF,s = α(m,n)RF,1 P (m,n)RF,s andQ(m,n)RF,R = α(m,n)RF,2 P(m,n)RF,R . By satisfying the well-known Karush-Khun-Tuker conditions, optimal solutionsto the relaxed convex optimization problem are obtained as (5.20a), (5.20b), (5.22a), and (5.22a).Such optimal solutions are feasible to the original problem (P3). Consequently, such solutions are alsooptimal to (P3). The detailed derivation is omitted for brevity,.Calculation of ω∗1 and ω∗2: ω∗1 and ω∗2 will be obtained by satisfying E[exp(−θ(3)TARR(RF )s,MC)]=E[exp(−θ(3)TARRE−RF,MC)], and constraint C8 of (5.19). Since ω∗1 and ω∗2 depend on the RF channelstatistics and instantaneous CSI, respectively; ω∗1 is determined offline, and ω∗2 is updated at each TS.Following sub-gradient methods, at the k + 1-th iteration, ω1 and ω2 are updated asω1[k + 1] =[ω1[k] + r1[k](E[exp(−θ(3)TARRE−RF,MC)]− E[exp(−θ(3)TARR(RF )s,MC)])]10,ω2[k + 1] =[ω2[k] + r2[k](L∑m=1Nsc∑n=1α(m,n)RF,1 P(m,n)RF,s +L∑m=1Nsc∑n=1α(m,n)RF,2 P(m,n)RF,R − Pmax)]+where r1[k] and r2[k] are small step sizes, and the values of α(m,n)RF,1 , α(m,n)RF,2 , P(m,n)RF,s , and P(m,n)RF,R areobtained from Proposition 5.4.1 for the given values of ω1[k] and ω2[k]. For suitably chosen step sizes,the aforementioned update equations rapidly converge to ω∗1 and ω∗2 within finite iterations.Special case of loose delay constraint with large channel gain-to-noise ratio: In this case, the QoS-aware water level in Proposition 5.4.1, Λ∗RF,i, will become constant for i = 1, 2. The RF sub-channelassignment metrics are written as ∆(i)m,n ≈ ω∗2c1(1− ln(c1h˜(m,n)RF,iφRF σ2RF)), for i = 1, 2, where c1 is a constant.The RF sub-channel assignment rules in (5.22a) and (5.22b) are reduced asα(m,n),∗RF,1 ={1, if h˜(m,n)RF,1 = max{maxm̂∈{1,2,··· ,L} h˜(m̂,n)RF,1 ,maxm̂∈{1,2,··· ,L} h˜(m̂,n)RF,2}0, otherwise.(5.26a)α(m,n),∗RF,2 ={1, if h˜(m,n)RF,2 = max{maxm̂∈{1,2,··· ,L} h˜(m̂,n)RF,1 ,maxm̂∈{1,2,··· ,L} h˜(m̂,n)RF,2}0, otherwise.(5.26b)In the presence of large channel gain-to-noise ratio, the constraint C8 in P3 is satisfied by equallyallocating total transmit power over the orthogonal RF sub-channels. Hence, P(m,n)RF,S → PmaxNsc andP(m,n)RF,R → PmaxNsc , ∀m,n. For the special case of loose delay constraint and shallow channel fading, thetotal RF power is uniformly allocated among all the RF sub-channels, and the RF sub-channels areassigned to the strongest link selected from all the MBS-to-RN and RN-to-SBS links.5.4.2 Optimal STM Selection and Transmit Power Allocation for FSOTransmissionWe denote NA as the number of transmit and receiver apertures at both hops of a given relayinglink; g˜(m,na,nb)FSO,i as the equivalent FSO channel gain in the i-th hop of m-th relaying link over (na, nb)-thaperture pairs where (na, nb) ∈ {1, 2, · · · , NA}; and PFSO as the maximum available transmit power985.4. Optimal AT for Multi-Carrier Hybrid RF/FSO Systemin each hop. We define a binary variable φ(m,i)z ∈ {0, 1} such that φ(m,i)z = 1 if the z STM, wherez ∈ {SM, SD, HT}, is selected in the i-th hop of the m-th relaying link, and φ(m,i)z = 0, otherwise.We define a(m,na)z,i ∈ [0, 1] as the transmit power allocation factor to the na-th transmit aperture inthe i-th hop of the m-th relaying link for z STM. For the analytical tractability, we consider that forHT in a given hop, the apertures at the transmitter (receiver) are divided into K disjoint sets whereeach set contains NA/K number of transmit (receive) apertures. In HT, K independent symbols aresimultaneously transmitted, and a given symbol is repeated over NA/K transmit apertures throughrepetition coding [195]. We consider that the transmit and receive apertures in a given hop experienceindependent fading, and cross-talk among the parallel optical beams is compensated at the receiverfor both SM and HT (see [68] for a method of compensating the cross-talk among the parallel opticalbeams). Accordingly, the achievable rates of the SM, SD, and HT, in the i-th hop of the m-th relayinglink, are given as, respectively,R(m,i)SM =NA∑na=1log2(1 + a(m,na)SM,i γ(m,na,na)FSO,i), (5.27a)R(m,i)SD = log21 + NA∑na=1a(m,na)SD,iNA∑nb=1γ(m,na,nb)FSO,i , (5.27b)R(m,i)HT =K∑l=1log21 + ∑na∈S(T )la(m,na)HT,i∑nb∈S(R)lγ(m,na,nb)FSO,i . (5.27c)Here, γ(m,na,nb)FSO,i =RPFSO g˜(m,na,nb)FSO,iφFSOσ2FSO, S(T )l and S(R)l are the l-th (l ∈ {1, 2, · · · ,K}) disjoint trans-mit and receive aperture sets at the transmitter and receiver, respectively, for performing HT inthe i-th hop of the m-th relaying link. The service rate of the FSO queue of MBS is given byR(FSO)s,MC = TFSOf WFSO∑Lm=1∑z∈{SM, SD, HT} φ(m,1)z R(m,1)z , and the service rate of the ER-FSO queueis given by R(FSO)E−FSO,MC = TFSOf WFSO∑Lm=1∑z∈{SM, SD, HT} φ(m,2)z R(m,2)z . The optimization problemfor maximizing the constant arrival rate to the FSO queue of the MBS is formulated asP4 : µ∗FSO,MC(ζ4, Q(4)max)= maxµ≥0,a(m,na)z,i ∈[0,1],φ(m,i)z ∈{0,1}µs.t. C10: µθ(4)TAR + logE[exp(−θ(4)TARR(FSO)s,MC)]= 0;C11: µθ(4)TAR + logE[exp(−θ(4)TARRE−FSO,MC)]= 0C12:∑z∈{SM, SD, HT}φ(m,i)z = 1,∀m, i, C13:NA∑na=1a(m,na)z,i = 1, ∀z ∈ {SM, SD, HT} ,m, i.(5.28)In (P4), θ(4)TAR = − 1Q(4)max(1 +W−1(− ζ4e)), C10 and C11 ensure the considered statistical-QoS con-straint, C12 and C13 provide the STM selection and transmit power allocation constraints for eachhop, respectively. Unlike RF transmission, the FSO relaying links in the considered system modelare mutually independent. Therefore, for FSO transmission, each relaying link can be indepen-dently optimized. Moreover, the maximum arrival rate to a buffer transmitting over multiple non-995.4. Optimal AT for Multi-Carrier Hybrid RF/FSO Systeminterfering and independent parallel links is the sum of individual EC of the parallel links [199,Proposition 4.3]. Consequently, the maximum traffic arrival rate to the FSO queue of the MBS willbe µ∗FSO,MC(ζ4, Q(4)max)=∑Lm=1 µ˜∗FSO,m(ζ4, Q(4)max)where µ˜∗FSO,m(ζ4, Q(4)max)is the maximum sup-portable traffic arrival rate over the m-th parallel relaying link. The value of µ˜∗FSO,m(ζ4, Q(4)max),∀m ∈ {1, 2, · · · , L}, is obtained from following optimization problem:P5 : µ˜∗FSO,m(ζ4, Q(4)max)= maxµ˜≥0,a(m,na)z,i ∈[0,1],φ(m,i)z ∈{0,1}µ˜s.t. C14: µ˜θ(4)TAR + logEexp−θ(4)TARTFSOf WFSOMN ∑z∈{SM, SD, HT}φ(m,1)z R(m,1)z = 0;C15: µ˜θ(4)TAR + logEexp−θ(4)TARTFSOf WFSOM ∑z∈{SM, SD, HT}φ(m,2)z R(m,2)z = 0C16:∑z∈{SM, SD, HT}φ(m,i)z = 1, C17:NA∑na=1a(m,na)z,i = 1,∀i ∈ {1, 2, }, z ∈ {SM, SD, HT} .(5.29)Proposition 5.4.2: We provide optimal solutions to P5 of (5.29) in two steps. At the first step,the optimal transmit power allocations among the transmit apertures of the i-th hop in the m-threlaying link, for performing SM, SD, and HT, are obtained. Next, based on the optimal transmitpower allocations, optimal STM selection for the i-th hop in the m-th relaying link, where i ∈ {1, 2}and m ∈ {1, 2, · · · , L}, is determined.Transmit power allocation for SM: We assume that the inequality γ(m,1,1)FSO,i > γ(m,2,2)FSO,i > · · · >γ(m,NA,NA)FSO,i holds. We define ψ(L,{γ(m,na,na)FSO,i}), β1Lη(4)T+1m∏Ln=1(γ(m,n,n)FSO,i) η(4)TLη(4)T+1 where βm is aconstant, and it depends on the channel fading statistics and statistical QoS-exponent. If there existsa maximum value of N ′A such that 2 ≤ N ′A ≤ NA and γ(m,N ′A,N′A)FSO,i ≥ ψ(N ′A,{γ(m,na,na)FSO,i})are satisfied,the optimal transmit power allocation for performing SM is obtained asa(m,na),∗SM,i =1C(m)SM,i(1ψ(N ′A,{γ(m,na,na)FSO,i}) − 1γ(m,na,na)FSO,i), na = 1, 2, · · · , N ′A0, na = N′A + 1, · · · , NA.(5.30)Otherwise, the optimal transmit power allocation for performing SM is obtained asa(m,na),∗SM,i ={1, na = 10, na = 2, 3, · · · , NA.(5.31)In (5.30), η(4)T =θ(4)TARTFSOf WFSOlog 2 , and C(m)SM,i is a scaler that is determined from∑NAna=1a(m,na),∗SM,i = 1.Transmit power allocation for SD: The optimal transmit power allocation for performing SD isgiven asa(m,na),∗SD,i ={1, if na = arg maxnˆ∈{1,2,··· ,NA}∑NAnb=1γ(m,nˆ,nb)FSO,i0, otherwise.(5.32)1005.4. Optimal AT for Multi-Carrier Hybrid RF/FSO SystemTransmit power allocation for HT: In each disjoint set of transmit apertures, only one transmitaperture will be active. The index of the active transmit aperture in the S(T )l disjoint transmit apertureset of the i-th hop, ∀l = 1, 2, · · · ,K, is given by nA,l = arg maxn∈S(T )l∑nb∈S(R)lγm,n,nbFSO,i . We alsodefine γ˜(m,nA,l)FSO,i ,∑nb∈S(R)lγm,nA,l,nbFSO,i , ∀l = 1, 2, · · · ,K. Without loss of generality, we assume thatγ˜(m,nA,1)FSO,i > γ˜(m,nA,2)FSO,i > · · · > γ˜(m,nA,K)FSO,i holds. If there exists a maximum value of l′ such that 2 ≤ l′ ≤ Kand γ˜(m,nA,l′ )FSO,i ≥ ψ(l′,{γ˜(m,nA,l)FSO,i})are satisfied, we obtaina(m,nA,l),∗HT,i =1C(m)HT,i 1ψ(l′,{γ˜(m,nA,l)FSO,i}) − 1γ˜(m,nA,l)FSO,i , l = 1, 2, · · · , l′0, l = l′ + 1, · · · ,K.(5.33)If such a condition is not satisfied, we obtain a(m,nA,l),∗HT,i = 1, if l = 1, and a(m,nA,l),∗HT,i = 0, ∀l 6= 1.Moreover, for the l-th disjoint transmit aperture set, we always obtain a(m,na),∗HT,i = 0, ∀na ∈ S(T )l andna 6= nA,l, ∀l = 1, 2, · · · ,K. In (5.33), C(m)HT,i is a scaler that satisfies∑NAna=1a(m,na),∗HT,i = 1.Optimal STM Selection: By substituting the aforementioned optimal transmit power allocations to(5.27a), (5.27b), and (5.27c), we obtain the optimal throughput of the i-th hop in the m-th relayinglink employing SM, SD, and HT, respectively. We denote such an optimal throughput as {R(m,i),∗z },∀i ∈ {1, 2},m ∈ {1, 2, · · · , L}, z ∈ {SM, SD, HT}. The optimal selection of the STM for the firstand second hops of the m-th relaying link are given by φ(m,1),∗z1 = 1, φ(m,1),∗z 6=z1 = 0 and φ(m,2),∗z2 = 1,φ(m,2),∗z 6=z2 = 0, respectively, where z1 = arg maxz R(m,1),∗z and z2 = arg maxz R(m,2),∗z .Proof (Outline): Since multiple STMs can not be used in a time-sharing approach, optimal solutionto (P5) can not be obtained by the method of problem relaxation. However, a given hop of each relayinglink has three possible options of selecting an STM. Moreover, for given {φ(m,i)z }, (P5) is a convexoptimization problem. For given selection(s) of the STM, the resultant convex optimization problem isoptimally solved in order to obtain optimal transmit power allocation(s) for a given hop, and such powerallocations are expressed as (5.30)-(5.33). For each hop, the STM providing the maximum throughputis selected. For brevity, we omit the detailed derivation.The constant value of βm in (5.30) and (5.33), ∀m = 1, 2, · · · , L, is determined such that theconstraints C14 and C15 in P5 are satisfied with equality for the optimal transmit power allocationsand STM selections provided in Proposition 5.4.2. Since βm depends only on the statistical CSIand statistical-QoS exponent, an offline method is used to determine the value of βm. By using thesolutions provided in Proposition 5.4.2, the maximum supportable arrival rate to the FSO queue ofMBS is expressed asµ∗FSO,MC(ζ4, Q(4)max)=L∑m=1−logE[exp(− log 2× η(4)T∑z∈{SM, SD, HT} φ(m,1),∗z R(m,1),∗z)]θ(4)TARTFSOf. (5.34)Special case of NA →∞: We consider that the number of transmit-receive apertures in both hopsof a given relaying link are asymptotically large, and both hops of a given relaying link have similarchannel statistics. We assume that φ(m,i)SM = 1 and a(m,na)SM,i = 1/NA, ∀i,m, na. For i.i.d fading, the max-1015.4. Optimal AT for Multi-Carrier Hybrid RF/FSO Systemimum supportable arrival rate for the m-th parallel relaying link is expressed as µ˜∗FSO,m(ζ4, Q(4)max)=−1θ˜logE[exp(−θ˜R˜)]where R˜ = NATFSOf WFSO log2(1 +γ(m,1,1)FSO,1NA)and θ˜ =θ(4)TARNA. Therefore, wecan show, limNA→∞ µ˜∗FSO,m(ζ4, Q(4)max)= NATFSOf WFSOE[log2(1 +γ(m,1,1)FSO,1NA)]. Consequently, from(5.34), we obtain, limNA→∞ µ∗FSO,MC(ζ4, Q(4)max)= NAWFSO∑Lm=1 E[log2(1 +γ(m,1,1)FSO,1NA)]. Sinceboth hops have similar channel statistics, E[log2(1 +γ(m,1,1)FSO,1NA)]= E[log2(1 +γ(m,1,1)FSO,2NA)], ∀m, is sat-isfied. Therefore, for the selection of φ(m,i),∗SM = 1 and a(m,na),∗SM,i = 1/NA, ∀i,m, na in P5 at each TS,the supportable arrival rate at the MBS approaches the maximum data rate received by the SBS. Asa result, for asymptotically large transmit-receive apertures with i.i.d fading, SM with equal powerallocation among the transmit apertures is the optimal transmission strategy for each hop.5.4.3 Maximum Supportable Arrival RateThe maximum supportable arrival rate to the MBS (in bits/second unit) for the proposed AT schemeis obtained as µ∗MC(ζ3, ζ4, Q(3)max, Q(4)max) = µ∗RF,MC(ζ3, Q(3)max)+µ∗FSO,MC(ζ4, Q(4)max). For given valuesof ω∗1, ω∗2, and {βm}, the AT schemes for RF and FSO transmissions, described in Proposition 5.4.1and Proposition 5.4.2, respectively, require computational complexity on the order of O (LN2SC) andO (LNA), respectively. Accordingly, the proposed AT schemes have affordable polynomial complexityfor online operation. For performance comparison, we consider the following BA relaying schemes withfixed transmission parameters.Fixed RF and FSO relaying-I: The total RF power is equally allocated among the RF sub-channelsand the RF sub-channels are uniformly distributed among all the relaying links. For FSO transmission,the available transmit power in each hop is equally allocated among all the transmit apertures, and SMis always selected. The maximum arrival rate is given as µI(ζ3, ζ4, Q(3)max, Q(4)max) = µFixedRF(ζ3, Q(3)max)+∑Lm=1 µEPA−SMFSO,m(ζ4, Q(4)max)whereµFixedRF(ζ3, Q(3)max)= mini=1,2−logE[exp(−η(3)T∑Lm=1∑n∈N (m)sc,iln(1 +Pmaxh˜(m,n)RF,iNscφRF σ2RF))]θ(3)TART˜fRF (5.35)µEPA−SMFSO,m(ζ4, Q(4)max)= mini=1,2− logE[exp(−η(4)T∑NAna=1ln(1 + γ(m,na,na)FSO,i /NA))]θ(4)TARTFSOf (5.36)and where N (m)sc,i is the set of allocated RF sub-channels to the i-th hop of the m-th relaying link. Inorder to obtain (5.35) and (5.36), we use the fact that the maximum supportable arrival rate in BArelaying with fixed transmission parameters is the minimum of the individual EC of the hops [200].Fixed RF and FSO relaying-II: Deterministic RF power allocation and RF sub-channel assignmentsimilar to the previous fixed relaying scheme is used over RF links. For the transmission over FSO links,the available transmit power in each hop is equally allocated among all the transmit apertures, and SDis always selected. The maximum arrival rate is given as µII(ζ3, ζ4, Q(3)max, Q(4)max) = µFixedRF(ζ3, Q(3)max)+1025.5. Simulation Results and Discussion∑Lm=1 µEPA−SDFSO,m(ζ4, Q(4)max)whereµEPA−SDFSO,m(ζ4, Q(4)max)= mini=1,2− logE[exp(−η(4)T ln(1 +∑NAna=1∑NAnb=1γ(m,na,nb)FSO,i /NA))]θ(4)TARTFSOf . (5.37)Nearest RF RS/fixed FSO relaying with SM: In both hops for RF communications, the nearestRN(s) to source and destination are selected, and the RF sub-channels (with equal power alloca-tion) are uniformly distributed among the selected hops. The maximum arrival rate is given asµIII(ζ3, ζ4, Q(3)max, Q(4)max) = µRSRF(ζ3, Q(3)max)+∑Lm=1 µEPA−SMFSO,m(ζ4, Q(4)max)whereµRSRF(ζ3, Q(3)max)= mini=1,2− 1θ(3)TART˜fRF logEexp−η(3)T ∑m∈LN∑n∈N (m)sc,iln1 + Pmaxh˜(m,n)RF,iNscφRFσ2RF .(5.38)Here, LN is the set of the selected RNs, and µEPA−SMFSO,m(ζ4, Q(4)max)is given in (5.36).Nearest RF RS/fixed FSO relaying with SD: By using (5.37) and (5.38), the maximum arrival rateis obtained as µIV (ζ3, ζ4, Q(3)max, Q(4)max) = µRSRF(ζ3, Q(3)max)+∑Lm=1 µEPA−SDFSO,m(ζ4, Q(4)max).Remark III: The RF resource allocation for multi-relay OFDMA network was performed by consid-ering NBA relaying in [201–203]. In these resource allocation schemes, either RF sub-channel pairingis required for enabling simultaneous transmission/reception at the RN without SI [203] or HD RFrelaying is considered in order to avoid SI and the complexity associated with RF sub-channel pairing[201]. Consequently, such RF resource allocations are not efficient. Moreover, such resource allocationsdo not provide link layer QoS guarantee. In [155], only sub-optimal transmit power allocation and RFsub-channel assignment with delay-QoS constraint were provided for a single relayed OFDMA backhaullink. By developing optimal RF power allocation/sub-channel assignment, our proposed AT schemeensures that the total (RF) queue-length of BA parallel relay network is bounded with a certain QLBviolation probability. Consequently, our proposed AT scheme (i.e., adaptive resource allocation) isdifferent compared to the conventional resource allocation schemes of MC multi-relay network.Remark IV: Selection of an STM in each hop of a given relaying link with finite transmit-receiveapertures depends on both statistical-QoS requirements and instantaneous SNR of the received aper-ture. We can show that in (asymptotically) large SNR regime, all the transmit apertures can remainactive with equal power allocation among the transmit apertures. Consequently, in asymptoticallylarge SNR regime, R(m,i)SM ≥ R(m,i)HT ≥ R(m,i)SD usually holds. On the other hand, in low SNR regime,all the transmit power is allocated to the aperture having largest channel gain. Hence, in low SNRregime, R(m,i)SD ≥ R(m,i)HT ≥ R(m,i)SM usually holds [195]. Therefore, SM is the optimal STM during the casehaving weak turbulence fading and negligible path loss, and SD is the optimal STM during the casehaving strong turbulence fading and severe path loss. By optimally adapting the STM, the proposedBA adaptive FSO relaying provides resilience to the weather-induced channel impairments.1035.5. Simulation Results and Discussion500 1000 1500 2000 2500 3000 3500 4000QLB for total queue occupancy, Qmax(1) (=Qmax(2) ) (in bits)1000200030004000500060007000Maximum supportable arrival rate (in Mbps)QLB violation probability, 1= 2=10-3QLB violation probability, 1= 2=10-7Proposed BA Hybrid RF/FSO RelayingFD NBA Selective RelayingFD NBA All-active Relaying(a) Weather condition: Clear weather.500 1000 1500 2000 2500 3000 3500 4000QLB for total queue occupancy, Qmax(1) (=Qmax(2) ) (in bits)0200400600800100012001400160018002000Maximum supportable arrival rate (in Mbps)QLB violation probability, 1= 2=10-3QLB violation probability, 1= 2=10-7Proposed BA Hybrid RF/FSO RelayingFD NBA All-active RelayingFD NBA Selective Relaying(b) Weather condition: Moderate fog.Figure 5.3: Maximum supportable arrival rate versus (vs.) QLB trade-off for SC hybrid RF/FSObackhaul network with L = 3 RNs and β(m)SI = 10−4, ∀m.5.5 Simulation Results and DiscussionFor simulation, we consider a multi-relay hybrid RF/FSO backhaul network with three RNs. Thecoordinates (in the unit of meter) of the RNs are given as [0, 1000], [0, 0], and [0,−1000], and thecoordinates of MBS and SBS are [−1000, 0] and [1000, 0], respectively. Without further specification,the simulation parameters are given as follows. (i) For RF link in SC hybrid RF/FSO network:Pmax = 2W (33 dBm), WRF = 20 MHz, TRFf = 5 × 10−6s, σ2RF = −114 dBm, and φRF = 1; (ii)For FSO link in SC hybrid RF/FSO network: P(s)FSO = 40mW, P(R)FSO = 40mW, WFSO = 108 Hz,TFSOf = 10−6s, R = 0.75 A/W, φFSO = 1, and σ2FSO = 5 × 10−12A2; (iii) For RF link in MC hybridRF/FSO network: Pmax = 2W (33 dBm), W˜RF = 1 MHz, T˜fRF= 10−4s, Nsc ∈ [30, 96], σ2RF = −114dBm, and φRF = 1; and (iv) For FSO link in MC hybrid RF/FSO network: PFSO = 1mW,WFSO = 108Hz, TFSOf = 10−6s, NA = 4, K = 2, R = 0.75 A/W, φFSO = 1, and σ2FSO = 5 × 10−12A2. TheRF channel fading of both MBS-to-RN (RN-to-SBS) and RN-to-RN links are modeled according toRice (4, 1) and Rayleigh distributions, respectively. The path loss of the RF links is modeled accordingto [108, eq. 5]. The FSO channel fading is modeled according to the Gamma-Gamma distribution withα = 2.23 and β = 1.54. The path loss of the FSO links is modeled according to [108, eq. 3], and weconsider path loss exponents (in the unit of dB/Km) 0.43, 4.2, 20, 42.2, and 125 for the weather withclear air, haze, lightfog, moderate fog, and dense fog, respectively.Figures 5.3(a) an 5.3(b) depict the maximum supportable arrival rate of the considered SC hybridRF/FSO communication system for different QLB and QLB violation probability in the presence ofclear weather and moderate fog, respectively. Due to the improved diversity over FSO link, FD NBAselective relaying supports larger arrival rate than FD NBA all-active relaying as depicted from both fig-ures 5.3(a) an 5.3(b). In both clear weather and moderate fog conditions, our proposed BA AT schemeoutperforms FD NBA selective and FD NBA all-active relaying schemes for all the considered QLB(s)and QLB violation probability. Specifically, such a performance improvement is more pronounced for1045.5. Simulation Results and Discussion0 5 10 15 20 25 30 35 40Maximum Total RF Transmit Power, Pmax (in dBm)15002000250030003500400045005000550060006500Maximum supportable arrival rate (in Mbps)Proposed BA Hybrid RF/FSO Relaying, SI=10-4Proposed BA Hybrid RF/FSO Relaying, SI=10-2FD NBA Selective Relaying, SI=10-4FD NBA Selective Relaying, SI=10-2FD NBA All-active Relaying, SI=10-4FD NBA All-active Relaying, SI=10-2 NBA Selective Relaying with HD RF Link(a) Weather condition: Clear weather.0 5 10 15 20 25 30 35 40Maximum Total RF Transmit Power, Pmax (in dBm)0100200300400500600Maximum supportable arrival rate (in Mbps)FD NBA Selective Relaying, SI=10-4FD NBA Selective Relaying, SI=10-2FD NBA All-active Relaying, SI=10-4FD NBA All-active Relaying, SI=10-2NBA Selective Relaying with HD RF LinkProposed BA Hybrid RF/FSO Relaying, SI=10-4Proposed BA Hybrid RF/FSO Relaying, SI=10-2(b) Weather condition: Dense fog.Figure 5.4: Maximum supportable arrival rate vs. RF transmit power for SC hybrid RF/FSO backhaulnetwork with L = 3 RNs, Q(1)max = Q(2)max = 3000 bits, ζ1 = ζ2 = 10−3, and β(m)SI = βSI , ∀m.large values of QLB. For example, in the presence of moderate fog with ζ1= ζ2= 10−7, our proposedAT scheme (given by Proposition 5.3.1 and Proposition 5.3.2 ) improves the maximum arrival rate ofFD NBA selective relaying by 42.20% and 88.93% at Q(1)max= Q(2)max= 500 bits and Q(1)max= Q(2)max= 3000bits, respectively. For similar weather condition and QLB violation probability, our proposed ATscheme can support 5.48 times and 7.03 times more arrival rate than FD NBA all-active relaying atQ(1)max= Q(2)max= 500 bits and Q(1)max= Q(2)max= 3000 bits, respectively. Note that, the considered FD NBAselective relaying requires similar CSI acquisition to our proposed BA AT schemes. By performing FDtransmission over both RF and FSO links, our proposed AT scheme efficiently improves the maximumsupportable arrival rate, especially for large QLB.Figures 5.4(a) an 5.4(b) illustrate the impact of RF transmit power budget and SIC factor on themaximum supportable arrival rate of the considered SC hybrid RF/FSO communication system in thepresence of clear weather and dense fog. In clear weather, increasing RF transmit power does notnoticeably improve the supportable arrival rate in the network. Moreover, in this case, RF SI at theRNs does not significantly deteriorate the total supportable arrival rate. From figure 5.4(a), we observethat the AT scheme over FSO links, given in Proposition 5.3.2, improves the supportable arrival ratecompared to the NBA selective/all-active relaying over FSO links. On the other hand, in a dense fog,the supportable arrival rate improves as the RF transmit power budget increases. Moreover, in thiscase, RF SI at the RNs noticeably reduces the supportable arrival rate. Therefore, mitigation of SI atthe RNs for RF transmission is crucial during severe weather conditions. Figure 5.4(b) depicts that asthe RF SIC worsens, in severe weather conditions, the arrival rate of the considered FD NBA relayingschemes approaches zero. Nevertheless, in the presence of severe RF SI/IRI, the proposed RF powerallocation (given by Proposition 5.3.1 ) allows RN(s) to operate in HD over RF links, and improves thesupportable arrival rate. As such, the proposed RF power allocation is efficient for SC hybrid RF/FSOnetwork during the extreme weather condition.Figure 5.5 illustrates the impact of the weather-induced FSO link attenuation on the arrival rate of1055.5. Simulation Results and Discussion0 20 40 60 80 100 120Weather dependent FSO path loss exponent (in dB/Km unit)01000200030004000500060007000Maximum supportable arrival rate (in Mbps)Proposed BA Hybrid RF/FSO, 3 RNProposed BA Hybrid RF/FSO, 2 RNProposed BA RF AT, All-active BA FSO Relaying, 3 RN Proposed BA RF AT, Selective BA FSO Relaying, 3 RN BA FSO Relaying With Proposed AT, 3 RNBA FSO Relaying With Proposed AT, 2 RNBA RF Relaying With Proposed AT, 3 RNBA RF Relaying With Proposed AT, 2 RN40 50 60 7080010001200140016001800Figure 5.5: Maximum supportable arrival rate vs. weather-dependent FSO link attenuation for SChybrid RF/FSO backhaul network with β(m)SI = 10−4, ∀m, Q(1)max = Q(2)max = 3000 bits, and ζ1 = ζ2 =10−3. From left to right, the vertical dashed lines represent weather conditions with clear air, haze,light fog, moderate fog, and dense fog [108].40 50 60 70 80 90 100 110 120 130Weather dependent FSO path loss exponent (in dB/Km unit)0200400600800100012001400160018002000Maximum supportable arrival rate (in Mbps) Proposed Hybrid RF/FSO ATFixed RF and FSO Relaying-IFixed RF and FSO Relaying-IINearest RF RS With FSO SMNearest RF RS With FSO SDBA FSO Relaying With Proposed ATBA FSO Relaying With Only SMBA FSO Relaying With Only SDFigure 5.6: Maximum supportable arrival rate vs. weather-dependent FSO link attenuation for MChybrid RF/FSO backhaul network with L = 3 RNs, Q(3)max = Q(4)max = 3000 bits, ζ3 = ζ4 = 10−3, andNsc = 30 RF sub-channels.1065.5. Simulation Results and Discussion10-7 10-6 10-5 10-4 10-3 10-2 10-1Maxium acceptable QLB violation probability ( 2)02004006008001000120014001600180020002200Maximum supportable arrival rate (in Mbps)Proposed Hybrid RF/FSO ATFixed RF and FSO Relaying-IFixed RF and FSO Relaying-IINearest RF RS With FSO SMNearest RF RS With FSO SDFigure 5.7: Maximum supportable arrival rate vs. QLB violation probability for MC hybrid RF/FSObackhaul network with L = 3 RNs, Q(3)max = Q(4)max = 3000 bits, and Nsc = 36 RF sub-channels.30 36 42 48 54 60 66 72 78 84 90 96Number of RF sub-channels, Nsc020040060080010001200140016001800Maximum supportable arrival rate (in Mbps)Proposed Hybrid RF/FSO ATFixed RF and FSO Relaying-IFixed RF and FSO Relaying-IINearest RF RS With FSO SMNearest RF RS With FSO SDFigure 5.8: Maximum supportable arrival rate vs. number of RF sub-channels in MC hybrid RF/FSOnetwork with L = 3 RNs, Q(3)max = Q(4)max = 3000 bits, ζ3 = ζ4 = 10−3.1075.5. Simulation Results and Discussionthe considered SC hybrid RF/FSO communication system. The arrival rate in figure 5.5 is calculatedfor 2 Km long FSO link. The backhaul network employing only BA FSO relaying with the proposedtransmit power allocation, given by Proposition 5.3.2, achieves near optimal data arrival rate for thesmall values of weather-induced link attenuation. However, for the large values of weather-induced linkattenuation, data arrival rate of BA FSO relaying with adaptive transmit power allocation approacheszero. As the number of parallel RN(s) increases, the proposed BA hybrid RF/FSO system can achieveimproved multiplexing gain in an FSO link. Consequently, the supportable arrival rate of the proposedBA hybrid RF/FSO system improves as the number of parallel RN(s) increases, especially in favorableweather condition, as depicted from figure 5.5. Figure 5.5 also depicts that all-active and selective BAFSO relaying converge to the proposed FSO transmit power allocation for the small-to-moderate andlarge values of the weather-induced link attenuation, respectively. Such an observation is consistentwith the analysis presented in Section 5.3.2. Therefore, as the weather-induced FSO link attenuationchanges, the FSO transmission strategy proposed in Proposition 5.3.2 switches from BA all-active toBA selective relaying.Figures 5.6 to 5.8 illustrate the statistical-QoS aware arrival rate for an MC hybrid RF/FSO com-munication system. It is considered that for the transmission over the FSO links, the multiple transmitand receive apertures in each hop experience i.i.d fading, and the cross-talk among the parallel opticalbeams is compensated at the receiver. Such assumptions are common in the literature [195]. For thescenario where the aforementioned assumptions do not hold, figures 5.6 to 5.8 will be the upper boundof the supportable arrival rate in MC hybrid RF/FSO system.Figure 5.6 depicts the impact of the weather-induced FSO link attenuation on the arrival rate ofan MC hybrid RF/FSO communication system. The arrival rate in figure 5.6 is also calculated for2 Km long FSO link. As expected, a standalone FSO based BA AT scheme, given by Proposition5.4.2, achieves near-optimal data arrival rate only for the small values of the weather-induced linkattenuation. Moreover, BA FSO relaying with only SM achieves better arrival rate in the small-to-moderate weather-induced link attenuation regime. In contrast, BA FSO relaying with only SDachieves better arrival rate in the large weather-induced link attenuation regime. Since our proposedAT scheme over the FSO links optimally selects the STM (from SM, SD, and HT) at each TS, such anAT scheme outperforms BA FSO relaying with both SM and SD techniques. Our proposed AT schemeover the RF links, given by Proposition 5.4.1, adaptively allocates RF power/sub-channels among allthe BA relaying links. Such an adaptive resource allocation outperforms the deterministic RF resourceallocation, as depicted from the large weather-induced link attenuation regime of figure 5.6. Becauseof performing AT over both RF and FSO links of an MC hybrid RF/FSO backhaul network, in allweather conditions, the proposed scheme supports larger arrival rate compared to the BA relayingschemes with fixed transmission parameters.Figure 5.7 depicts the supportable arrival rate to an MC hybrid RF/FSO backhaul network fordifferent acceptable QLB violation probability. We observe that the proposed AT scheme supportsmuch larger arrival rate compared to considered BA fixed relaying schemes for both strict and looseQLB violation probability. For instance, at ζ3= ζ4= 10−7, our proposed AT scheme improves themaximum arrival rate of the considered fixed RF and FSO relaying-I, fixed RF and FSO relaying-II,the nearest RF RS with FSO SM, and the nearest RF RS with FSO SD by 22.14%, 29.19%, 22.14%, and1085.6. Chapter Summary29.19%, respectively. At ζ3= ζ4= 10−1, our proposed AT scheme improves the maximum arrival rateof the considered fixed RF and FSO relaying-I, fixed RF and FSO relaying-II, the nearest RF RS withFSO SM, and the nearest RF RS with FSO SD by 17.25%, 17.56%, 39.29%, and 39.72%, respectively.In figure 5.7, we consider the moderate fog condition with 42.2 dB/Km link attenuation. In such acondition, over FSO link, an SM based transmission strategy outperforms an SD based transmissionstrategy as confirmed from figure 5.6. Consequently, for all the considered QLB violation probability,fixed RF and FSO relaying-I outperforms fixed RF and FSO relaying-II, and the nearest RF RS withFSO SM outperforms the nearest RF RS with FSO SD based BA relaying.Figure 5.8 illustrates the supportable arrival rate to an MC hybrid RF/FSO backhaul network fordifferent numbers of RF sub-channels. In this figure we consider 50 dB/Km FSO link attenuation,and in this region, over the FSO link, an SD based transmission strategy outperforms an SM basedtransmission strategy as confirmed from figure 5.6. Consequently, in figure 5.8, fixed RF and FSOrelaying-II and the nearest RF RS with FSO SD achieve larger data arrival rate compared to the otherBA fixed relaying schemes. As the number of RF sub-channels increases, the RF link can support morearrival rate while satisfying the given QoS constraint. Consequently, the supportable data arrival rateof an MC hybrid RF/FSO backhaul network improves as the number of RF sub-channels increases.However, due to the deterministic RF resource allocation, the considered BA fixed relaying schemesdo not efficiently exploit the time-varying characteristics of the RF sub-channels. In contrast, theproposed AT scheme exploits the time-varying characteristics of the RF sub-channels, thanks to theRF sub-channel assignment/power allocation of Proposition 5.4.1. Therefore, as the number of RF sub-channels increases, the proposed AT scheme always supports much higher data arrival rate than theconsidered BA fixed relaying schemes. For example, with Nsc = 90 RF sub-channels, our proposed ATscheme improves the maximum supportable arrival rate of the considered fixed RF and FSO relaying-I,fixed RF and FSO relaying-II, the nearest RF RS with FSO SM, and the nearest RF RS with FSO SDby 25.79%, 20.86%, 28.26%, and 23.13%, respectively.5.6 Chapter SummaryIn this chapter, we have developed AT schemes for a hybrid RF/FSO based backhaul networkemploying BA parallel DF relaying. Our proposed AT schemes maximize the supportable arrival rate tothe MBS by ensuring that the total-queue occupancy in the considered multi-buffer system is boundedwith certain QLB violation probability. The simulation results have demonstrated the efficiency of ourproposed BA AT schemes for different weather conditions and link-layer QoS-requirements.109Chapter 6Statistical-Delay-QoS Aware JointPower Allocation and Relaying LinkSelection for FSO Fronthaul NetworksIn the Chapters 3, 4, and 5 of this thesis, we investigated point-to-point FSO communication systemsand cooperative hybrid RF/FSO based backhaul for small-cell network. As mentioned in Chapter 1,FSO systems offer promising fronthaul solutions for the 5G C-RAN architecture. Although severalrecent works have investigated different aspects of the FSO based fronthaul network (see [123–126]and references therein), the link-layer QoS-aware performance was not investigated in state-of-the-artliterature of FSO fronthaul. In this chapter, by considering statistical-delay constraints, we investigatejoint power allocation and relaying link selection for an uplink FSO fronthaul network having multipleRRHs, RNs, and aggregation nodes (ANs). The organization of this chapter is given as follows. InSection 6.1, we summarize the accomplished works and research contributions. The system modelis described in Section 6.2. Section 6.3 provides the problem formulation. Joint power allocationand RRH-relaying link assignments are developed at Section 6.4. Section 6.5 presents the selectedsimulation results, and finally, Section 6.6 provides the concluding remarks.6.1 Accomplished Works and Research ContributionsThe contributions of this chapter are summarized as follows.1. In this work, we investigate a delay-QoS aware AT scheme for a fronthaul network employingmultichannel coherent FSO communications. In the considered fronthaul network the RRHs areplaced far from the BBU pool, and as a result, they use relay assisted FSO communications inorder to overcome the weather dependent path losses. For enhancing the reliability of the FSOfronthaul network, the RRHs in the considered fronthaul network are equipped with buffer suchthat RRHs can (temporarily) store the arrived data. We aim to maximize the supportable arrivalrate at the input of the RRHs’ buffer subject to certain statistical-delay constraints. Specifically,our aim is to maximize the end-to-end EC of the RRHs over the fronthaul network. Towardssuch an objective, we present a joint multichannel power allocation and relaying link selection(JMCPARLS) scheme for uplink of the considered FSO fronthaul network. Our proposed schemejointly performs the following two tasks: (1) assignment of the available RNs and aggregationnodes (ANs) to the RRHs and (2) allocation of the available transmit power among the orthogonalFSO channels at RRHs and RNs.1106.2. System OverviewFigure 6.1: A block diagram of a single fronthaul cluster.2. The joint power allocation and relaying link selection are formulated as an MINLP problem. Weobtain near optimal solution to such an MINLP problem by using Lagrangian dual decomposi-tion and minimum weight matching techniques. Our analysis reveals that the proposed schemeachieves the channel capacity of the conventional WF power allocation and a constant channelcapacity at the loose and strict statistical-delay constraints, respectively. A semi-distributedalgorithm of polynomial computational complexity is developed for implementing the proposedscheme. In this algorithm, every RRH distributively calculates transmit power allocations. Onthe other hand, a global network controller (GNC) centrally calculates the RRH-relaying linkassignments.3. Our simulation results confirm the effectiveness of the proposed scheme for the strict statistical-delay constraints, especially in strong turbulence fading. Particularly, simulation results showthat equal power allocation among orthogonal FSO channels only provides near optimal EC atthe loose statistical-delay constraints. Simulation results also depict that in the strict statistical-delay constraints, our proposed scheme outperforms a statistical-delay-QoS aware scheme wherethe relaying links from a given RRH are independently optimized.6.2 System Overview6.2.1 System ModelWe consider a fronthaul network that is divided into multiple non-overlapping and non-interferingfronthaul clusters. Here, non-overlapping cluster means that the RRHs in each cluster are associatedwith only the RNs and ANs of the corresponding fronthaul cluster. As such, resource allocation for each1116.2. System Overviewfronthaul cluster can be independently optimized. Note that, in a general scenario, some RRH(s) maydirectly connect with the AN(s) and/or BBU pool. However, due to simplicity of the system model,such a general scenario is not considered. Figure 6.1 illustrates the block diagram of a typical fronthaulcluster. A fronthaul cluster has one or more ANs which aggregate the traffic from the RRHs in FSOlinks and forward these traffic to the BBU pool through optical fiber links. Without loss of generality,we do not consider the capacity constraint of the optical fiber links. The RRHs in a fronthaul clustercan be located remotely from the ANs. Consequently, in order to overcome the weather dependentpath losses, RRHs send the data traffic to the ANs by using the relay assisted FSO links. In oursystem model, the duration of a typical TS is approximately same as the channel coherence time, andtransmission parameters are adapted once in each TS. In a given TS, an RRH transmits the modulatedoptical beam to an RN selected from a group of available RNs, and the RN forwards this beam to anAN selected from a group of available ANs. Each RRH is equipped with multiple apertures pointedtowards different RNs so that the RRH can select the best possible relaying link for data transmission.Each FSO RN is also equipped with multiple apertures pointed towards different RRHs and/or ANsso that in a given transmission slot an FSO RN can opportunistically serve the best possible RRH. Weconsider that the lengths of all the FSO links (i.e., the locations of RRHs, RNs, and ANs) are given.Usually, the length of an FSO link is selected in such a way so that the end-to-end outage probabilitybecomes less than a certain threshold [116]. FSO based fronthaul link can provide reliable performanceover a link length from 1 to 3 Kilometers [27]. Consequently, we consider that the predefined FSO linklengths in our system model are in the range of 1 to 3 Kilometers20. For the considered system model,we make the following assumptions.A1: RRHs, RNs, and ANs are fixed (i.e., static) nodes, and the data arriving at a particular RRHhave similar statistical-delay-QoS requirements and constant arrival rates. However, the arrived datafor different RRHs can have different statistical-delay-QoS requirements and different (constant) arrivalrate. As explained in Section 4.2 that the assumption of constant data arrival rate can be justifiedin the practical scenarios. In such a case, the data arrival rate remains constant over a large numberof independent channel fading realizations. However, we would like to note that the proposed powerallocation and relaying link selection can still be applied when the arrival process is stochastic. Inparticular, for stochastic data arrival with a discrete-time on-off Markov process, the average arrivalrate is a monotonic function of the EC [162]. Therefore, the proposed work of this chapter can beapplied in order to maximize the average rate of a discrete-time on-off Markov arrival process.A2: The considered RRHs have the decoding capability that facilitates an RRH to receive in RFdomain (i.e., from the UE(s)) and transmit over FSO link. RRH is also equipped with buffer fortemporarily storing the incoming data. Note that, in the conventional C-RAN architecture, RRHincludes only radio functionality. However, enabling the decoding capability at the RRH(s) reducesburden over fronthaul link (see [205, 206] and references therein). Moreover, buffers enable the RRH(s)to support enhanced arrival rate from the access links. Note that, when the RRHs have the buffers20Note that for given locations of RRHs and ANs, optimal FSO link length selection problem becomes an optimalRN placement problem in 2D plane [204]. However, optimal RN placement in an FSO fronthaul network is an entirelydifferent optimization problem compared to our considered optimization problem. Consequently, optimal RN placementin an FSO fronthaul network is beyond the scope of our current work. A simple suboptimal RN placement procedure isto place a unique RN at the middle of each RRH-AN link. We illustrate the effectiveness of such a simple RN placementfor improving the end-to-end EC of an FSO fronthaul network in Section 6.5.1126.2. System Overviewand decoding capability, the link between BBU pool and RRHs can also be referred as “backhaul”.However, following the terminology proposed by the C-RAN architecture, we denote such link(s) as“fronthaul.” Such a practice is also common in state-of-the-art literature [205, 206].A3: RNs forward the incoming traffic to the ANs by using an AF relaying protocol. In addition,the RNs do not have their own traffic. The later assumption simplifies the considered optimization andit is also considered in the existing cooperative FSO literature [80, 86, 108].A4: A given relaying link supports maximum one RRH in uplink. Such an assumption is consideredfor the simplification of the RRH-relaying link assignment problem. Due to such an assumption, theconsidered work is applicable to the fronthaul cluster where the number of RRHs is upper bounded bythe number of total relaying links.A5: The complete knowledge about the received CSI of all the possible transmission links isavailable at the transmitting nodes (RRHs and RNs) so that they can adapt the transmission poweraccordingly. Transmitting nodes can obtain reliable CSI estimates through feedback from the receiversover an FSO or RF feedback channel. Moreover, due to the channel reciprocity of atmospheric turbu-lence fading, the transmitting nodes can also estimate CSI from the received signal for the bi-directionalFSO communication systems. The detailed justification of such an assumption can be found in Section3.3.1 of this thesis.Remark I: The proposed scheme allows an RRH to transmit through a relaying link having morefavorable channel conditions. Accordingly, our proposed scheme provides robustness against weather-dependent performance degradation of one or more FSO fronthaul links. The proposed scheme usuallyrequires increased number of transmit apertures at RRHs and RNs in order to improve the weatherdependent performances. However, the proposed scheme offers little performance improvement if all theavailable relaying links experience deep outage due to dense fog. Fog induced FSO signal attenuationcan be overcome by transmitting optical carrier of long infrared wavelengths (8µm -10µm). HybridRF/FSO is another solution to combat fog induced link outage. As shown in the previous chapterthat hybrid RF/FSO can provide backhaul connectivity even in the dense fog. However, the mainchallenge for the hybrid RF/FSO based fronthaul in the considered architecture is the increased resourceallocation complexity. In particular, hybrid RF/FSO system experiences interference from the existingcellular/RF wireless communication links. Moreover, the interference among the active RF links andSI (if FD RF relaying is considered) also degrade the achievable throughput of a fronthaul network. Inorder to mitigate such interference, additional resource allocations, such as, sub-channel allocation andtime-slot scheduling are required when hybrid RF/FSO is used in the considered architecture. Due tothe limited bandwidth over RF fronthaul, quantization is also required [126]. Overall, hybrid RF/FSObased fronthaul for the considered architecture requires complex resource allocation. In contrast, FSOfronthaul does not require complex quantization [126], and FSO RNs operate in FD manner suchthat they can simultaneously transmit and receive without creating SI and/or interference to nearbyfronthaul link(s). Consequently, for the considered architecture, FSO based fronthaul is appealing dueto less complex resource allocation.1136.3. Problem Formulation6.2.2 Link Signal-to-Noise-RatioWe assume that every RRH transmits by using multiple coherent modulated orthogonal FSO chan-nels. Orthogonal FSO channels can be created by employing WDM and/or POLMUX at the RRHs.We denote the set of the RRH as S, the set of orthogonal FSO channels at each RRH as N , the set ofRNs as R, and the set of ANs as P. Without loss of generality, we assume that the m-th RRH sendsdata to the p-th AN through the l-th RN. We denote transmit power of the i-th optical channel fromthe m-th RRH at first and second hop as P(i),(1)m,l,p and P(i),(2)m,l,p , respectively. A CSI assisted AF relayingscheme is considered where the RN amplifies the received signal with the inverse of the channel gainof the first hop. An electrical amplification is used in the considered AF RNs [77, 78]. We assume thataccurate estimations of CSI are available at the RNs. Pilot symbols are inserted at the beginning ofthe symbol blocks transmitted from an RRH, and an RN estimates the channel gain of the first hopby observing such pilot symbols. Following [78, eq. 1], the end-to-end SNR of the i-th orthogonal FSOchannel is obtained asγ(i),e2em,l,p = 2∑n=11P(i),(n)m,l,p γ(i),(n)m,l,p−1 (6.1)where γ(i),(n)m,l,p is the received channel-gain-to-noise ratio of the i-th channel at the n-th hop, and it isdefined as γ(i),(n)m,l,p =Rg(n)m,l,pqBmI(i),(n)m,l,p . Here, Bm is the bandwidth of an orthogonal FSO channel; I(i),(n)m,l,p isthe channel gain of the i-th channel at the n-th hop impaired by both atmospheric turbulence fadingand pointing error; and g(n)m,l,p is the path loss coefficient of the n-th hop. We use the Gamma-Gammadistribution and (2.23) to characterize the atmospheric turbulence induced channel fading and thezero-boresight pointing error, respectively. However, our developed resource allocation scheme canbe applied to any atmospheric turbulence fading and pointing error model. We assume ergodic andi.i.d. block fading process such that the channel fading co-efficient remains same in each TS, andindependently varies from one TS to another TS. We also assume that the accumulated phase noisedue to the atmospheric turbulence and/or lasers can be tracked and corrected almost perfectly followingthe photodetection. Such an assumption can be justified by using the arguments presented in Section2.3.1 and Section 4.1.6.3 Problem FormulationSimilar to the previous chapters, we interpret the statistical-delay-QoS requirements in terms ofthe statistical-delay-QoS exponents. We denote θm and T(m)f , respectively, as the statistical-delay-QoSexponent and frame duration for the data transmitted from the m-th RRH. We also denote R(m) asthe set of accessible RNs to the m-th RRH, and P(l) as the set of the accessible ANs to the l-th relaynode. Finally, we define an indicator variable, ρm,l,p ∈ {0, 1}, such as, ρm,l,p = 1 if the p-th AN and thel-th RN are assigned to the m-th RRH and ρm,l,p = 0 otherwise. Therefore, we define the end-to-end1146.3. Problem FormulationEC of the m-th RRH asE(m)c , −1θmlogE{γ(i),e2em,l,p}exp−θmT (m)f Bm ∑l∈R(m)∑p∈P(l)∑i∈Nρm,l,p log2(1 + γ(i),e2em,l,p) . (6.2)The objective of the proposed resource allocation is to maximize the data arrival rate at the input ofeach RRH’s buffer subject to certain statistical-delay constraints. As per definition of the EC, such anobjective can be satisfied by maximizing the EC of each RRH. Therefore, we consider an optimizationproblem with an objective of maximizing each RRH’s achievable EC over FSO fronthaul link. Weconsider the following constraints:Transmit power constraint at RRHs and RNs: In order to avoid the potential harm of human eyeand skin caused by the laser beam, a safety regulation is imposed on the maximum transmit power forcommercial laser transmitters. We denote the maximum transmit power from the m-th RRH as Pm.We write transmit power constraint for the m-th RRH as∑l∈R(m)∑p∈P(l)∑i∈Nρm,l,pP(i),(1)m,l,p ≤ Pm, ∀m ∈ S. (6.3)We denote S(l) as the set of RRHs having access to the l-th RN and Pl as the maximum transmitpower from the l-th RN. We write transmit power constraint for the l-th RN as∑m∈S(l)∑p∈P(l)∑i∈Nρm,l,pP(i),(2)m,l,p ≤ Pl, ∀l ∈ R. (6.4)The justification of the transmit power allocation constraints, given by (6.3) and (6.4), is providedas follows. In the considered system model, both RRHs and RNs can transmit N parallel opticalbeams (i.e., N orthogonal optical channels). According to the explanation provided in Section 4.1, thetransmit power allocation among these optical channels subject to the total transmit power constraintis meaningful. However, for a given RRH, the transmit power allocation among these optical channelsdepends on both the turbulence fading experienced by these channels as well as the selection of therelaying link. For example, the transmit power allocation among the optical channels from the m-thRRH depends on the selected RN for the m-th RRH, and the transmit power allocation among theoptical channels from the l-th RN depends on the selected AN for the l-th RN. In addition, both hopsneed to be jointly optimized since the EC of each RRH depends on the end-to-end SNR. Accordingly,we need to jointly optimize the transmit power allocation among the parallel optical beams from eachRRH and the relaying link selection for each RRH. The transmit power allocation constraints, givenby (6.3) and (6.4), facilitate such a joint optimization.Relaying link selection constraints: If an RRH sends information to an AN through multiple RNs,it is necessary to synchronize transmissions from all the RNs. Such a synchronization ensures thatsignals from all the RNs simultaneously reach to the AN. However, synchronizing all the RN-to-ANlinks for high speed optical communications is challenging [80]. Moreover, due to the limited transmitpower budget, an RRH should assign all of the available transmit power to the best possible RN. Byusing a similar argument, we also justify that an RN should forward the data of a particular RRHto only one AN. Accordingly, a given RRH transmits information through only one relaying link. We1156.3. Problem Formulationwrite relaying link selection constraint for an RRH as∑l∈R(m)∑p∈P(l)ρm,l,p = 1, ∀m ∈ S. (6.5)Moreover, we assume that a given relaying link supports maximum one RRH in uplink. Consequently,we have the following constraint21:∑m∈S(l)ρm,l,p ≤ 1, ∀l ∈ R, ∀p ∈ P(l). (6.6)The corresponding optimization problem is formulated as{maxP ,ρE(1)c ,maxP ,ρE(2)c , · · · ,maxP ,ρE(m)c , · · ·}s.t. (6.3), (6.4), (6.5), (6.6),ρ ∈ {0, 1},P ≥ 0
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Statistical quality-of-service aware adaptive transmission for free space optical communication systems Hassan, Md. Zoheb 2019
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Title | Statistical quality-of-service aware adaptive transmission for free space optical communication systems |
Creator |
Hassan, Md. Zoheb |
Publisher | University of British Columbia |
Date Issued | 2019 |
Description | Despite the growing attention for free space optical (FSO) networks, state-of-the-art literature lacks appropriate adaptive transmission (AT) schemes that can exploit the stochastic propagation channel of the FSO networks and guarantee delay quality-of-service (QoS) in the link-layer. Specifically, weather-induced channel impairments not only affect the error-rate or outage probability but also increase the end-to-end queueing-delay of the FSO network. This dissertation aims to improve QoS-aware throughput of the terrestrial FSO communication systems by designing innovative AT schemes. The key goal of the developed AT schemes is to maximize the supportable arrival rate while ensuring the QoS in terms of certain delay-bound violation probability constraints. We first analyze the effective capacity (EC) of terrestrial FSO communication systems. We derive accurate closed-form expressions of the achievable EC by considering several FSO channel impairments. Through asymptotic analysis, we reveal insights on the EC increment. Next, we present delay-QoS aware discrete-rate AT schemes for FSO communication systems with parallel optical beams and average/peak transmit power constraints. Our results suggest that to improve the delay-throughput trade-off, only suitable optical channels need to be activated. Simulation results demonstrate that joint adaptation of transmission parameters of the active optical beams improve throughput of the FSO communication systems in the strict statistical-QoS constraints. Subsequently, we develop AT schemes for FSO backhaul/fronthaul networks. We first study AT schemes for buffer-aided parallel decode-and-forward relaying assisted hybrid radio-frequency (RF)/FSO backhaul networks. Two different hybrid RF/FSO system configurations are considered, and AT schemes for both configurations are developed. These schemes maximize the arrival rate subject to the total queue-occupancy constraint. Next, we develop delay-QoS aware joint power allocation and relaying link selection for amplify-and-forward relay assisted uplink FSO fronthaul networks. Finally, we investigate joint FSO fronthaul and millimeter-wave access link optimization for the downlink cloud small cell network subject to end-to-end queue-length-bound violation probability constraints. Extensive simulations are performed to evaluate the performance of the proposed AT schemes by considering several FSO channel impairments and statistical-QoS requirements. Simulation results demonstrate that our proposed AT schemes substantially improve the statistical-QoS aware arrival rate in the FSO backhaul/fronthaul networks. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2019-05-29 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
DOI | 10.14288/1.0379184 |
URI | http://hdl.handle.net/2429/70388 |
Degree |
Doctor of Philosophy - PhD |
Program |
Electrical and Computer Engineering |
Affiliation |
Applied Science, Faculty of Electrical and Computer Engineering, Department of |
Degree Grantor | University of British Columbia |
GraduationDate | 2019-09 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
AggregatedSourceRepository | DSpace |
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