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In-band full-duplex power line communications Prasad, Gautham 2019

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In-Band Full-DuplexPower Line CommunicationsbyGautham PrasadM.S., University of Florida, 2014B. Eng., PES Institute of Technology, 2012A 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)March 2019© Gautham Prasad, 2019The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:In-Band Full-Duplex Power Line Communicationssubmitted by Gautham Prasad in partial fulfillment of the requirements for thedegree of Doctor of Philosophy in Electrical and Computer Engineering.Examination Committee:Lutz Lampe, Electrical and Computer EngineeringSupervisorSudip Shekhar, Electrical and Computer EngineeringSupervisory Committee MemberMartin Ordonez, Electrical and Computer EngineeringUniversity ExaminerRuben Zamar, StatisticsUniversity ExaminerAdditional Supervisory Committee:Cyril Leung, Electrical and Computer EngineeringSupervisory Committee MemberiiAbstractPower line communication (PLC) exploits the existing power-grid infrastructure forsignal transmission at various avenues from large-scale transmission and distributionnetworks to smaller-scale in-home and in-vehicle electrical wiring frameworks. PLCprovides gigabit-range throughput, which also makes it a viable solution for multi-media communication in indoor local area networks. However, the low-pass nature ofpower line channels and the strict electromagnetic compatibility regulations govern-ing PLC hinder adequate data rate gains that can be further achieved by traditionalmeans of increasing transmit power and/or bandwidth. One solution to improve datarate under such restrictions is to use in-band full-duplexing (IBFD), which doubles thespectral efficiency for a given channel quality by enabling simultaneous bidirectionaldata communication in the same frequency band. With the backdrop of existingIBFD implementation in various communication systems from analog telephones tomore recent proposals for wireless communications, we investigate the requirementsfor an IBFD PLC system and propose solutions that counter the unique challengesencountered in the harsh power line environment. Simulation results show that ourlow-cost and low-complexity design achieves over 80% increase in median bidirec-tional data rates under typical in-home power line networking conditions withoutany additional power or bandwidth requirement.Aside from improving spectral efficiency, IBFD allows us to solve several electro-magnetic compatibility issues observed at PLC deployments. By using IBFD, PLCiiiAbstracttransceivers can simultaneously transmit data packets while also sensing the oper-ating spectrum. We use this spectrum aware transmission ability of IBFD-enabledPLC modems to propose cognitive coexistence techniques to eliminate or reduce theimpact of the electromagnetic interference caused by unintentional PLC radiationon broadcast radio services, digital subscriber line communications, and neighboringPLC systems in a heterogeneous PLC environment.Along with obtaining physical layer advancements, we further apply IBFD toachieve medium access control (MAC) layer enhancements to improve its efficiency,which is known to deteriorate under heavily loaded network conditions. We proposean IBFD priority resolution procedure and a combined frequency domain contentionresolution and preamble collision detection technique that improve the MAC effi-ciency by reducing the time spent in resolving priorities and contentions by up to85%.ivLay SummaryPower Line Communication (PLC) enables data transmission over the existing elec-trical wiring infrastructure in both indoor (residential and industrial) and outdoor(power transmission and distribution) environments. In this thesis, we present solu-tions that allow data transfer on a power line channel to be simultaneously bidirec-tional (full-duplex) and also use the same frequency band in both directions (in-band),by minimizing the impact of our own transmitted signal, i.e., self-interference. Thisnot only doubles the two-way data rate without any additional power or bandwidthrequirement, but also enables various other functionalities, e.g., simultaneous datatransfer and spectrum sensing, secure communication via simultaneous data recep-tion and jamming, instantaneous repeating with simultaneous packet reception andforwarding, and a medium access control protocol design of carrier sense multipleaccess with collision detection, which were all previously considered to be infeasiblefor PLC.vPrefaceThis thesis is based on original research that I conducted under the supervision ofProfessor Lutz Lampe in the Department of Electrical and Computer Engineering atthe University of British Columbia, Vancouver, Canada.Versions of Chapter 2 appear in• G. Prasad, L. Lampe, and S. Shekhar, “In Band Full Duplex Broadband PowerLine Communications,” IEEE Trans. Commun., vol. 64, no. 9, pp. 3915–3931,Sep. 2016.• G. Prasad, L. Lampe, and S. Shekhar, “Enhancing Transmission Efficiencyin Broadband Power Line Communications using In-band Full Duplexing,” inProc. IEEE Int. Symp. Power Line. Commun. Applicat. (ISPLC), pp. 46–51,Bottrop, Germany, Mar. 2016.• G. Prasad and L. Lampe, “Introducing In-band Full Duplexing for BroadbandPower Line Communications,” in Proc. 9th Workshop Power Line Commun.(WSPLC), Klagenfurt, Austria, Sep. 2015.I was responsible for all contributions in Chapter 2, including reviewing literature,formulating the problems, developing solutions, evaluating them through simulations,and preparing publication manuscripts. Professor Lutz Lampe supervised all mywork and also helped me choose the problem statement. The hybrid-circuit designcomponent of the above work was also supported by Professor Sudip Shekhar.viPrefaceVersions of Chapter 3 appear in• G. Prasad, L. Lampe, and S. Shekhar, “Digitally Controlled Analog Cancel-lation for Full Duplex Broadband Power Line Communications,” IEEE Trans.Commun., vol. 65, no. 10, pp. 4419–4432, Nov. 2017.• G. Prasad, L. Lampe, and S. Shekhar, “Analog Interference Cancellation forFull Duplex Broadband Power Line Communications,” in Proc. IEEE Int.Symp. Power Line. Commun. Applicat. (ISPLC), pp. 1–6, Madrid, Spain,Apr. 2017.I was responsible for all contributions in Chapter 3, including selecting the problemstatement, developing the idea, reviewing literature, formulating the problems, de-signing solutions, evaluating them through simulations, and preparing publicationmanuscripts. Professor Lutz Lampe supervised all my work. The hybrid-circuit de-sign component of the above work was also supported by Professor Sudip Shekhar.Versions of Chapter 4 appear in• G. Prasad and L. Lampe, “Feasibility of Full-Duplex Dynamic Spectrum Man-agement for PLC-DSL Coexistence,” in Proc. IEEE Int. Symp. Power Line.Commun. Applicat. (ISPLC), pp. 1–6, Manchester, UK, Apr., 2018. (BestStudent Paper Award)• G. Prasad, Y. Huo, L. Lampe, and V. C. M. Leung, “Electromagnetic Com-patibility of Power Line Communications in Energy Storage Units,” in Proc.IEEE Int. Symp. Power Line. Commun. Applicat. (ISPLC), pp. 1–6, Manch-ester, UK, Apr. 2018.• G. Prasad, Y. Huo, L. Lampe, and V. C. M. Leung, “Frequency DomainAccess Control for Power Line Communications in Home Area Networks,” inviiPrefaceProc. IEEE Int. Conf. Smart Grid Commun. (SmartGridComm), pp. 302–307Dresden, Germany, Oct. 2017.• G. Prasad and L. Lampe, “Full Duplex Spectrum Sensing for BroadbandPower Line Communications,” in Proc. IEEE Int. Symp. Power Line. Com-mun. Applicat. (ISPLC), pp. 1–6, Madrid, Spain, Apr. 2017.• G. Prasad and L. Lampe, “Simultaneous Data Transmission and SpectrumSensing for Broadband Power Line Communications,” in Proc. 10th WorkshopPower Line Commun. (WSPLC), Paris, France, Oct. 2016.I led the research for all contributions in Chapter 4, including selecting problemstatements, developing the ideas, reviewing literature, formulating the problems, de-signing solutions, evaluating them through simulations, and preparing publicationmanuscripts. My work was supervised by Professor Lutz Lampe. Professor Victor C.M. Leung provided inputs on evaluation methodologies for Section 4.4.4, and feed-back on publication manuscripts based on Sections 4.3 and 4.4. Mr. Yinjia Huoassisted me in simulations presented in Sections 4.3.4 and 4.4.4.viiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiNotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxviiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 In-Band Full-Duplex PLC: Why and How? . . . . . . . . . . . . . . 31.2 IBFD: Beyond Doubling Spectral Efficiency . . . . . . . . . . . . . . 101.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18ixTable of Contents2 Introducing IBFD for BB-PLC . . . . . . . . . . . . . . . . . . . . . 192.1 Feasibility and Requirements of IBFD for BB-PLC . . . . . . . . . . 202.2 Proposed Two-step Cancellation Procedure . . . . . . . . . . . . . . 232.2.1 Analog Isolation . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.2 Digital Echo Cancellation . . . . . . . . . . . . . . . . . . . . 272.2.3 Rate of Convergence and Cancellation Gain . . . . . . . . . . 332.2.4 Implementation of IBFD . . . . . . . . . . . . . . . . . . . . 362.3 LMS Modification for LPTV PLC channels . . . . . . . . . . . . . . 362.3.1 The LPTV-LMS Adaptation . . . . . . . . . . . . . . . . . . 372.3.2 Performance Illustration . . . . . . . . . . . . . . . . . . . . . 402.4 Data Rate Gain Analysis . . . . . . . . . . . . . . . . . . . . . . . . 422.4.1 Echo Cancellation Gain . . . . . . . . . . . . . . . . . . . . . 432.4.2 Theoretical Data Rate Gains . . . . . . . . . . . . . . . . . . 442.4.3 Simulation Results of the Overall Date Rate Gain . . . . . . 462.5 Extension to MIMO BB-PLC Systems . . . . . . . . . . . . . . . . . 482.5.1 Analog Isolation . . . . . . . . . . . . . . . . . . . . . . . . . 492.5.2 Digital Cancellation . . . . . . . . . . . . . . . . . . . . . . . 512.5.3 Performance Results . . . . . . . . . . . . . . . . . . . . . . . 522.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 Digitally Controlled Analog Cancellation . . . . . . . . . . . . . . . 563.1 Analog SI Cancellation Solutions . . . . . . . . . . . . . . . . . . . . 583.2 Proposed AIC Solution . . . . . . . . . . . . . . . . . . . . . . . . . 613.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . 613.2.2 Proposed Echo Cancellation Procedure . . . . . . . . . . . . . 623.2.3 ADC Distortion and Quantization Noise . . . . . . . . . . . . 63xTable of Contents3.2.4 Impact on ADC Bit Loss . . . . . . . . . . . . . . . . . . . . 643.3 AIC for MIMO IBFD BB-PLC . . . . . . . . . . . . . . . . . . . . . 663.4 Effect of Non-linear SI Components . . . . . . . . . . . . . . . . . . 703.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.5.1 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . 723.5.2 Channel and Noise Models . . . . . . . . . . . . . . . . . . . 733.5.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 733.6 Discussion on the Proposed AIC Solution . . . . . . . . . . . . . . . 803.6.1 Notable Characteristics . . . . . . . . . . . . . . . . . . . . . 803.6.2 Implementation Costs . . . . . . . . . . . . . . . . . . . . . . 823.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834 Spectrum Aware Transmission with IBFD PLC . . . . . . . . . . . 854.1 IBFD-PLC: Cognitive of Broadcast Radio . . . . . . . . . . . . . . . 864.1.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.1.2 Spectrum Sensing with IBFD . . . . . . . . . . . . . . . . . . 884.1.3 Proposed Solutions . . . . . . . . . . . . . . . . . . . . . . . . 914.1.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 954.1.5 Quantifying the Gains . . . . . . . . . . . . . . . . . . . . . . 1004.2 IBFD-PLC: Cognitive of DSL Communications . . . . . . . . . . . . 1024.2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.2.2 IBFD DSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.2.3 Data Rate Gains . . . . . . . . . . . . . . . . . . . . . . . . . 1064.2.4 Feasibility Analysis . . . . . . . . . . . . . . . . . . . . . . . 1084.3 IBFD-PLC: Cognitive of Neighboring PLC . . . . . . . . . . . . . . 1164.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117xiTable of Contents4.3.2 EMI Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 1214.3.3 EMI Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 1264.3.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 1294.4 IBFD-PLC: Upper Layer Enhancements . . . . . . . . . . . . . . . . 1344.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1344.4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354.4.3 Proposed Schemes . . . . . . . . . . . . . . . . . . . . . . . . 1374.4.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 1464.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1495 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1525.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1525.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1555.3 Further Research Directions . . . . . . . . . . . . . . . . . . . . . . . 157Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160AppendicesA Channel and Noise Models . . . . . . . . . . . . . . . . . . . . . . . . 187A.1 SISO Channel Generation . . . . . . . . . . . . . . . . . . . . . . . . 187A.1.1 LPTV Channels . . . . . . . . . . . . . . . . . . . . . . . . . 187A.1.2 Channels to Determine DRG . . . . . . . . . . . . . . . . . . 188A.2 MIMO Channel Generation . . . . . . . . . . . . . . . . . . . . . . . 188A.3 PLC Noise Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 189A.3.1 Colored Background Noise . . . . . . . . . . . . . . . . . . . 189A.3.2 Narrowband Noise . . . . . . . . . . . . . . . . . . . . . . . . 189xiiTable of ContentsA.3.3 Impulse Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 189B Transfer Function of the Echo Channels . . . . . . . . . . . . . . . . 192B.1 Self-Interference Channel in SISO IBFD Operation . . . . . . . . . . 192B.2 Self- and Cross-Interference Channels in MIMO-IBFD Operation . . 195C An Approximate Expression for γADC . . . . . . . . . . . . . . . . . . 197D ADC Bits lost in IBFD . . . . . . . . . . . . . . . . . . . . . . . . . . 200E Interference Channel Transfer Functions at the Stand-alone Re-ceiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202xiiiList of Tables2.1 Number of computations per OFDM symbol with mixed-domain andtime-domain echo cancellations . . . . . . . . . . . . . . . . . . . . . 342.2 DRG per sub-carrier as a function of sub-carrier channel attenuation(SCA) and channel noise level NR. . . . . . . . . . . . . . . . . . . . 453.1 A Comparison of the Theoretical Data Rate Gains Per Sub-carrier withDIC and AIC Solutions under Different Sub-Carrier Attenuations witha Noise Floor of −130 dBm/Hz. . . . . . . . . . . . . . . . . . . . . . 753.2 Caption table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 954.2 VDSL2 Transceiver Parameters [137] . . . . . . . . . . . . . . . . . . 1074.3 Transmission parameters of DSL standards whose operating frequen-cies overlap with BB-PLC bands [137–140] . . . . . . . . . . . . . . . 1144.4 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 147A.1 Noise Statistics Used to Generate the Different Noise Levels . . . . . 191xivList of Figures1.1 Evolution of PLC with emphasis on BB-PLC standards. . . . . . . . 31.2 Impact of the large SI during IBFD operation. . . . . . . . . . . . . . 51.3 The different types of possible SI cancellation methods. P1, P2, andP3 indicate three ports of the hybrid. . . . . . . . . . . . . . . . . . . 51.4 Nodes A and C are hidden from each other, while node B is in conver-sation with C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 Some examples of non-PLC services that share the 2−100 MHz band-width, which is also used for BB-PLC. . . . . . . . . . . . . . . . . . 121.6 Portion of the BB-PLC spectrum that is also used by DSL communi-cations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.7 Impact of the number of network nodes on the percentage of time spentat the MAC layer on all activities other than data payload transmission. 162.1 ADS schematic of the simplified hybrid implementation with only twoop-amps, and the resistances tuned to provide port impedances ofZ1 = Z2 = Z3 = 100 Ω. . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2 Hybrid isolation Phyb from port 1 to port 3 as a function of PLCline impedance ZPLC. Phyb is maximum when the line impedance ismatched to the hybrid P2 impedance, i.e., ZPLC = Z2 = (100 + j0) Ω. 26xvList of Figures2.3 Transceiver block diagrams for IBFD for BB-PLC using OFDM. (a)EC in time and frequency domain (only one of the shaded blocks isused). (b) Mixed-domain EC. For brevity, we include addition andremoval of cyclic prefix with the IDFT and DFT blocks, respectively. 282.4 Magnitude of channel gain of (a) sample PLC channels under differentin-home network conditions, and the (b) frequency and (c) impulseresponses of their corresponding SI/echo channels. . . . . . . . . . . . 302.5 MSE after EC versus transmitted OFDM-symbol time for a sam-ple PLC channel. Comparison of 40-tap TDEC filter and a 917-tapMDEC. LMS with step-size µ = 0.025. . . . . . . . . . . . . . . . . . 332.6 MSE as a function of MDEC iteration for sample PLC channels gen-erated with [107]. MDEC with fixed and variable step-size LMS. (a)One change of PLC channel. (b) Multiple changes of PLC channel. . 352.7 MSE versus iteration number for MDEC using the conventional LMSand the proposed LPTV-aware LMS algorithms for an LPTV PLCchannel. Total duration is nine HCs. LMS step size is µ = 0.025. . . . 402.8 Per sub-carrier PSD levels at different locations in the PLC trans-mission system, providing an illustration of achievable data-rate gains(DRGs) using IBFD. . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.9 Scatter plot of ECG as a function of sub-carrier attenuation. PLCsample channels generated with [107]. Noise scenario as described inSection 2.2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44xviList of Figures2.10 DRG (overall increasing curves - in blue) and MSE (overall decreasingcurves - in green) versus iterations for LPTV-LMS with step-sizes of(a) µ = 0.025, (b) µ = 0.05, and (c) µ = 0.075. Approximate DRGsaturation points are shown by the dashed line. . . . . . . . . . . . . 462.11 Empirical CDF of overall DRG (2.17) using IBFD for a set of 1500random channels under different noise conditions. . . . . . . . . . . . 492.12 Port connections of the active hybrids in a 2× 2 MIMO configuration. 502.13 Block diagram for digital EC for one received signal in an IBFD en-abled MIMO transceiver. . . . . . . . . . . . . . . . . . . . . . . . . . 522.14 Total ECG for SI and CI with respect to SI ECG for SISO. . . . . . . 532.15 Empirical CDF of overall MIMO DRG (2.17) using IBFD for a set of1500 random channels under different noise conditions. . . . . . . . . 553.1 Transceiver block diagram of an IBFD BB-PLC system with our pro-posed AIC solution. External band-pass filter and transient protectioncircuitry are not explicitly shown. LPF: low-pass filter, PA: power am-plifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.2 A schematic representation of an IBFD-enabled 2× 4 MIMO BB-PLCtransceiver setup. The line-hybrid interface is highlighted in red, andthe echo canceler of transceiver-1 and transceiver-3 are highlightedin green and blue, respectively. T and R indicate the front-ends ofthe transmitter and receiver chains, respectively, and H represents thehybrid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.3 A block diagram of the ith transceiver (shown in green in Fig. 3.2) ofan NT × NR MIMO IBFD BB-PLC node with our proposed AIC. Asimilar structure follows for all NT transceivers. . . . . . . . . . . . . 68xviiList of Figures3.4 Variation of ECG with sub-carrier PLC channel attenuation. . . . . . 743.5 CDF plots of DRGs obtained for a SISO IBFD system under twodifferent noise levels using the DIC and AIC solutions, with DRGcomputed as (3.18). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.6 Variation of ECG for SI (3.19) and CI (3.20) with SOI strength, for theDIC and AIC solutions. A plot with hybrid represents the ECG at thereceivers accompanied by a transmitter on the same conductor pair,while a plot without the hybrid indicates the ECG at the stand-alonereceiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.7 CDF plots of DRGs obtained at one of the receivers of the MIMOIBFD system under two different noise levels using the DIC and AICsolutions, with DRG computed as (3.18). . . . . . . . . . . . . . . . . 794.1 Structure of one configuration of our proposed two conductor-pairspectrum sensing solution. . . . . . . . . . . . . . . . . . . . . . . . . 934.2 The equivalent decompositions of the line-device interface shown inFig. 4.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.3 PSD of the monitored signal under HD and IBFD operations usingDIC. A cross (X) on top of a peak indicates that the IBFD implemen-tation fails to satisfy condition (4.1). . . . . . . . . . . . . . . . . . . 964.4 PSD of the monitored signal under IBFD operation with 12-, 14-, and16-bit ADCs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.5 PSD of the monitored signal under HD operation, IBFD using the twoconductor-pair setup for passive isolation, and IBFD with the hybrid. 984.6 PSD of the monitored signal under HD operation, and IBFD with DICand AIC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99xviiiList of Figures4.7 CDF of throughput gained by using broadcast radio bands. . . . . . . 1014.8 (a) PLC-to-DSL coupling channel gains under four different conditions(surrounding environment) from [141], and (b) their correspondingVDSL-2 downstream data rates with and without PLC PSD reduc-tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.9 Heat map showing the required PN,PLC to achieve different ΨDSL[k] forvarying DSL channel attenuations and DPIC conditions. . . . . . . . 1104.10 Empirical CDF plot of ΨDSL observed on the power line under high-and low-noise conditions [115]. . . . . . . . . . . . . . . . . . . . . . . 1124.11 Percentage rate loss of PLC and downstream DSL communications inthe downstream DSL bands. . . . . . . . . . . . . . . . . . . . . . . . 1154.12 The energy storage facility at the Vancouver campus of The Universityof British Columbia, powered by Alpha Technologies Inc. and CorvusEnergy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.13 A zoomed image of Fig. 4.12 showing an individual battery and thecentral BCU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.14 Illustrations of (a) the fields generated by signals in opposing directionsinterfering destructively in conventional PLC, and (b) cables carryingsignals in opposing directions being too far away from each other fortheir fields to completely cancel each other out in PLC-B. . . . . . . . 1204.15 The method-of-images model for a single conductor that is at a heighth above the ground plane and carrying a current Inet. . . . . . . . . 1224.16 The Cartesian coordinates representation of the electric field producedat a distance d from the conductor by its nth dipole element that isoriented along the z-axis. . . . . . . . . . . . . . . . . . . . . . . . . 125xixList of Figures4.17 Variation of the electric field strength for PLC-B and conventionalPLC applications (a) across frequency, and (b) for varying observationdistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1304.18 (a) Feeding voltage limit across different frequencies that PLC-B de-vices need to adhere to, in order to conform with the FCC Part 15 emit-ted radiations regulation, and (b) the obtained electric field strengthacross all frequencies by injecting a signal of power spectral density−80 dBm/Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1324.19 The median power coupling factor across all frequencies varying withdistance of separation. . . . . . . . . . . . . . . . . . . . . . . . . . . 1334.20 Illustration of the initiation procedure of a MAC frame transmissionat a node under the conventional HPGP CSMA/CA protocol. (PB:Preamble) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1374.21 Illustration of the MAC frame transmission at a node and the timesaved using our proposed frequency domain CAP and contention res-olution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1404.22 CDF plot (zoomed) of the average SNR obtained over 1000 randomlygenerated power line channel and noise conditions. . . . . . . . . . . . 1434.23 Percentage of time spent on CAP and contention resolution for vary-ing number of network nodes using the conventional solution and ourproposed solution under two different CAP3 network traffic conditions. 1484.24 MAC efficiency versus the data payload frame length using the con-ventional solution and our proposed solution under different CAP3network traffic conditions. . . . . . . . . . . . . . . . . . . . . . . . . 1495.1 A one-hop IBFD relay network with three PLC nodes. . . . . . . . . 158xxList of FiguresB.1 Port connections of the active hybrid in SISO configuration. . . . . . 193C.1 Variation of γADC,dB from (C.2) and γˆADC,dB of (C.3) with m. . . . . . 198E.1 Equivalent circuits of the power line-hybrid interface (shown in redin Fig. 3.2) using the Z-parameters described by the input impedancematrix of the power line. . . . . . . . . . . . . . . . . . . . . . . . . 203xxiList of AbbreviationsADC Analog-to-Digital ConverterADS Advanced Design SystemAFE Analog Front-endAIC Analog Interference CancellationAM Amplitude ModulationAMI Advanced Metering InfrastructureAMR Automatic Meter ReadingAVLN Audio Video Logical NetworkAWG American Wire GaugeBB-PLC Broadband Power Line CommunicationBC Back-off CounterBCU Battery Control UnitBER Bit Error RateBMS Battery Management SystemBPL Broadband over Power LinesCAP Channel Access PriorityCB Citizens BandCCo Central CoordinatorCDF Cumulative Distribution FunctionCI Cross-InterferencexxiiList of AbbreviationsCIFS Contention Inter-Frame SpacingCM Common ModeCN Central NetworkCSMA/CA Carrier Sense Multiple Access with Collision AvoidanceCSMA/CD Carrier Sense Multiple Access with Collision DetectionCTS Clear-to-SendDAC Digital-to-Analog ConverterDB Derivation BoxDFT Discrete Fourier TransformDIC Digital Interference CancellationDM Differential ModeDPIC DSL-to-PLC Interference ChannelDRG Data Rate GainDRM Digital Radio MondialeDSL Digital Subscriber LineDSLAM Digital Subscriber Line Access MultiplexerEC Echo CancellationEM ElectromagneticEMC Electromagnetic CompatibilityEMI Electromagnetic InterferenceEMS Energy Management SystemFCC Federal Communications CommissionFDD Frequency Division DuplexingFDEC Frequency Domain Echo CancelerFIR Finite Impulse ResponsexxiiiList of AbbreviationsHAN Home Area NetworkHC Half CycleHD Half-duplexHPAV HomePlug Audio VideoHPGP HomePlug Green PHYIBFD In-Band Full-DuplexIEEE Institute of Electrical and Electronics EngineersIoT Internet-of-ThingsI/Q In-phase/QuadratureL Live or LineLAN Local Area NetworkLCL Longitudinal Conversion LossLMS Least Mean SquaresLV Low VoltageMAC Medium Access ControlMDEC Mixed Domain Echo CancelerMIMO Multi-input multiple-outputMSD Most Significant DigitMSE Mean Squared ErrorN NeutralNB-PLC Narrowband Power Line CommunicationNMSE Normalized Mean Squared ErrorOFDM Orthogonal Frequency Division MultiplexingOL OutletOp-Amp Operational AmplifierxxivList of AbbreviationsPA Power AmplifierPCo Proxy CoordinatorPDIC PLC-to-DSL Interference ChannelPE Protective EarthPGA Programmable Gain AmplifierPLC Power Line CommunicationPN Proxy NetworkPOTS Plain Old Telephone ServicePR Primary ReceiverPRP Priority Resolution ProcedurePRS Priority Resolution SignalPSD Power Spectral DensityPT Primary TransmitterPUL Per-Unit LengthRADAR Radio Detection and RangingRBW Resolution BandwidthROC Rate-of-ConvergenceRSI Residual Self-InterferenceRTS Request-to-SendRXA Receiver-end AttenuatorSCA Sub-carrier AttenuationSI Self-interferenceSINAD Signal-to-Noise-and-DistortionSINR Signal-to-Interference-plus-Noise RatioSISO Single-input single-outputxxvList of AbbreviationsSNR Signal-to-Noise RatioSOI Signal-of-interestSQNR Signal-to-Quantization Noise RatioSR Secondary ReceiverST Secondary TransmitterSTA StationTDD Time Division DuplexingTDEC Time Domain Echo CancelerTDMA Time Division Multiple AccessTL Transmission LineUSRP Universal Software Radio PeripheralV2I Vehicle-to-InfrastructureVDSL Very-high-data-rate Digital Subscriber LineVSS-LMS Variable Step Size Least Mean SquaresV-VDSL Vectored Very-high-data-rate Digital Subscriber LinexxviNotation∗ Linear convolution|N | Cardinality of a set N|x| Magnitude of the complex number x◦ Hadamard product or element-wise multiplication(·)∗ Complex conjugationFN Discrete Fourier transform operator of size N={x} Imaginary part of the complex number xQ(·) Tail distribution function of the standard normal distribution<{x} Real part of the complex number xσ2x Variance of the signal xx(t) Continuous time analog signal x at any time instant tx[n] = x(nTs) Discrete time counterpart of x(t) sampled with a frequency of1TsxxviiAcknowledgmentsI am sincerely thankful to Prof. Lutz Lampe for the opportunity to be a part of hisresearch group. Prof. Lampe has always supported and encouraged me throughoutmy doctoral studies, not only in my work that appears in this dissertation, but also inhelping me grow professionally and academically. I am constantly amazed by his timemanagement skills, his ability to work on diverse research topics, and his approach toproblems, some of which I have, on several occasions, tried to emulate. He has been,and will continue to be, an inspiration in my career. I also thank him for allowingme to present our work at various conferences and workshops around the globe.I am deeply grateful to Prof. Sudip Shekhar for his guidance and assistancethroughout my doctoral journey. Prof. Shekhar has been a patient teacher to meand has always been supportive of my work and my academic pursuits.I thank Prof. Naofal Al-Dhahir of The University of Texas at Dallas for takingthe time out to serve as the external examiner for my final exam. His comments andcritiques have enriched my disseration.Over the course of my PhD, I have been fortunate to have collaborated withseveral researchers from all over the world. I thank them all: Prof. Victor Leung,Prof. Ralf Lehnert, Prof. Rudolf Mathar, Dr. Hao Ma, Dr. Jahidur Rahman, Dr.Fariba Aalamifar, Dr. Ievgenii Tsokalo, Dr. Stanislav Mudriiyevski, Dr. Anıl Mengi,Dr. Omid Tagizadeh, Mr. Yinjia Huo, and Mr. Lazar Atanackovic for all researchcontributions that resulted from our collaborative work.xxviiiAcknowledgmentsI am thankful to my Masters supervisor Prof. Haniph Latchman at the Universityof Florida for encouraging me to continue my grad studies and work with Prof. Lampe.I am grateful to my colleague, Yinjia, for all the brainstorming sessions. I speciallythank him for working with me several times at odd hours to catch deadlines in time-lines that seemed ridiculously impossible.Many thanks to UBC G+PS Graduate Student Travel Fund and the IEEE Com-Soc Student Travel Grant for funding some of my conference travels in part.I thank my lab mates at 4090: Mrinmoy, Naveen, Yinjia, Ayman, Hao, Jahidur,Fariba, Yanan, and Roee for all the insightful discussions we have had. I also thankNaveen and Ranjini for giving me a home away from home in Vancouver.MITACS funded a portion of my work in Germany. I thank Prof. Holger Hirschat the Universita¨t Duisburg – Essen for hosting my MITACS Globalink ResearchAward tenure, and Dr. Jo¨rg Honerla for helping me out with measurements in theirlab. I thank Dr. Anıl Mengi and Prof. Michael Koch for giving me the opportunityto intern at Devolo AG. It is probably not an overstretch to say that my internshipcould have been rough if not for Dr. Christoph July, who helped me in every possibleway from my first day to the last. I also thank Andreas and Nico for letting me be apart of Devolo’s contributions to standardization activities at the European Telecom-munications Standards Institute (ETSI). Many thanks to all my friends in Aachenand Duisburg for keeping me safe and sane. Vielen Dank Monish and Krithika, formaking Mu¨nchen so much fun.Finally, I thank my parents for all the love, encouragement, and support theyhave showered on me from thousands of miles away.xxixDedicationTo my parentsxxxChapter 1IntroductionPower line communication (PLC) enables data transfer over the electrical wiringinfrastructure [1]. PLC, therefore, finds application in every conceivable avenue wherepower lines are available in some form, e.g., transmission and distribution grids [2, 3],indoor environments [4–7], in-vehicle and vehicle-to-infrastructure (V2I) networks [8–11], and even in energy management systems or battery storage units (smart batterypacks) [12–14]. PLC, also known by other names such as carrier communication [15]or power line telecommunication [16], is an old technology dating back as early as1898 [17], when it was used for remote meter reading. Other patents filed during thisperiod also indicate that PLC has been historically considered to be a suitable meansto achieve remote asset monitoring [18, 19], which forms an integral part of today’sSmart Grid [20–22].The readily available communication infrastructure provided by PLC for bidirec-tional communication makes it ideally suited in the context of smart grids to achieveautomatic meter reading (AMR) [23], advanced metering infrastructure (AMI) [24],and demand-side management [25]. PLC systems for these purposes often use a rel-atively small bandwidth of less than 500 kHz, as these services prefer coverage andreliability over speed. Such systems are classified as narrowband PLC (NB-PLC)systems [26].Toward the end of the 20th century, advances in signal processing techniquesfor PLC accomplished high-speed communication over power lines using frequency1Chapter 1. Introductionbands of over 25 MHz [27]. Such systems are classified as broadband PLC (BB-PLC)systems (also known as Broadband over Power Lines (BPL) [28]). This motivatedpower utility companies to investigate using PLC to provide Internet access to itscustomers [27, 29, 30]. But the strict electromagnetic compatibility (EMC) restric-tions, and limitations such as severe signal attenuation at transformers and presenceof feeder segmentation eventually hindered successful deployments of BB-PLC toprovide Internet access to households [2]. BPL has, however, found renewed interestfrom commercial telecommunication enterprises that have developed new network ar-chitectures and proposed the use of alternative signal transmission methods to reviveBB-PLC for Internet access [31].Nevertheless, the most attractive application of BB-PLC has been in in-home lo-cal area networks (LANs), where the high speed it provides suit multimedia commu-nication for applications such as high-definition and 3-dimensional video streamingand LAN gaming. Conventional BB-PLC operates in a single-input single-output(SISO) manner by applying differential signal transmission over a pair of conductors.The availability of a third wire, i.e., protective earth (sometimes also referred to as“ground”) in most in-home wiring infrastructure (over 64% and 70% of households inthe United States and Canada, respectively [32]) allows for a multiple-input multiple-output (MIMO) transmission by coupling and decoupling signals over more than onepair of conductors [33]. This has shown to provide data rates up to 2024 Mbit/s [34],which makes BB-PLC a competitive technology for in-home multimedia communica-tion, either as a standalone solution or as a backbone to the wireless LAN. Fig. 1.1shows the evolution of high-speed BB-PLC over time [34–37].In this thesis, we consider designing and tailoring our solutions to BB-PLC sys-tems as they pose a more challenging application environment than NB-PLC systems,21.1. In-Band Full-Duplex PLC: Why and How?2001 –HomePlug1.02005 –HomePlug AV2008 –ITU-T G.99602010 –IEEE 19012011 –ITU-T G.9963 (MIMO)2012 –HomePlugAV2 (MIMO)Figure 1.1: Evolution of PLC with emphasis on BB-PLC standards.as we describe in detail in Chapter 2. However, a simplified version of our solutioncan also be applied on NB-PLC products.1.1 In-Band Full-Duplex PLC: Why and How?While a simplex communication was sufficient for early PLC applications such as re-mote meter reading, bidirectional communication is required for modern applicationsof PLC, e.g., for monitoring and control in the smart grid, and in enabling a robustindoor LAN. Current PLC modems typically implement duplexing in time, i.e., timedivision duplexing (TDD). This results in inefficient spectral utilization, since theentire frequency band is used for communications in only one direction. The spectralefficiency can be doubled if we could instead transmit and receive data simultaneouslyin the same band. Although doubling the spectral utilization efficiency is attractivefor all forms of communication, it is particularly appealing in PLC for the followingtwo reasons. Power line channels are known to display a low-pass behavior, with chan-nel attenuation drastically increasing with frequency [38–40]. This behavior is seenacross the spectrum, including in the 2− 100 MHz frequency range that is typicallyused in BB-PLC. Therefore, improving spectral efficiency in PLC has greater appealalong with or in place of expanding the transmission spectrum. Further, although31.1. In-Band Full-Duplex PLC: Why and How?power consumption is not of the highest consideration in PLC modem design, asPLC devices are typically not battery operated and are always connected to a powerline, EMC regulations around the world restrict the transmitted signal power spectraldensity (PSD) on the power lines to limit the electromagnetic radiation caused dueto the unshielded and unbalanced nature of electrical power lines. Therefore, furtherincrease in transmit PSD is not a feasible solution to improve data rates. Hence, amethod to enhance throughput without requiring expansion in bandwidth or increasein transmit PSD is ideally suited for PLC.With this backdrop, we consider the application of in-band full-duplex (IBFD)operation1, which has long been used in other wired and wireless communicationsystems [41–47]. IBFD in PLC allows for simultaneous bidirectional data transferover the same power line channel in the same frequency band. The fundamentalimpediment in achieving successful IBFD is the impact of self-interference (SI) onthe received signal. We illustrate the issue of distortion introduced by the echo/SI2in Fig. 1.2. Depending on the communication system parameters like transmit powerand channel attenuation, the SI could be up to several billion times stronger thanthe signal-of-interest (SOI).The impact of SI can be reduced by using different suppression and/or cancellationtechniques (see Fig. 1.3). Suppression involves passively reducing the amount oftransmitted signal that interferes with the SOI. This is typically achieved in wirelessIBFD systems by using a ferrite circulator in case of single antenna systems [47].For multi-antenna systems, suppression can be obtained by using methods like (a)1The term full-duplex is often used in the literature to refer to IBFD. This is not to be confusedwith simultaneous bidirectional communication over different frequency bands, i.e., frequency divi-sion duplexing (FDD), which may also use echo cancellation techniques to achieve superior spectralisolation. To avoid this confusion, we use the term IBFD throughout this thesis.2The term echo is more commonly used in IBFD literature related to wire-line communications,while SI is used more often in describing wireless IBFD systems. We use the terms interchangeablythroughout this thesis.41.1. In-Band Full-Duplex PLC: Why and How?To/From channelTXRXTransmit signalSignal-of-Interest (SOI)SOI Echo/SIFigure 1.2: Impact of the large SI during IBFD operation.TXDigital SI estimatorRXTo/From lineP1P2P3Analog SIestimatorPropagation domainHybridCancellation SuppressionFigure 1.3: The different types of possible SI cancellation methods. P1, P2, and P3indicate three ports of the hybrid.antenna spacing [48], which involves strategic placement of the transmit and receiveantennas to achieve destructive interference cancellation at the receive antenna, or(b) antenna separation [49], in which the two antennas are located at farthest distanceon the device to increase path loss, so that the transmitted signal is fairly attenuatedbefore reaching the receive antenna, or (c) antenna isolation [50], where either anartificial barrier is placed between the transmit and receive antennas (absorptiveshielding) or the antennas are directed in such a way to introduce additional isolation51.1. In-Band Full-Duplex PLC: Why and How?of the transmitted signal in the direction towards the receive antenna (directionalisolation). In wire-line IBFD systems, a three-port hybrid circuit (also referred to as2-to-4 wire interface [51]) is commonly used to achieve some isolation between thebidirectional signals. Due to the nature of suppression, it can only be implementedin the analog domain.Cancellation, on the other hand, is an active signal removal technique, that in-volves replicating the echo using the known transmitted signal, and canceling it fromthe received signal to discern the SOI. Cancellation can be performed either in theanalog or digital domain. Analog interference cancellation (AIC) involves tapping thetransmitted signal just before it enters the analog front-end (AFE) and filtering it toreconstruct the interference signal. This process essentially emulates the SI channeland can be achieved using analog delays and attenuations. AIC implementations areoften found in wireless and Ethernet IBFD systems [46, 52]. Digital interference can-cellation (DIC) is the most common cancellation scheme among all IBFD systems.DIC is similar to AIC in principle, where the SI channel is estimated to reconstructthe echo. However, the signal recreation is performed in the digital domain usinga finite impulse response (FIR) filter. Several hybrid methods can also be found inthe literature, where the SI estimation is performed in the digital domain but thesignal is canceled in analog, or vice-versa. [52] and [53] provide detailed surveys ofvarious interference cancellation methods to achieve IBFD in the context of wirelesscommunications.In this thesis, we answer the open question: what are the most suitable suppressionand/or cancellation methods for IBFD BB-PLC systems? We answer this question byconsidering the various techniques already implemented in different IBFD solutionsacross communication media, and evaluating whether they can be directly applied in61.1. In-Band Full-Duplex PLC: Why and How?the context of BB-PLC. IBFD has been used in continuous wave RADAR systemssince the 1940s, where the SI (referred to as “transmitter leakage”) was reduced us-ing the antenna separation technique [54]. Suppression-based IBFD was also laterimplemented in analog plain old telephone service (POTS) communications using ahybrid module placed at the device-line interface [55]. However, with the advent ofhigh-speed modems using digital communications, additional cancellation methodsin the digital domain were implemented, e.g., in full-duplex digital subscriber line(DSL) communications [56]. To supplement such digital echo cancellation methodsand further reduce the impact of the residual echo on the SOI, analog cancellationtechniques were developed, especially targeting full-duplex Ethernet and coaxial cablecommunications [45, 46]. The concept of echo cancellation for PLC is also not new.It has previously been considered for NB-PLC systems to improve spectral efficiencyin the small transmission bandwidth available. The IEC 62488 standard [57], whichspecifies PLC for power utility applications, includes an optional use of echo cancel-lation to improve bandwidth utilization in full-duplex operation. Implementation ofdigital echo cancelers for such systems is relatively uncomplicated, typically makinguse of an adaptive filter tuned using, for example, the least mean squares (LMS) al-gorithm, to emulate the echo channel. Advancements to such LMS-driven filters haverecently been proposed in [58, 59], which have suggested effective methods to resetthe filter weights under abrupt channel changes. However, these techniques cannotdirectly be used for BB-PLC systems. For example, echo cancellation for NB-PLCaddressed in [58, 59] consider a sampling rate of 25.6 kHz, and hence a bandwidth ofless than 15 kHz. BB-PLC systems typically work with a sampling rate of 75 MHzover a bandwidth of 28 MHz [35, 36, 60, 61]. This results in much longer responsesof the SI channel, and it is thus preferable not to do cancellation in time domain71.1. In-Band Full-Duplex PLC: Why and How?as in [57–59]. Furthermore, channel attenuation varies widely in the transmissionband of BB-PLC. For example, [58] considered a constant channel attenuation ofabout 32 dB for NB-PLC. But for realistic BB-PLC channels, we consider channelattenuations between 10 dB and 80 dB in the frequency band of interest. This makescancellation challenging since, as we will show in Chapter 2, low attenuation im-pedes adaptation of the echo cancellation filter while high attenuation leads to highquantization noise from the SI. Finally, the PLC network impedance varies widelyin the BB-PLC spectrum, which, compared to NB-PLC, complicates signal isolationthrough the AFE. In Chapter 2, we present the unique challenges that are encoun-tered in BB-PLC, and propose IBFD designs that are tailored for BB-PLC systems.We draw parallels with other IBFD implementations in not only NB-PLC, but alsofrom old-fashioned POTS to state-of-the-art SI cancellation techniques proposed forwireless communications, to better appreciate the unique considerations required forBB-PLC.One of the fundamental design challenges for IBFD in BB-PLC is at the hardwareinterface of BB-PLC modems. For effective half-duplex (HD) operation, BB-PLCmodems are designed with a low output impedance (transmit-path) and a higherinput impedance (receive-path). Simultaneous operation of both these paths dur-ing IBFD skews the voltage drop across these paths and introduces significant sig-nal attenuation. To address this issue, we propose the use of a broadband activeimpedance-stabilizer in the form of a hybrid circuit in Chapter 2, where we describeits circuit design, including our proposed customizations to reduce its power con-sumption. This hybrid circuit serves the dual purpose of impedance stabilization bypresenting a constant input/output impedance of the modem during IBFD operation,as well as providing initial echo suppression.81.1. In-Band Full-Duplex PLC: Why and How?Another significant uniqueness observed in BB-PLC is the unknown and contin-uously varying broadband access impedance seen by the PLC modem. In contrastto the SI channels observed in, say, wireless communications scenario, where thechannel between the transmitter and receiver antennas may be assumed to changerather slowly, the echo channel in PLC is dependent on the access impedance atthe line-modem interface, which is influenced by activities in all parts of the net-work. Therefore, the variation of access impedance is similar to the changes that areobservable in the end-to-end channel frequency response. We propose solutions inChapters 2 and 3 to address this issue by proposing adaptive SI estimation solutionsthat operate in the presence of the SOI, without requiring a silent (HD-only) periodat start-up or any other time during operation that is a common requirement in manywireless IBFD solutions [49, 62].Furthermore, power lines exhibit two kinds of channel changes, namely short-term and long-term change [63]. While long-term changes are caused due to networkactivities, e.g., connection/disconnection of electrical appliances, short-term changesare a consequence of internal operation of devices connected to the network, andare shown to present a periodic impedance variation with respect to the 50/60 Hzmains. These rapid short-term changes hinder efficient operation of typical adaptiveSI estimation algorithms. Hence, in Chapter 2, we also propose solutions that canexploit the periodic nature of these short-term changes to ensure that our adaptivealgorithm converges to its saturation point.Beyond the aforementioned aspects, our IBFD design is also based on a com-prehensive analysis of the cancellation requirements of typical BB-PLC systems, thequantization noise limitation caused due to a finite precision analog-to-digital con-verter (ADC) at the receiver, the non-linear distortion introduced by practical line91.2. IBFD: Beyond Doubling Spectral EfficiencyFigure 1.4: Nodes A and C are hidden from each other, while node B is in conversationwith C.drivers in the modem AFE, and the implementation cost and computational com-plexity involved. Furthermore, we also expand and analyze our solution for MIMOBB-PLC systems, including the design and choice of cancellation and suppressiontechniques for each of the transceivers and stand-alone receivers in a MIMO modem.1.2 IBFD: Beyond Doubling Spectral EfficiencyAside from doubling bidirectional data rates, IBFD provides a variety of networkingbenefits. For example, as a direct consequence of IBFD operation, the well-knownhidden node problem [64, Ch. 6] can be resolved without the use of Request-to-Send (RTS) and Clear-to-Send (CTS) message exchange [48]. Consider a typicalHomePlug AV Logical Network (AVLN) [60, Fig. 2.3], a part of which is shown inFig. 1.4. If nodes A and C are hidden from each other, and B is in conversationwith C, B can simultaneously start transmission as soon as it receives data from C,thereby indicating to A that it is currently busy. If B has nothing to transmit or ifC is not an IBFD enabled device, B can send a busy signal or duplicate the signalfrom C to announce its busy state.Another important benefit provided by IBFD is the enhancement of relaying ca-101.2. IBFD: Beyond Doubling Spectral Efficiencypacity in a multi-hop network [65, 66]. Considering the same scenario of a largeAVLN, as in [60, Fig. 2.3], one of the nodes in the central network (CN) is desig-nated as a Proxy Coordinator (PCo) of a proxy network (PN) consisting of stations(STAs) hidden from the Central Coordinator (CCo) of the CN. Such scenarios aretypically encountered in large PLC networks where the PCo acts as a relay nodebetween the CCo and the hidden STAs. Depending on the forwarding mechanismused (e.g., amplify-and-forward or decode-and-forward), an IBFD enabled PCo cantransmit packets to the CCo as soon as it starts receiving packets from an STA in thePN, and vice versa. In this way, IBFD accelerates the setup and functioning of PNs,virtually creating a larger CN. With several relay nodes present in BB-PLC in-homeand access networks for range extension, the ability of a relay node to simultaneouslytransmit and receive packets in the same band doubles the efficiency of such networks.Furthermore, bidirectional data transfer ensures that the information being com-municated is unintelligible to an eavesdropper, since only the legitimate users areaware of their transmitted signal, while the eavesdropper intercepts two superim-posed signals that it is unable to decode. Under conditions when either of the legiti-mate users does not have any data to transmit, the receiver can choose to transmit ajamming signal to degrade the decoding ability of the eavesdropper, while being ableto interpret the SOI itself using echo cancellation techniques. An analysis of such aphysical layer security scheme for MIMO BB-PLC can be found in [67].Apart from the above detailed advantages, which are also obtainable in generalacross different communication systems [48, 66, 68], IBFD allows us to solve variousEMI and networking issues specific to PLC that we face today in practical deploy-ments. PLC signals are typically injected in a differential manner so that the uninten-tional radiations cancel each other out. However, due to non-idealities in the network,111.2. IBFD: Beyond Doubling Spectral EfficiencyHarmful EMI 32 MHz 100 MHzHAMDRMCB FMfFigure 1.5: Some examples of non-PLC services that share the 2 − 100 MHz band-width, which is also used for BB-PLC.a portion of the differential-mode signal is converted into common-mode [69]. Theradiated emissions from the in-phase common-mode components add up, and henceare the primary sources of EMI from BB-PLC signals. Since power lines are electro-magnetically unshielded, the radiations cause EMI with non-PLC services that sharethe operating frequency spectrum with BB-PLC. The converse also holds true, wherecommon-mode signal ingress onto the power lines are converted into differential-modecomponents, which distort the BB-PLC signals.Several smart-notching and dynamic spectral adaptation techniques are suggestedby PLC standards to address EMC in BB-PLC to minimize the impact of BB-PLCsignal egress and ingress [70, 71]. Integrating IBFD into these techniques allows usto increase the efficiency of operation. IBFD enables PLC modems to simultaneouslytransmit PLC signals while also sensing the operating spectrum. In Chapter 4, wediscuss three different types of services that are affected by EMI from BB-PLC signals,and propose IBFD solutions to counter the adversities.1. Interference of unintentional radiation caused by PLC on broadcast radio appli-cations : BB-PLC operates in the 2−100 MHz frequency range, and thus sharesthis spectrum with other broadcast and amateur radio services. Fig. 1.5 showsexamples of the non-PLC services, such as amateur radio (also known as “HAMradio”), digital radio mondiale (DRM), citizens band (CB) radio, and frequency121.2. IBFD: Beyond Doubling Spectral Efficiencymodulated (FM) radio services. Traditionally, BB-PLC standards have ensuredthat PLC modems comply with a tone map that masks transmission in someof these frequencies to protect non-PLC services from interference caused bythe unintentional radiation [34–36]. However, this leads to a considerable lossin BB-PLC throughput. Therefore, several studies have investigated spectrumsensing techniques to enable the use of the frequency band when the allottednon-PLC services are absent [72–75]. Such a dynamic frequency exclusion tech-nique is also accommodated in the newer PLC standard of EN 50561-1 [71].With a traditional HD approach, BB-PLC modems are required to suspendtransmission at regular intervals to sense the spectrum for non-PLC activities,which leads to an inefficient use of the idle spectra. We therefore evaluate theuse IBFD to achieve 100% spectrum sensing efficiency by transmitting PLCsignals while simultaneously looking for active radio services. In the first partof Chapter 4, we apply IBFD solutions designed in Chapters 2 and 3 to examineif sufficient SI cancellation is achievable to successfully detect the presence ofDRM and broadcast radio services using the detection guidelines mandated bythe European Telecommunications Standards Institute (ETSI) [76].2. Interference of unintentional radiation caused by PLC on DSL communications :Narrowband non-PLC services can be protected from unintentional PLC radi-ation by switching off PLC transmission on the overlapping frequency bandswhen the spectrum is busy. However, this approach is unsuitable when theoverlapping frequency bands are broad enough to significantly or completelysubsume one another. An illustrative example of this issue is the mutual in-terference caused by unintentional signal ingress and egress of BB-PLC andDSL communications. Fig. 1.6 shows the various DSL communication stan-131.2. IBFD: Beyond Doubling Spectral EfficiencyHarmful EMI 32 MHz 100 MHzVDSL2, V-VDSL2 G.fast, XG-fastfFigure 1.6: Portion of the BB-PLC spectrum that is also used by DSL communica-tions.dards that specify the partial or complete use of the 2 − 100 MHz frequencyrange used for BB-PLC. A reactive solution to address this issue is to estimateand cancel the interference on both the power lines and the DSLs, as required.However, we detail the numerous drawbacks of such a solution in Chapter 4,and instead adopt a proactive approach, where we adaptively vary the trans-mit PSD mask for PLC transmission to reduce the PLC-to-DSL interference tobenign levels. We also show that such a solution is warranted without a similarapproach to be employed by DSL communications, since PLC-to-DSL interfer-ence adversely impacts DSL data rates, while this phenomenon is not noticedin the opposite direction. Such a proactive PLC PSD adaptation technique hasalso been suggested by ETSI to be the practically implementable solution infuture BB-PLC modems [70]. We present a feasibility analysis of this methodin Chapter 4 with a conventional HD approach, where we suspend PLC trans-mission at regular intervals to estimate the PLC-to-DSL interference channelby sensing for the DSL signal on the power line. We then analyze the feasibilityof the PSD adaptation approach with IBFD operation where we estimate thePLC-to-DSL channel in an IBFD manner by also simultaneously transmittingBB-PLC signals.3. Interference of unintentional radiation caused by PLC on neighboring PLC :141.2. IBFD: Beyond Doubling Spectral EfficiencyEMI caused by PLC is a cause for concern in heterogeneous PLC networks aswell. In Chapter 4, we consider a case study of EMI between conventional indoorBB-PLC and PLC over battery cables in an energy storage facility, to determinethe permissible transmit PSD limits on battery cables to ensure benign inter-ference on neighboring indoor BB-PLC (similar to the analysis we performedpreviously for PLC-to-DSL interference). However, since the concept of PLCover battery cables is yet to be implemented in practical energy managementsystems (EMSs), interference measurements between the two heterogeneousnetworks are currently unavailable. Therefore, we analytically characterize theradiation that is caused by broadband signal transmission over battery cablesby considering the uniqueness associated with signal propagation on batterycables that is distinctive from conventional BB-PLC. Differential transmissionover conventional power lines have the benefit that the two closely spaced con-ductors ensure that the unintentional electromagnetic radiation from both theselines nearly cancel each other out. However, in the case of PLC over batterycables, the two single-core cable pairs are not necessarily in close proximity witheach other. This results in an increased electromagnetic radiation as comparedto conventional PLC. Thus, we begin our analysis by first deriving the BB-PLCtransmit PSD limits on battery cables to conform with the radiation regula-tions. To this end, we model the cable as a concatenation of infinite number ofinfinitesimally small Hertzian dipoles and compute the total radiated electricfield. Using the field limits imposed by regulations, we then compute the maxi-mum permissible PSD on battery cables. Furthermore, we use reception factorvalues measured for indoor power lines [75] to also determine the EMI causedon conventional BB-PLC by PLC transmission over battery cables. Our first151.2. IBFD: Beyond Doubling Spectral EfficiencyIssue with Green PHY410 20 30 40 50Number of active network nodes5055606570758085% time wastedFigure 1.7: Impact of the number of network nodes on the percentage of time spentat the MAC layer on all activities other than data payload transmission.analysis and suggested PSD values pave the way for standardization activitieson PLC applied in EMSs.Apart from designing physical layer solutions for EMI issues, simultaneous datatransmission and spectrum sensing can be applied to also improve the operating effi-ciency at the medium access control (MAC) layer. The MAC layer efficiency in cur-rent BB-PLC standards, e.g., IEEE 1901/HomePlug AV (HPAV)/HomePlug Green-PHY (HPGP) [36, 61, 77], operating with carrier sense multiple access with collisionavoidance (CSMA/CA) protocol, drastically reduces with increasing number of nodesconnected to the network. As an application scenario, we consider a smart-home net-work with several PLC devices connected as a part of the in-home Internet-of-Things(IoT) environment. Accordingly, we choose the HPGP standard tailored for smart-home PLC conditions, and evaluate its MAC layer performance with varying numberof network nodes. We notice from our investigation result in Fig. 1.7 that the timewasted, tw, i.e., time spent in the MAC layer on all activities other than data payloadtransmission, increases with the number of connected network nodes. This perfor-161.2. IBFD: Beyond Doubling Spectral Efficiencymance is also consistent with prior HPGP MAC layer evaluations [78, 79]. Amongthe various MAC layer activities contributing to tw, the ones that consume the mostamount of time are collision recovery and contention resolution. Our successful IBFDsolution proposed in Chapters 2 and 3 enables the implementation of the carrier sensemultiple access with collision detection (CSMA/CD), which was previously conceivedto be infeasible in PLC networks [80, Ch. 5], to substantially reduce the time spenton collision recovery. The results in [81, 82] show that CSMA/CD implemented us-ing our IBFD design provides significant improvement in MAC efficiency, which alsoremains constant with increasing number of network nodes. With this backdrop,we propose further enhancements at the MAC layer to reduce the other major timeconsuming activity of contention resolution. Conventional CSMA operation involvesa random back-off procedure, during which, the network nodes compete by countingdown from a chosen back-off counter (BC) value to zero, where the node with the low-est BC value wins the contention. This countdown duration increases as nodes choosea larger BC value, which is more probable in busier networks. With a goal of de-creasing the time spent in the random back-off procedure, we use a frequency domainback-off approach, where the contentions are resolved in single time-shot [83, 84]. Wedetail this technique in Chapter 4, where we also propose solutions that address thechallenge of incorporating such a method for PLC scenarios, where we operate in apower line environment with frequency selective channels containing deep notches andthe power line noise contaminated with several narrowband noise components. Wefurther reduce tw by devising a method to integrate CSMA/CD operation within thefrequency domain contention resolution. We show that our MAC layer enhancementscollectively reduce tw by up to 85%.171.3. Outline1.3 OutlineThe remainder of this dissertation is organized as follows. We present the first anal-ysis and solution to achieve IBFD in BB-PLC in Chapter 2. We enhance our IBFDsolution to counter the practical hardware component limitations in Chapter 3. InChapter 4, we use IBFD-PLC to provide solutions to various open issues affectingPLC. We conclude the dissertation in Chapter 5 by summarizing our work, offeringconcluding remarks, and providing possible future research directions. All supple-mentary details are relegated to the Appendices.18Chapter 2Introducing In-band FullDuplexing for Broadband PowerLine CommunicationsAgainst the background of existing IBFD schemes for different media and systems [43–49, 52, 85–91], in this chapter, we present the first design for IBFD-enabled BB-PLCtransceivers. We start in Section 2.1 with an analysis for the cancellation gain re-quired, the dynamic range of typical ADCs, and the level of non-linear signal com-ponents in a BB-PLC scenario. This analysis guides us to propose a two-step SIcancellation scheme3 in Section 2.2. This SI cancellation scheme uses a hybrid mod-ule for suppression in the analog domain, and a subsequent time/frequency domainadaptive cancellation scheme in the digital domain. Our design takes the effect ofunknown and varying network impedances into account and facilitates simultaneousoperation of a low impedance transmitter path and a high impedance receiver paththat is commonly the case in BB-PLC modems [1, Ch. 4.2.7]. To address linear pe-riodically time varying (LPTV) channel conditions that are often observed in powerline channels [63], in Section 2.3, we propose a new LPTV-aware LMS algorithm thatprovides more accurate echo estimates by exploiting the cyclic nature of short-term3Note that we use the terms SI cancellation and echo cancellation interchangeably to refer toan integrated solution with one or more types of cancellation and suppression methods shown inFig. 1.3.192.1. Feasibility and Requirements of IBFD for BB-PLCchannel variations. We demonstrate the benefits of our IBFD design in Section 2.4,by showing the results of a simulative performance study as well as theoretical datarate gain calculations obtained under different channel and noise conditions focusingon in-home PLC network scenarios. We then extend our solution to a MIMO systemand provide its performance analysis in Section 2.5. Finally, we offer conclusions inSection 2.6.2.1 Feasibility and Requirements of IBFD forBB-PLCThe amount of cancellation required for a successful IBFD functioning depends onthe SOI strength, as well as the noise floor at the receiver (NR). To completely erasethe effects of SI, ideally, the PSD of the residual SI (RSI), PRSI, should be less thanNR. In such a case, data rates can be successfully doubled through IBFD.Admissible transmit PSDs of BB-PLC standards vary mainly as a function offrequency band and geographical region, so as to meet the applicable EMC regulations[1, Chs. 3, 9], [33, Ch. 6.4]. We adopt a maximum PSD of PTX = −50 dBm/Hz,which is specified in the HPAV standard for North America [60] and corresponds to aworst-case analysis for IBFD, as it produces the largest gap between SI and noise floorand thus requires the greatest cancellation gain. The value of NR varies significantlybased on frequency band, and network conditions such as number of loads connectedto the line, types of loads, types of interconnections, and the overall network topology.Typical values of NR for in-home PLC environments are greater than −130 dBm/Hz[7, 92–94]. This produces a maximum cancellation gain requirement of less than−50− (−130) = 80 dB.202.1. Feasibility and Requirements of IBFD for BB-PLCNext, we consider the possibility of ADC saturation due to relatively high SI inthe analog domain. Typical BB-PLC receivers use a 12-bit ADC, which gives anideal signal-to-quantization-noise ratio (SQNR) of 74 dB. However, commercial 12-bit ADCs, such as AD98664, provide a typical Signal-to-Noise-and-Distortion-Ratio(SINAD) of 69 dB. This is further reduced considering the application of multi-carriertransmission and in particular orthogonal-frequency division multiplexing (OFDM)as used in BB-PLC. For an n-bit ADC with an effective number of bits of ENOB, wehave [95, Ch. 6]SINAD =σ2xσ2e=12(2ENOB−1)2PAPR(2.1)and thus,SINADdB = 6.02ENOB− PAPRdB + 4.77 dB , (2.2)where PAPRdB is the peak-to-average-power ratio of the input signal in dB, and σ2xand σ2e are the variances of the input signal and the uniformly distributed quantizationerror, respectively. For OFDM transmission, the value of PAPR depends on thenumber of sub-carriers used for data transmission. For example, although the HPAVspecification uses a 3072-point discrete Fourier transform (DFT), only Nused = 917 ofthose sub-carriers are used for data transmission in the 2− 28 MHz bandwidth [60].Such systems can have a maximum PAPR of 10 log10(917) = 29.67 dB, which wouldsignificantly decrease the SINAD in (2.2). However, to reduce the PAPR in suchscenarios, signals beyond a certain maximum amplitude Vclip are clipped, resultingin additional clipping noise that decreases with increasing Vclip. But setting a large4AD9866 is manufactured specifically for power line networking and works up to 80 Msps thatsuits the 75 MHz HPAV applications.212.1. Feasibility and Requirements of IBFD for BB-PLCVclip incurs substantial quantization noise [96, 97]. We therefore need to choose anoptimized clipping amplitude V optclip , and it has been shown that Voptclip = 5σx is agood choice for a 12-bit ADC [97]. With this V optclip , our simulation results indicatea SINAD of 60 dB for a 12-bit ADC, closely matching the theoretical values in [97].As a consequence, the IBFD system contains a quantization noise level of at mostPQN = −50 − 60 = −110 dBm/Hz. Note that, in reality, PQN < −110 dBm/Hz,depending on the amount of analog signal suppression experienced by the SI beforereaching the ADC. Hence, the quantization noise becomes comparable to the noisefloor in typical PLC scenarios.High SI also generates non-linear signal components in the AFE, which thenintroduce additional interference with the SOI. Such interferences are mitigated inEthernet and wireless systems by AIC circuits [46, 52, 90]. However for BB-PLC,efficient AFEs [98] hold total non-linear distortion levels at 75 dB to 80 dB belowthe transmit power. With a PTX of −50 dBm/Hz, the non-linear distortion levels areless than −50−75 = −125 dBm/Hz, which are lower than typical NR values and lessthan PQN, and hence have negligible additional effect on SOI.The above analysis shows that the isolation required is significant, but notablyless than what is needed in wireless IBFD (about 110 dB or more). This suggeststhat we may not need a three-step cancellation approach consisting of analog isolationthrough a hybrid, circuit-based AIC, and digital EC as often considered in wirelesscommunications [47, 49, 52]. Toward a simpler design, we suggest to omit the AICcomponent, as digital EC has the advantages of better reconfigurability and adaptiv-ity. These features are essential for IBFD in BB-PLC where the interference-channelconditions can vary widely over installation, and over time for a given installation,due to the widely varying network impedance. Furthermore, AIC schemes based on222.2. Proposed Two-step Cancellation Proceduredelay-line solutions presented in e.g., [47] would be difficult to adopt for BB-PLC dueto the length of expected delays. On the other hand, digital EC schemes consideredfor DSL systems (e.g., [43, 87–89]) seem to be an excellent starting point for digitalEC in BB-PLC.2.2 Proposed Two-step Cancellation ProcedureFollowing the discussion in the previous section, we propose the two-step cancellationprocedure consisting of(a) an analog domain isolation using a hybrid(b) a digital domain echo cancellation.2.2.1 Analog IsolationIBFD techniques in wireless communications use a ferrite circulator to gain up to15 dB of analog isolation between the transmitted signal and the SOI [47]. Due to costand size limitations of ferrite circulators, a simpler transformer-based hybrid was alsodeveloped for such applications [99]. But the size of the magnets and transformersin ferrite circulators and transformer hybrids, respectively, prohibits their use inlow frequency applications (say, for < 100 MHz) such as BB-PLC. We thereforechoose an active hybrid circuit as in [100], and similar to the ones used in DSLoperations [85, 101]. This circuit uses three amplifier and voltage divider stages toprovide complete voltage transfer from one port to its adjacent port in one direction,and utilizes the high reverse isolation of operational amplifiers (op-amps) to provideisolation in the opposite direction.232.2. Proposed Two-step Cancellation ProcedureR1_x = 200 OhmR2_x = 647.2 OhmPort1-TXend_AFEPort2-PLC_ChannelPort3-RXend_AFEAMP_2AMP_1R1_9R2_5R1_7R2_4R2_2R1_4R1_3R2_3R1_1R2_1R1_2R1_6R1_5R1_8OpAmpOpAmpFigure 2.1: ADS schematic of the simplified hybrid implementation with only two op-amps, and the resistances tuned to provide port impedances of Z1 = Z2 = Z3 = 100 Ω.The location of the hybrid in the overall IBFD system can be seen from Fig. 2.3(which is discussed in detail in Section 2.2.2), where the port 1 (P1) of the hybrid isconnected to the transmitter-end AFE, port 2 (P2) to the power line channel, andport 3 (P3) to the receiver-end AFE of the transceiver. For our application, since thehybrid has only two inputs, at P1 from the transmitter and at P2 from the channel,we simplify the existing circuit from [100] by abandoning the amplifier stage at P3,as there is no voltage transfer required from P3 to P1. Fig. 2.1 shows the circuitschematic of the simplified active hybrid using the Advanced Design System (ADS)software. This simplification reduces the power consumption of the hybrid by over30%, without compromising its operation for the use case considered here.The hybrid circuit also gives us the flexibility to set the impedance at each port,Zi, individually, where i ∈ {1, 2, 3} indicates the port number. The hybrid circuitin Fig. 2.1 operates in such a way that when a voltage is applied at port i, it is242.2. Proposed Two-step Cancellation Proceduretransferred out of port i + 1 across a matched load, for i = 1, 2. Therefore, wewould ideally want to match P2 and P3 to the power line channel and receiver-endAFE, respectively. Additionally, impedance matching at P2 also prevents reflectionsfrom the hybrid-to-channel interface that are then transferred to the receiver at P3causing SI. But impedance matching at P2 is not an easy exercise since the power linechannel impedance is unknown and varies with both time and frequency. Adaptiveimpedance matching circuits (e.g., [102]) are not able to achieve matching over theentire operating frequency range of BB-PLC. We therefore set Z2 = 100 Ω, which isthe typical impedance of a power line channel in our frequency range of interest, cf.e.g., [33, Ch. 1]. Similarly, we match the impedance Z3 = ZRX at P3. Although thereceiver-end AFE usually presents a high impedance [103], it is typically precededby an impedance matching section which attempts to match the receiver-end inputimpedance to the line impedance of about 100 Ω [103]. Hence, it makes sense to setZ3 = 100 Ω. On the other hand, at P1, we desire to bridge the impedance to obtainmaximum voltage transfer and draw minimum current. We achieve this by havingZ1  Zs, where Zs is the output impedance of the transmitter-end AFE. Typically,the value of Zs is very low, e.g., of the order of 3 Ω [103]. Hence, Z1 = 100 Ω sufficesto achieve impedance bridging.5 Therefore, we tune the resistances in our hybridcircuit to set Zi = 100 Ω, i = 1, 2, 3, which is shown in Fig. 2.1. This can easilybe achieved by doubling all the resistances from the original circuit of [100], whichpresents an impedance of 50 Ω at all ports. Doubling all the impedances also ensuresappropriate functioning of the voltage divider sections.From the above it follows that the hybrid circuit has a two-fold purpose in IBFDfor BB-PLC. It provides well defined impedances for the transmitter and receiver5Alternatively, we could match the impedances at P1 by setting Z1 = Zs, but this would halvethe voltage transfer into the channel, and line drivers typically cannot drive such low impedances(e.g., less than 10 Ω [103]).252.2. Proposed Two-step Cancellation Procedure0 50 100 150 200 25005101520253035404550Re(ZPLC), ΩPhyb, dBIm(ZPLC) = −100 ΩIm(ZPLC) = −50 ΩIm(ZPLC) = −25 ΩIm(ZPLC) = 0 ΩIm(ZPLC) = 25 ΩIm(ZPLC) = 50 ΩIm(ZPLC) = 100 ΩFigure 2.2: Hybrid isolation Phyb from port 1 to port 3 as a function of PLC lineimpedance ZPLC. Phyb is maximum when the line impedance is matched to the hybridP2 impedance, i.e., ZPLC = Z2 = (100 + j0) Ω.chains of the AFE and it isolates them from each other. While, due to the hybrid,there is no direct SI path from the transmitter to the receiver, the isolation is im-perfect because of reflections at P2. More specifically, with a channel impedanceZPLC(f) for some frequency f , we have the reflection coefficientΓPLC(f) =ZPLC(f)− Z2(f)ZPLC(f) + Z2(f), (2.3)where Z2(f) = Z2 = 100 Ω. For the hybrid shown in Fig. 2.1, we obtain the voltagetransfer function from P1 to P3 as HSI(f) = 0.9 ΓPLC(f). The derivation is relegatedto Appendix B.1. The resulting hybrid isolation Phyb = −20 log10|HSI| is shown asa function of ZPLC in Fig. 2.2. We observe an isolation of about 45 dB when P2 isnearly matched. But as ZPLC deviates from the matched value of Z2 = 100 Ω, theisolation Phyb drops quickly. Phyb also depends on the bandwidth of the op-amps usedin Fig. 2.1, where op-amps with a larger bandwidth provide a more constant hybrid262.2. Proposed Two-step Cancellation Procedureisolation across frequencies. Considering the cost and availability, we apply op-ampswith a 300 MHz operating bandwidth.Since Phyb is insufficient to improve the signal-to-interference-plus-Noise (SINR) ofthe received signal to a sufficient level under the commonly encountered mismatched-port scenario, the remaining cancellation is performed by an echo canceler in thedigital domain.2.2.2 Digital Echo CancellationSince all recently standardized BB-PLC systems apply multi-carrier transmission andmost of them in the form of OFDM, it is meaningful to consider implementations ofdigital EC in time and frequency domain as well as their combination. For this wemake use of designs presented in previous work in the context of DSL [43, 87–89].Fig. 2.3 shows the block diagrams for the corresponding IBFD solutions, includingthe connection of digital EC and the hybrid circuit discussed in the previous section.In the following, we briefly review the different digital EC schemes and discuss andcompare their applicability for IBFD in BB-PLC.Time-Domain CancellationThe time-domain based cancellation is shown in the right part of Fig. 2.3(a). Thetime-domain transmit signal x is tapped just before it enters the AFE and is usedtogether with the time-domain received signal y to tune the weights g = [g1, . . . , gM ]Tof an adaptive filter to learn the effective echo channel hSI from P1 to P3.To derive the filter update, we express the received signal sample at discrete time272.2. Proposed Two-step Cancellation ProcedureModulator IDFT Demodulator x y(n) = (x*hSI)(n) + (xSOI*hPLC)(n) + w(n) + + DFT LMS Update G(l) LMS Update g(n) X(l) X(l).G(l) xT(n)g(n) Time Domain Cancellation Frequency Domain Cancellation Active hybrid hSI To/From PLC P1 P3 P2 AFE AFE e(n) E(l)	  (a)Modulator IDFT IDFT DFT DFT LMS Update G(l) + Active hybrid hSI Demodulator To/From PLC P1 P3 P2 x y(n) = (x*hSI)(n) + (xSOI*hPLC)(n) + w(n) e(n) AFE AFE X(l) E(l) (b)Figure 2.3: Transceiver block diagrams for IBFD for BB-PLC using OFDM. (a) ECin time and frequency domain (only one of the shaded blocks is used). (b) Mixed-domain EC. For brevity, we include addition and removal of cyclic prefix with theIDFT and DFT blocks, respectively.282.2. Proposed Two-step Cancellation Proceduren as (‘∗’ indicates linear convolution)y(n) = (x ∗ hSI)(n)︸ ︷︷ ︸echo+ (xSOI ∗ hPLC)(n)︸ ︷︷ ︸SOI+ w(n)︸ ︷︷ ︸cumulative noise, (2.4)where xSOI is the far-end transmitted signal which passes through the PLC channelwith impulse response hPLC, and w(n) represents the noise at the receiver end. Theecho estimate yˆ(n) produced by the filter g is given byyˆ(n) = xT(n)g(n) , (2.5)where x(n) = [x(n−M + 1) . . . x(n)]T. As a low-complexity solution for tuning thefilter weights, we apply the LMS updateg(n+ 1) = g(n) + µx(n)e(n) , (2.6)wheree(n) = y(n)− yˆ(n) (2.7)and µ > 0 is the step size of the LMS adaptation. We note that baseband transmissionis applied for BB-PLC and thus no complex-conjugate operator is required in (2.6).The number of weights M in the adaptive filter is decided based on the actuallength of typical echo channels. Fig. 2.4 shows the frequency responses for foursample PLC channels (Fig. 2.4(a)) and their corresponding SI channels (Fig. 2.4(b))considering different in-home PLC network conditions. The channels are generatedusing the procedure described in Appendix A.1. Considering a sampling frequencyof fs = 75 MHz and a 3072-point DFT as applied in HPAV [60], Fig. 2.4(c) shows292.2. Proposed Two-step Cancellation Procedure0 1 2 3x 107−100−80−60−40−200Frequency, HzMagnitude of channel gain |HPLC|, dB(a)0 1 2 3x 107−25−20−15−10−50Frequency, HzMagnitude of channel gain |HSI|, dB2DB, 2OL, no load5DB, 5OL, variable loads10DB, 10OL, no load10DB, 10OL, variable loads(b)0 10 20 30 40 50−0.6−0.4−0.200.20.4Time samplesAmplitude of impulse response hSI(c)Figure 2.4: Magnitude of channel gain of (a) sample PLC channels under differentin-home network conditions, and the (b) frequency and (c) impulse responses of theircorresponding SI/echo channels.the corresponding impulse response of the echo channel hSI. We observe that aboutM = 40 would be a reasonable filter length to fully capture the effect of echoes.302.2. Proposed Two-step Cancellation ProcedureFrequency-Domain CancellationEC can also be implemented in the frequency domain, which typically reduces thecomputational complexity associated with the estimation step (2.5). The frequency-domain EC for BB-PLC is shown in the left part of Fig. 2.3(a). Let us define the `thfrequency-domain transmit vector (i.e., OFDM symbol)X(`) = [X1(`), . . . , XNused(`)]T ,and the corresponding received and error vector Y (`) and E(`), respectively. Thenumber of elements in the adaptive filter vector G is equal to the number of usedOFDM sub-carriers, i.e., M = Nused. The echo estimate in the frequency domain isthen obtained as (‘◦’ denotes element-wise multiplication)Yˆ (`) = X(`) ◦G(`) , (2.8)with the LMS filter updateG(`+ 1) = G(`) + µdiag(X(`))∗E(`) , (2.9)where diag(X) is the diagonal matrix with the elements of X on the principal diag-onal, and the error signal in the frequency domain follows fromE(`) = Y (`)− Yˆ (`) . (2.10)We notice from Eqs. (2.8)-(2.10) and the block diagram in Fig. 2.3(a) that a successfulfrequency-domain cancellation with this setup requires synchronous transmission andreception with respect to the OFDM-symbol timing of the transmitted signal andthe SOI. To accommodate a frame-asynchronous operation, we move to a simplifiedmixed-domain EC.312.2. Proposed Two-step Cancellation ProcedureMixed-Domain CancellationMixed-domain cancellation captures favorable aspects from both its time- and frequency-domain counterparts, by employing frequency-domain estimation as in (2.8) for areduced number of computations, and time-domain cancellation as in (2.7) for ef-ficient asynchronous cancellation. The corresponding implementation is shown inFig. 2.3(b). This type of simplified mixed-domain cancellation is made possible bythe fact that BB-PLC systems such as HPAV [60] use a cyclic prefix that essentiallyeliminates interference between successive OFDM symbols, which avoids the needfor the traditional cyclic echo synthesis performed in mixed-domain cancellation inDSL systems [43, 87, 89]. As shown in Fig. 2.3(b), mixed-domain EC requires twoadditional DFT/IDFT blocks for time/frequency-domain transformation.The number of computations required in a time-domain echo canceler (TDEC)depends on M . Since the signals and filter taps are real, every LMS iteration requires2M + 1 real multiplications and 2M real additions [104, Ch. 6]. Hence, for everyOFDM symbol of size N , the total number of real computations required is (4M +1)N . In reality, this value is a little higher depending on the length of the cyclic prefix.In the mixed-domain echo canceler (MDEC) on the other hand, the LMS updateis performed block-wise, and M = Nused. The total number of real computationsrequired is approximately(4 · (2 ·1+1)+2 · (2 ·1+1)+2 · (2 ·1))Nused = 22Nused [104,Ch. 6]. However, MDEC uses two additional IDFT/DFT blocks. When implementedusing a prime factor FFT, where N = 2p3q5r, these DFT blocks add an approximateoverhead of 2N(1.375p + 2.67q + 4r − 1) + 2 real additions and 2N(0.75p + 2q +2.8r − 2) + 4 real multiplications [105]. The overall numbers of computations perOFDM symbol for the TDEC and MDEC schemes are summarized in Table 2.1. Forexample, for the HPAV specification, using a DFT size of N = 3072 and Nused = 917322.2. Proposed Two-step Cancellation Procedure500 1000 1500 2000−60−50−40−30−20−10OFDM−symbol time indexMSE, dBAveraged TDEC adaptationActual TDEC adaptationMDEC adaptationFigure 2.5: MSE after EC versus transmitted OFDM-symbol time for a sample PLCchannel. Comparison of 40-tap TDEC filter and a 917-tap MDEC. LMS with step-sizeµ = 0.025.usable carriers, and assuming an echo channel length of 40, TDEC requires 60% morecomputations than MDEC.2.2.3 Rate of Convergence and Cancellation GainWe implement the transceiver designs of Fig. 2.3(a) for TDEC and Fig. 2.3(b) forMDEC to compare the rate of convergence (ROC) of the mean-squared error (MSE)using LMS filters. To this end, we adopt the HPAV system specifications for transmis-sion in the 2−28 MHz band and use different in-home channel and noise realizationsgenerated as explained in Appendix A.1 and Appendix A.3, respectively.Fig. 2.5 shows the MSE for both TDEC and MDEC for one particular power linechannel as a function of the time index of the transmitted OFDM symbol, whichcorresponds to one update in the MDEC implementation. The MSE for MDEC isthe average value for all Nused sub-carriers. We also plot the moving average of thefluctuating TDEC MSE that is calculated on a sample-by-sample basis. The small332.2. Proposed Two-step Cancellation ProcedureTable 2.1: Number of computations per OFDM symbol with mixed-domain and time-domain echo cancellationsMixed-domain Time-domainDFT 4N(2.125p+ 4.67q + 6.8r − 3) + 12 -Add/Multiply 22Nused (4M + 1)NTotal 4N(2.125p+ 4.67q + 6.8r − 3) + 12 (4M + 1)N+22NusedLMS step-size of µ = 0.025 is chosen to better notice the ROC. We observe thatthe ROC is quite similar for both methods. However, the results indicate a higherEC gain in the steady state for MDEC. This trend has been confirmed in simulationexperiments for several PLC channels. Therefore, and because of the computationalcomplexity advantages, we adopt MDEC for our BB-PLC IBFD solution.Before proceeding, we briefly discuss methods to improve the speed of convergencefor MDEC.Least Squares InitializationWe can reduce the number of iterations for convergence by replacing a traditionalall-zero initialization of G with a least-squares (LS) error estimate [43]. The LSestimate of the echo channel at sub-carrier k can be obtained asHˆSI,k =YkXk.. (2.11)We observed that instead of the all-zero vector initialization, assigning G(0) = HˆSI,where HˆSI = [HˆSI,1, HˆSI,2, . . . , HˆSI,k, . . .]T for all k, increases the ROC significantly,essentially due to a lower MSE starting point.342.2. Proposed Two-step Cancellation Procedure150 200 250 300−20−15−10−50510Iteration numberMSE, dB  Constant step size LMSVariable step size LMSChannel changes(a)0 50 100 150−18−16−14−12−10−8−6Number of iterationsMSE, dB  Constant step size LMSVariable step size LMS(b)Figure 2.6: MSE as a function of MDEC iteration for sample PLC channels generatedwith [107]. MDEC with fixed and variable step-size LMS. (a) One change of PLCchannel. (b) Multiple changes of PLC channel.Variable Step Size LMSTo further increase the ROC, we could employ a variable step size LMS (VSS-LMS) al-gorithm that varies the LMS step size dynamically to provide faster convergence [106].Fig. 2.6(a)6 illustrates this by showing the MSE as a function of the MDEC iterationfor the case that the PLC channel changes abruptly due to load changes and thusa new adaptation is required. On the other hand, we observe from Fig. 2.6(b) thatwhen the channel changes relatively frequently, there is little improvement achievedby using VSS-LMS compared to a constant step size LMS with a larger µ. In Sec-tion 2.3, we present a solution specifically tailored for PLC transmission consideringthe case that the frequent channel variations have an underlying periodicity.6Note that the difference in saturated MSE level before the channel change is a result of SNRbeing conducive for the VSS-LMS to provide a slightly lower MSE with a lower minimum µ comparedto the µ of the constant step-size LMS. But once the channel changes, both the curves saturate tonearly the same value in the new SNR conditions.352.3. LMS Modification for LPTV PLC channels2.2.4 Implementation of IBFDThe proposed two-stage cancellation structure in Fig. 2.3(b) requires fairly littlechanges to the existing modem structure to accommodate IBFD. Traditional BB-PLCtransceivers are TDD devices that use a line-driver control to turn off the transmitor receive path when the other is in operation. Migration of such systems to IBFDis uncomplicated, since it only requires the line driver control to switch on both thetransmit and receive paths at the same time to allow simultaneous bidirectional com-munication. We also note that this ensures complete coexistence and interoperabilitywith the existing HD modems.The active hybrid circuit also consumes additional power. Our simplified hybridconsists of only two power consuming amplifier sections. With the maximum signalvoltage not exceeding 6 V [60], and a typical op-amp supply current of 9 mA [108],the hybrid, on an average, consumes about 108 mW of additional power. Our hybridport impedance selection also ensures that there is no added power loss in either thetransmitted or received signal when compared to a conventional HD system.2.3 LMS Modification for LPTV PLC channelsThe characteristics of PLC channels are determined by the network configuration andtopology, the electromagnetic properties of the power lines, and the loads connectedat the outlets. Especially the latter are responsible for recurring variations of thePLC channel, as they can be modeled as periodically time-varying impedances inthe frequency band of interest for PLC [109]. Such channel changes can cause MSEbursts in the EC performance as illustrated in Fig. 2.6. Furthermore, the LPTVnature of the changes does not often provide enough time for the LMS algorithm to362.3. LMS Modification for LPTV PLC channelsconverge close to its stationary value. In this section, we propose a new LPTV-awareLMS algorithm that specifically exploits the periodic pattern of changes to improvethe adaptation.2.3.1 The LPTV-LMS AdaptationLPTV loads vary periodically with the period equal to one half of the mains cycle[109]. We therefore divide our LMS adaptation into periods of one half cycle (HC)each. This is also facilitated by typical BB-PLC systems, such as HPAV, which areaware of the mains cycle period [60, Ch. 3]. Denoting ` as the LMS iteration variableand Φ(`) as the MSE after the `th iteration, Algorithm 1 shows the pseudo-code ofthe proposed LPTV-LMS adaptation.During the “first HC”, when ` < LHC, where LHC is the number of OFDM symbolsin one HC, the MSE is constantly monitored to determine the time locations whichexperience a cyclic channel change (CCC). Assuming the LMS algorithm does notconverge in the first HC7, the MSE decreases with increasing ` when there is no changein channel conditions. Therefore, the time at which the MSE increases compared tothe previous iteration is identified as the location where a CCC occurs. We recordthe iteration index ` of the jth such CCC as cj. When a CCC occurs, we havetwo options: (a) Reset filter weights with an LS estimate, or (b) continue with noreset. If the magnitude of the MSE increase is larger than a preset positive thresholdΦreset thresh, we reset the filter weights with an LS estimate. Φreset thresh is chosen basedon an average MSE increase caused by an LS estimate reset. This value is obtainedfrom several test runs performed with and without the LS reset. If the MSE increaseis less than Φreset thresh, it indicates that Φ(`+ 1) with option (a) would be higher7This assumption is valid since the coherence time of LPTV PLC channels [63] is typically muchsmaller than the LMS convergence time with a legitimate step size.372.3. LMS Modification for LPTV PLC channelsAlgorithm 1 Pseudo-code for LPTV-LMS algorithmFirst HC: ` = 0, j = 01: Standard LMS update2: for ` = 1 : LHC − 1 do3: if Φ(`)− Φ(`− 1) > 0 then4: Save ` −→ cj # Location of a CCC5: j = j + 16: if Φ(`)− Φ(`− 1) ≥ Φreset thresh then7: Reset G(`+ 1) with LS estimate8: else9: Standard LMS update10: end if11: else12: Standard LMS update13: end if14: ` = `+ 115: end forAdaptation HC: ` = 0, j = 016: while 1 do # Until an N-CCC is encountered17: if ` ∈ C then18: G(`) = G(cj⊕1 − 1)19: j = j ⊕ 120: if Φ(`)− Φ(cj⊕1 − 1) > Φcyclic thresh then21: Reset G(`+ 1) with LS estimate22: Jump to First HC23: end if24: Standard LMS update25: else26: if Φ(`)− Φ(`− 1) > Φchange thresh then27: Reset G(`+ 1) with LS estimate28: Jump to First HC29: else30: Standard LMS update31: end if32: end if33: ` = `+ 134: end whilethan Φ(`+ 1) with option (b). In such cases, we let the standard LMS adaptationcontinue without any weight reset. At the end of the first HC, the algorithm contains382.3. LMS Modification for LPTV PLC channelspositions of CCCs in the set C = {cj| j = 0, 1, ..., J − 1}, where J indicates the totalnumber of CCCs identified in one HC.After the completion of the first HC, the algorithm jumps to an “adaptation HC”,where the values updated in the previous HC are reused to minimize adaptationtime. For every jth CCC in the current HC, we reset the LMS weights with thelast updated value for the corresponding jth CCC in the previous HC, i.e., G(`) =G(cj⊕1 − 1),∀` ∈ C . The symbol ‘⊕’ indicates a modulo J addition to account forcyclic reuse of weights after J CCCs. This way, we continue the LMS adaption fromwhere we stopped in the previous HC, by reusing the last LMS update of the samechannel condition in the previous HC.We note that the channel conditions undergo non-LPTV changes too. For exam-ple, a load connected/disconnected from the line causes a non-CCC (N-CCC). Suchchanges can occur at positions ` /∈ C or ` ∈ C .1. To detect N-CCCs at ` /∈ C , we monitor the MSE difference Φ(`) − Φ(`− 1)at all ` /∈ C , to check if the value is greater than a threshold Φchange thresh.Φchange thresh is chosen such that false positives are rarely detected. This isaccomplished by setting Φchange thresh larger than the MSE fluctuations in thesteady state of the LMS. Once an N-CCC is detected, we reset the filter weightswith an LS estimate and re-start the adaptation by jumping to the “first HC”.2. To detect N-CCCs at ` ∈ C , we verify if Φ(`) − Φ(cj⊕1 − 1) < Φcyclic thresh.If the condition is not met, we conclude that there has been an N-CCC. Wethen reset the filter weights with an LS estimate and jump to the “first HC”.Generally, Φ(`) ≈ Φ(cj⊕1 − 1), since G(`) = G(cj⊕1 − 1). We therefore set asmall threshold Φcyclic thresh whose value is close to zero.392.3. LMS Modification for LPTV PLC channels0 500 1000 1500−50−45−40−35−30−25−20−15−10−5Number of iterationsMSE, dB  LPTV−aware LMSConventional LMSFirst HC Adaptation HC Adaptation HC Adaptation HC Adaptation HC Adaptation HC Adaptation HC Adaptation HC Adaptation HC= Re−use weightsSAT = SaturatedΦ(l) − Φ(l−1) > Φreset_threshSATSATFigure 2.7: MSE versus iteration number for MDEC using the conventional LMSand the proposed LPTV-aware LMS algorithms for an LPTV PLC channel. Totalduration is nine HCs. LMS step size is µ = 0.025.2.3.2 Performance IllustrationTo test MDEC with the proposed LPTV-aware LMS algorithm, we consider in-homechannel and noise scenarios as described in Appendix A.1.1 and Appendix A.3, re-spectively.Fig. 2.7 shows the MSE as a function of the adaptation iteration against a conven-tional LMS adaptation. As can be seen in Fig. 2.7, the CCC locations are determinedin the first HC and are subsequently re-used and updated in the following adaptionHCs. Notice that for the selected in-home environment, there are two locations inthe first HC where the MSE difference crosses the reset threshold limit. These arethe locations where the loads displaying commuted behavior switch their impedancesand therefore cause a significant change in channel conditions. At these locations,402.4. Data Rate Gain AnalysisPSD, dBm/Hz PTX NR PSOI SCA When RSI PSD is in -  DRG < 1 1 ≤ DRG < 2 DRG = 2  !50 EC gain SNRHD  SINR RSI: Residual Self-Interference DRG: Data Rate Gain EC: Echo Cancellation PSD: Power Spectral Density SCA: Sub-carrier Attenuation SINR: Signal-to-Interference-plus-Noise Ratio (in IBFD mode) SI: Self-Interference SNRHD: Signal-to-Noise Ratio in half-duplex mode SOI: Signal of Interest max{PRSI, NR, PQN} Figure 2.8: Per sub-carrier PSD levels at different locations in the PLC transmissionsystem, providing an illustration of achievable data-rate gains (DRGs) using IBFD.the weights are reset with an LS estimate. For all other CCCs in the first HC, theconventional LMS update is followed. Fig. 2.7 also clearly demonstrates the superiorperformance of the LPTV-aware LMS algorithm over the conventional LMS adap-tion. The re-use of previously updated filter weights results in consistently decreasingMSE over time, which leads to improved SI estimates.We note that regardless of what LMS algorithm is used, PLC impulse noise, whichis known to significantly affect the detection of the SOI, has relatively little effect onthe adaptation for SI cancellation, which is due to the relatively large power of theSI signal.412.4. Data Rate Gain Analysis2.4 Data Rate Gain AnalysisIn this section, we evaluate the gains achievable with the proposed IBFD structure.To this end, we compare the relevant signal-to-noise ratio (SNR) and SINR figureswhen using HD and IBFD PLC transmission, respectively. Fig. 2.8 illustrates therelations of the PSDs at different points of the transmission system, consideringa single sub-carrier associated with a given sub-carrier attenuation (SCA). In HDtransmission, the transmit signal with level PTX is attenuated through the channel,and the SOI is received at the level PSOI. Hence, the per sub-carrier SNR is given by(sub-carriers indexes are omitted for brevity)SNRHD = PSOI −NR . (2.12)In the IBFD case, the transmitted signal is also interference, which after EC by thehybrid and digital adaptive cancellation is experienced at the level PRSI. At the sametime, as discussed in Section 2.1, the quantization noise level PQN may be increaseddue to the still strong SI signal at the output of the analog hybrid. Hence, theeffective noise level is equal toPeff = PRSI +NR + PQN ≈ max{PRSI, NR, PQN} , (2.13)where the approximation assumes the domination of one noise or interference com-ponent. This yieldsSINR = PSOI − Peff (2.14)as the SINR for IBFD.Comparing SNR for HD and SINR for IBFD leads to the three shaded regions in422.4. Data Rate Gain AnalysisFig. 2.8. As commonly done, we consider the use of adaptive modulation that allo-cates bits onto sub-carriers to maintain a certain reliability level, commonly expressedthrough a bit-error rate (BER) target P tb . Given a modulation with constellation sizeMk on a sub-carrier k, the BER Pb can be approximated as [110],Pb(SNRk,Mk) =4log2(Mk)·(1− 1√Mk)· Q(√3 · SNRkMk − 1), (2.15)where SNRk takes the value of SNRHD,k and SINRk for half-duplex and IBFD mode,respectively, and Q(x) = 1√2pi∫∞xe−t22 dt. From (2.15), we can observe that a decreasein SNR should be accompanied by a reduction in modulation order to maintain aconstant target reliability. Therefore, for SINR  SNRHD, the overall data-rategain (DRG) will be smaller than one, as the one-directional transmission rate forIBFD will be less than half of that of HD. For a range SINR . SNRHD, the loss inone-directional rate will be more than compensated by simultaneous bi-directionaltransmission and thus 1 ≤ DRG < 2. Finally, for SINR ≈ SNRHD, the full duplexinggain will be reaped and thus DRG = 2. The region in which we lie depends on theEC gain (ECG)ECG = PTX −max{PRSI, NR, PQN} . (2.16)2.4.1 Echo Cancellation GainThe exact value of ECG depends on the prevalent PLC channel conditions. In partic-ular, as can be seen in (2.4), the received signal, which is used as a reference signal toupdate the LMS weights, consists of echo, SOI, and noise components. The latter twoact as disturbance for the echo estimator. Hence, since the SOI component increasesas the channel attenuation decreases, lower channel attenuation is expected to affectthe accuracy of the SI estimate and thus the digital echo cancellation. Fig. 2.9 shows432.4. Data Rate Gain Analysis0 10 20 30 40 50 60 703540455055606570Sub−carrier Attenuation, dBECG, dBFigure 2.9: Scatter plot of ECG as a function of sub-carrier attenuation. PLC samplechannels generated with [107]. Noise scenario as described in Section 2.2.3.a scatter plot of the ECG from (2.16) (i.e., the gain from both the digital cancella-tion gain and the hybrid isolation) as a function of channel attenuation in OFDMsub-carriers. The results are obtained for 1000 randomly generated PLC channelsusing the simulator from [107] and the noise scenario as described in Appendix A.3.We observe that the ECG increases with increase in sub-carrier attenuation. We alsoobserve from Fig. 2.9 that ECG saturates after a certain point, which is when thePQN becomes dominant in (2.13).2.4.2 Theoretical Data Rate GainsWe can now use the results from Fig. 2.9 to quantify the achievable DRGs, i.e., inwhich region of Fig. 2.8 we operate, as a function of the channel attenuation andnoise level NR. This is presented in Table 2.2, which shows the DRG as a functionof the sub-carrier attenuation SCA = −20log10|HPLC,k| and for two different noiselevels. Depending on the resulting SNR and SINR values, we select constellationsizes MHD and MFD for the modulation scheme in conventional half-duplex and IBFD442.4. Data Rate Gain AnalysisTable 2.2: DRG per sub-carrier as a function of sub-carrier channel attenuation(SCA) and channel noise level NR.NR = -110 dBm/Hz NR = -130 dBm/HzSCA (dB) ECG SNRHD MHD SINR MFD DRG SNRHD MHD SINR MFD DRG5 37 55 1024 32 1024 2 75 1024 32 1024 210 40 50 1024 30 256 1.6 70 1024 30 256 1.615 45 45 1024 30 256 1.6 65 1024 30 256 1.620 47 40 1024 27 256 1.6 60 1024 27 256 1.625 52 35 1024 27 256 1.6 55 1024 27 256 1.630 57 30 256 27 256 2 50 1024 27 256 1.635 59 25 64 24 64 2 45 1024 24 64 1.240 61 20 16 20 16 2 40 1024 21 64 1.245 62 15 16 15 16 2 35 1024 17 16 <150 62 10 4 10 4 2 30 256 12 4 <155 62 5 2 5 2 2 25 64 7 4 <160 62 0 1 0 1 N/A 20 16 2 1 <1transmission, respectively. The modulation schemes are selected based on an adaptivemodulation algorithm with P tb = 10−3 [33, Ch. 9]. We limit max(Mk) = 1024, inaccordance with the HPAV specifications [60].For the relatively higher noise level of NR = −110 dBm/Hz, the values in Table 2.2show that IBFD consistently provide DRGs, often at the maximum of a factor of two.For relatively low channel attenuation, i.e., SCA . 25 dB, the DRG is diminishedas PRSI rises above the noise floor. However, in this region of operation, the SNRis very high and the rate of HD is limited by max(MHD,k). If the noise level is aslow as NR = −130 dBm/Hz, then PRSI and PQN dominate the effective noise levelPeff (2.13) in IBFD, and we observe a DRG smaller than one for channels with highattenuation. If channel attenuation decreases, HD with practical signal constellationscannot further increase the rate due to increasing SNR, and IBFD becomes againbeneficial in terms of achievable rate.452.4. Data Rate Gain Analysis0 500 1000 1500 2000 250000.20.40.60.811.21.41.6Number of iterationsDRG−50−40−30−20−10MSE, dB(a)0 500 1000 1500 2000 250000.20.40.60.811.21.41.6Number of iterationsDRG−50−40−30−20−10MSE, dB(b)0 500 1000 1500 2000 250000.20.40.60.811.21.41.6Number of iterationsDRG−50−40−30−20−10MSE, dB(c)Figure 2.10: DRG (overall increasing curves - in blue) and MSE (overall decreasingcurves - in green) versus iterations for LPTV-LMS with step-sizes of (a) µ = 0.025,(b) µ = 0.05, and (c) µ = 0.075. Approximate DRG saturation points are shown bythe dashed line.2.4.3 Simulation Results of the Overall Date Rate GainThe DRG values computed in the previous section correspond to individual sub-carriers experiencing a given sub-channel attenuation. In this section, we provide theoverall DRG obtained across all OFDM sub-carriers of a channel.462.4. Data Rate Gain AnalysisLPTV DRG EvolutionWe first consider an LPTV channel condition described in Appendix A.1.1 and alow-noise scenario as explained in Appendix A.3 and Table A.1, with the transceiverrunning our LPTV-LMS algorithm for EC. After every LPTV-LMS iteration, wecalculate the overall DRG asDRG =2 · ∑k∈Nlog2(MFD,k)∑k∈Nlog2(MHD,k), (2.17)where N is the set of all data carrying sub-carriers, and MFD,k and MHD,k arethe constellation size of the modulation applied on the kth sub-carrier in IBFDand HD modes, respectively. The factor of two in the numerator in (2.17) ac-counts for the simultaneous bidirectional communication in IBFD. Fig. 2.10 showsthe evolution of DRG with LPTV-LMS iterations for the three different step-sizes ofµ = 0.025, 0.05, 0.075. For completeness, we also show the MSE of the LMS algorithmin the same figure. As expected, we notice that the DRG convergence is fastest forthe largest µ. However, increase in µ also elevates the final MSE saturation value thataffects the ECG, and in turn DRG. We find that µ = 0.05 achieves a good trade-offbetween rate of convergence and final overall DRG. With µ = 0.05, we observe thatDRG convergences to its eventual value by about 900 iterations. This correspondsto 900 OFDM blocks, or a time duration of 45 ms for an extended OFDM blocklength of 50 µs [60, Table 4.2]. This duration is negligible when compared to therate of N-CCC that a typical PLC network would experience. N-CCCs are causedby induced activities on the line, such as plugging in/out devices, or when there isa change in the state of operation of components connected to the line. Even on abusy in-home network, we do not expect such changes to occur more than, say, 20472.5. Extension to MIMO BB-PLC Systemsper minute. This gives a worst-case transient period of 45 ms3 s= 1.5%. We note thatthe results in Fig. 2.10 are for poor channel conditions of high attenuations. Whenchannel attenuations are lower, Fig. 2.9 shows that the ECG is lower, indicating ahigher saturated MSE. In such cases, the transient time is even lesser. Furthermore,we expect N-CCCs to occur much less frequently in a typical in-home power linenetwork. Hence, we use the saturated value of ECG to evaluate DRGs for a largerset of channel conditions in the next section.Overall DRGsWe now present results for the overall DRG obtained by running the IBFD systemof Fig. 2.3(b) for a set of 1500 randomly generated channels and three different noiseconditions as described in Appendix A.1.2, and in Appendix A.3 and Table A.1,respectively.Fig. 2.11 shows the empirical cumulative distribution function (CDF) of the DRGfrom (2.17) for the three noise environments. We observe that the overall DRG issmaller than one only for less than 1% of the channels with our proposed IBFDsolution even under relatively low noise conditions. For high noise levels, IBFD givesa minimum DRG of 1.6. Under medium noise conditions, IBFD is seen to consistentlyoutperform conventional HD rates to provide a median DRG of 76%.2.5 Extension to MIMO BB-PLC SystemsIn this section, we extend our IBFD solution to MIMO BB-PLC systems. MIMOBB-PLC has recently been standardized in the HomePlug AV2 and ITU-T G.9963standards [37, 111] to enable data rates in the Gbps range. MIMO BB-PLC exploitsthe fact that often more than two conductors are available, which enables coupling482.5. Extension to MIMO BB-PLC Systems0.8 1 1.2 1.4 1.6 1.8 200.10.20.30.40.50.60.70.80.91xPr(DRG ≤ x)  Low Noise LevelMedium Noise LevelHigh Noise LevelFigure 2.11: Empirical CDF of overall DRG (2.17) using IBFD for a set of 1500random channels under different noise conditions.of multiple input and decoupling of multiple output signals. The most commonscenario is the use of three conductors, namely live or phase (L or P), neutral (N),and protective earth (PE), which enables a 2 × 2 MIMO system. This has beenextended to a 2 × 4 setup, where a third differential signal and the common modeare included at the reception stage [33, Ch. 1]. We propose an IBFD solution forMIMO BB-PLC whose structure follows our two-step structure for the SISO case.In particular, we initially isolate the bidirectional signals in the analog domain andthen cancel the remaining interference using a digital canceler.2.5.1 Analog IsolationFig. 2.12 shows the block diagram for the integration of the hybrids for analog isola-tion in a 2× 2 MIMO BB-PLC system (we refer to [112, Fig. 12] [33, Ch. 1] for theschematic of a MIMO PLC coupler). As it can be seen, we require two 3-port hybrids,one at each transmit-end AFE. Each of these hybrids isolates the transmitted signalfrom the SOI on their pair of wires. If a 2×4 MIMO is being implemented, the other492.5. Extension to MIMO BB-PLC SystemsHybrid-1 Hybrid-2 PLC coupling circuitry on to the line N L PE P1 P2 P3 P1 P2 P3 ZPLC, 11 ZPLC, 12 ZPLC, 21 ZPLC, 22 ZPLC = VS!ZS V’S ZRX ZS ZRX a1 a2 b1 b2 a’1 b’1 a’2 b’2 a3 b3 b’3 a’3 V3 ΓPLC V’3 Zhyb Figure 2.12: Port connections of the active hybrids in a 2× 2 MIMO configuration.two reception modes use only the digital cancellation.The amount of isolation provided by the hybrid depends on the extent of reflec-tions caused due to impedance mismatch at the hybrid-line interface. The coun-terparts to reflection co-efficient ΓPLC, line impedance ZPLC, and hybrid outputimpedance Z2 in the SISO system are the voltage reflection matrix ΓPLC, the chan-nel impedance matrix ZPLC, and the dual-hybrid output impedance matrix Zhyb,respectively, which are shown in Fig. 2.12. Since P1 and P3 of each of the hybridsare still connected to the transmit- and receive-end AFEs, respectively, we chooseZ1 = Z3 = 100 Ω for both the hybrids, following the analysis in Section 2.2. Z2 ofeach of the hybrids, which are the principal diagonal elements of Zhyb, should be cho-sen in such a way that ΓPLC is kept at a minimum. Measurement results in [33, Chs.1, 5] indicate that the median impedance of typical MIMO channels between anytwo wire pairs is about 88 Ω. We also obtained some channel realizations from the502.5. Extension to MIMO BB-PLC Systemsopen-source MIMO PLC channel generator tool [113] and found the impedance to bearound 100 Ω. We thus conclude that Z2 = 100 Ω is still a good choice. Given thesehybrid parameters and a channel impedance matrix ZPLC, we can determine the SIand cross-interference (CI) channel frequency responses, Hii and Hij, i, j ∈ {1, 2},i 6= j, respectively, using an analysis similar to the SISO scenario. The details of thederivation are given in Appendix B.2.2.5.2 Digital CancellationWe apply the previously validated mixed-domain digital cancellation procedure to aMIMO system by using two LMS filters at each transceiver, one to estimate the SIchannel and the other for the CI channel. Fig. 2.13 illustrates the digital EC structurefor canceling SI from the output of one of hybrids from Fig. 2.12. Denoting the twotransmit signals of the MIMO system as x1 and x2, we can express the sampledoutput of the first hybrid asy1(n) = (x1 ∗ h11)(n)︸ ︷︷ ︸SI/self-echo+ (x2 ∗ h12)(n)︸ ︷︷ ︸CI/cross-echo+ ySOI(n)︸ ︷︷ ︸SOI+ w(n)︸ ︷︷ ︸cumulative noise, (2.18)with the impulse responses h11 and h12 of the SI and CI channels, respectively. Wenote that the SOI usually contains components of two signals sent from the far-endtransmitter, which, however, is irrelevant for the EC step. The SI and CI estimatesare canceled simultaneously to produce a common error signal e1. The LMS filtersare updated in the frequency domain asG11(`+ 1) = G11(`) + µdiag(X1(`))∗E1(`) (2.19)G12(`+ 1) = G12(`) + µdiag(X2(`))∗E1(`), (2.20)512.5. Extension to MIMO BB-PLC Systemsh11 P1 P3 P2 AFE AFE Active hybrid IDFT IDFT DFT LMS-1 G11(l) LMS-2 G12(l) y1(n) = (x1*h11)(n) + (x2*h12)(n) + ySOI(n) + w(n) To/From PLC x1 e1(n) X1(l) X2(l) Figure 2.13: Block diagram for digital EC for one received signal in an IBFD enabledMIMO transceiver.where G11(`) and G12(`) are the weights of the SI and CI estimation filters, re-spectively in the `th iteration, and X1(`), X2(`), and E1(`) are the `th iterationfrequency domain versions of x1, x2, and e1, respectively. Similar adaptive cancella-tion is performed at the other transceiver path as well. When more than two receivemodes are used, the same digital cancellation procedure is employed at the otherreceiver(s) to cancel the two CIs.2.5.3 Performance ResultsFor performance evaluation, we consider one of the two transceivers to determine theamount of SI and CI cancellation achieved by the EC solution described in Fig. 2.13.We operate under the same system settings and noise conditions reported in Sec-tion 2.4, while we generate MIMO channels as specified in Appendix A.2.522.5. Extension to MIMO BB-PLC Systems10 20 30 40 50 60303540455055606570Sub−carrier attenuation, dBECG, dB  SISO SIMIMO SIMIMO CIFigure 2.14: Total ECG for SI and CI with respect to SI ECG for SISO.Echo Cancellation GainsFor the MIMO BB-PLC case, interference is caused by both SI and CI. Hence, wedefine ECGSI and ECGCI as the ECG obtained for SI and CI, respectively, which aregiven byECGSI = PTX −max{PRSI, NR, PQN} (2.21)ECGCI = PTX −max{PRCI, NR, PQN} , (2.22)where PRCI is the PSD of the residual CI. Fig. 2.14 shows the smoothing spline curve-fit data for ECGSI and ECGCI for 1000 different channel realizations, in comparisonto the ECG obtained in SISO operation. We notice that ECGSI and ECGCI showthe same trend as the SISO ECG with gains increasing with higher sub-carrier at-tenuations. We also observe that ECGSI ≈ ECGCI across all sub-carriers. However,the specific gain values deviate from the ECG for the SISO case. This is due toa larger pre-digital attenuation of the SI signal. In particular, the multi-conductor532.6. Conclusionline-hybrid interface provides an average of 12 dB of isolation in the MIMO scenarioas opposed to 7 dB of average isolation seen in the SISO case. This higher isolationresults in lower SI and CI strengths entering the LMS estimator. Under low sub-carrier attenuations, this leads to a smaller difference between the signal strengths ofSI/CI and SOI, which produces less accurate SI/CI estimates, leading to lower digitalcancellation gains. As the sub-carrier attenuation increases, the difference betweenthe signal strengths increases. This produces higher digital cancellation gain, whichwhen combined with a greater pre-digital isolation produces a larger overall MIMOECG.Overall Data Rate GainsWe measure the DRG as defined in (2.17) for 1500 randomly generated MIMO chan-nels (see Appendix A.2). The empirical CDF of the DRG is shown in Fig. 2.15 forthe three different noise levels described in Appendix A.3 and Table A.1. We observethat in almost all cases, the DRG is larger than one for all three noise conditions.However, the DRGs are generally lower than those for the SISO case. The reason forthis is the lower ECG values for relatively smaller sub-carrier attenuations as shownin Fig. 2.14. We obtain a median DRG of about 1.6 under typical (medium) noiseconditions and nearly double the data rates for 20% of the cases under high noiselevels.2.6 ConclusionIn this chapter, we considered the application of IBFD for BB-PLC as a means tosignificantly enhance data rates under typical channel and noise conditions, and tosolve several prevalent networking problems. We motivated and developed a two-step542.6. Conclusion0.8 1 1.2 1.4 1.6 1.8 200.10.20.30.40.50.60.70.80.91xPr(DRG ≤ x)  High Noise LevelMedium Noise LevelLow Noise LevelFigure 2.15: Empirical CDF of overall MIMO DRG (2.17) using IBFD for a set of1500 random channels under different noise conditions.implementation, consisting of an active hybrid to provide initial analog isolation anda mixed time-frequency domain digital echo cancellation for effective SI reduction.Furthermore, we addressed the problem of LPTV channel behavior typically seen inPLC, by developing a new LPTV-aware LMS adaptation algorithm, which exploitsthe cyclic nature of the channel changes to provide better error convergence and moreaccurate echo channel estimates. We also extended our solution for application inMIMO BB-PLC systems. The presented quantitative results suggest that our IBFDsolution provides significant data rate gains over conventional TDD BB-PLC trans-mission for a range of channel and noise scenarios. The proposed IBFD scheme canbe readily integrated into the existing HD systems and also ensures interoperabilitywith the non-upgraded HD devices. We use the IBFD design proposed in this chapteras the foundation to further investigate the potential of integrating AIC to achievehigher EC and DRGs in Chapter 3 by overcoming the limitation imposed by the ADCquantization noise.55Chapter 3Digitally Controlled AnalogCancellationOur IBFD solution in Chapter 2 focused on the design of a custom hybrid and amixed-domain digital EC procedure, and accomplished up to 63 dB of echo cancel-lation gain (ECG). While this was sufficient to significantly increase data rates intypical in-home BB-PLC scenarios, we learn from Section 2.1 that an ECG of up to80 dB is typically required to bring the SI level down to the minimum power linenoise floor [7, 114, 115]. The solution in Chapter 2 chose not to use AIC techniques asthey suffer from adaptivity and reconfigurability issues under rapidly changing echochannel conditions, which is commonly the case in PLC environments where any net-work change is reflected in the echo channel response. However, the maximum ECGachieved by this solution, which we will henceforth refer to as the DIC solution, islimited by the dynamic range of the ADC used at the receiver. The quantization noiseand distortion introduced by the ADC restricts the achievable ECG due to insuffi-cient pre-digital isolation. This motivates us to investigate AIC methods, either tocomplement DIC or function independently, that are capable of not only counteringthe critical ADC dynamic range constraint but also of providing precise adaptivityand reconfigurability. This would allow us to further improve the achievable ECGand accomplish a two-times DRG in a broader range of in-home power line networkconditions.56Chapter 3. Digitally Controlled Analog CancellationIn Section 3.1, we first motivate the choice and applicability of our AIC designapproach to BB-PLC systems, as opposed to other AIC techniques available in theliterature. We present the details of our proposed solution in Section 3.2, where weanalyze its impact on the distortion and quantization noise produced by the ADC.Further, we relate this ADC distortion and quantization noise to the loss of precisionin the ADC for quantizing the SOI, by formulating the number of ADC bits lost forresolving the residual SI. For this purpose, we also derive an approximate expressionfor the SINAD ratio of the ADC that operates on an OFDM signal. We eventuallyshow that by using our solution, we lose nearly zero ADC bits for resolving the residualSI. Next, in Section 3.3, we adapt our proposed solution to a generic MIMO BB-PLCscenario. We present our solution by describing its implementation at the PLC signalcoupling interface and by analytically characterizing the interference channel transferfunctions at the receivers of an IBFD-enabled MIMO BB-PLC device. Further, inSection 3.4, we analyze the effects of non-linear SI components on EC, as they becomemore pronounced due to the reduction in ADC distortion and quantization noise.We then present simulation results of the performance of our proposed solution inSection 3.5 for both SISO and MIMO configurations under realistic in-home PLCchannel and noise environments, and compare it to the performance of the DICsolution under a similar setup. Finally, in Section 3.6, we provide a discussion on ourproposed solution by describing the notable features and the costs associated with apractical implementation. We conclude the chapter in Section 3.7, with derivationsrelegated to the Appendices.Nomenclature followed in this chapter : x(t) is used to represent a continuoustime analog signal x at any time instant t, and x[n] = x(nTs) is its discrete timecounterpart sampled with a frequency of 1/Ts. X[k] = FN{x[n]} is used to denote573.1. Analog SI Cancellation Solutionsthe frequency domain version of x[n], where FN{·} is the discrete Fourier transform(DFT) operator of size N . X = [X[k]]T is the vector of all X[k], ∀k ∈ N , whereN (|N | ≤ N) is the set of all data carrying sub-carriers. BB-PLC regulations acrossgeographical locations restrict the usage of certain intermediate frequencies in the2−100 MHz bandwidth to protect non-PLC service frequencies such as amateur radiobands, citizen band, aeronautical bands, etc. [4]. N contains the non-contiguous setof sub-carriers that are not excluded by such regulations, and are used by BB-PLCdevices for data transfer.3.1 Analog SI Cancellation SolutionsAIC ensures that the residual SI does not introduce ADC distortion and quantizationnoise that is large enough to limit the achievable ECG. Several AIC techniques areavailable in the literature, which are used in full-duplex systems across communicationmedia, e.g., [45–47, 65, 116]. An LMS adaptive analog cancellation solution wasproposed in [46] for full-duplex Ethernet communication, where a four-tap analogFIR filter was used to estimate and cancel the echo in time domain. However, weshowed in Chapter 2 that a time domain canceler for BB-PLC requires at least 40 tapsto completely capture the effects of the echo channel. Extending the structure in [46]to 40 taps requires using 40 additional digital-to-analog converter (DAC) units, whichis both costly and introduces additional distortions. Further, this solution and similarones only managed to achieve ECG of about 20 dB, which is sufficient in Ethernetsystems to prevent ADC saturation and allow subsequent digital cancellations of theecho and near-end crosstalk [117, 118]. However, these values are highly insufficientfor BB-PLC scenarios that require ECG of up to 80 dB. A similar AIC technique withsign-sign LMS adaptation filters was also proposed for coaxial cable communications583.1. Analog SI Cancellation Solutionsin [45], providing a gain of only about 15 dB.Improved ECGs were obtained by a delay-line based AIC solution proposed forwireless IBFD systems [47], where a part of the transmitted analog signal was passedthrough delay lines of different lengths to recreate the attenuation and propagationdelay experienced by the echo in the SI channel. However, such a solution is notapplicable for BB-PLC scenarios where the echo consists of multiple notable signalreflections that are caused from discontinuities along the power lines. Recreatingsuch long delays would require excessively lengthy delay lines. Alternatively, anadaptive AIC method for wireless systems was introduced in [65], similar to the onesin [45, 46]. Although this solution manages to achieve sufficient ECG, multi-tapFIR filter realization in the analog domain restricts the ability to quickly reconfigurefilter weights and delays to widely varying PLC channel conditions. Thus, an analogcancellation solution that incorporates digital echo estimation is appropriate for IBFDPLC scenarios.IBFD designs with analog cancellation and digital estimation were implementedfor wireless communication systems in [49, 116, 119]. However, these solutions arenot adaptive in nature. The echo estimator relies on a rather long silent periodper frame, where the transceiver operates in HD mode, to provide a least squareschannel estimate. A slowly varying wireless echo channel between the transmitterand receiver antenna facilitates such an operation. In case of BB-PLC scenarios, thevariation in the echo channel is driven by the changes in the overall PLC network.Hence, an adaptive channel estimation is more suitable. Next, since RF systems usemixers in the transmit and receive chains, digitally controlled AIC does not counterthe additional phase noise and in-phase/quadrature (I/Q) imbalance that limit theperformance of such IBFD systems [52]. Hence, for wireless systems, AIC solutions593.1. Analog SI Cancellation Solutionsthat tap-in and process the transmitted signal in the analog domain provide greaterSI cancellation, as they are able to better capture the above stated effects [47, 52].Since typical BB-PLC systems operate completely in baseband, we do not face thislimitation. This allows us to implement a digitally controlled AIC to obtain sufficientECGs, uninhibited by phase noise or I/Q imbalance constraints. Since the digitalecho estimation of [49, 116, 119] does not completely capture the effects of analog RFcomponents, they rely primarily on suppression techniques, like antenna separation,to provide the required SI attenuation. On the other hand, we use a single “antenna”transceiver system where we use the same power line conductor-pair for bidirectionalcommunication. Alternatively, the coupling loss between multiple conductor-pairscould be exploited to achieve “antenna separation”. Although this coupling loss be-tween the conductor-pairs provides an isolation of about 12 dB, which is higher thanthat achieved with the hybrid module used in a “single-antenna” system [120], weshow through our results that our solution achieves the target ECG using the singlewire-pair configuration. Additionally, a higher suppression adversely affects the can-cellation performance as our LMS adaptation algorithm relies on the relative strengthof the echo component in the received signal. Furthermore, this multi-conductor setupdoes not provide us the physical flexibility of freely placing “antennas”, and wouldonly double the resources (conductor-pairs) used for transmission. Thus, we proposean IBFD solution that achieves simultaneous in-band bidirectional communicationon the same wire-pair by relying predominantly on cancellation for EC. Finally, weaddress the distinctive challenges posed by the PLC coupling mechanism for an IBFDimplementation, which have not been studied in any of the above.In the following sections, we present our proposed adaptive AIC solution, where wecancel the echo in the analog domain by digitally estimating the echo channel. We use603.2. Proposed AIC Solutiona one-tap FIR filter per sub-carrier to estimate the channel frequency response withminimal complexity using an adaptive LMS update algorithm. We then demonstratethe procedure to extend our solution to a MIMO BB-PLC scenario.3.2 Proposed AIC Solution3.2.1 System ModelWe recap the point-to-point IBFD BB-PLC link introduced in Chapter 2, with twoidentical transceivers at each end, where the transmitter transmits an OFDM signal,x. The signal is coupled on to the power line with an active hybrid circuit (Fig. 2.1)used in between the AFE and the PLC coupler. The hybrid isolates x and thecontinuous time received signal, y, which is expressed asy(t) = (x ∗ hSI)(t)︸ ︷︷ ︸echo+ (xSOI ∗ hPLC)(t)︸ ︷︷ ︸signal-of-interest+ r(t)︸︷︷︸cumulative noise, (3.1)where ‘∗’ indicates linear convolution, hSI is the impulse response of the SI channel,xSOI is the signal transmitted by the far-end transmitter traveling through a PLCchannel with impulse response hPLC, and r is the cumulative noise seen at the near-end receiver8. The received signal is then passed through a receiver-end attenuator(RXA) that is present to handle large signals possibly transmitted from a nearbyoutlet. To accomplish cancellation at the receiver, an adaptive echo canceler usesa copy of x to generate an echo estimate, yˆ, which is subtracted from the receivedsignal, y. The resultant error signal, y − yˆ, is fed back to the estimator to adapt itsfilter weights to produce an improved estimate in the next iteration.8Note the difference of (3.1) with (2.4), where w(n) included the ADC noise within, while r(t)is the analog noise before the ADC.613.2. Proposed AIC SolutionIDFT DAC LPF PGA PAHybridRXAPGADAC LPF PGAIDFTDFTDFT Gain ControlADCScaler +To/from lineX(l)W(l)E(l)y(t) = (x*hSI)(t) + (xSOI*hPLC)(t) + r(t)e[n]yˆ(t)e(t)x(t)Figure 3.1: Transceiver block diagram of an IBFD BB-PLC system with our proposedAIC solution. External band-pass filter and transient protection circuitry are notexplicitly shown. LPF: low-pass filter, PA: power amplifier.3.2.2 Proposed Echo Cancellation ProcedureA block diagram of an IBFD-enabled transceiver with our proposed solution is shownin Fig. 3.1. We perform signal cancellation in the analog domain using an activedifferential amplifier circuit to obtain an error signal, e, given bye(t) = y(t)− yˆ(t). (3.2)We then convert e(t) to discrete time samples using an ADC, which is precededby a programmable gain amplifier (PGA). A gain control module forces the PGA toscale the input signal appropriately to minimize the distortion and quantization noiseintroduced by the ADC. We use this scaling factor to de-scale the quantized error,e[n], and send these digital samples to an FIR filter that we implement alike the oneemployed in the DIC solution in Chapter 2. We adapt the filter-weights vector, W (`),using the LMS adaptive update algorithm at every `th iteration, which corresponds623.2. Proposed AIC Solutionto the `th OFDM block, as [104, Ch. 5]W (`+ 1) = W (`) + µdiag(X(`))∗E(`) , (3.3)where (·)∗ is the complex conjugation operator, µ is the step-size of the LMS update,and X(`) and E(`) are the frequency domain versions of x[n] and e[n], respectively.Next, we obtain the echo estimate,Yˆ (`) = X(`) ◦W (`), (3.4)where ‘◦’ represents the Hadamard product. We then transform Yˆ (`) to time domainand convert it to a continuous analog signal, yˆ, using an additional DAC in the echoreconstruction chain. We also include a PGA after the DAC to provide any furtheramplification required.Since we cancel the echo in the analog domain as per (3.2), the signal entering thePGA at the receiver has a lower power as the LMS adaptation improves the accuracyof yˆ. As a result of reduction in the total power of the signal entering the PGA, thedistortion and quantization noise introduced by the ADC also decreases.3.2.3 ADC Distortion and Quantization NoiseThe power of the quantization and distortion noise introduced by the ADC is givenbyPN,ADC =σ2inpγADC, (3.5)where σ2inp is the power of the input signal entering the quantizer, and γADC is SINADratio of the ADC. σ2inp is primarily driven by the transmit signal power and the extentof pre-digital EC. In case of the DIC solution of Chapter 2, pre-digital EC is achieved633.2. Proposed AIC Solutionby hybrid suppression. Therefore, σ2inp = PTXGhyb + PTXGPLC + PN, where PTXis the transmit signal power used by both near- and far-end transmitters, Ghyb issuppression gain obtained by the hybrid, GPLC is power line channel attenuation,and PN is overall noise power at the near-end receiver (not including ADC-inducednoise)9. Hence, the power of the ADC distortion and quantization noise isP(DIC)N,ADC =PTX(Ghyb +GPLC) + PNγADC. (3.6)Due to the relatively low isolation typically provided by the hybrid (see Fig. 2.2),Ghyb  GPLC, and P (DIC)N,ADC ≈ PTXGhyb/γADC.However, pre-digital cancellation in our proposed solution contains both hybridsuppression and the AIC. Therefore, σ2inp is a function of the LMS iteration, `, andreduces with increasing `. We have σ2inp(`) = PTXGhybGAIC(`)+PTXGPLC+PN, whereGAIC(`) is the AIC gain produced in the `th LMS iteration. Hence, the power of theADC distortion and quantization noise isP(AIC)N,ADC(`) =PTX(GhybGAIC(`) +GPLC) + PNγADC. (3.7)As the accuracy of yˆ increases with ` and GAIC approaches zero, P(AIC)N,ADC(`) tendstoward the value of PN,ADC observed under an HD operation. This assures thatP(AIC)N,ADC is no longer a limiting factor for the achievable ECG.3.2.4 Impact on ADC Bit LossTo better understand the impact of distortion and quantization noise on the SOIand thus gain insight into the extent of degradation caused by IBFD operation, we9We do not explicitly indicate the attenuation of the RXA since it works along with the PGA ofthe ADC, and applies equally to both DIC and AIC scenarios.643.2. Proposed AIC Solutionmap PN,ADC to the number of ADC bits lost in an IBFD operation for quantizing theadditional residual SI.Due to the high PAPR of OFDM signals, the gain control module lets the PGAscale the input signal to accommodate some clipping in the ADC, in order to minimizethe overall clipping distortion and quantization noise [96]. Under such an operation,γADC is given by [121]γ−1ADC =1/322m(Vclipσinp)2+√8pi(σinpVclip)3exp(−Vclip22σ2inp), (3.8)where m is the ADC resolution, and any part of the input signal beyond a voltage|Vclip| is clipped. The number of ADC bits lost for quantizing the residual SI canbe computed by determining the ADC dynamic range per-bit using (3.8). In Ap-pendix C, we show that γADC is approximately linear with m in logarithmic scale,and can be expressed asγˆADC,dB = 5.5m− 3.6, (3.9)where γˆADC,dB is a linear approximation of γADC in dB. Clearly, the dynamic rangeof every bit of the ADC under our operation is 5.5 dB. Thus, we can represent thenumber of bits lost for quantizing the SOI asblost =10 · log10(σ2inpPTXGPLC)5.5. (3.10)In Appendix D, we show using (3.10) that the number of ADC bits lost for thequantization of the SOI in an IBFD operation is given byblost = λ · log10(1 +PTXGtotalPTXGPLC + PN), (3.11)653.3. AIC for MIMO IBFD BB-PLCwhere Gtotal is the total ECG of both suppression and cancellation before the ADC,and λ is a constant of value 20/11.As explained in Section 3.2.3, pre-digital isolation in the DIC solution is achievedonly using the hybrid. Therefore, Gtotal,DIC = Ghyb, while Gtotal,AIC includes theadaptive AIC, and is therefore a function of the LMS iteration, `. Thus, Gtotal,AIC(`) =GhybGAIC(`). This gives usblost,DIC = λ · log10(1 +PTXGhybPTXGPLC + PN)(3.12)blost,AIC(`) = λ · log10(1 +PTXGhybGAIC(`)PTXGPLC + PN). (3.13)AsGAIC(`) reduces and approaches zero with increase in `, (3.13) reduces to blost,AIC(`) ≈λ log10(1) = 0.3.3 AIC for MIMO IBFD BB-PLCIn this section, we use our AIC design developed in Section 3.2 to propose anIBFD MIMO BB-PLC system. As detailed in Chapter 1, a MIMO operation issupported over power lines by utilizing the three conductors available in most in-home single-phase electrical installations [33]. For multi-phase electrical distributioninfrastructures, more than three wires are available to support even more transmis-sion streams [122, Ch. 13]. The usage of MIMO has also been ratified in the latestBB-PLC standards of HomePlug AV2 and ITU-T G.9963 [37, 111].To propose an AIC solution for a MIMO system, we consider a point-to-pointMIMO BB-PLC link with two IBFD-enabled nodes at each ends. The near-end nodeuses NnearT and NnearR active transmitters and receivers, respectively, while the far-endnode uses N farT and NfarR . In typical in-home BB-PLC scenarios NR > NT, as the num-663.3. AIC for MIMO IBFD BB-PLCber of usable transmitter chains is limited by Kirchoff’s law [33, Ch. 1]. However, thepresence of parasitic components allows non-redundant information to be extractedfrom signals on all available conductor pairs. Furthermore, irrespective of the type ofdecoupling used for obtaining the differential signals, an additional reception modecan be realized through common-mode decoupling by extracting the common-modesignal on all the conductors [123]. This type of a structure can incorporate the hybridcircuit for suppression only on the NT transceiver chains, as the hybrid isolates bidi-rectional signals on the same conductor pair. For the remaining (NR −NT) receiverchains, suppression can be accomplished through the coupling losses present acrossdifferent conductor pairs. A conceptual structure of such a setup is shown in Fig. 3.2for a single-phase power line infrastructure. The three available conductors, L, N,and PE, allow coupling and decoupling on a maximum of two transmitter chains(NT = 2) and four receiver chains (NR = 4), respectively.Consider a near-end MIMO node with NnearT transmitter chains. This node trans-mits NnearT OFDM signals, xi, i = 1, 2, ..., NnearT , and receives NfarT streams. The ithreceived signal can be represented asyi(t) =NnearT∑j=1(xj ∗ hij)(t) +N farT∑j=1(xSOI,j ∗ hPLC,ij)(t) + ri(t), ∀i = 1, 2, ...NnearR , (3.14)where hij is the interference channel impulse response from the jth transmitter to theith receiver at the near-end node, xSOI,j is the jth far-end transmitted signal, hPLC,ijis the power line channel impulse response from the jth far-end transmitter to theith near-end receiver, and ri is the cumulative pre-ADC noise at the ith receiver ofthe near-end node.An echo estimate, yˆi, is generated by a filter bank present at every receiver chain.The echo estimate is removed from yi, and the resultant error is sent back to the echo673.3. AIC for MIMO IBFD BB-PLCT1T2R1R2R3R4LNPEH1H2+-+-+-+-TX-endTX-endRX-endRX-endRX-endRX-endEcho EstimatorEcho EstimatorEcho EstimatorEcho EstimatorCommon-mode decouplingFigure 3.2: A schematic representation of an IBFD-enabled 2 × 4 MIMO BB-PLCtransceiver setup. The line-hybrid interface is highlighted in red, and the echo can-celer of transceiver-1 and transceiver-3 are highlighted in green and blue, respectively.T and R indicate the front-ends of the transmitter and receiver chains, respectively,and H represents the hybrid.IDFT DAC LPF PGA PAHybridRXAPGADAC LPF PGAIDFTDFTDFT Gain ControlADCScaler +To/from lineXi(l)Ei(l)yi(t)ei[n]xi(t)Wij(l)ŷi(t)ei(t)j={1,2,…,NT}+X1(l)Xj(l)…j ≠ iFigure 3.3: A block diagram of the ith transceiver (shown in green in Fig. 3.2) of anNT × NR MIMO IBFD BB-PLC node with our proposed AIC. A similar structurefollows for all NT transceivers.683.3. AIC for MIMO IBFD BB-PLCchannel estimator for filter-weights adaptation.A block diagram of the ith transceiver with our proposed AIC solution is shownin Fig. 3.3. Every transceiver associated with a hybrid also contains an identicalstructure, but with a different set of LMS filters. The LMS adaptive cancellationprocedure is essentially an NnearT -times scaled version of the SISO solution in Fig. 3.1.The NnearT filters estimate the SI and CI channel transfer functions adaptively. Thestructure of the stand-alone receivers (i.e., receivers without an associated transmit-ter) is also similar to Fig. 3.3. While its structure does not contain a transmit chainand therefore no hybrid, it uses the same digital interference channel estimation andAIC procedure as in Fig. 3.3. Suppression in this case is achieved through couplinglosses between the conductor pairs. In Chapter 2, we provided the suppression gainby deriving the echo channel transfer function at the transceivers through the hybrid,i.e., considering a 2×2 MIMO system with no stand-alone receivers. In Appendix E,we proceed further to derive the transfer function of the echo channel caused by thecoupling losses between conductor-pairs at a stand-alone receiver using circuit theoryapproach. We show by way of numerical results in Section 3.5 that the suppressionobtained at the stand-alone receivers through coupling losses is nearly identical tothat gained using the hybrid.The proposed MIMO-IBFD solution with analog EC provides similar reduction inADC distortion and quantization noise to a SISO case, and consequently loses similarnumber of ADC bits in resolving the SI. The exact expression for the number of bitslost at every ith ADC is given by (D.3) in Appendix D.693.4. Effect of Non-linear SI Components3.4 Effect of Non-linear SI ComponentsOne of the implications of the significant reduction in PN,ADC is that the non-linearcomponents of the SI are no longer insignificant for EC, as it was the case in the DICsolution. Non-linear components are typically generated by the active componentsin the transceiver. For baseband applications, non-linear SI components are largelygenerated by the amplifiers in the device. The total power of these componentsdepends on the transmitted signal power and the type of amplifiers used. In thetransmitter chain, the line driver or power amplifier (PA) is the main source of non-linear distortions as it operates with the largest signal power. Baseband PAs canbe modeled using several different approaches [124]. Among these, the Hammersteinmodel is a generic baseband PA model using which the output signal of the PA canbe written as [125]x(t) =P∑p=1p oddap · xφ(t) (|xφ(t)|)p−1 , (3.15)where xφ is the pre-amplified signal entering the PA, ap is the scaling factor for thepth order of distortion, and P indicates the total number of significant orders ofdistortion. The summation is only over odd powers of p, since the components ofxφ(t) raised to even powers typically lie outside the band of interest for basebandsignals. The term corresponding to p = 1 is the linear component of xφ(t), while theothers are the non-linear distortions introduced by the PA. We determine the scalingfactors ap, ∀p > 1, based on the specifications of the PA used by the transmitter.Typical PLC line drivers, such as [98], specify that the total non-linear distortions liein the range of 75 dB to 80 dB below the transmit power. This amplified signal thenpasses through the hybrid, which we implement using active operational amplifiers(op-amps). Commercially available low-distortion op-amps can be used in this circuit703.4. Effect of Non-linear SI Componentsto ensure insignificant non-linear distortions [126]. The echo then interferes with theSOI and enters the receiver chain. Unlike radio-frequency systems, BB-PLC receiverdoes not use a low-noise amplifier since the power line induced noise is significantlyhigher than the thermal noise floor. Instead, BB-PLC receivers use an RXA to handlea large signal that could possibly enter from a nearby power outlet. Baseband RXAcan be implemented using simple passive components and thus does not contributeto any non-linear distortions.The above analysis suggests that the total non-linear SI components are at least75 dB below the transmit PSD. Thus, for a North American transmit PSD mask of−50 dBm/Hz [60, Ch. 4], non-linear components require a worst-case cancellation ofup to 5 dB to bring them down to the minimum noise floor of −130 dBm/Hz that istypically seen in in-home BB-PLC networks for the considered transmission band [7,115]. For the European transmit PSD limit of −55 dBm/Hz [36], the non-lineardistortions are brought down to this noise floor without any additional cancellationsrequired. Nevertheless, non-linear SI components undergo suppression through thehybrid. Although we obtain sufficient hybrid isolation of about 7 dB on an average,the isolation gain is frequency selective in nature. In particular, the gain obtained ata frequency f is given by (see (B.8))Ghyb(f) = c ·∣∣∣∣ZPLC(f)− Zhyb(f)ZPLC(f) + Zhyb(f)∣∣∣∣2 , (3.16)where ZPLC is the line impedance seen by the hybrid port connected to the power line,Zhyb is the port impedance of the hybrid port connected to the line, and c is a scalingfactor capturing the effects of impedance bridging and matching at the hybrid ports.Due to this frequency dependence, we learn from Fig. 2.2 that the hybrid isolationcan be as low as 2 dB for certain frequencies. In such a case, the worst-case PSD713.5. Simulation Resultsof the non-linear components, with a maximum transmit PSD of −50 dBm/Hz, lies3 dB above the noise floor.Toward proposing a low-complexity and a low-power overhead solution, we de-cide to tolerate the outlier scenario, without including a non-linear SI cancellationmodule either digitally, or by introducing an additional power-hungry PA in the echoreconstruction chain for analog non-linear cancellation.3.5 Simulation ResultsIn this section, we present numerical results of echo cancellation and practical datarate gains obtained by simulations performed under realistic BB-PLC channel andnoise settings. We run our simulations with the proposed AIC scheme for both SISOand MIMO system configurations and compare our results with the performance ofthe DIC solution of Chapter 2.3.5.1 Simulation SettingsThroughout our simulations, we use system parameters from the HPAV standard [35].We implement baseband OFDM using a fast Fourier transform of size 3072, withthe North American amplitude map and tone mask specified in [35, Figure 3-24]and [35, Table 3-23], respectively. For SISO simulations, we implement the transceivershown in Fig. 3.1 for our proposed AIC solution, and the transceiver block shown inFig. 2.3(b) for a comparison with the DIC solution. For the MIMO configuration, weimplement the transceivers for the AIC and DIC solutions as shown in Fig. 3.3 andFig. 2.13, respectively. To emulate the infinite precision analog signal, we use the de-fault 64-bit double precision of MATLAB, and we use a 12-bit ADC with 11 effectivenumber of bits to quantize the converted digital signal sampled at 75 MHz [35]. We723.5. Simulation Resultsmodel the power amplifier using (3.15), with a1 set according to the amplitude mapof the HomePlug AV standard, and ap, ∀p 6= 1, set as per the non-linear distortionpowers specified in [98].3.5.2 Channel and Noise ModelsWe use the same channel and noise models employed in Chapter 2, since they providecomprehensive models for realistic in-home power line network settings, and alsoenable a fair comparison between our solutions. A detailed description of these isprovided in Appendix A.3.5.3 Numerical ResultsEcho Cancellation Gain in SISO ModeWe define the ECG as the ratio of the SINR of the SOI after EC to SINR of theSOI before EC. To facilitate a precise data rate gain analysis in later sections, wecompute the ECG on a per sub-carrier basis. Considering that one of either noise orthe interference component dominates, we use the approximation,ECG ≈ PTXmax{PRSI, PN,ADC, PN} , (3.17)where PRSI is the power of the RSI including both linear and non-linear components.For the sake of brevity, we drop denoting the sub-carrier index in (3.17). ECGincludes the effects of both suppression and cancellation. The cancellation gain isobtained from analog and digital LMS cancellation for the AIC and DIC solution,respectively, and is computed after the LMS iterations reach convergence.Fig. 3.4 shows a scatter plot of the variation of ECG with the channel attenuation733.5. Simulation Results0 20 40 60 8030405060708090100Sub−carrier attenuation, dBECG, dB  DICAICFigure 3.4: Variation of ECG with sub-carrier PLC channel attenuation.of the kth sub-carrier, 1/|HPLC[k]|2, over 1000 random channels generated using [107].To isolate the interference cancellation ability of our proposed solution, we performour simulations under zero-noise conditions. This ensures that the effects of RSI,and not the ambient noise, limit the achieved ECG. Since PLC noise is always aneventual limiting factor for the achieved ECG, overcoming the RSI limitation is thekey performance indicator when comparing the DIC and our proposed AIC solutions.When PRSI and PN,ADC are sufficiently reduced, complete IBFD gains are achievedfor any given PN level.We notice that, as with the DIC solution, the achieved ECG improves with in-creasing channel attenuation due to more accurate echo estimates. Fig. 3.4 alsodemonstrates that while ECG for DIC is limited by PN,ADC, and hence saturatesat around 63 dB, ECG for AIC continues to grow further with increase in channelattenuation to reach up to 90 dB. At this point ECG begins to saturate due to thepresence of residual non-linear SI components. With our proposed AIC solution, weare able to obtain an ECG > 80 dB at higher sub-carrier attenuations, which is thetarget gain required to bring the SI down to the minimum noise floor commonly743.5. Simulation ResultsTable 3.1: A Comparison of the Theoretical Data Rate Gains Per Sub-carrier withDIC and AIC Solutions under Different Sub-Carrier Attenuations with a Noise Floorof −130 dBm/Hz.SCA ECGDIC,k ECGAIC,k SNRk,HD Mk,HD SINRk,DIC Mk,DIC DRGk,DIC SINRk,AIC Mk,AIC DRGk,AIC(dB) (dB) (dB) (dB) (dB) (dB)5 37 36 75 1024 32 1024 2 31 1024 210 40 39 70 1024 30 256 1.6 29 256 1.620 47 47 60 1024 27 256 1.6 27 256 1.630 57 57 50 1024 27 256 1.6 27 256 1.640 61 68 40 1024 21 64 1.2 28 256 1.650 62 79 30 256 12 4 <1 30 256 260 62 85 20 16 2 2 <1 20 16 270 62 87 10 4 -8 1 <1 10 4 2seen in in-home power line networks. Reducing the SI level down to the noise floorallows true doubling of data rates. However, since we do not achieve ECG > 80 dBunder all sub-carrier attenuations, we do not successfully double data rates under allconditions.Data Rate Gain in SISO ModeThe attainable DRG is not only dependent on ECG, but also on the prevalent noiseconditions. Under a high noise scenario, a lower ECG is sufficient to double the datarate by bringing the SINR to the signal-to-noise ratio in the HD mode (SNRHD),while a larger ECG is required under a low noise scenario. Hence, we expect toattain higher DRGs at higher noise levels, and lower gains at lower noise levels.In order to determine DRGs obtained under a low-noise scenario, we compute thetheoretical gains with the DIC and AIC solutions for different sub-carrier attenuationsin Table 3.1. We use an adaptive bit loading algorithm [127] that allocates bitson the kth sub-carrier with a quadrature amplitude modulation constellation sizeof Mk, based on the received sub-carrier SNR, SNRHD,k or SINRk, to maintain atarget bit error rate (BER) Pb, expressed as [110, Eq. (8)]. We set Pb = 10−3,which is a conservative target unencoded BER, and limit Mk ≤ 1024 in accordance753.5. Simulation Results0.8 1 1.2 1.4 1.6 1.8 200.10.20.30.40.50.60.70.80.91xPr(DRG ≤ x)  Low Noise LevelHigh Noise Level1.33xDICAICFigure 3.5: CDF plots of DRGs obtained for a SISO IBFD system under two differentnoise levels using the DIC and AIC solutions, with DRG computed as (3.18).with the HPAV specifications [60, Ch. 4]. We then compute DRGk,φ =2 log2(Mk,φ)log2(Mk,HD),for φ = {AIC,DIC}. Since PN,ADC limits the max(ECG) for the DIC solution, weobserve in Table 3.1 that DRGk,φ < 1 for higher sub-carrier attenuations (SCAs). Incontrast, with our AIC solution, ECG continues to improve with increasing SCA andis able to achieve DRGk,AIC = 2. However, we notice that under lower SCAs, we stillencounter a sub-optimal DRGk,AIC < 2 due to insufficient ECGs (see Fig. 3.4).Since DRGk,φ is computed on a per sub-carrier basis, it is not indicative of theoverall DRG that is eventually obtained. To investigate the overall DRGs that wecan expect to procure under practical in-home PLC channel and noise scenarios,we simulate the transceiver block of Fig. 3.1 under two different noise levels. Thecumulative PLC noise generator tool of [115] provides a control to generate noisesamples at different levels by varying various noise parameters, for example, maximumamplitude of the impulses, or the roll-off factor of the colored background noise. Wechoose a low- and a high-noise setting in [115] to evaluate the achievable DRGs underthe two extreme conditions. We compute the overall DRG in both these cases as the763.5. Simulation Resultsratio of the physical layer sum-rate across all data carrying sub-carriers in IBFD andHD modes,DRGφ =2 · ∑k∈Nlog2(Mk,φ)∑k∈Nlog2(Mk,HD), (3.18)for φ = {AIC,DIC}. Fig. 3.5 shows the CDF plot of DRGs obtained over 1500random channel realizations that were generated using [107]. For typical power linenoise conditions, we expect the CDF values of DRG to lie in between the two curvesshown in Fig. 3.5 for both the DIC and AIC solutions. We observe that with theAIC solution, we are able to double the data rates for over 60% of the cases underhigh noise levels. Even under a low noise condition, we achieve DRGAIC ≥ 1.6, andeliminate any conditions under which DRG < 1.Echo Cancellation Gain in MIMO ModeTo determine the ECG in a MIMO IBFD system, we run simulations with an NT×NRMIMO configuration. Since most in-home installations are wired for single-phasepower distribution, we use NT = 2. We also set NR = 3, where two of the receiversare associated with a transmitter each on the same conductor-pair with suppressionachieved through a hybrid, and the other is a stand-alone receiver where the inter-ference signal undergoes suppression as a result of the coupling losses between theconductor pairs. We use the interference channel transfer functions of the hybrid pro-vided in Appendix B.2 at the two transceivers. For suppression at the stand-alonereceiver, we derive the channel transfer function in Appendix E as a function of thereflection co-efficient seen at the line-device interface.Such a configuration produces SI and CI components that need to be canceled at773.5. Simulation Results−60 −70 −80 −90 −100 −110 −120304050607080PSD of the SOI, dBm/HzECG, dB  SI − DIC w/ hybCI − DIC w/ hybSI − AIC w/ hybCI − AIC w/ hybCI − AIC w/o hybFigure 3.6: Variation of ECG for SI (3.19) and CI (3.20) with SOI strength, for theDIC and AIC solutions. A plot with hybrid represents the ECG at the receiversaccompanied by a transmitter on the same conductor pair, while a plot without thehybrid indicates the ECG at the stand-alone receiver.each of the NR receivers. We define ECG for both SI and CI individually asECGSI =PTXmax{PRSI, PN,ADC, PN} (3.19)ECGCI =PTXmax{PRCI, PN,ADC, PN} , (3.20)where PRCI is the power of the residual CI including both linear and non-linearcomponents. We refer to both interference signals at the stand-alone receiver as CIs,and compute ECGCI as (3.20).Fig. 3.6 shows a smoothing spline fit of ECGSI and ECGCI for both DIC and AICsolutions, obtained at one of the two transceivers for 1000 random MIMO channelsgenerated using [113]. The gains at the other transceiver are also identical. Similarto the results in Fig. 3.4, ECGSI and ECGCI for the AIC solution grow with increasein SCA without being limited by ADC distortion and quantization noise. We furtherobserve that the ECG for the CI at the stand-alone receiver (i.e., without the hybrid)783.5. Simulation Results0.8 1 1.2 1.4 1.6 1.8 200.10.20.30.40.50.60.70.80.91xPr(DRG ≤ x)  Low Noise LevelHigh Noise LevelDICAIC1.44xFigure 3.7: CDF plots of DRGs obtained at one of the receivers of the MIMO IBFDsystem under two different noise levels using the DIC and AIC solutions, with DRGcomputed as (3.18).also presents a similar curve, indicating analogous values of suppression. Note thatwe represent the x-axis as the PSD of the SOI to present results that are independentof the value of N farT .Data Rate Gain in MIMO ModeTo determine the overall DRG that we can expect to gain under practical power linenetwork conditions, we run the system shown in Fig. 3.3 under two different noisescenarios as used in Section 3.5.3. The CDF plot of the DRGs computed as (3.18)is provided in Fig. 3.7, which is obtained for a set of 1500 random MIMO PLCchannels [113]. Considering the results from Fig. 3.6, we show the DRG for the firstreceiver chain in Fig. 3.7. We observe that the AIC solution significantly improvesDRGs compared to the use of the DIC solution, with DRGAIC = 2 obtained for over70% of the cases under a high noise level, and a median gain of 1.8 under low noiselevels.793.6. Discussion on the Proposed AIC Solution3.6 Discussion on the Proposed AIC SolutionIn this section, we reflect on our proposed AIC solution to discuss the salient featuresand provide costs associated with its implementation.3.6.1 Notable Characteristics1. Upward and Downward Compatibility : Although we use HPAV specificationsthroughout our simulations, our echo estimation and cancellation procedurecan be applied to any OFDM system with arbitrary number of sub-carriers andtransmission/reception chains, i.e., our solution can be implemented on olderHomePlug releases like HomePlug 1.0 as well as newer standards like HomePlugAV2, ITU-T G.9963, and other OFDM-based standards [37, 111].2. Training Period : One of the marked features of our proposed solution is thatit requires no additional start-up time or a silent training period that are typi-cally required by most IBFD solutions commonly seen in other communicationsystems [46–49]. The LMS filter that we use, adapts its filter weights usingthe received signal, by exploiting the higher power of the echo in the presenceof the SOI. When a silent period is however available, where the transceiver isonly transmitting, the filter weights adapt to their optimal value and providethe maximal ECG, i.e., the highest value in Figs. 3.4 and 3.6, for any givenchannel condition.3. Tracking Channel Changes : Our solution inherently tracks changes on the linein real time as a consequence of using the LMS adaptive filter. However, onencountering a channel change, the filter requires an additional transient timeto reach its saturation value, when it can provide the maximum possible ECG.803.6. Discussion on the Proposed AIC SolutionThis transient time is dependent on the step-size of the LMS adaptation algo-rithm, and also on the channel and noise conditions. For typical PLC networkconditions, we showed the transient time in Chapter 2 to be around 1.5% of thetime between two different channel conditions on a busy power line network.Since we use the same LMS adaptation procedure, we expect to encounter simi-lar values of transient time. Apart from such long-term channel changes, powerlines are also subject to short-terms changes, which are LPTV in nature [63]. Toadapt to such changes, the LMS filters use a customized LPTV-LMS algorithmthat we previously developed in Chapter 2. Since our AIC solution estimatesthe echo channel digitally, it is capable of quickly adapting and reconfiguringthe filter weights to changing network conditions.4. Application Scenarios : Throughout our work, we provide analyses and resultsfor a point-to-point communication link. However, we can also to adopt oursolution to other scenarios, like IBFD relaying, or IBFD spectrum sensing [66,128]. Since our solution requires no wait times or dedicated pilot/trainingsignals, it provides a seamless IBFD relaying operation without any initializa-tion period. Further, while using our solution for simultaneous transmissionand spectrum sensing, the maximal ECG can be achieved under all conditions,since the signal being monitored is only the noise on the line and not a PLCsignal [120]. We provide a detailed analysis of various application scenarios ofIBFD BB-PLC in Chapter 4.5. Processor and DAC Complexity : In our simulations and analyses, we considerthe transceiver processor and the DACs used in the transmission and echoreconstruction chains to have sufficient precision to replicate an analog channeldigitally. From Fig. C.1, we observe that this precision needs to be at least 16813.6. Discussion on the Proposed AIC Solutionbits to obtain a SINAD ratio of over 80 dB. If a lower resolution DAC is usedin the transmitter chain, it introduces additional distortion and quantizationnoise. However, this can be countered by tapping the transmitted signal afterthe DAC quantizer module for use at the LMS filter (see Figs. 3.1 and 3.3), sothat the input signal entering the filter already consists of the DAC distortionand quantization noise effects [129]. Further, to avoid similar such effects, theecho reconstruction chain demands a high-resolution DAC of 16 bits or more.This solution also requires an additional DFT block to convert the tapped timedomain signal into a frequency domain input to the LMS filter.3.6.2 Implementation CostsSI cancellation in the analog domain requires the use of an analog adder. Thiscan be implemented using an active operational amplifier (op-amp) based differentialamplifier circuit to ensure no additional signal power loss. Due to the large amplitudeof PLC signals and a tight restriction on the non-linear SI cancellation, a wide voltagerange, low distortion op-amp such as LMH6702 [126] is appropriate. A similar op-amp is also required to build the active hybrid circuit. With a maximum PLC signalvoltage of ±6 V [36], and an op-amp supply current of 12.5 mA [126], the adder andhybrid together consume an additional power of 225 mW. For an NT × NR MIMOIBFD system, this value is scaled by a factor of NT, and an additional power of(NR − NT) · 75 mW is required for the analog adders in the stand-alone receiverchains.Apart from these AFE overheads, the companion PHY/MAC transceiver chip setwill also require NR additional DACs. Commercially available DACs of 18-bit resolu-tion consume about 4 mW each [130]. Unlike the DIC solution, the additional power823.7. ConclusionsTable 3.2: Additional Power Consumption Overhead for DIC and AIC solutionsSISO 2× 4 MIMOComponent DIC AIC DIC AICQuantity Power (mW) Quantity Power (mW) Quantity Power (mW) Quantity Power (mW)Hybrid 1 150 1 150 2 300 2 300Additional DAC 0 0 1 4 0 0 4 16Analog adder 0 0 1 75 0 0 4 300LMS filter 1 7.6 1 7.6 8 60.8 8 60.8Total 157.6 236.6 360.8 676.8consumption by the analog adders and the DACs are specific to our AIC solutions.However, the computation overhead introduced by the LMS adaptation filters appliesequally for both the DIC and AIC solutions. For the system parameters specifiedin the HomePlug AV standard [35], the frequency-domain LMS adaption procedurerequires about 7, 369 million operations per second (MOPS) (see Table 2.1). Theadditional power consumption introduced by these operations depends on the type ofprocessor implementation. It has been shown that newer processor architectures areable to provide an energy efficiency of 970 MOPS per mW [131, Ch. 5]. Therefore, theadditional processor power consumption can be computed to be(NT ·NR · 7,369970)mW.We present the overall comparative power consumption overheads associated with theDIC and our proposed AIC solutions in Table 3.2.In total, the overall increase in power consumption for a 2× 4 MIMO IBFD BB-PLC system is less than 0.7 W. Considering that the device is always connected tothe power line, and that the typical power consumption of a HD MIMO BB-PLCdevice is about 8 W [132], this additional power requirement adds a relatively smalloverhead.3.7 ConclusionsIn this chapter, we proposed an IBFD solution for BB-PLC devices using an op-ampbased hybrid for suppression and an adaptive analog cancellation procedure using833.7. Conclusionsthe DIC solution designed in Chapter 2 as a foundation. By canceling the echo inthe analog domain, we successfully countered the critical constraint imposed by thedistortion and quantization noise introduced in the ADC. Further, we extended oursolution to a MIMO BB-PLC system and analytically characterized the echo channeltransfer function by illustrating the PLC signal coupling mechanism for an IBFD-enabled MIMO BB-PLC transceiver. With our proposed solution, we showed thebenign effects of the residual non-linear SI components on the signal-of-interest. Usingrealistic power line channel and noise settings, we demonstrated through simulationresults that our solution is capable of successfully doubling median data rates undertypical in-home power line network conditions in a SISO configuration, and achieveat least a 1.8 times median data rate gain over HD MIMO BB-PLC using IBFD inMIMO operation.84Chapter 4Spectrum Aware Transmissionwith IBFD PLCWe have thus far investigated point-to-point IBFD communication links and quanti-fied the benefits using the bidirectional throughput gains that we achieve. However,a true doubling of data rate even with successful SI cancellation techniques designedin Chapter 3 is achievable only under symmetrical bidirectional data flow, i.e., underconditions where the upstream and downstream data demand are in equal propor-tions. Several activities, e.g., downloading multimedia or uploading live stream video,predominantly consists of unidirectional data flow. Hence, IBFD for simultaneousdata transmission in such cases may not be appealing. Furthermore, based on thePLC application scenario, several other networking issues are more compelling to beaddressed in place of doubling data rates. We discussed some of the current openissues in power line networks in Chapter 1 that can be solved using IBFD-PLC.In this chapter, we use the spectrum-aware transmission ability provided by IBFDPLC to solve several prevalent issues in PLC networks. The ability to simultaneouslytransmit and receive data can instead be used by an IBFD-enabled BB-PLC modemto transmit packets while listening to the spectrum, i.e., sensing the spectrum forother activities. This could include, sensing for non-PLC ingress in the operatingfrequency band and/or other radiated or conducted PLC signals.We present our problem descriptions, analyses, solutions, and numerical simula-854.1. IBFD-PLC: Cognitive of Broadcast Radiotion results of each considered issue in this chapter independently in Sections 4.1−4.4.In Section 4.1, we address the issue of EMI caused by unintentional PLC radiation onbroadcast radio services. Following the recommendations in the EN 50561-1 specifi-cation to include dynamic frequency exclusion corresponding to the broadcast radiospectra [71], we examine the use of IBFD to simultaneously transmit data and sensefor broadcast radio signals. Subsequently, we use the same underlying technique inSection 4.2 to address the issue of coexistence in in-home LANs to protect PLC andDSL communications from EMI caused by each other. To this end, we conduct a fea-sibility analysis of dynamic spectrum management (DSM) suggested by ETSI [70],where we dynamically estimate the PLC-to-DSL interference channel on power lineswhile also simultaneously transmitting BB-PLC signals using IBFD. We illustratethe challenges introduced by the harsh power line noise environment for a successfulDSM operation in both HD and IBFD operating modes. In Section 4.3, we con-duct an EMC analysis by exploring the EMI caused in heterogeneous PLC networks.As an example, we analyze the EMI caused by PLC over battery cables in a smartbattery pack on the neighboring BB-PLC network within an energy storage facility.Finally, in Section 4.4, we use IBFD to propose MAC protocol enhancements, whichsignificantly reduce the time spent on congestion control activities that hamper theMAC efficiency. We finally conclude the chapter in Section 4.5.4.1 IBFD-PLC: Cognitive of Broadcast Radio4.1.1 PreliminariesWe illustrated in Chapter 1 that several non-PLC services, like broadcast, amateur,and citizens band radio, operate in the frequency band of 2−100 MHz that is used for864.1. IBFD-PLC: Cognitive of Broadcast RadioBB-PLC. To protect these services from EMI caused by PLC, regulatory authoritiesrestrict BB-PLC devices from using most of these frequencies. BB-PLC standardscomply with these regulations and enforce a transmission tone-mask consisting ofseveral intermediate spectral notches [60, Ch. 4]. Since these bands are frequentlyidle, permanent notching wastes valuable spectral resources.Newer BB-PLC standards, like EN 50561-1, allow the use of dynamic notchingto utilize the spectra allotted to broadcast radio services whenever they are idle [71].Many cognitive PLC campaigns have been conducted to determine efficient strategiesand criteria to detect the presence of these broadcast radio interferences [72–75].However, all of them consider an HD operation, where the PLC device suspends itstransmission at regular intervals to sense the spectrum. We define the efficiency, η, insuch cases as η = tsTp, where ts is the time duration used by the secondary user (i.e.,PLC transceiver) for data transmission, and Tp is the total time during which theprimary user (i.e., broadcast radio transmitter) is inactive. Therefore, Tp − ts is thetime spent on spectrum sensing, and other wait times. The efficiency of such systemscan be increased if the secondary users develop the ability to sense the spectrum aswell as transmit data at the same time on the line.IBFD provides a means for BB-PLC transceivers to simultaneously transmit andreceive data in the same frequency band over the same power line. Hence, IBFDprovides a powerful technique to accomplish 100% efficiency in cognitive PLC sce-narios by allowing spectrum sensing and data transmission at the same time. Whencombined with an SNR-based interference detection method [72], IBFD enables PLCdevices to transmit and receive data, as well as detect non-PLC interferences, all atthe same time.Our solutions in Chapters 2 and 3 have shown that IBFD can be accomplished874.1. IBFD-PLC: Cognitive of Broadcast Radiofor BB-PLC with the use of an operational amplifier based analog hybrid and a dig-ital/analog echo cancellation to estimate and cancel the SI. By using the standard-ized broadcast radio detection procedure detailed in EN 50561-1 and ETSI TS 102578 [71, 76], we show that while the DIC-based IBFD solution proposed in Chapter 2can increase bidirectional data rates considerably, using such a solution for spectrumsensing deteriorates the performance as compared to an HD operation due to theeffects of the RSI. Since the higher RSI is caused due to the limited precision of theADC used in the receiver, we propose two alternative solutions apart from AIC to al-leviate this constraint. We show the improvements in spectrum sensing performanceachieved by our proposed solutions, through simulations performed under a limitinglow noise floor condition. Further, we also compute throughput gains obtained underrealistic BB-PLC channel and noise settings by using IBFD dynamic notching in thebroadcast radio bands.4.1.2 Spectrum Sensing with IBFDWe perform spectrum sensing for broadcast radio services in the frequency domainby monitoring the PSD of the received signal. We use the detection criteria specifiedin ETSI TS 102 578 for HD operations [76], and adapt it to spectrum sensing withIBFD operation. The specification stipulates M specific broadcast radio bands to bemonitored for the presence of a radio signal. Hence, we perform spectrum sensing inevery mth radio band, for all m = 1, 2, ...,M . A radio broadcast signal is considered884.1. IBFD-PLC: Cognitive of Broadcast Radioto be present at a frequency fk, if both the following conditions are met [76]:NR(fk)12|Nm|(N(low,m)R +N(high,m)R) ≥ α1 (4.1)NR(fk) ≥ α2, (4.2)whereN(low,m)R =|Nm|∑i=1NR(fkm1 − i∆f), (4.3)N(high,m)R =|Nm|∑i=1NR(fkm|Nm| + i∆f), (4.4)NR represents the PSD of the signal being monitored (i.e., in HD mode, it representsthe noise floor PSD at the receiver), ∆f is the spacing between two frequency bins,Nm = {km1 , km2 , ..., km|Nm|} is the set of sub-carrier indexes that lie in the mth pre-defined radio band with kmi < kmi+1, and k ∈ Nm. N (low)R and N (high)R indicate theaggregate noise floor on either sides of the radio band (i.e., lower- and higher-ends),with values summed over a bandwidth equal to that of the radio band itself10. Thevalues in [76] specify α1 = 101.4 and α2 = 10−13.5. Thus, (4.1) ensures that thedetected interference is at least 14 dB above the noise floor on either side of the radioband, and (4.2) ensures that its power is at least −95 dBm in a bandwidth of 9 kHz,which translates to a PSD of −95 dBm−10log10(9 kHz) ≈ −135 dBm/Hz.With the IBFD operation, the received signal contains not only the noise at thereceiver, but also the RSI signal that is present due to non-ideal SI cancellation.Therefore, the average noise floor on either side of the mth radio band is increased10In view of minimizing implementation complexity, we replace computing the median noise floor,as suggested in [76], with computing the mean instead in (4.3), (4.4), and (4.1), by enforcing noout-of-band radio interferences outside Nm, ∀m = 1, 2, ...,M , as suggested in [74].894.1. IBFD-PLC: Cognitive of Broadcast Radioby a factor ofγm = 1 +P(low,m)RSI + P(high,m)RSIN(low,m)R +N(high,m)R, (4.5)whereP(low,m)RSI =|Nm|∑i=1PRSI(fkm1 − i∆f),P(high,m)RSI =|Nm|∑i=1PRSI(fkm|Nm| + i∆f),and PRSI represents the RSI PSD including any effects introduced due to the RSI, suchas additional distortion and quantization noise. This increase in noise floor affectscondition (4.1), which examines the relative power level of a potential radio interfer-ence to the adjacent noise floor. By applying the HD threshold of α1 for IBFD op-erations, we increase the probability of missed detections, as we fail to detect interfer-ences with PSD levels from α12|Nm|(N(low,m)R +N(high,m)R)to α1γm2|Nm|(N(low,m)R +N(high,m)R).Alternatively, to maintain the same probability of missed detections as that obtainedin HD operations, we are required to determine a new α′1 ≤ α1 for every mth radioband, based on the value of γm. This results in a possible increase in false alarm rates,as non-broadcast radio interferences could be detected as one, due to a reduced ver-ification threshold. An increase in false alarm rates partially defeats the purpose ofdynamic notching. Additionally, γm dynamically varies with changes in PLC channelconditions as the extent of SI cancellation provided by the IBFD solution varies withchange in the network impedance. Furthermore, determining the value of γm wouldrequire an accurate estimation of N(low,m)R and N(high,m)R at every mth radio bandregularly, which in turn requires a silent period (i.e., HD operation). Therefore, toaddress these issues, we propose solutions in the next section that accomplish γm ≈ 1for all m = 1, 2, ...,M .904.1. IBFD-PLC: Cognitive of Broadcast Radio4.1.3 Proposed SolutionsWe begin by considering the DIC-based IBFD solution presented in Chapter 2. Sincethe hybrid isolation is relatively weak, the SI is not sufficiently attenuated to producebenign values of distortion and quantization noise at the ADC. Hence, under low noiseconditions at the receiver, it can be seen from (4.5) that this potentially producesγm  1. The distortion and quantization noise power introduced by the ADC isgiven byPADC =PinpSINAD, (4.6)where Pinp is the power of the input signal entering the ADC. Thus, to reduce PADC,we propose two different solutions in the following, apart from the AIC solution ofChapter 3, each of which either reduces Pinp or increases SINAD.Improving ADC SDQNROur first solution is fairly straightforward and attempts to increase SINAD providedby an ADC. The ADC in the receiver chain is preceded by the AGC block thatscales the input signal such that it occupies the entire dynamic range of the ADC.However, since OFDM signals possess a high PAPR, the AGC scales the input signalto accommodate some clipping, in order to minimize the overall clipping distortionand quantization noise [96]. Under such an operation, the SDQNR of the ADC isgiven by [121]SINAD−1 =1/322b(Vclipσinp)2+√8pi(σinpVclip)3exp(−Vclip22σ2inp), (4.7)where b is the number of ADC bits, σ2inp is the variance of the input signal, and Vclipis the voltage beyond which the signal is clipped. It has been shown in [97] that914.1. IBFD-PLC: Cognitive of Broadcast Radiothere exists an optimal(Vclipσinp)for every b, which maximizes SINAD. Therefore, bytuning the AGC to provide the ADC with the optimal(Vclipσinp), the only other avenueto improve SINAD further is by increasing b. We show later in Section 4.1.4 that byusing a 16-bit ADC in place of the default 12-bit resolution that current BB-PLCdevices use, we nearly achieve γm ≈ 1.We recognize that increasing ADC precision to improve SINAD is a fairly simplis-tic solution that introduces additional complexity to the transceiver chip-set. There-fore, we proceed to present an alternative that attempts to reduce Pinp, to therebydecrease PADC.Increasing Passive IsolationAs our second solution, we propose a method to decrease Pinp by improving thepassive isolation provided at the line-device interface. The IBFD solutions proposedin both Chapters 2 and 3 achieve passive isolation using a three-port hybrid circuit.One of the ports is connected to the power line channel and the other two to thetransmitter and receiver chains of the transceiver front-end. The isolation obtainedusing this circuit is given byIhyb(f) =c′|Γ(f)|2 , (4.8)where c′ is a scaling factor capturing the extent of impedance bridging and matchingat the hybrid ports connected to the transmitter and receiver ends of the transceiver,respectively. Since the constant resistive Zhyb is often mismatched to a widely varyingcomplex ZPLC, Ihyb(f) obtained is relatively weak (see Fig. 2.2). This results inPinp that is large enough to produce γm  1 under low NR conditions. Thus, wepropose the following solution to increase the passive isolation. Many in-home wiring924.1. IBFD-PLC: Cognitive of Broadcast RadioLineNeutralProtective EarthTransmissionSpectrum SensingZTXZRXVTXVRXFigure 4.1: Structure of one configuration of our proposed two conductor-pair spec-trum sensing solution.installations consist of three wires, line, neutral, and protective earth, for powerdistribution [33, Ch. 1.2]. By using one of the pairs for transmission, and another forspectrum sensing, we achieve higher passive isolation of SI at the line-device interfacewithout the use of a hybrid. Such a technique is similar to antenna separation orantenna isolation achieved in IBFD wireless communication systems. A conceptualstructure of this setup is shown in Fig. 4.1. The passive isolation obtained under thisscenario is expressed asIpas(f) =∣∣∣∣VRX(f)VTX(f)∣∣∣∣−2 , (4.9)where VTX and VRX are the voltages at the transmitter and receiver ends of the device,respectively. To derive the transfer function VRX/VTX, we decompose the line-modeminterface of Fig. 4.1 into two equivalent circuits shown in Fig. 4.2, where ZPLC,ij isthe (i, j)th element of the effective input power line impedance matrix, ZPLC, andZTX and ZRX are the device front-end impedances of the transmitter and receiverchains, respectively. We drop the index f for brevity. Using Kirchoff’s voltage lawin both the transmit and receiver loops carrying the currents I1 and I2, respectively,934.1. IBFD-PLC: Cognitive of Broadcast Radio𝑉𝑉TX𝑍𝑍TX𝑍𝑍 RX𝑉𝑉RX𝑍𝑍PLC,11𝑍𝑍PLC,12𝐼𝐼2 𝑍𝑍PLC,21𝐼𝐼1𝑍𝑍PLC,22𝐼𝐼2𝐼𝐼1Figure 4.2: The equivalent decompositions of the line-device interface shown inFig. 4.1.we obtainVTX = I1 (ZTX + ZPLC,11) + I2ZPLC,12 (4.10)I2ZRX + I2ZPLC,22 + I1ZPLC,21 = 0 (4.11)By representing I1 in terms of I2 using (4.11) and substituting it in (4.10), we haveVTX = I2(ZPLC,12 − (ZTX + ZPLC,11) (ZRX + ZPLC,22)ZPLC,21). (4.12)Further, with (4.12) and the knowledge that VRX = −I2ZRX, we obtainVRXVTX=ZPLC,21ZRX(ZTX + ZPLC,11)(ZRX + ZPLC,22)− ZPLC,12ZPLC,21 . (4.13)We show through numerical results in Section 4.1.4 that this setup improves thepassive isolation over that obtained by the hybrid. Nevertheless, we find that thisisolation is insufficient to provide γm ≈ 1. We also recognize that this solution usesan additional resource (wire-pair) to accomplish a SISO communication. However,this solution is most suitable when PLC product manufacturers choose to apply aDIC-based technique for SISO IBFD BB-PLC.944.1. IBFD-PLC: Cognitive of Broadcast RadioTable 4.1: Simulation ParametersTransmission bandwidth 2− 28 MHzSampling frequency 75 MHzFFT Size 3072Number of data carrying sub-carriers 917Sub-carrier spacing 24.414 kHzTransmit PSD −50 dBm/HzSpectrum Sensing RBW (∆f) 300 HzNumber of AM interferences 10Number of DRM interferences 104.1.4 Numerical ResultsSimulation ConfigurationTransceiver Settings : We consider a BB-PLC transceiver that operates as per HPAVspecifications [60]. We transmit in a bandwidth of 2−28 MHz, and apply the perma-nent tone-mask specified in [35] to notch out intermediate frequencies that overlapwith the HAM bands of amateur radio. We use a 3072-point DFT to load dataon to 917 orthogonal sub-carriers with a sampling rate of 75 MHz. Furthermore,we adopt the North American amplitude mask to transmit with a maximum PSDof −50 dBm/Hz on all data carrying sub-carriers [60]. For spectrum sensing, wechoose a DFT size that provides a resolution bandwidth (RBW) of 300 Hz as rec-ommended by [76]. We summarize the simulation parameters in Table 4.1. For allour simulations using a b-bit ADC, we operate with an optimal clipping ratio of(Vclipσinp)opt= −0.0053b2 + 0.3763b+ 1.2627 [97].Channel and Noise Generation: We use the channel generator tools of [107]and [113] to realize random realistic indoor channels consistent with our previousevaluations in Chapters 2 and 3. Since the performance of IBFD spectrum sensingdeteriorates as γm increases, we use a white noise of NR = −130 dBm/Hz to simu-late a low-noise environment. Under practical colored background power line noise954.1. IBFD-PLC: Cognitive of Broadcast Radio0.5 1 1.5 2 2.5x 107−130−120−110−100−90PSD across a 100 Ω load, dBm/HzFrequency, Hz  IBFDHDXX XXXXXFigure 4.3: PSD of the monitored signal under HD and IBFD operations using DIC.A cross (X) on top of a peak indicates that the IBFD implementation fails to satisfycondition (4.1).conditions, the detection performance is only improved.Broadcast Radio Interferences : We use an interference signal with 10 amplitudemodulation (AM) radio and 10 DRM interferences. We adopt the test signal providedin [76], which contains interferences near the borders of the pre-defined radio bandsto test the effectiveness of our spectrum sensing procedure. However, we reduce theinterference amplitudes to demonstrate the impact of the increased noise floor underIBFD operation. Each of the AM and DRM interferences in the signal appear inpairs in the frequency domain, i.e., the signal contains 10 pairs of interferences, withevery pair containing an AM signal of a larger amplitude and a DRM signal of asmaller amplitude.Simulation Results1. Increased Noise Floor : Our first result in Fig. 4.3 shows the impact of IBFDoperation on spectrum sensing using the DIC-based IBFD solution from Chap-964.1. IBFD-PLC: Cognitive of Broadcast Radio0.5 1 1.5 2 2.5x 107−130−120−110−100−90Frequency, HzPSD across a 100 Ω load, dBm/Hz  12−bit14−bit16−bitFigure 4.4: PSD of the monitored signal under IBFD operation with 12-, 14-, and16-bit ADCs.ter 2. As this solution is limited by the ADC dynamic range, it provides a max-imum SI cancellation gain of about 63 dB. Therefore, the PSD floor of the mon-itored signal in IBFD mode is around −113 dBm/Hz, which produces γm ≈ 50.With the specified α1 = 101.4 [76], any interference between −116 dBm/Hz and−99 dBm/Hz satisfies condition (4.1) only with HD spectrum sensing but notwith IBFD. As a result, we observe in Fig. 4.3 that spectrum sensing fails todetect interferences corresponding to DRM signals.2. Impact of Higher Precision ADCs : Fig. 4.4 shows the results of our first solu-tion. We use ADCs of varying precision at the receiver along with the DIC-based IBFD proposed in Chapter 2. Increasing the ADC precision provideshigher SINAD of the ADC. Therefore, the resultant distortion and quantiza-tion noise is reduced. This ensures that PADC limiting the cancellation gainobtained by DIC is maintained at a lower level to provide higher digital cancel-974.1. IBFD-PLC: Cognitive of Broadcast Radio0.5 1 1.5 2 2.5x 107−135−130−125−120−115−110−105−100−95−90Frequency, HzPSD across a 100 Ω load, dBm/Hz  IBFD − hybridIBFD − multiple wiresHDFigure 4.5: PSD of the monitored signal under HD operation, IBFD using the twoconductor-pair setup for passive isolation, and IBFD with the hybrid.lation gains. We observe from Fig. 4.4 that by using the default 12-bit ADC,we obtain an increased noise floor, as also evident in Fig. 4.3. However, with a16-bit ADC, we achieve PRSI ≈ −130 dBm/Hz, producing γm < 2. Althoughthis value is sufficient to produce accurate spectrum sensing under all scenar-ios with a suitable α1, deployment of this solution requires new chip-sets ofincreased complexity with higher precision ADCs.3. Increase in Passive Isolation with an Additional Conductor Pair : The resultof our second proposed solution can be seen in Fig. 4.5. We design a couplinginterface where we use one conductor pair for data transmission and another forspectrum sensing considering a three-conductor channel generated using [113].However, we persist with DIC for active cancellation. The SI signal undergoespassive isolation at the line-device interface due to coupling losses between thetwo conductor-pairs. Our simulation results indicate a typical passive isolation984.1. IBFD-PLC: Cognitive of Broadcast Radio0.5 1 1.5 2 2.5Frequency, Hz #107-130-120-110-100-90PSD across a 100 + load, dBm/Hz IBFD - DICIBFD - AICHDFigure 4.6: PSD of the monitored signal under HD operation, and IBFD with DICand AIC.of the two conductor-pair setup to be around 14 dB, which is more than fivetimes the average hybrid suppression. However, we observe from Fig. 4.5 thatwe do not achieve γm ≈ 1 as the PSD of the monitoring signal is still about10 dB above the noise floor.4. Increase in Active Cancellation Gain with AIC : We finally present the result ofusing AIC for spectrum sensing in Fig. 4.6, where we compare the accuracy ofspectrum sensing using DIC- and AIC-based IBFD and the HD operation. Sincewe operate with analog signals in our proposed method, we use the default 64-bit double precision of MATLAB to simulate an infinite precision analog signal,and use a 12-bit ADC for digitizing. The results in Fig. 4.6 show that the PSDof the monitored signal in IBFD operation using AIC is nearly the same asthat under HD operation. This signifies γm ≈ 1, which indicates the samespectrum sensing accuracy in both HD and AIC-based IBFD operations. We994.1. IBFD-PLC: Cognitive of Broadcast Radioalso note that AIC can also be implemented without the hybrid by using a twoconductor-pair setup (see Fig. 4.1) for passive isolation.4.1.5 Quantifying the GainsIncrease in ThroughputThe increase in throughput by using dynamic notching is directly proportional to thebandwidth alloted to broadcast radio services. EN 50561-1 specifies a pre-defined setNm, covering a total bandwidth of 5.8 MHz, in which transmission sub-carriers caneither be permanently or dynamically notched out by PLC transceivers depending onthe spectrum sensing ability of the device. We compute the maximum throughputgained by using all sub-carriers in Nm asC =∑m∈Nmfkm|Nm|∫fkm1log2(1 +PTX(f)|HPLC(f)|2PRSI(f) +NR(f))df, (4.14)where PTX is the transmit PSD used by the PLC device and HPLC is the power linechannel transfer function. To obtain realistic values of C, we limit the maximummodulation order to 1024-QAM as per HPAV specifications [35], and also allow aguard band of 12 kHz at either ends of a broadcast band to emulate practical notchingabilities of band-pass filters.We compute (4.14) for 1500 random PLC channel and noise conditions that wegenerate using the random network setting in [107] and [115]. Since we achieve γm ≈ 1using AIC for IBFD, we let PRSI(f) +NR(f) ≈ NR(f) for all 2 MHz ≤ f ≤ 28 MHzin our computations. The empirical CDF plot of the resultant throughput gains areshown in Fig. 4.7. We observe that we obtain a maximum throughput gain of up to1004.1. IBFD-PLC: Cognitive of Broadcast Radio0 10 20 30 40 50 6000.20.40.60.81x, Mb/sProb(C ≤ x)Figure 4.7: CDF of throughput gained by using broadcast radio bands.53 Mb/s, with a median of about 35 Mb/s.Increase in Spectrum Sensing EfficiencyThe maximum throughput gain computed in Section 4.1.5 is only applicable whenall the broadcast radio bands are idle for use by PLC devices. During this interval,only a portion of this time, η, as defined in Section 4.4.1, is used for actual datatransmission. Using our proposed IBFD spectrum sensing techniques, we achieve theoptimal efficiency of ηFD = 1, as we transmit and sense the medium simultaneously atall times. In contrast, a portion of this total time is consumed by sensing-only oper-ations in a HD operation. Spectrum sensing timings have not been comprehensivelytested and are not strictly enforced. Practical sensing-only and other wait times inHD spectrum sensing are dependent on the typical coherence time of the surroundingwireless environment in the broadcast radio bands. Using the values suggested forpossible sensing times in [76, Sec. 4.2], the efficiency could be as low as, ηHD = 0.3.1014.2. IBFD-PLC: Cognitive of DSL CommunicationsUnder such conditions, we obtain over a three-time increase in ergodic throughputgain using IBFD spectrum sensing over the HD operation.4.2 IBFD-PLC: Cognitive of DSLCommunicationsIn this section, we continue the use of IBFD-PLC to achieve spectrum-aware trans-mission, and apply it to combat our second considered issue of EMI between in-homeBB-PLC and DSL communications.4.2.1 BackgroundA home area network consists of a multitude of communication requirements forapplications ranging from low data rate home automation to high-speed multimediacommunications [4, 6, 133], for which PLC provides an attractive alternative dueto the ubiquitous nature of the electrical wiring infrastructure and the widespreadavailability of power outlets in an indoor environment. One of the drawbacks of PLCapplied in in-home communication networks is the EMI to and from the PLC signalproduced due to the presence of asymmetric (common-mode) components on theunshielded and unbalanced power lines. One example is the issue of BB-PLC signalegress in the frequency range of 2−100 MHz interfering with neighboring applicationssuch as, broadcast, amateur, and digital radio services [60, Ch. 3][1, Ch. 3], which weconsidered in Section 4.1. Radiated BB-PLC signals have also been found to causeinterference in wired access networks, like DSL communications, where broadbandsignal on the telephone line is distorted as a result of a common-to-differential modeconversion as in the case of PLC [134–136].1024.2. IBFD-PLC: Cognitive of DSL CommunicationsInterference CancellationA smart notching, or dynamic spectral notching, which we analyzed in Section 4.1,is suitable to combat interference that occupies a relatively small portion of the PLCtransmission bandwidth. The short-wave and digital broadcast radio services, forexample, occupy a maximum of only 5.7 MHz of the 85 MHz of total bandwidththat is used by newer BB-PLC devices [76, 111]. However, recent DSL standards ofvery-high-data-rate DSL 2 (VDSL2), vectored-VDSL2, G.fast, and XG-fast occupynearly the entire BB-PLC operating bandwidth [137–140]. Thus, dynamic notchingto accommodate these services could render PLC completely inoperable.A reactive solution to counter EMI between PLC and DSL communications isto implement interference cancellation at the customer-end DSL modems using acooperative communications protocol [141, 142]. However, this intrusive techniquerequires a new physical connection between the DSL modem and the CCo of thePLC network. Given that the CCo could dynamically change among several op-erating PLC nodes, we potentially require a physical connection between the DSLmodem and all available PLC nodes. Furthermore, this protocol also requires PLCto be synchronized with the DSL super-frames. Under non-trivial network load con-ditions with devices operating under the CSMA mode (as opposed to a time divisionmultiple access (TDMA) mode), such a solution presents a significant increase in net-work latency. In addition, this interference cancellation solution functions only whenthe PLC modems operate with the delayed acknowledgment scheme [141], whichensures that not more than one PLC node transmits in a given DSL super-frameduration. Hence, it lacks backward compatibility with current and older BB-PLCproducts, operating with say, the HPAV standard, which only support an immediateacknowledgment procedure [35].1034.2. IBFD-PLC: Cognitive of DSL CommunicationsContributionsWith this backdrop, in this section, we investigate an appealing alternative approachto proactively counter the EMI between PLC and DSL communications using DSM inthe LAN. Along with such a method already being popular in the domain of wirelesscommunications [143], DSM has also been envisioned by ETSI as a potential solutionto ensure coexistence between DSL and PLC in a home area network (HAN) [70].To this end, we examine the technique of adapting the PSD of the transmitted PLCsignal on different sub-carriers based on a dynamic PLC-to-DSL interference channelestimate obtained at the PLC node using IBFD spectrum sensing. Since the interfer-ence channel estimation accuracy drives the PSD adaptation efficiency, we empiricallydetermine the required normalized mean squared error performance of the channelestimation procedure to approximately preserve the throughput performance of bothDSL and PLC systems. Further, we simulate an indoor communications network onpower lines and DSL, and use real interference channel measurements data to inves-tigate the SNR of the DSL signal available at the power line modems for channelestimation. Finally, we also explore the impact of duplexing on DSM to examineits applicability with next-generation DSL standards of G.fast and XG-fast that donot use the traditional FDD. We show through our analyses and simulations thata non-intrusive DSM approach, although appealing and widely applied in wirelesscommunications scenarios, has limited applicability in practical indoor environmentsunder both HD and IBFD PLC operations.4.2.2 IBFD DSMAs a first step toward DSM, an elementary PSD reduction at the PLC modems canbe performed on a trial-and-error basis until satisfactory data rates are achieved in1044.2. IBFD-PLC: Cognitive of DSL Communicationsthe DSL network [70, 144]. However, such a method is evidently inefficient time- andthroughput-wise, especially under varying interference channel conditions. Alterna-tively, a more potent solution is to dynamically estimate the PLC-to-DSL interferencechannel (PDIC) and selectively reduce the transmit PSD at the PLC modem suchthat the PLC interference on the DSL transmission is below a pre-defined minimumthreshold. Although solely reducing PSD on the PLC network appears to be an unfairpower allocation strategy at the outset, the fact that the DSL access network formsthe backbone of indoor communications makes the DSL nodes the primary usersof the spectral resource, and justifies requiring a higher priority. Furthermore, onshort power line links that enjoy conducive PLC channel conditions, PSD reductiondoes not result in a noticeable decrease in data rates due to adequate SNRs that areguaranteed to the adaptive bit allocation algorithm. To determine the desired PSDreduction, we make use of the known sync-symbol that is transmitted in every DSLsuper-frame, and estimate the DSL-to-PLC interference channel (DPIC) [141]. SincePDIC and DPIC here refer to the indoor wireless channel between the customer-endDSL modem and the PLC node, the channel can be assumed to be reciprocal [144].As a result, we can compute PDIC at the PLC node simply by monitoring the DSLsignal ingress on the power line and estimating the DPIC.Traditional HD methods of signal monitoring, or spectrum sensing, require PLCmodems to periodically suspend their transmission in order to estimate the DPIC.This leads to a loss in PLC throughput especially for DPIC with low coherence time.However, simultaneous transmission and reception achieved by IBFD allows us toestimate the interference channel without interrupting PLC data transmission [120].In this case, PLC modems monitor the noise on the power line that is affected by RSI.Intuitively therefore, the accuracy of the estimated channel is driven by the extent of1054.2. IBFD-PLC: Cognitive of DSL CommunicationsSI cancellation provided by the IBFD solution. We have shown in Chapter 3 that ourAIC-based IBFD solution provides an SI cancellation of about 90 dB, through whichwe can reduce a typical BB-PLC SI PSD of −50 dBm/Hz to a benign −140 dBm/Hz.Once the RSI is sufficiently reduced, we then estimate the DPIC transfer func-tion, HDPIC, using well-known channel estimation methods that use a known pi-lot/preamble sequence, i.e., the sync-symbols transmitted in every DSL super-framefor our application scenario [145, 146]. Accordingly, we reduce the transmit PSD onevery kth PLC sub-carrier, PTX,PLC[k], such thatPTX,PLC[k] ≤ Pthresh[k]|HPDIC[k]|2 , (4.15)where HPDIC = HDPIC is the estimated PDIC transfer function, and Pthresh[k] is a pre-determined interference threshold tolerable on the DSL, which is chosen such that itdoes not cause noticeable effects on the DSL data rates, i.e., Pthresh[k] is negligiblecompared to the prevalent DSL noise floor. In this respect, older DSL standardscan afford higher values of Pthresh due to the effects of far-end cross-talk [147]. Onthe other hand, DSL access multiplexers (DSLAMs) that use vectored transmissionrender the downstream signals more vulnerable to external interferences, and hencedemand lower values of Pthresh.4.2.3 Data Rate GainsWe now show the potential of IBFD DSM by presenting the DSL data rate gainachieved with dynamic PSD adaptation. Current DSL standards of VDSL, VDSL-2,and V-VDSL2 use FDD for bidirectional communication [137, 138]. Consequently,to compute the DSL data rates, we only consider the downstream signals that aresignificantly more prone to PLC interference effects due to the DSL channel attenu-1064.2. IBFD-PLC: Cognitive of DSL CommunicationsTable 4.2: VDSL2 Transceiver Parameters [137]Operating bandwidth 1.1− 17.6 MHzFFT Size 8192Sampling rate 35.328 MHzSub-carrier spacing (∆fDSL) 4.3125 kHzTransmit PSD (PTX,DSL) [137, Table. A7]Noise PSD (PN,DSL) −140 dBm/HzMax. constellation size (Mmax) 32768SNR gap (Ψgap) 9.75 dBation, whereas upstream transmission has sufficient transmit SNR to be resilient toPLC interference [70]. We calculate the downstream DSL rate asC =∆fDSL∑k∈Dmin[log2 (Mmax) ,log2(1 +PTX,DSL[k]|HDSL[k]|2Ψgap (PN,DSL + PTX,PLC[k]|HPDIC[k]|2))], (4.16)where D is the set of all DSL sub-carrier indexes that are used in downstream trans-mission [137, Annex. A], Ψgap is the SNR-gap that accommodates practical non-idealities, and HDSL is the DSL channel transfer function from the central office tothe customer premise equipment. Please refer to Table 4.2 for other notation descrip-tions, where we also summarize the transceiver parameters that we adopt from theVDSL2 standards [137]. Throughout our analysis of DSL rates, we consider vectoringat the DSLAM that achieves complete far-end cross-talk nullification.For the purposes of demonstration, we consider a matched 300 meter 26-gaugeAmerican wire gauge (AWG) cable with no bridge taps to compute |HDSL|2 [148].Further, we use four different HPDIC conditions that were measured in a real in-home environment [141]. With the assumption of perfect HPDIC estimate at the PLCnode, we perform dynamic PSD reduction for PLC transmission such that power line1074.2. IBFD-PLC: Cognitive of DSL Communications0 10 20-140-120-100-80-60Condition 1Condition 2Condition 3Condition 4(a)1 2 3 4Conditions050100150With PSD ReductionWithout PSD Reduction(b)Figure 4.8: (a) PLC-to-DSL coupling channel gains under four different conditions(surrounding environment) from [141], and (b) their corresponding VDSL-2 down-stream data rates with and without PLC PSD reduction.interference is negligible compared to the DSL noise. We then compute the data ratesusing (4.16) and show the results in Fig. 4.8. We observe that Conditions 1 and 2,which present relatively higher coupling of PLC signals on to the DSL, produce lowerVDSL2 data rates and consequently stands to gain the highest, of up to 80% datarate increase, with the introduction of DSM. Similar analysis follows for the othertwo conditions, which indicate that DSL communication stands to gain substantiallywith a lower BB-PLC interference. These results are also comparable with the datarate loss values reported by a comprehensive measurement campaign conducted on24-gauge AWG cables in different indoor DSL network architectures over variousgeographic locations [136, Fig. 12].4.2.4 Feasibility AnalysisWe have thus far considered the VDSL2 standard that operates under FDD, wherenon-overlapping upstream and downstream bands allowed precise PSD adaptation1084.2. IBFD-PLC: Cognitive of DSL Communicationsby the PLC modems. At the same time, we also assumed the availability of anideal channel estimate at the PLC node. In this section, we analyze the impact ofPLC noise on the DPIC estimation accuracy, and discuss the effects of alternativemethods of duplexing, such as TDD and IBFD, that are applied in next-generationDSL standards.Impact of PLC NoisePLC systems are typically affected by three types of noise, namely, colored back-ground noise, narrow-band noise, and impulse noise [149]. For typical in-home condi-tions, the noise PSD varies between −80 dBm/Hz and −130 dBm/Hz [7, 115], whichis well above the RSI PSD produced with our AIC-based IBFD solution developedin Chapter 3. Hence, the extent of power line noise primarily limits the accuracy ofthe DPIC estimation at the PLC node under both HD and IBFD modes.Several channel estimation procedures can be found in the literature that arespecifically targeted for preamble-based OFDM systems [146, 150]. In any suchmethod, the accuracy of the channel estimate depends on the SINR of the train-ing signal used. In our case, we use the DSL sync-symbol for DPIC estimation, andwe compute its SINR seen on the kth power line sub-carrier asΨDSL[k] =PTX,DSL[k]|HDSL[k]|2|HDPIC[k]|2PN,PLC[k] + PTX,PLC|HSI[k]|2 , (4.17)where PN,PLC is the power line noise PSD and |HSI[k]|2 is the total SI cancellationachieved by the IBFD solution. We have shown in Chapter 3 that the attainable ECGis frequency dependent and varies inversely with the strength of the received signal-of-interest [151]. Given the DSL transmit PSD, the channel attenuation undergone bydownstream DSL signals, and the weak DPIC gains (Fig. 4.8(a), [136, 141]), we can1094.2. IBFD-PLC: Cognitive of DSL Communications5040-30 30-2080-1020600401010-200-180-160-140-120-100-80Figure 4.9: Heat map showing the required PN,PLC to achieve different ΨDSL[k] forvarying DSL channel attenuations and DPIC conditions.reliably consider a constant maximum SI cancellation performance of |HSI|2 = 90 dBacross all sub-carriers.With PTX,PLC = −50 dBm/Hz and PTX,DSL = −53 dBm/Hz [35, 137], we plot thePLC noise conditions required to achieve different ΨDSL[k] in Fig. 4.9. We vary theHDPIC axis from 35 dB to 95 dB, which are the statistical minimum and maximumvalues of HDPIC reported in the measurement campaign of [136]11. We present HDPICslices at 50 dB, 60 dB, and 75 dB, which are found to be the statistical 99th, 90th,and 50th percentile coupling values, respectively [136]. We observe from Fig. 4.9 thattypically seen power line noise conditions between −80 dBm/Hz to −130 dBm/Hzcan produce positive values of ΨDSL[k] under limited conditions of HDPIC and HDSL.11The percentile statistics reported in [136] are for the frequency range of 2−100 MHz. However,Fig. 6 of [136] shows a similar trend of the probability density functions of the coupling levels forthe VDSL2 frequency profile of “998ADE17”, which is between 1.1− 17.6 MHz [137].1104.2. IBFD-PLC: Cognitive of DSL CommunicationsFor example, with a 90th percentile coupling of 60 dB, an SINR of 5 dB is achievedonly when the DSL attenuation is less than 20 dB even under a low PN,PLC[k] =−130 dBm/Hz. This gives us an indication that the channel estimation procedurecould be prone to significant inaccuracies in typical indoor environments.Subsequently, we determine how likely useful SINR values are achievable in a re-alistic in-home communications network. To this end, we use 10 real HDPIC channeltransfer functions that were measured in different locations of a residential environ-ment [141], and the same 300 meter 26-gauge AWG cable for downstream DSL trans-mission. We then compute the average SINR for varying power line noise conditionsasΨDSL = 10 · log10(1|D′|∑k∈D′ΨDSL[k]),where D′ is the set of all BB-PLC sub-carrier indexes lying in the DSL downstreamband. We use an open-source cumulative power line noise generator to simulaterandom PLC noise under two extreme conditions [115]. We then calculate ΨDSL for1000 different “high”- and “low”-noise conditions with a randomly chosen HDPIC eachtime. The empirical CDF plot of ΨDSL is shown in Fig. 4.10. As expected, we noticepoor SINR values under a high-noise environment. But the achieved SINR in lowerpower line noise conditions also appears insufficient for a favorable channel estimationperformance using typical estimation procedures [146, 150]. We therefore ascertainwhat accuracy of the channel estimate could be considered to be acceptable.The channel or SINR estimation performance can be characterized in terms ofthe normalized mean squared error (NMSE) of the estimated value. As the NMSEof the estimated SINR, DPIC, increases, the PSD adaptation accuracy at the PLCnode reduces. When |HDPIC|2 is overestimated, the PLC transmission rate suffers,as the transmit PSD is reduced more than required. Conversely, DSL throughput is1114.2. IBFD-PLC: Cognitive of DSL Communications-50 -40 -30 -20 -1000.20.40.60.81HighLowFigure 4.10: Empirical CDF plot of ΨDSL observed on the power line under high- andlow-noise conditions [115].affected as a result of under-compensated PSD adaptation by the PLC node when|HDPIC|2 is underestimated. In order to quantify the exact effect of inaccurate channelestimation on both DSL and PLC systems, we study the impact of varying DPIC onthe PLC transmission rate and the DSL downstream data rate. We denote PˆTX,PLC[k]and P˜TX,PLC[k] as the adapted PSD for the estimated channel HˆDPIC and the idealchannel HDPIC, respectively, that are determined using (4.15). We then compute theachieved PLC transmission rate, CˆPLC, asCˆPLC =∆fPLC∑k∈D′min[log2(MPLC),log21 + PˆTX,PLC[k]|HPLC[k]|2Ψgap(PN,PLC + PˆTX,PLC[k]|HSI|2)], (4.18)where ∆fPLC = 24.414 kHz is the OFDM sub-carrier spacing, and MPLC = 4096 is themaximum modulation order, both chosen as per the HomePlug AV2 standard [111],1124.2. IBFD-PLC: Cognitive of DSL Communicationsand HPLC is the PLC channel transfer function. Similarly, we also compute the idealPLC transmission rate C˜PLC asC˜PLC =∆fPLC∑k∈D′min[log2(MPLC),log21 + P˜TX,PLC[k]|HPLC[k]|2Ψgap(PN,PLC + P˜TX,PLC[k]|HSI|2)], (4.19)On the same lines, we calculate the achieved DSL downstream transmission rate,CˆDSL =∆fDSL∑k∈Dmin[log2(Mmax),log21 + PTX,DSL[k]|HDSL[k]|2Ψgap(PN,DSL[k] + PˆTX,PLC[k]|HDPIC[k]|2)], (4.20)and the ideal DSL rate, C˜DSL, asC˜DSL =∆fDSL∑k∈Dmin[log2(Mmax),log21 + PTX,DSL[k]|HDSL[k]|2Ψgap(PN,DSL[k] + P˜TX,PLC[k]|HDPIC[k]|2)], (4.21)We then determine the rate loss in both DSL and PLC systems to beρφ =C˜φ − CˆφC˜φ× 100 [%], (4.22)where φ ∈ {DSL,PLC}.The empirical values of ρPLC and ρDSL are shown in Fig. 4.11. Each of thePLC transmission rates are computed for a randomly generated indoor PLC chan-1134.2. IBFD-PLC: Cognitive of DSL CommunicationsTable 4.3: Transmission parameters of DSL standards whose operating frequenciesoverlap with BB-PLC bands [137–140]VDSL VDSL2 G.fast XG-fastBandwidth (MHz) 0.13-12 1.1-35 2.2-212 2.2-500Max. PSD (dBm/Hz) −60 −53 −65 −89Duplexing FDD FDD TDD IBFD/TDDnel using [107] and a power line noise condition produced using [115]. Further,we compute PˆTX,PLC[k] in each case using (4.15) for a channel estimate, HˆDPIC,that is randomly generated for the chosen DPIC and an ideal HDPIC. Since typi-cal PN,DSL = −140 dBm/Hz [136], we set Pthresh = −150 dBm/Hz over all sub-carriersto limit the impact of PLC-to-DSL interference.It can be seen in Fig. 4.11 that we achieve ρ ≈ 0 for DPIC ≤ 10−3, which indicatesthe ideal channel estimation performance that we desire. However, as DPIC grows, wenotice that the rate loss begins to increase, with PLC transmission rate loss increasingfaster than that of the downstream DSL rates, as an over-compensated PSD reductionhurts PLC rates more severely than an under-compensated PSD reduction does to theDSL rates due to our chosen Pthresh. We can conclude from Fig. 4.11 that DPIC ≈ 5×10−2 could be considered to be an acceptable trade-off value that relaxes the requiredchannel estimation performance without significantly impacting the DSL and PLCtransmission rates. However, typical channel estimators for OFDM systems indicatesuch an estimation performance requires ΨDSL ≥ 2 dB [146, 150], and Fig. 4.10suggests that such conditions are unavailable in our simulated network conditions.Further, recall that we have considered a matched 300 meter copper cable withno bridge taps for our simulations. But typical VDSL2 loops span longer lengths(e.g., about 1.5 km [136]) with multiple bridge taps in between that introduce greaterchannel attenuation and higher frequency selectivity. Additionally, greater bandwidthprofiles of VDSL2, such as the “998ADE35” profile, restrict PTX,DSL ≤ −76.7 dBm/Hz1144.2. IBFD-PLC: Cognitive of DSL Communications10 -4 10 -3 10 -2 10 -1 10 001020304050 (%)PLCDSLFigure 4.11: Percentage rate loss of PLC and downstream DSL communications inthe downstream DSL bands.above 30 MHz [136]. Furthermore, newer standards of G.fast and XG-fast also uselower PTX,DSL, as tabulated in Table 4.312. This signifies that the attainable ΨDSL isfurther reduced, leading to poorer values of DPIC.Effect of DuplexingImplementing dynamic spectral adaptation on PLC devices over the downstream DSLbands is straightforward for FDD systems, such as VDSL, VDSL2, and V-VDSL2,due to the non-overlapping orthogonal nature of the bidirectional frequency bands.However, the recent G.fast standard specifies the use of TDD to accommodate bidirec-tional data streams [139]. This requires PLC nodes to be synchronized with the G.fastdevices to implement DSM during downstream G.fast data transfer. Furthermore,duplexing through IBFD is being considered for the future XG-fast standard [140],12The specifications of XG-fast are not publicly available yet. −89 dBm/Hz is the transmit PSDused in an initial hardware proof-of-concept [152].1154.3. IBFD-PLC: Cognitive of Neighboring PLCwhich demands a PSD reduction by PLC nodes on all frequency bands at all times.OutcomeWe have thus learned that while PLC-to-DSL interference is large enough to causea significant loss in downstream DSL data rates, the DSL-to-PLC interference ishardly noticeable on the power line, thereby limiting the DPIC estimation accuracy.We therefore require more effective channel estimators that are capable of operatingunder harsh SINR conditions. Thus, we conclude that the practical applicability ofdynamic spectral adaptation is limited, irrespective of the operating mode (HD orIBFD) on the PLC device, despite the potential benefits it presents at the outset overits competitor EMI-management solutions [70].4.3 IBFD-PLC: Cognitive of Neighboring PLCAs our third application scenario of IBFD-PLC, we investigate methods to combatEMI caused between neighboring PLC systems. To this end, we consider a heteroge-neous PLC network within an energy storage facility, which consists of several smartbattery packs placed in an indoor environment, with conventional BB-PLC enablingthe indoor LAN and BB-PLC over battery cables in a smart battery pack enablingcommunications between the battery control unit and the individual cells. Since EMIin such a network scenario has not been studied thus far, we present the first analysisof characterizing the radiated EMI from PLC over battery cables in this section, witha goal of suggesting signal transmission levels that not only ensure conformity withEMC regulations, but also assure benign EMI on the neighboring indoor BB-PLC.1164.3. IBFD-PLC: Cognitive of Neighboring PLC4.3.1 BackgroundThe growth of distributed energy generation through renewable sources demandsincreased energy storage abilities due to the irregular and discontinuous nature ofrenewable energy generation [153–155]. On a smaller scale, battery storage facilitiescan also be found in road and rail transport applications [156, 157]. In all theseuse-cases, the battery storage units are equipped with a digital battery managementsystem (BMS) that primarily achieves cell monitoring, cell balancing, ensuring bat-tery safety and protection, state-of-health estimation, charging control, and thermalmanagement [158, and references therein]. The BMS is therefore required to con-stantly monitor the voltage, temperature, and state-of-charge of all cells in the unit.This is typically achieved by using cell-boards that monitor these parameters of in-dividual batteries and convey it to a central battery control unit (BCU).Fig. 4.12 shows an example of an energy storage facility at The University ofBritish Columbia – Vancouver campus. We further zoom into an individual batteryin Fig. 4.13, where we notice that the BMS uses dedicated cables (black cables inFigs. 4.12 and 4.13) to enable bidirectional communication between the cell-boardsand the BCU (specified in Fig. 4.13). Such a communication infrastructure is em-blematic of present-day conventional BMSs [159]. Alternatively, the physical archi-tecture can be simplified by using PLC, which exploits the existing infrastructure,i.e., battery power cables (orange cables in Figs. 4.12 and 4.13), to provide robustand cost-efficient communications [12, 160, 161].As we have seen in the previous sections, one of the fundamental aspects thathas regulated PLC in any field of application from home area networks to smart-gridcommunications is its associated EMI and susceptibility [162]. Although recent workshave demonstrated the feasibility of PLC for communications in BMSs in the context1174.3. IBFD-PLC: Cognitive of Neighboring PLCFigure 4.12: The energy storage facility at the Vancouver campus of The Universityof British Columbia, powered by Alpha Technologies Inc. and Corvus Energy.1184.3. IBFD-PLC: Cognitive of Neighboring PLCFigure 4.13: A zoomed image of Fig. 4.12 showing an individual battery and thecentral BCU.of both electric vehicles and grid storage facilities [13, 163, 164], the EMC issues ofPLC inside these energy storage units is not well-investigated. Apart from the needto comply with regulatory EMC limits, the issue of EMI is especially important inbattery storage units at distributed generation locations, where multiple cell-boardsthat are part of different heterogeneous communication networks operate in closeproximity. Furthermore, PLC radiations could also interfere with neighboring wiredcommunication networks, such as broadband PLC operating in the smart-grid orindoor environment.Various facets of EMI in power line networks have already been extensively stud-ied in the literature, e.g., [165–168]. However, we notice a crucial difference in thearchitectures of traditional PLC and PLC for BMSs (referred to as PLC-B here-after), as illustrated in Fig. 4.14. For traditional PLC, where the conductors carryingthe outgoing and return signals are bundled together, the radiation effects of the1194.3. IBFD-PLC: Cognitive of Neighboring PLCTX RX(a)BCUTXCell-boardRX(b)Figure 4.14: Illustrations of (a) the fields generated by signals in opposing directionsinterfering destructively in conventional PLC, and (b) cables carrying signals in op-posing directions being too far away from each other for their fields to completelycancel each other out in PLC-B.differential-mode (DM) signals cancel each other out. As a result, the common-mode(CM) signal is the primary source of electromagnetic radiation. On the other hand, inPLC-B scenarios, the feeding conductor and return conductor could be spaced wideapart from each other (e.g., Fig. 4.14(b); also see [13, Figs. 1 and 10]). This leadsto negligible destructive interference of the electromagnetic (EM) radiations. Thus,a signal of the same strength causes much stronger net radiation in PLC-B vis-a-visconventional PLC. Therefore, the transmission limits imposed on conventional PLCtransmission is not directly applicable to PLC-B systems.Contributions: In this section, we investigate the effects of EMI caused by PLC-B in an energy storage unit. We first use the transmission line theory with themethod-of-images to model the signal propagation over the battery cable. Next, werepresent the conductor as a concatenation of several infinitesimally small Hertziandipoles to compute the radiated electric field at any point in space. We then use theelectric field limits imposed by the U.S. Federal Communications Commission (FCC)regulations for radiated emissions [169], and determine the maximum permissible1204.3. IBFD-PLC: Cognitive of Neighboring PLCPLC signal strength that can be injected into the cable13. Further, we investigatethe impact of the injected PLC-B signal on a neighboring broadband PLC network,by modeling the power line as a non-ideal receiving antenna. We use measuredreception factor values reported in the literature to determine the interference signalmagnitude that is radiated into a nearby broadband PLC application as a result of aPLC-B transmission. Finally, we suggest usable transmission signal strength limitsthat not only conform to the FCC standards, but also cause benign interference onneighboring BB-PLC networks.4.3.2 EMI FormulationWe consider a battery storage unit where multiple cells are connected in both seriesand parallel to obtain the desired current and voltage levels, similar to Fig. 4.12.Every cell has a cell-board connected between the positive and negative terminals ofthe battery [160, Fig. 1.2]. The central BCU has the ability to communicate indi-vidually to each of these cell-boards in a master-slave topology to enable operationssuch as cell balancing and charging control [13] [160, Ch. 3]. As a result, the out-going and return current paths are not physically close to each other. This leads tounintentional radiation that is not canceled by opposing fields.Current Propagation ModelEM radiation is quantified by the magnitude of the radiated electric field,∣∣∣ #»E(f)∣∣∣, atany given distance for a frequency14 f . To compute#»E radiated from a power cable,13Although we use the FCC regulations, the same procedure that we present can also be usedto obtain transmission limits for any given specifications. We choose to apply the FCC regulationas it explicitly specifies the maximum permissible field strength levels for radiated emissions, whileEuropean regulations, such as EN 50561, indicate the value through conducted emissions [170].14Henceforth, until we present numerical results in Section 4.3.4, we drop the indexing of f forbrevity.1214.3. IBFD-PLC: Cognitive of Neighboring PLCGroundre↵hh}InetInet2Figure 4.15: The method-of-images model for a single conductor that is at a heighth above the ground plane and carrying a current Inet.we consider a single conductor with current I flowing through it. However, in general,there could be multiple conductors in close proximity with each other that connectdifferent cells with each other and the BCU. Since we are interested in determiningthe electric field strength at a distance that is significantly larger than the dimensionsof the cable, we can view this as a single conductor with an effective radius of reffand a net cross-sectional current of Inet [171].Further, as the cross-sectional dimensions of the cable are also electrically smallcompared to the wavelength of PLC signal, Inet can be viewed as propagating with thequasi-transverse-electromagnetic mode along the wire, which can be modeled usingtransmission line (TL) theory [172, Ch. 1]. The TL theory models the propagation ofcurrents by TL equations using the per-unit-length (PUL) parameters of the cable.In the following, we derive the PUL parameters of resistance (R), inductance (L),capacitance (C) and conductance (G) for our considered scenario.For the current propagation similar to what is shown in Fig. 4.14(b), we canview the condition as a current flow in a single conductor over the ground plane withheight h, which can be modeled by TL theory using the method of images [172, Ch. 4].1224.3. IBFD-PLC: Cognitive of Neighboring PLCThis setup is also shown in Fig. 4.15. Using the method of images, the consideredscenario is equivalent to replacing the ground plane with an identical conductor thatis symmetrical with respect to ground, i.e., an identical conductor is placed below theground plane with a height h and the two conductors lie on the same vertical plane. Inaddition, the conductor below the ground plane has a current −Inet flowing through.We also consider the conductor to be cylindrical, and the surrounding medium to benon-ferromagnetic so that the permeability of the surrounding medium equals thatof free space, i.e. µ = µ0.The computation of R depends on the relationship between reff and the skin depth,δ, which is defined asδ =1√fpiµσcond, (4.23)where σcond is the conductance of the conductor. For a copper conductor, σcond =5.96× 107 S, and thus, the maximum value of δ over the considered frequency rangeof 1.8 MHz to 30 MHz is δmax = 4.86 × 10−5 m. Since δmax  reff , we use [172, Eq.4.103b] to calculate R asR =12reffpiσcondδ. (4.24)Next, for the computation of L, C, and G, we consider h  2reff , which isclearly a typically observable condition (see Fig. 4.15). For computational simplicity,we approximate the medium to be homogeneous in the insulation permittivity, ins,and insulation conductance, σins. Under such conditions, we obtain the closed form1234.3. IBFD-PLC: Cognitive of Neighboring PLCexpressions for the PUL parameters as [172, Eq. 4.45 - 4.47]C =2piinsln(2hreff) , (4.25)L =µ2piln(2hreff), (4.26)G =2piσinsln(2hreff) . (4.27)Typically, cable insulation materials are characterized with the complex relativepermittivity, comp. In such cases, we have ins = 0<{comp} and σins = −2pif0={comp},where 0 is the free space permittivity, and <{·} and ={·} denote the real and imag-inary parts of a complex number, respectively. We consider the commonly usedinsulation of polyvinyl chloride, and use reff = rw = 4.25 mm from [173] for ourevaluations.Using the PUL parameters, we compute the characteristic impedance of the line,and TL propagation constant, γ, as [172, Eqs. 6.60, 6.73]Zc =√R + j2pifLG+ j2pifC, (4.28)γ =√(G+ j2pifC)(R + j2pifL), (4.29)where j =√−1. We then use γ to obtain [172, Eq. 6.60]Inet(z) = I+nete−γz + I−neteγz, (4.30)where z is the length variable along the line, and I+net and I−net are the forward andbackward components of the propagating current Inet, respectively. The values ofI+net and I−net are contingent on the load conditions that determine the extent of the1244.3. IBFD-PLC: Cognitive of Neighboring PLCrnxˆyˆzˆ!nΔzConductorHertzian dipoleE(n)yE(n)z(0, d, zn)Figure 4.16: The Cartesian coordinates representation of the electric field producedat a distance d from the conductor by its nth dipole element that is oriented alongthe z-axis.forward traveling wave that is reflected back, which is captured by the reflectioncoefficient [172, Ch. 6.2.1].Electric Field ComputationNext, we model the conductor as a concatenation of N Hertzian dipoles, each ofwhose length ∆z  λ, where λ is the wavelength of the radiated wave. This setupis also shown in Fig. 4.16. We then compute the electric field caused due to the nthdipole at a distance d. For computational simplicity, we first represent the generatedfield in 3-dimensional spherical coordinates (rˆ, θˆ, φˆ) as#»E(n)(rn, θn) = E(n)r rˆ + E(n)θ θˆ=Inet(−zn)∆z2piη(1rn− jkr2n)exp(−jkrn)rncos θn rˆ+Inet(−zn)∆zjωµ4pi(1 +1jkrn− 1k2r2n)exp(−jkrn)rnsin θnθˆ, (4.31)1254.3. IBFD-PLC: Cognitive of Neighboring PLCwhere η = 120pi Ω is the free-space impedance, k = 2piλis the wave number, andw = 2pif is the angular frequency. Further, for the ease adding the field vectors ofeach of the N dipoles, we convert#»E(n) to Cartesian coordinates (xˆ, yˆ, zˆ) as#»E(n)(d) = Ey yˆ + Ez zˆ=(drnE(n)r +znrnE(n)θ)yˆ +(znrnE(n)r +−drnE(n)θ)zˆ. (4.32)Note that by the orienting the axes in such a way that the dipole stays at the originand the point-of-interest lies on the yˆ − zˆ plane, we obtain no component in the xˆdirection. We then compute the overall electric field#»E at a perpendicular distanced from the line as the vector sum#»E(d) = limN→∞N∑n=−N#»E(n)(d). (4.33)4.3.3 EMI AnalysisIn this section, we formulate the limits on the allowed feeding signal based on themaximum electric field regulations. Further, we also examine the effects of the gen-erated#»E on neighboring broadband PLC applications.Electric Field Limits by FCCRegulatory authorities across the world limit the maximum radiation limits that aretolerable from intentional and unintentional radiation caused in the radio-frequencybands. In our work, we consider the regulations imposed by FCC that is applicablein the North American region in the frequency band of interest between 2 MHz and30 MHz [169]. Naturally, the same procedure we follow here can also be applied with1264.3. IBFD-PLC: Cognitive of Neighboring PLCany specifications.The Code of Federal Regulations by FCC limits the unintentional radiation byPLC systems to be∣∣∣ #»EFCC(d = 30 m)∣∣∣ = 30 µV/m [169, 174, 175]15. To determinethe maximum feeding signal strength using this limit, we first compute the com-monly used field coupling factor, βV =| #»E||V | [162], by injecting a net current, Inet,corresponding to a unit voltage signal, and determining its associated∣∣∣ #»E(d)∣∣∣ us-ing (4.31)−(4.33). We then set∣∣∣ #»EFCC(d = 30 m)∣∣∣ = 30 µV/m to obtain the voltageand power feeding limits, which we present in Section 4.3.4.Impact on Neighboring BB-PLC ApplicationsSimilar to the battery power cables emitting EM radiations as a transmitting antenna,a communication cable located in vicinity of PLC-B is conversely also susceptible tothese radiations as a receiving antenna. For a receiving antenna, the incident powerdensity Pinc and the maximum received power PR,max are related by the effective area,i.e., the aperture of the antenna, A, as [176, Eq. 16.3.1]A =PR,maxPinc. (4.34)Further, the aperture A can be expressed with respect to the maximum directivityof the antenna, Gmax, as [176, Eq. 16.3.5]A =Gmaxλ24pi, (4.35)15This is the value used to derive the −50 dBm/Hz transmit PSD limit in HPAV standard thatwe have been using throughout our analysis in the previous chapters.1274.3. IBFD-PLC: Cognitive of Neighboring PLCwhereGmax =max [U(θ, φ)]14piφ=2pi∫φ=0θ=pi∫θ=0U(θ, φ) sin θdθdφ, (4.36)with U(θ, φ) being the radiant intensity, i.e., the power per unit solid angle.The incident power density is the magnitude of the Poynting vector of the incidentelectromagnetic wave. Thus,Pinc =∣∣∣∣12 #»E × # »H∣∣∣∣ = 12 ∣∣∣ #»E∣∣∣ ∣∣∣ # »H∣∣∣ = 12∣∣∣ #»E∣∣∣2η, (4.37)where the simplifications arise from the orthogonality of#»E and the magnetic field,# »H , and the far-field approximation. From (4.34), (4.35) and (4.37), we getPR,max =Gmaxλ2∣∣∣ #»E∣∣∣28piη. (4.38)Since the power line does not act as an ideal antenna with matched impedance, thepractically obtainable received power is PR = κPR,max, where κ < 1. This effect canbe captured using a reception factor that is defined asαrec , 10 log10∣∣∣ #»E∣∣∣2PR = 10 log10( 8piηκGmaxλ2). (4.39)Note that the term κGmax is specific to the considered cable and its location. Inorder to obtain a realistic value of κGmax, we use the measurement results from [75,Ch. 5]. In particular, we set the value of κGmax such that the median of αrec over2 to 20 MHz computed with (4.39) matches the values presented in [75, Fig. 54]16.16Although the term κGmax could be frequency dependent in practice, we set a fixed value due tothe lack of a frequency characterization of αrec in [75, Ch. 5].1284.3. IBFD-PLC: Cognitive of Neighboring PLCWith this procedure, we obtain κGmax =120.Further, with knowledge of the characteristic impedance through (4.28), we cancompute∣∣∣ #»E∣∣∣ for any transmitted signal with power, PT, using (4.31)−(4.33). Thereby,we define the power coupling factor,βP , 10 log10(PRPT), (4.40)which indicates the power of the interference signal that is generated on a neighboringpower line as a result of a nearby PLC-B operation with a signal transmitting witha power PT.Since we use the measured αrec values that are reported for indoor power lines, theresults of βP presented in Section 4.3.4 are limited to EMI caused on PLC applica-tions. However, we remark that the same procedure is also applicable to characterizeEMI on any wired communication network using the associated αrec values.4.3.4 Numerical ResultsIn this section, we present the numerical results of nominal radiated emissions, feedinglimits, and the extent of interference caused by PLC-B operations on nearby PLC.Throughout this section, we consider an RBW of ∆f = 9 kHz to maintain conformitywith the measurement apparatus and methods specified in the regulations [169, 177].We also consider h to be high enough such that the field from the image line doesnot impact final effective field strength measured at any d.Increased RadiationAs our first result, we show the increase in electric field caused due to increasedseparation between the outgoing and the return paths in the PLC-B scenario. First,1294.3. IBFD-PLC: Cognitive of Neighboring PLC0 1 2 310 7-40-20020406080PLC-BConventional PLCFCC Limit(a)0 5 10406080100120140PLC-BConventional PLC(b)Figure 4.17: Variation of the electric field strength for PLC-B and conventional PLCapplications (a) across frequency, and (b) for varying observation distance.to determine∣∣∣ #»E(f, d)∣∣∣ caused by conventional PLC, we feed a signal with a transmitPSD of P˜TX = −50 dBm/Hz, as per the HPAV standard [35]. Accordingly we get theDM current,|IDM(f)| =√P˜TX ·∆fZc, (4.41)for field computation using (4.30)− (4.33). To evaluate the worst-case emission, weconsider the current close to the feeding point on the cable before the signal has un-dergone any noticeable attenuation, i.e., Inet(z, f) = IDM(f), where z is comparativelysmall. Further, we also assume matched load conditions to let I−net = 0 in (4.30).In conventional PLC, where the conductors carrying the outgoing and return cur-rents are in close proximity with each other, the CM current is the primary source ofelectromagnetic radiation. Thus, we compute a corresponding CM current, ICM(f),for the DM current of (4.41) using a longitudinal conversion loss (LCL) factor. Com-monly reported LCL values in the literature are between 30 − 50 dB [178, 179].For emulation purposes, we generate Gaussian distributed random CM voltage val-ues (and their corresponding CM currents) across varying frequencies such that1304.3. IBFD-PLC: Cognitive of Neighboring PLCthe mean and variance of LCL are 40 dB and 5 dB, respectively. We then useICM(f) in (4.31)−(4.33) to obtain the radiated electric field for conventional PLC,∣∣∣ #»EPLC(f, d)∣∣∣. On the other hand, we use the same P˜TX = −50 dBm/Hz and (4.41)to get IDM(f) for use in (4.30)−(4.33) to obtain∣∣∣ #»EPLC−B(f, d)∣∣∣. The field strengthresults obtained for both applications are shown in Fig. 4.17(a). The large vari-ation in∣∣∣ #»EPLC(f, d = 30 m)∣∣∣ is a result of the random LCL values that we usedin our computations. We can clearly notice that for the same feeding limit ofP˜TX = −50 dBm/Hz, PLC-B produces about 40 dB of additional radiated emis-sions, which corresponds to the mean LCL value used. We also notice that while∣∣∣ #»EPLC(f, d = 30 m)∣∣∣ ≤ 30 dBµV/m, which is the FCC limit for field strength [169],the electric field of PLC-B radiation well exceeds the permitted limits at most fre-quencies.Further, in Fig. 4.17(b), we also plot the variation of the maximum field magnitudeacross all frequencies, maxf[∣∣∣ #»EPLC−B(f, d)∣∣∣] and maxf[∣∣∣ #»EPLC(f, d)∣∣∣], between 2 −30 MHz, with the observed distance d. Yet again, we observe that while both valuesdrop with increasing d as anticipated, the radiated emissions from PLC-B is well overthe FCC regulations threshold [169].Feeding LimitsTo conform to the norms specified in the FCC Part 15 emitted radiations regula-tions [169], we compute the maximum possible voltage and power spectral densityfeeding limits, Vlimit(f) and P˜limit, respectively, using the procedure described in Sec-tion 4.3.3. Accordingly, we first compute the field coupling factor asβV (f)∣∣d=30 m=∣∣∣ #»E(f, d = 30 m)∣∣∣ , (4.42)1314.3. IBFD-PLC: Cognitive of Neighboring PLC0 1 2 310 7-50-40-30-20-10-48dBV(a)0 1 2 310 7-10010203029.5 dBuV/m(b)Figure 4.18: (a) Feeding voltage limit across different frequencies that PLC-B devicesneed to adhere to, in order to conform with the FCC Part 15 emitted radiations reg-ulation, and (b) the obtained electric field strength across all frequencies by injectinga signal of power spectral density −80 dBm/Hz.for a signal of V (f) = 1 V on the line. We then determine the feeding limit voltageas|Vlimit(f)| =∣∣∣ #»EFCC(f, d = 30 m)∣∣∣βV (f)∣∣d=30 m. (4.43)In Fig. 4.18(a), we show the |Vlimit(f)| that is permissible on the line to satisfythe radiated emission limits of FCC. We then use minf[Vlimit(f)] to determine a con-servative maximum permissible feeding power spectral density limit asP˜limit =∣∣∣∣minf [Vlimit(f)]∣∣∣∣2Zc∆f, (4.44)in 2 MHz ≤ f ≤ 30 MHz. Using∣∣∣∣minf [Vlimit(f)]∣∣∣∣ = −48 dBV shown in Fig. 4.18(a),we get the P˜limit = −80 dBm/Hz. This PSD feeding limit serves as a reference toPLC-B products for compliance with FCC regulations.Further, in Fig. 4.18(b), we show the emitted radiation field strength obtained atan observation distance of 30 m from the line, when the injected signal strength1324.3. IBFD-PLC: Cognitive of Neighboring PLC5 6 7 8 9 10-65-60-55-50-45-40-35Figure 4.19: The median power coupling factor across all frequencies varying withdistance of separation.is −80 dBm/Hz. We clearly notice that the field strength now lies well within30 dBµV/m.Interference to Neighboring PLCAs our final result, we show the impact of PLC-B operation on a nearby conventionalbroadband PLC network, as formulated in Section 4.3.3. We consider different sepa-ration distances between the PLC-B and the broadband PLC network, i.e., betweena battery cable and a neighboring power line, and plot the power coupling factor, βP ,for different separations in Fig. 4.19.We observe that the coupling factor reduces with increase in separation dis-tance as expected. With a nominal separation distance of, say, d = 10 m, and anoperating power spectral density of P˜limit = −80 dBm/Hz as determined in Sec-tion 4.3.4, PLC-B causes a median interference power spectral density of about−80 − 62 = −142 dBm/Hz, which is well below most indoor power line noise lev-els [7, 115]. Fig. 4.19 also serves as a reference to determine the required physical1334.4. IBFD-PLC: Upper Layer Enhancementsseparation between the battery pack and the indoor electrical wiring installation forany chosen transmission level.4.4 IBFD-PLC: Upper Layer EnhancementsAs our final application scenario of IBFD-PLC, we examine the use of SI cancella-tion techniques for resolving contentions in the frequency domain and implementingCSMA/CD in BB-PLC networks to improve the MAC layer performance efficiencyin heavily loaded PLC networks, e.g., a smart-home IoT environment.4.4.1 BackgroundThe space for PLC in HANs has historically been occupied by low bandwidth andultra-low data rate products of X-10, CE Bus, and LonWorks [1, Ch. 7]. How-ever, BB-PLC alternatives, such as HPGP, offer low-cost low-power solutions whilealso providing significantly higher data rates, with specifications tailored for smartgrid functionalities in HANs [180]. Furthermore, HPGP also provides complete in-teroperability with other BB-PLC standards, such as HPAV, HPAV2, and IEEE1901, which are commonly used by indoor high-speed multimedia communicationdevices [4]. Thereby, HPGP enables a single PLC network for all communicationrequirements in a HAN [60, Ch. 15].The increasing congestion in HANs caused by the growing number of devicesconnected in a smart-home environment results in the performance degradation oftypical HPGP networks. A conventional HPGP-compliant network functions poorlyunder heavily loaded network conditions as the efficiency of the MAC layer decaysrapidly with increasing number of nodes. Our evaluation result shown in Fig. 1.7and many prior works have shown that the efficiency rapidly degrades, and could1344.4. IBFD-PLC: Upper Layer Enhancementsbe as low as 10% [78, 79]. One of the reasons for this reduced MAC efficiency isthe extended time periods that are lost during frame collisions under the CSMA/CAscheme. A method to reduce this collision recovery time is to implement CSMA/CDto immediately terminate transmission in case of a collision. However, CSMA/CDrequires the PLC nodes to operate in an IBFD manner [80, Ch. 5]. Our IBFDdesigns proposed in Chapters 2 and 3 have been used to show a successful CSMA/CD-based MAC protocol operation for BB-PLC applications [81, 82, 181]. Although thecollision recovery time is significantly reduced by a CSMA/CD operation, the priorityresolution procedure (PRP) and the random back-offs still consume a relatively largetime duration during which no data payload is transferred.In this section, we aim to further reduce the MAC layer overheads, particularly,the time spent during PRP and back-offs, to increase the MAC efficiency of in-homePLC networks. We propose a solution to implement PRP in the frequency domain byallotting orthogonal frequency bands for each priority levels. Further, we use the sameunderlying principle to also perform contention resolution in the frequency domainwithout backing off slot-by-slot as in its time domain counterpart. Concurrently,we use the IBFD operation to simultaneously detect collisions during this period bysensing for other potential frame transmissions. We show through simulation resultsthat our solutions provide a considerable gain in the MAC efficiency for typicallyencountered HAN traffic conditions.4.4.2 Related WorkAlthough we find no previous implementations of PRP in the frequency domain, theworks in [83, 84] have proposed a solution to apply frequency domain contention res-olution for wireless networks. This solution allocates a unique OFDM sub-carrier to1354.4. IBFD-PLC: Upper Layer Enhancementsthe individual BC values. During the back-off period, the network nodes transmit asignal on the OFDM sub-carrier mapped to its BC value. In this way, the time duringwhich the BC is counted down to zero is reduced to a single OFDM block durationwherein all nodes are informed of each others BC status. However, apart from thedrawback that this limits the range of the possible BC values to the available numberof OFDM sub-carriers [182], this scheme may not be effective in BB-PLC systems,since the power line channel consists of multiple deep-notches in the frequency do-main [109, 183]. The presence of narrowband noise components on the power linefurther compromises the effectiveness of this implementation. Therefore, along withpresenting a solution that provides a wider frequency band for every BC value tocounter the frequency selective nature of the PLC channel, we also propose a methodto combat the harsh narrowband noise that could potentially affect the accuracy ofdetection. Furthermore, we use the IBFD operation during this period to performcontention resolution and collision detection at the same time.The solution of [83, 84] was further adapted in [184, 185] to reduce the probabilityof collisions after the frequency domain random back-off. However, such schemes arenot applicable to our scenario as we do not wish to alter the procedure in which theBCs are updated by the HPGP protocol. Instead, we apply the CSMA/CD operationthat is able to detect and avoid potential frame collisions with minimal overheads [81].In the following sections, we present our proposed schemes based on frequencydomain resolution of the priorities and contentions among network nodes, and demon-strate the effectiveness of our solution through network simulations performed undera realistic smart-home environment with varying HAN traffic conditions.1364.4. IBFD-PLC: Upper Layer EnhancementsPRS0 PRS1 PB Frame	control	+	PayloadPRPBack-offCIFSFigure 4.20: Illustration of the initiation procedure of a MAC frame transmission ata node under the conventional HPGP CSMA/CA protocol. (PB: Preamble)4.4.3 Proposed SchemesPriority ResolutionThe conventional CSMA/CA operation adopted by the HPGP standard is shown inFig. 4.20. When the channel is sensed idle by the node for a time duration correspond-ing to the contention inter-frame spacing (CIFS), a frame transmission is initiatedstarting with the PRP. During the PRP, every node indicates its frame priority asone of the four channel access priority (CAP) levels available in HPGP. The CAPsof all nodes are resolved in two slots in a bit-by-bit manner starting with the mostsignificant bit. A node transmits a priority resolution signal (PRS) to indicate a bit‘1’, and remains silent otherwise. Each PRS spans seven OFDM blocks, and is sensedat every silent node in the time domain.To reduce the time spent in PRP, we propose to resolve the CAPs in the frequencydomain. The fundamental idea that we use is to divide the available spectrum intofour separate frequency bands and map each CAP to an individual sub-band indi-vidually to a CAP, so that a two-step bit-by-bit resolution procedure can insteadbe performed in just one step. We let a node with a priority-p message, i.e., CAPpMAC frame, transmit its PRS only on the pth frequency sub-band. We could furtherinclude multiple repetitions as in [77] to guarantee performance under poor channeland noise conditions. At the same time, the node also receives PRSs from all theother active nodes. The node then examines the received PRS spectrum to detect1374.4. IBFD-PLC: Upper Layer Enhancementswhether a CAP greater than its own has been transmitted. Under conditions whenthe node does not detect a CAP greater than its own, it wins the PRP and proceedsto the back-off stage. Note that a node is only required to detect a CAP greater thanits own, and not required to learn the CAPs of all other network nodes. Althoughthis can, in theory, be achieved in a HD mode, using an IBFD operation to cancel theSI signal provides superior detection accuracy in the presence of closely spaced activesub-carriers in adjacent sub-bands. Furthermore, IBFD PRP implementation alsohelps in identifying a contention-free condition where the random back-off procedurecould be eliminated when there is a sole PRP winner.Contention ResolutionAll the nodes winning the PRP proceed to the back-off stage where they back-off forrandom durations of time decided by the value of their BC. Network node n ∈ Ψselects a random BC value, Wn, drawn from a uniformly distributed random variablein the range [0,CW], where CW is the contention window size determined by thenetwork protocol, and Ψ is the set of all network nodes that have won the PRP.Since CWmax = 63 for HPGP, this random back-off time can be as long as 63 ×35.84 µs = 2.25 ms, which is over 70% longer than even the maximum allowed dataframe length [77]. In order to reduce this time duration, we propose to performback-off in the frequency domain.Advertising BC: We described in Section 4.4.2 that prior works have proposed afrequency domain back-off scheme by transmitting a signal on one particular OFDMsub-carrier based on the chosen Wn [83, 84]. However, such a method suffers fromdetection errors in BB-PLC, as power line channels are highly frequency selectiveand experience narrowband noise [92, 109, 149, 183]. To alleviate this problem, wedecide to use a larger bandwidth, i.e., a larger number of sub-carriers, to send Wn,1384.4. IBFD-PLC: Upper Layer Enhancementssuch that each node n can advertise its Wn by transmitting a preamble signal on thenth sub-band of carriers reserved for Wn. HPGP generates OFDM preambles usinga 384-point inverse DFT, which provides 192 available sub-carriers to transmit on.After permanently notching sub-carriers lying in the amateur radio frequency bands,only 113 of the total sub-carriers are available for data transmission [77]. Therefore,with CWmax = 63, less than two sub-carriers are available to be alloted to representeach Wn. Further, given that the sub-carrier spacing is 195 kHz [77], and that themedian coherence bandwidth of BB-PLC channels is about 200 kHz [109], using twosub-carriers is not likely to provide a satisfactory improvement in detection accuracy.Therefore, to further increase the bandwidth available per Wn, we consider resolvingthe contentions using two OFDM blocks. We divide the frequency spectrum into tensub-bands and let the nodes resolve contentions in a digit-by-digit manner startingwith the most significant digit (MSD). In the first OFDM-block contention round,all nodes use the IBFD operation to simultaneously transmit and receive the MSD oftheir Wn. Only the nodes winning the first OFDM-block contention round, i.e., thenodes with the smallest MSD, then proceed to advertise their least significant digit.The nodes that also win the second OFDM-block contention round win the contentionresolution procedure. This solution provides each digit of Wn with a bandwidth ofover 2 MHz, which is sufficient to compensate for the deep fades in the channel.However, since CWmax = 63 for HPGP, three sub-bands (representing the digits 7,8, and 9) remain unused while resolving the MSD. To effectively utilize the entireavailable spectrum, we could further represent Wn in an octal representation andthen divide the total bandwidth into eight sub-bands. This provides every octal-digitwith a bandwidth of over 2.7 MHz.The operation of our proposed schemes at a frame transmission initiation is shown1394.4. IBFD-PLC: Upper Layer EnhancementsFrame	control	+	PayloadPRPBack-offTotal	time	savedCIFSPRS0 PRS1 PB Frame	control	+	PayloadPRPBack-offCIFSFigure 4.21: Illustration of the MAC frame transmission at a node and the time savedusing our proposed frequency domain CAP and contention resolution.in Fig. 4.21, which also illustrates the amount of time saved by applying our proposedsolution. We again highlight that a node only needs to learn the min∀n∈ΨWn, and notWn of each node, as obtained in [83, 84].Reassigning Wn for Losing Nodes: The node that wins the contention round setsits BC value to zero, and proceeds to transmit the frame control and the data payload.However, the nodes that lose the contention are required to reassign their Wn for thenext contention opportunity. Recall that in a conventional time-domain randomback-off, the nodes count down Wn to zero, or until it senses a preamble transmissionon the line. Thus, every node, m, that loses a contention round eventually assignsWm ← Wm − min∀n∈Ψn6=mWn. (4.45)With our frequency domain contention resolution procedure, we also apply (4.45)without counting down in time. Although we do not specifically identify Wn of eachnode, every listening node is able to deduce minn∈Ψn6=mWn by learning the smallest digitin each of the OFDM-block contention rounds. In this way, we only modify thetechnique in which the channel access contention is resolved, without altering thealgorithm prescribed in the HPGP protocol to determine Wn in the random back-off1404.4. IBFD-PLC: Upper Layer EnhancementsAlgorithm 2 Our proposed algorithm at the mth network node.1: Start: When message is ready to be transmitted2: while sense the channel do3: if channel is idle for CIFS then4: Transmit and receive CAPs5: if CAPm ≥ maxn∈ΨCAPn then6: Pick Wm predetermined from previous round, or7: Wm ← U [0,CW]8: Transmit Wm, and sense for Wn, ∀n ∈ Ψ, n 6= m9: if Wm < min∀n∈Ψn6=mWn then10: Win contention; transmit frame control11: else12: if Wm = min∀n∈Ψn6=mWn then13: Indicate collision; transmit jamming signal14: else15: Wm ← Wm − min∀n∈Ψn6=mWn16: end if17: end if18: end if19: end ifprocedure.Collision DetectionMultiple nodes winning the back-off leads to an eventual frame collision. To avoiddata payload collisions and save the associated collision recovery time, we use theIBFD operation during contention resolution to also achieve collision detection. Sincethe nodes transmit and receive their Wn simultaneously, each such node is informed ofat least one other winner when multiple nodes win the second OFDM-block contentionround, thereby indicating a future payload collision. Under such a condition, thenodes transmit a jamming signal to inform all the network nodes of a collision. Inthis way, we use IBFD to combine both contention resolution and collision detection1414.4. IBFD-PLC: Upper Layer Enhancementsto be performed in the same time slot. The pseudo-code of our proposed protocol isgiven in Algorithm 2.Signal DetectionA common approach to detect the presence of a signal in a given sub-band is tocompare the relative level of the power spectral density (PSD) of the signal with thenoise floor. This process is relatively straightforward under additive white Gaussiannoise conditions where the signal level can be compared to the noise floor on any silentsub-bands. However, power line noise is colored [92, 149]. It is therefore prudent topre-compute the noise floor of each sub-band individually. This can be accomplishedduring the silent periods. Since the PRP begins only after the channel is sensed idlefor CIFS = 35.84 µs, the noise floor in each sub-band can be computed during thisperiod. Given that our proposed frequency domain PRP and contention resolutioncompletes within τ = 30.72 µs, the noise floor can be assumed to be stationary withinthis duration of CIFS + τ .Effect of Narrowband Noise: Most power line environments are subject to nar-rowband noise whose PSD is typically orders of magnitude larger than the backgroundnoise [92, 149]. This increases the probability of missed detection as the narrowbandnoise increases the computed average noise floor in the affected sub-band. However,measurement results suggest that, on an average, three such narrowband compo-nents with a mean bandwidth of less than 450 kHz each, i.e., spanning less thanthree sub-carriers, are typically present on the power line [92, Table 2]. Therefore,the sub-carriers that are affected by narrowband noise can be easily identified andexcluded from the noise floor computation and signal identification during the silentand the resolution periods, respectively.Detection Threshold: Once we compute the average noise floor in each sub-band,1424.4. IBFD-PLC: Upper Layer Enhancements2 4 6 8012345x 10−3x, dBPr(SNR ≤ x)  4 sub−bands8 sub−bands10 sub−bandsFigure 4.22: CDF plot (zoomed) of the average SNR obtained over 1000 randomlygenerated power line channel and noise conditions.we can determine the relative threshold that a signal energy should cross in order to bedetected. A low detection threshold increases the probability of false alarms, while alarge one increases missed detections. To obtain an empirical indication on the rangeof possible detection thresholds, we examined the average SNR in each sub-bandacross 1000 randomly generated power line channel and noise conditions to find theminimum SNR17. We divided the available spectrum into four sub-bands for the PRP,and eight sub-bands for the contention resolution. A CDF plot of the average SNR isshown in Fig. 4.22. We notice that smaller number of sub-bands (i.e., larger number ofsub-carriers in each sub-band) provides a higher minimum SNR as the notches in thechannel transfer function are better averaged over greater number of sub-carriers.Fig. 4.22 also indicates that the probability of encountering low SNR conditionsis minimal. Furthermore, the detection threshold can be dynamically assigned foreach contention opportunity based on the SNR profile obtained over a previous data17Please refer to Appendix A for a detailed description on the channel and noise generationprocedure and statistics.1434.4. IBFD-PLC: Upper Layer Enhancementspayload reception. Hence, for evaluating numerical results in Section 4.4.4, we runour simulations with assumption of zero detection errors or false alarms.Detection Errors and False Alarms in Collision Detection: The application ofIBFD is indispensable for collision detection as the transmitted and monitored signalsoccupy the same sub-band. We have shown in Chapter 3 that IBFD with AIC iscapable of reducing SI to the minimum power line noise floor on idle sub-bands.This ensures that collision detection is devoid of false alarms due to SI. However, SIcancellation could be incomplete in the presence of a received signal [151]. But anincompletely canceled SI can only trigger an alarm and not cause a missed detection.Therefore, a sub-optimal SI cancellation performance does not adversely affect thedetection error rate.Discussion on the ImplementationIn this final part of Section 4.4.3, we discuss some salient features of our proposedschemes and possible limitations associated with a practical implementation.1. Operation in a Heterogeneous HAN: Throughout our analysis in Section 4.4.3and simulation results we present in Section 4.4.4, we consider devices operatingwith the HPGP protocol. However, a HAN is also expected to consist of PLCdevices for high-speed communication purposes, which typically function usingthe HPAV or IEEE 1901 protocol. HPGP is known to provide complete interop-erability with HP1.0, HPAV, HPAV2, and IEEE 1901 BB-PLC standards, andalso uses the same PRP and random channel access schemes as them [60, Ch.15], [77]. Hence, our proposed solutions are not only interoperable with thesehigh throughput BB-PLC standards, but are also applicable to each of thesecompatible standards in a heterogeneous HAN. We further emphasize that the1444.4. IBFD-PLC: Upper Layer Enhancementsfunctioning of the Green PHY preferred allocation and distributed bandwidthcontrol, which guarantee a minimum and maximum time-on-wire for HPGPdevices in a hybrid network, respectively [60, Ch. 15], are independent to theoperation of our proposed schemes, and can completely coexist with each other.2. Operation of the Legacy Back-off Procedure: As explained in Section 4.4.3,our proposed schemes do not alter the procedure in which the back-off, back-offprocedural, or the deferral counter is updated for a given network. We onlymodify the manner in which the CAPs and contentions are resolved. Thus, ourschemes can be applied together with other solutions proposed to improve theBC update algorithm, e.g., [78, 79].3. Hidden Node Collisions: The CSMA/CD scheme used in Section 4.4.3 doesnot address the frame collisions caused due to hidden nodes. However, theIBFD operation could be used by the network nodes as a potential solution toachieve a virtual RTS/CTS handshake and eliminate hidden-node collisions, asdiscussed in Chapter 1.4. Application with Non-IBFD Nodes: Our proposed schemes, without the colli-sion detection procedure, are in principle also implementable with HD devices.However, an uncanceled SI signal is strong enough to potentially saturate theADC in the receiver. The resulting increase in quantization noise could resultin a drastic increase in false alarms. Thus, an IBFD solution with AIC is mostsuitable for our application.5. Extending to Larger CWmax: In Section 4.4.3, we presented a collision resolu-tion procedure for a CWmax = 63. However, extending our solution to largervalues of CWmax is straightforward, either by adding a supplementary OFDM-1454.4. IBFD-PLC: Upper Layer Enhancementsblock contention round, or allocating a smaller bandwidth per Wn by using ahigher base representation to denote Wn. The optimal solution then dependson the network conditions.6. Interleaving Sub-carriers: While allotting different sub-bands for Wn andCAPs in Section 4.4.3, we divided the frequency spectrum into sub-bands thatcontain contiguous sub-carriers. However, our empirical SNR evaluations indi-cate that the frequencies below∼ 2 MHz suffer from lower SNRs when comparedto higher frequencies. Thus, every CAP and Wn can alternatively be mappedto a different set of sub-carriers each, that spans across the entire frequencyspectrum, in order to possibly allow applying a higher detection threshold.4.4.4 Simulation ResultsIn this section, we present the network simulation results obtained by using ourproposed schemes for a typical indoor PLC HAN.Simulation SettingsWe model a heavily loaded indoor PLC network with up to 80 network nodes. Toemulate realistic data packets and network node interactions, we run our simulationsfor varying number of active nodes and different frame lengths.Since examining MAC efficiency under a saturated network traffic condition is acommonly used metric for the evaluation of the network performance [186, 187], wesimulate a network that is saturated with CAP0 MAC frames18. However, the inter-arrival time between messages transmitted by devices inside a typical HAN scenariois found to be well emulated by an exponential random distribution [5, 188, 189].18Recall that CAPp MAC frames carry priority-p messages. HPGP has four CAP classes, withp = 3 being the highest and p = 0 being the lowest CAP.1464.4. IBFD-PLC: Upper Layer EnhancementsTable 4.4: Simulation ParametersParameter ValueSimulation time (TS) 30 sCIFS 35.84 µsPRS, preamble, and Back-off slot time (tp) 35.84 µsFrame control length 133.92 µsMaximum frame length (MaxFL) 1293.64 µsExtended inter-frame space (EIFS) 1695 µstOFDM 5.12 µsRoll-off interval (at both ends) 0.5× tOFDMWe thus also generate network traffic in which CAP3 MAC frame arrival follows aPoisson process. Hence, we evaluate the performance of our solutions for two differentnetwork traffic scenarios with a common CAP0 MAC frame saturation condition: (a)a saturated network where all active network nodes constantly contend with CAP3MAC frames, and (b) a comparatively more realistic network in which the higherCAP message arrival follows a Poisson process, where the network nodes contend forthe channel with CAP3 MAC frames that have an exponentially distributed randominter-arrival time. In addition, we set the mean inter-arrival times for the CAP3 MACframes in condition (b) such that they only occupy 50% of the available networkresource (time duration), while the rest can be used for CAP0 messages, possiblecollisions and recovery, and other non data payload transmissions. We tabulate theremaining simulation parameters in Table 4.4, which we obtained from the HPGPspecification [77].Numerical ResultsVarying Number of Network Nodes: For our first result in Fig. 4.23, we vary thenumber of network nodes between 10 and 80 to determine the amount of time, τc,spent in resolving CAPs and contentions using the conventional approach of [77],1474.4. IBFD-PLC: Upper Layer Enhancements10 20 30 40 50 60 70 80051015202530Number of network nodes with data to transmitτc/Ts,(%)  Conventional solution; Poisson arrivalProposed solution; Poisson arrivalConventional solution; saturated networkProposed solution; saturated networkFigure 4.23: Percentage of time spent on CAP and contention resolution for varyingnumber of network nodes using the conventional solution and our proposed solutionunder two different CAP3 network traffic conditions.and our proposed frequency domain resolution procedure. We fix the transmittedframe length to tFL = MaxFL (refer Table 4.4). We observe from Fig. 4.23 thatunder a saturated network condition, τc increases exponentially with the number ofnodes due to increased collisions, while τc remains fairly stable with a Poisson CAP3message arrival process. In both cases, Fig. 4.23 shows that τc is considerably smallerfor a frequency domain resolution procedure when compared to its time domaincounterpart.Varying Frame Lengths: Our second result shows the variation of the MACefficiency (η) with tFL in Fig. 4.24. We vary tFL in 10% steps of MaxFL, and set thetotal number of active network nodes to 10. We then compute η as (see Table 4.4 forparameters)η =tFLτc + EIFS−MaxFL + tFL . (4.46)We observe from Fig. 4.24 that η improves with increase in tFL due to a longer1484.5. Conclusions0 0.2 0.4 0.6 0.8 100.10.20.30.40.50.60.70.8tFL/MaxFLη  Time domain; saturated networkFrequency domain; saturated networkTime domain; Poisson arrivalFrequency domain; Poisson arrivalFigure 4.24: MAC efficiency versus the data payload frame length using the con-ventional solution and our proposed solution under different CAP3 network trafficconditions.duration of time used for data payload transmission. It is noticeable that our solutionprovides a considerable improvement in η over the time domain resolution procedure.It is also evident from Fig. 4.24 that a saturated network condition causes largernumber of collisions and therefore a smaller η. However, by detecting a collision andimmediately terminating the transmission, our solution is seen to be resilient to theeffects of collisions, providing a similar η for both traffic conditions.4.5 ConclusionsIn this chapter, we have investigated the application of spectrum-aware transmissionenabled by IBFD operation to solve several prevalent EMI and networking issues inBB-PLC systems.In this first part, we proposed solutions to counter the impact of RSI on IBFDspectrum sensing. Recognizing the limitation imposed due to inadequate dynamic1494.5. Conclusionsrange of the ADC, we proposed solutions other than our AIC-enabled IBFD techniqueto counter this constraint by either increasing SINAD ratio of the ADC, or by reducingthe power of the input signal entering the ADC. We demonstrated through simulationresults that our proposed solutions overcome the restriction of limited ADC precisionto provide nearly identical spectrum sensing accuracy as that achieved with HDoperation. Due to the ability to transmit and sense the medium simultaneously usingIBFD operation, we achieved the maximum spectrum sensing efficiency of 100%.In the next section, we addressed the issue of EMI between indoor communicationsystems over power lines and DSLs. We investigated the use of dynamic spectraladaptation in PLC systems to reduce its EMI on DSL communications. To thisend, we considered the use of an IBFD spectrum sensing approach that allows powerline modems to estimate the extent of PLC-to-DSL interference while simultaneouslytransmitting PLC data. However, our feasibility analyses showed that such a non-intrusive spectrum sensing based PLC-DSM approach potentially suffers from severedrawbacks, in both HD and IBFD modes, due to the harsh effects of power linenoise and the substantial EMI reduction demands of newer DSL standards operatingover extended bandwidths. This suggests that, in spite of its drawbacks, a customizedinterference cancellation implemented on the DSL customer premise equipment couldbe more suitable in practice.As a part of our third investigation for the use of IBFD-PLC to solve EMI issuesin heterogeneous PLC networks, we presented the first analysis of EMC for PLC inenergy storage units. By recognizing the unique challenges faced in applying PLC forsuch scenarios, we derived limits on the signal strength that can be injected on thebattery cables to comply with the FCC regulations on radiated emissions. Further-more, we showed numerical results to determine the feeding PLC-B signal strength1504.5. Conclusionsand the inter-network separation distance that results in a benign radiated interfer-ence with a neighboring broadband PLC network. Our work provides a theoreticalframework for eventually standardizing PLC operation in EMSs.Finally, we used the IBFD operation to present a channel access procedure forBB-PLC systems in which priorities and contentions of the network are resolved in thefrequency domain. We further used SI cancellation techniques to propose a frequencydomain collision detection procedure that achieves a CSMA/CD operation with areduced collision detection time. The application scenario for such access improvedBB-PLC systems are HANs with increased number of devices at the consumer-endas foreseen in the evolution of smart grids. We showed through network simulationresults for different HAN traffic conditions and HPGP system parameters that oursolutions achieve up to 85% reduction in the time spent on CAP and contentionresolution over a conventional time domain approach. We have thereby increased theMAC efficiency of the HPGP protocol to improve its applicability in a heavily loadedsmart-home environment.151Chapter 5ConclusionWe conclude the dissertation in this chapter and identify potential areas of futurework. We summarize our contributions and provide conclusions in Sections 5.1and 5.2, respectively. We present possible research directions for future work inSection 5.3.5.1 SummaryIn this thesis, we presented an IBFD solution for BB-PLC. In light of IBFD imple-mented in various communication systems from RADAR and analog telephones towireless communications, we analyzed the requirements for and challenges faced inBB-PLC systems for successful IBFD operation. Our solution consists of a two-stepapproach to combat the issue of SI. We use an op-amp based analog hybrid modulefor initial SI suppression. Along with providing signal isolation, we designed ourhybrid circuit such that it also presents well-defined device impedance to the lineunder IBFD operation when both the low-impedance transmitter path and the high-impedance receiver path are activated simultaneously within the modem. We thenproposed a digitally controlled AIC solution for active echo cancellation within thetransceiver AFE, using which we combined the benefits of digital adaptation for quickreconfigurability and low-cost implementation, and analog cancellation to address theissue of finite precision of practical ADCs. We further investigated time-, frequency-,1525.1. Summaryand mixed-domain digital filter adaptation techniques in terms of the achieved MSEperformance and ROC of the adaptation. Our adaptive AIC solution successfullyadapts to changing echo channel conditions that is affected by changes in any part ofthe PLC network, unlike, say, wireless communication scenarios, where SI channelsare fairly immune to activities that are sufficiently far away from the IBFD device.We further addressed the issue of short-term changes in power line channels thathamper the performance of LMS adaptation. We exploit the linear periodically timevarying nature of these changes to design a novel LPTV-LMS algorithm that ensuresthat the algorithm converges to its saturation value under all channel conditions.Furthermore, we expanded our solution to MIMO PLC systems that couple powerline signals on to more than one pair of conductors. Our simulation results show thatwe double the median data rates in SISO scenarios and obtain over 80% increasein median MIMO throughput under typical in-home power line channel and noiseconditions. As a part of this evaluation study, we developed a cumulative power linenoise generator tool, which we have released as open-source at [115].Beyond improving spectral efficiency, IBFD allows us to solve several prevalentnetworking issues in PLC systems. The simultaneous bidirectional data communica-tion ability allows PLC modems to transmit data signals while also sensing the oper-ating spectrum. We used the spectrum-aware transmission ability of IBFD-enabledPLC modems to implement an IBFD dynamic frequency exclusion technique to en-sure EMC between PLC and broadcast radio services. Based on recommendationsfrom EN 50561-1 specification, we applied smart notching at PLC transmission toeliminate unintentional radiation disturbance caused by power line signals on broad-cast radio reception. Using IBFD operation we achieved 100% spectrum sensingefficiency and showed that we obtain up to 35 Mbit/s of median data rate increase1535.1. Summaryby cognitively using the idle broadcast radio frequency bands.We then investigated using this cognitive transmission ability of IBFD PLCmodems to also ensure coexistence between indoor PLC and DSL communicationnetworks in an in-home environment. We analyzed the feasibility of implementing adynamic spectral adaptation approach at the PLC modems to reduce the EMI fromPLC on to DSL by estimating the PLC-to-DSL interference channel in real-time bymonitoring the DSL signal ingress while also transmitting PLC data using the IBFDoperation. Our analysis showed that such a solution is limited by the harsh power linenoise conditions, and therefore requires more effective channel estimation algorithmsover the state-of-the-art to ensure successful operation in both HD and IBFD modes.As our next application scenario, we considered the EMI between two differentheterogeneous PLC networks. We examined the EMC constraints in an energy stor-age facility, where the BMS uses BB-PLC over battery cables and indoor LAN isalso enabled by BB-PLC technology operating in overlapping frequency bands. Sincethe unintentional electromagnetic radiation of BB-PLC signals over battery powercables has not been investigated in the past, we presented the first analysis of theradiated field strength by modeling the cable as a concatenation of infinite number ofinfinitesimally small Hertzian dipoles. By using the PUL parameters of typical bat-tery power cables and the interconnection architecture of individual cells in a batterystorage unit, we characterized the radiated electric field strength and determined thatPLC violates EMC regulations by applying the maximum transmit PSD allowed forconventional BB-PLC. We suggested new reduced transmission limits for PLC overbattery cables to ensure conformity with EMC regulations, and also result in benignEMI on neighboring BB-PLC applications.Finally, we used IBFD operation in PLC to reduce the time spent on congestion1545.2. Conclusionscontrol at the MAC layer to improve its efficiency. We resolved the contentions andpriorities in the frequency domain and proposed solutions to adapt this techniquefor application on frequency selective power line channels where signals are also sub-ject to narrowband noise. We further integrated CSMA/CD operation within ourfrequency domain contention resolution procedure to reduce the time spent in con-gestion control activities at the MAC layer by up to 85%. Our solution providescomplete interoperability with all BB-PLC standards and can be augmented withother MAC layer enhancements proposed in the literature, as we do not modify theoperation of the underlying random back-off procedure.5.2 ConclusionsAlthough IBFD is an old technology, adopting it to different communication sys-tems (Ethernet, coax, DSL, wireless, NB-PLC, BB-PLC) requires detailed analysisto address the specific design considerations required to counter the unique challengesposed by each of them. For example, we learned from Chapter 2 that while a ferritecirculator is acceptable for analog SI suppression in wireless communications oper-ating in the GHz range, an op-amp based active hybrid, which can also be designedto provide broadband impedance stabilization, is more suitable for BB-PLC appli-cations owing to the feasibility constraints of the size of magnets and transformersrequired to operate in frequencies as low as 2 MHz. Our proposed IBFD solutionaddresses various such design considerations for BB-PLC systems, many of whichrequired significant enhancements to existing IBFD techniques.Our simulation results show that we achieve the target of doubling data ratesin over 70% of the tested in-home PLC network conditions. A comparative studyof in-home and smart-grid power lines [190] has shown that outdoor low-voltage1555.2. Conclusions(LV) networks present greater channel attenuation but lower power line noise, whencompared to typical in-home conditions. Therefore, based on our results in Figs. 3.4and 3.5, we could expect to obtain similar data rate gains in LV smart-grid networksas we did in in-home LANs. Examining the scalability of IBFD throughput gains atoutdoor LV and medium voltage networks is an interesting future work.Research ImpactSuccessful simulation results of our solution have proven that our IBFD design isready for prototype development and practical implementation. Furthermore, follow-ing our system evaluations [191, 192], the upcoming G.hn2 BB-PLC standard fromITU-T has also proposed to integrate full-duplexing as a part of PLC operation [193].Our IBFD solution has also been used by researchers to incorporate IBFD BB-PLC for designing efficient low-cost smart-grid monitoring and diagnostics techniques.Our SI cancellation method inherently estimates the SI channel, which is indicativeof the multiple signal reflection paths along the power line network. The impulseresponse of the SI channel provides insights into the status of the power line health,and has been used to develop machine learning techniques to monitor the SI channelvariations and automatically diagnose a cable degradation or fault [21]. Anotherwork has proposed a method to use our IBFD design to implement the joint-time-frequency-domain reflectometry [194] within a power line modem for cable diagnosticsby using the echo estimated during SI cancellation [195]. SI estimation techniquesfor BB-PLC have also been used to determine the broadband access impedance [196],using the direct relationship between the SI channel and the access impedance, with afixed hybrid port impedance (see Appendix B.1). The estimated line input impedancecan be used for various tasks, including to diagnose cable anomalies [196], and to1565.3. Further Research Directionscalculate the input return loss for adaptive transmit power boosting [34, Sec. 3.4.2].5.3 Further Research DirectionsIn the final portion of this dissertation, we present potential avenues for future re-search works.• Physical layer security in BB-PLC with intentional jamming : Our SI cancel-lation techniques that we designed in Chapters 2 and 3 can be used to obtainseveral other power line networking benefits apart from the ones we discussedin Chapter 4. For example, [67] introduced the concept of secure MIMO BB-PLC using intentional jamming, along the lines of jamming-based physical layersecurity achieved in wireless communications [68]. A point-to-point IBFD com-munication link is inherently immune to eavesdropper attacks from unintendednodes present between the two legitimate network actors due to the super-position of two signals, which makes the received signal unintelligible to aneavesdropper. However, when either of the legitimate nodes has no data totransmit, it can send a jamming signal, which can be optimally beamformed todegrade the signal decoding performance at the eavesdropper. The first anal-ysis of the achievable secrecy rates in such secure MIMO BB-PLC links canbe found in [67]. Further analysis for different network topologies, locations ofthe eavesdropper, and power line channel and noise conditions are importantextensions.• IBFD relaying : IBFD can also be used to improve the relaying capacity in amulti-hop PLC network. Consider a typical AVLN we introduced in Chapter 1,a part of which is shown in Fig. 5.1. The primary transmitter (PT) transmits1575.3. Further Research DirectionsPT PR/ST SRFigure 5.1: A one-hop IBFD relay network with three PLC nodes.packets to the destination node, the secondary receiver (SR), via the interme-diate relay node. Such a network operation is characteristic of STAs in a CNcommunicating with the PCo in a PN via the CCo (see [60, Fig. 2.3]). AnIBFD relay node, which acts as the primary receiver (PR) and the secondarytransmitter (ST) can simultaneously forward packets to the SR while receiv-ing data from the PT. This reduces the end-to-end delay in the relay network.While such an IBFD relaying mechanism has been studied in the context ofwireless communications [65, 66], analysis for PLC in terms of the reductionin end-to-end delay, possible increase in SINR due to inter-node interferencefrom the PT, and achievable diversity gains with cooperative IBFD relaying inpower line channels that possess the keyhole property [197] is missing.• Proof-of-concept prototype: Prototype implementation, as with any systemsdesign, is a natural next step to verify practical gains achievable in powerline links using IBFD. A universal software radio peripheral (USRP) basedimplementation is a suitable beginning. Point-to-point communication linktesting requires at least one of the USRPs to be IBFD-capable, i.e., to use full-duplex daughter-boards, such as UBX–40 or UBX–160 [198]. 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Electron., vol. 48, no. 4, pp. 913–918,2002.[206] H. Meng, Y. L. Guan, and S. Chen, “Modeling and analysis of noise effectson broadband power-line communications,” IEEE Trans. Power Del., vol. 20,no. 2, pp. 630–637, 2005.[207] W. Chen and J. Choma, Feedback Networks: Theory and Circuit Applications(Advanced Series in Circuits and Systems). World Scientific Press, 2007.[208] D. Korpi, T. Riihonen, V. Syrja¨la¨, L. Anttila, M. Valkama, and R. Wichman,“Full-duplex transceiver system calculations: Analysis of ADC and linearitychallenges,” IEEE Trans. Wireless Commun., vol. 13, no. 7, pp. 3821–3836,2014.186Appendix AChannel and Noise ModelsA.1 SISO Channel GenerationTo generate SISO PLC channels, we use the open-source channel generator tool [107],which implements the bottom-up approach from [183]19. It allows us to choose differ-ent network conditions for an in-home setting by assigning the number of derivationboxes (DB), number of outlets (OL) associated with each box, the cable types andlengths, and the loads connected at each of the OL. It also provides an option togenerate a random network topology in which it automatically creates an in-homenetwork setting by randomly choosing the above parameters.A.1.1 LPTV ChannelsTo generate an LPTV channel condition, we consider an in-home scenario with har-monic and commuted load variations at some of the OLs in the network [109]. Theindoor topology that we have selected for the results in this paper consists of 25 OLs,of which 7 are without any load, each 5 are connected to commuted and to harmoni-cally varying loads that are both resistive and frequency-selective in nature, and theremaining 8 are connected to other time invariant resistive and frequency-selective19We note that a bottom-up approach is required for the performance evaluation of the proposedIBFD method, as it provides realizations for the frequency response together with the associatedaccess impedance. This would not be the case using phenomenological descriptions for the channelfrequency response as provided in e.g. [201–203].187A.2. MIMO Channel Generationloads. We consider a minimum channel coherence time of Tc = 700 µs for in-homepower lines, as reported in [63]. For North American mains frequency of 60 Hz, thisresults in 160·2·700·10−6 = 12 channel changes in one HC. We therefore generate 12 timeinvariant channels and switch from one to the other after every Tc. We apply this inevery HC to replicate the LPTV behavior in an actual PLC setting. These 12 chan-nels have a minimum and maximum sub-carrier attenuations of 30 dB and 78 dB,respectively, with a mean of about 53 dB for the selected network setting.A.1.2 Channels to Determine DRGFor generating a large set of channels, we use the random network generator settingin [107]. We limit the maximum number of DBs and OLs to 15 each to simulate arealistic in-home network. With such a setting, we obtain channels with sub-carrierattenuations varying between 6 dB to 77 dB with a mean of 40 dB. The statisticsof the channel frequency responses generated using [107] have been shown to closelymatch those from [109] whose average coherence bandwidth is about 200 kHz.A.2 MIMO Channel GenerationTo generate a set of 1500 random MIMO channels, we use the channel generator toolof [113]. To simulate a realistic in-home network setting, we lay a tree topology of 15outlet nodes and 20 branches, and vary the branch lengths from 1 to 100 meters, anddifferent loads conditions at each outlet varying between 1 Ω to 2 kΩ. We also varythe backbone conductor with the two available options of symmetric and ribbon-typecables. This results in channels with sub-carrier attenuations varying between 10 dBand 70 dB with a mean of 42 dB.188A.3. PLC Noise GenerationA.3 PLC Noise GenerationWe consider the PLC noise as a sum of background, narrowband, and impulse noise,as described in [36, Annex. F]20. The former two can be assumed stationary and aredescribed through their PSDs.A.3.1 Colored Background NoiseThe PSD for the colored background noise is modeled as a first order exponential,S(f) = a+ b|f |c, (A.1)where a, b, and c can be varied for different noise conditions, as specified in Table A.1.A.3.2 Narrowband NoiseThe narrowband noise PSD follows a parametric Gaussian function. We do notvary narrowband noise parameters for different noise levels as they are typicallyindependent of the network conditions and are usually introduced by interfering short-wave or amateur radio signals.A.3.3 Impulse NoiseThe impulse noise is generated in time domain using the sum-of-sinusoids model,p(t) = (u(t)− u(t− Td)) ·Nd−1∑i=0AiNde−αi|t|e−j2pifit,20The noise model described in the IEEE standard document [36] is the result of studies over manyyears published in e.g. [7, 204, 205]. We note that especially noise models can vary for differentscenarios. For example, [206] reports a set of measurements suggesting a non-Gaussian backgroundnoise.189A.3. PLC Noise Generationwhere u(·) is the unit step function, Nd is the number of damped sinusoids in animpulse, Td is the duration of the impulse, Ai is the impulse amplitude, and αi andfi are the damping factor and pseudo frequency of the ith sinusoid, respectively. Wegenerate NT such impulses for every mains cycle, spread by an inter-arrival time,tint. Nd = 3 and αi = 0.3 × 106 are fixed, and other parameters are adjusted togenerate different types of impulse noise, namely periodic synchronous (PS), periodicasynchronous (PA), and aperiodic (AP) impulse noise, and to account for differentnoise levels specified in [149], as shown in Table A.1.To enable reproducibility of our experiments, we have made the noise generatoravailable online [115].190A.3. PLC Noise GenerationTable A.1: Noise Statistics Used to Generate the Different Noise LevelsHigh Medium Lowfi (MHz)PS U [0.25, 0.5] U [0.25, 0.5] U [0.25, 0.5]PA U [2, 13] U [2, 13] U [2, 13]AP U [0.5, 1] U [0.5, 1] U [0.5, 1]Td(µs)PS 300 U [2,300] 2PA 10 U [1.5, 10] 1.5AP 150 U [15, 150] 15Ai (mV)PS 1500 U [5, 1500] 5PA 40 U [4, 40] 4AP 150 U [5, 150] 5tint (ms)PS U [10, 200] U [10, 200] U [10, 200]PA U [10, 200] U [10, 200] U [10, 200]AP E(λ−1 = 100) E(λ−1 = 100) E(λ−1 = 100)NTPS 10 U [1, 10] 1PA 5 U [0, 5] 0AP 10 U [1, 10] 1S(f) (dBm/Hz)a -145 U [-140, -145] -140b 53.23 U [52.23, 38.75] 38.75c -0.337 U [-0.337, -0.72] -0.72U [z1, z2] denotes a random number that is drawn from a uniform distribution between z1 and z2.E [λ−1 = λ0] denotes a random number drawn from an exponential distribution with mean of λ0.191Appendix BTransfer Function of the EchoChannelsB.1 Self-Interference Channel in SISO IBFDOperationWe consider the SISO-IBFD scenario illustrated in Fig. B.1 to derive an expression forthe echo channel transfer function HSI(f) =V3(f)VS(f)for a given frequency f . For brevity,we do not include the frequency-dependency in the following. We first express HSIin terms of the S-parameters of the hybrid and then represent the S-parameters interms of the outward reflection coefficient at P2 (ΓPLC). To this end, we terminate P2with impedance ZPLC and view the hybrid as a 2-port network between P1 and P3.With a reference impedance Z0 at P1 and P3, we obtain HSI from the S-parametersas [207, Ch. 3]HSI =V3VS=S21(1 + ΓL)(1− ΓS)2(1− S22ΓL)(1− ΓinΓS) , (B.1)192B.1. Self-Interference Channel in SISO IBFD Operation  a1b1a2b2a3b33-portActive HybridP1 P2P3ZPLCZSVSZRXV1 V2V3Z1 Z2Z3GPLCFigure B.1: Port connections of the active hybrid in SISO configuration.whereΓin = S11 +S12S21ΓL1− S22ΓLΓS =ZS − Z0ZS + Z0ΓL =ZRX − Z0ZRX + Z0.Our modified hybrid circuit of Fig. 2.1 has no transfer connection from P3 to P1,which results in S12 = 0 due to the reverse isolation of the op-amps. This results inΓin = S11. Therefore,HSI =S21(1 + ΓL)(1− ΓS)2(1− S22ΓL)(1− S11ΓS)= c · S21 , (B.2)193B.1. Self-Interference Channel in SISO IBFD Operationwhere c = (1+ΓL)(1−ΓS)2(1−S22ΓL)(1−S11ΓS) .Next, we represent S21 in terms of ΓPLC. By definition we have,S21 =b3a1∣∣∣∣∣a3=0(B.3)ΓPLC =a2b2, (B.4)where ai and bi are the inward and outward traveling waves of the hybrid, respectively.The amplifier and voltage divider stages and the reverse isolation of the op-amps usedin the hybrid ensure that the signal entering one port is completely transferred tothe next [100], resulting inb2 = a1 (B.5)b3 = a2 . (B.6)From (B.4)-(B.6) it follows thatb3a1=b3b2=a2ΓPLCa2= ΓPLC . (B.7)Finally, combining (B.2), (B.3), and (B.7), we have,HSI = c · ΓPLC . (B.8)The factor c depends on ΓL, ΓS, S11, and S22. Without loss of generality, we choosereference impedance Z0 = 100 Ω, which results in ΓL = 0. On the other hand, ZS istypically low [103], and gives ΓS ≈ −1. The values of S11 and S22 are independentof ZPLC, and only depend on Z1, Z2, ZS, ZRX, and Z0. Furthermore, since these194B.2. Self- and Cross-Interference Channels in MIMO-IBFD Operationimpedances are purely resistive, S11 and S22 are also frequency independent. ADSsimulations of our circuit in Fig. 2.1 indicate S11 = S22 = 0.1 for the given Z1, Z2,ZS, ZRX, and Z0. With these values, we obtain c = 0.9 for our hybrid.B.2 Self- and Cross-Interference Channels inMIMO-IBFD OperationWe consider the block diagram for a 2 × 2 MIMO PLC system in Fig. 2.12. Thevoltage reflection matrix ΓPLC is calculated as [172, Ch. 7]ΓPLC =Γ11 Γ12Γ21 Γ22 = [ZPLC −Zhyb][ZPLC +Zhyb]−1.We first study SI on Hybrid-1 (see Fig. 2.12). Following the same approach as forthe SISO case in Appendix B.1, we view the hybrid as a 2-port network with portsP1 and P3 as the two ports. From the derivation in Appendix B.1, we obtain the SIchannel transfer functionH11 =V3VS= c11Γ11 , (B.9)where c11 =(1+ΓL)(1−ΓS)2(1−S22ΓL)(1−S11ΓS) and Sij are the S-parameters of Hybrid-1.We extend this analysis further to the CI channel from transmitter 2 to receiver1, i.e., P1 of Hybrid-2 and P3 of Hybrid-1 are the two ports. Considering the signaldefinitions in Fig. 2.12 and analogous to (B.4) and (B.5), we now havea2 = Γ12b′2 (B.10)b′2 = a′1 . (B.11)195B.2. Self- and Cross-Interference Channels in MIMO-IBFD OperationFrom (B.6), (B.10), and (B.11), we obtainb3a′1=b3b′2=a2b′2=Γ12b′2b′2= Γ12 (B.12)and thusH12 =V3V ′S= c12 · Γ12 , (B.13)where c12 =(1+ΓL)(1−ΓS)2(1−S22ΓL)(1−S11ΓS) . Following the same analysis leads to the SI and CIchannel observed at Hybrid-2,H21 =V ′3VS= c21 · Γ21 (B.14)H22 =V ′3V ′S= c22 · Γ22 , (B.15)where we replace the S-parameters from the Hybrid-1 with those from Hybrid-2 tocompute the constants c21 and c22.196Appendix CAn Approximate Expression forγADCIn this appendix, we formulate an approximate expression of γADC for an ADC op-eration that incorporates signal clipping of high PAPR OFDM signals, in order tominimize the overall distortion and quantization noise power. We begin with theexact relation of (3.8), and express it in logarithmic scale asγADC,dB = −10 · log10(1/322m(Vclipσinp)2+√8pi(σinpVclip)3exp(−Vclip22σ2inp)). (C.1)It is evident from (C.1) that γADC,dB is dependent on the clipping ratio,Vclipσinp. Ithas been shown that the optimal clipping ratio,(Vclipσinp)opt, nearly varies quadraticallywith m, and that its least squares fit can be expressed as(Vclipσinp)opt= αm2 + βm+ δ,where α, β, and δ are the quadratic polynomial coefficients [97]. By tuning our GainControl to force the PGA to consistently provide this optimal clipping ratio of the197Appendix C. An Approximate Expression for γADC0 2 4 6 8 10 12 14 160102030405060708090mSignal−to−noise−and−distortion ratio, dB  ActualApproximateFigure C.1: Variation of γADC,dB from (C.2) and γˆADC,dB of (C.3) with m.received signal to the ADC, we can rewrite (C.1) asγADC,dB =− 10 · log10((αm2 + βm+ δ)23 · 22m +√8pi(αm2 + βm+ δ)3exp(− (αm2 + βm+ δ)22)).(C.2)It is clear from (C.2) that γADC,dB is not strictly linearly with m. However, a plotof γADC,dB versus m in Fig. C.1 shows that γADC,dB is nearly linear in m. We cantherefore find an approximate linear expression for γADC,dB using a first-order Taylorseries expansion of (C.2).Since we use a 12-bit ADC, we evaluate the first order Taylor series expansion ofγADC,dB at m = 12. By using {α, β, δ} = {−0.0053, 0.3763, 1.2627} [97], we find the198Appendix C. An Approximate Expression for γADClinear approximation for γADC,dB to beγˆADC,dB = 5.5m− 3.6. (C.3)We observe from Fig. C.1 that this approximation provides a close fit to (C.2).199Appendix DADC Bits lost in IBFDThis derivation of the number of ADC bits lost with an IBFD operation followsa similar derivation in [208]. However, we use the γˆADC,dB expression derived inAppendix C and the system model described in Section 3.2.The additional ADC bits lost due to IBFD can be expressed as the differencebetween the loss of bits for quantizing the SOI in HD and IBFD modes. Therefore,we use (3.10) to writeblost =105.5(log10(σ2inp,FDPTXGPLC)− log10(σ2inp,HDPTXGPLC))= λ · log10(σ2inp,FDσ2inp,HD), (D.1)where λ = 20/11.SISO : For a point-to-point SISO link, σ2inp,FD = PTX(Gtotal + GPLC) + PN, andσ2inp,HD = PTXGPLC + PN. We can thus re-write (D.1) asblost = λ · log10(1 +PTXGtotalPTXGPLC + PN). (D.2)MIMO : For a MIMO scenario, σ2inp,FD,i = PTX(∑NnearTj=1 Gtotal,ij +∑N farTj=1 GPLC,ij)+PN,i and σ2inp,HD,i = PTX∑N farTj=1 GPLC,ij + PN,i, at the ith receiver. Hence, (D.1) for200Appendix D. ADC Bits lost in IBFDMIMO can be re-written for the ith receiver asblost,i = λ · log101 +PTXNnearT∑j=1Gtotal,ijPTXN farT∑j=1GPLC,ij + PN,i . (D.3)201Appendix EInterference Channel TransferFunctions at the Stand-aloneReceiverIn this appendix, we consider a 2×3 MIMO transceiver and derive the channel transferfunctions of the two CI channels at the stand-alone receiver (i.e., operating withoutan associated transmitter). Throughout this derivation, we consider a frequencyselective interference channel created as a result of a frequency selective networkimpedance. However, we drop the frequency index for brevity.We first derive the interference channel transfer function from the first transceiverto the stand-alone receiver. To aid our derivation, we decompose the line-hybridinterface (shown in red in Fig. 3.2) into three equivalent circuits shown in Fig. E.1,by viewing the interface as a three port network whose Z-parameters are describedby the power line input impedance matrix,ZPLC =Z11 Z12 Z13Z21 Z22 Z23Z31 Z32 Z33 . (E.1)Fig. E.1(a) shows the equivalent circuit at the first transceiver. We replace the202Appendix E. Interference Channel Transfer Functions at the Stand-alone ReceiverVhyb,1=2VTX,1ZhybZ11Z12I2Z13I3Z21I1Z23I3Z31I1Z32I2Zhyb ZRXZ22 Z33VRXI1 I2 I3(a)Vhyb,1=2VTX,1ZhybZ11Z12I2Z13I3Z21I1Z23I3Z31I1Z32I2Zhyb ZRXZ22 Z33VRXI1 I2 I3(b)Vhyb,1=2VTX,1ZhybZ11Z12I2Z13I3Z21I1Z23I3Z31I1Z32I2Zhyb ZRXZ22 Z33VRXI1 I2 I3(c)Figure E.1: Equivalent circuits of the power line-hybrid interface (shown in red inFig. 3.2) using the Z-parameters described by the input impedance matrix of thepower line.hybrid with its Thevenin equivalent source voltage and impedance. Since the hybridis designed to completely transfer voltage from one port to a matched load at theadjacent port in one direction [100], the Thevenin equivalent voltage of the hybrid,Vhyb,1 = 2VTX,1, where VTX,1 is the signal voltage at the hybrid port connected to thetransmitter. The Thevenin equivalent impedance is the hybrid impedance shown tothe power line, Zhyb = 100 Ω, which is set to match the typical power line impedance.At the second transceiver, shown in Fig. E.1(b), we short the voltage source in ac-cordance with the superposition theorem, and replace the hybrid with its Theveninequivalent impedance of Zhyb. Finally, we represent the stand-alone receiver with itsimpedance of ZRX in Fig. E.1(c).203Appendix E. Interference Channel Transfer Functions at the Stand-alone ReceiverApplying Kirchoff’s voltage law in these three circuits provides usI1(Zhyb + Z11) + I2Z12 + I3Z13 = 2VTX,1, (E.2)−I1Z21 − I2(Zhyb + Z22)− I3Z23 = 0, (E.3)−I1Z31 − I2Z32 − I3(ZRX + Z33) = 0, (E.4)where I1, I2, and I3 are the currents flowing in the circuits of Fig. E.1(a), Fig. E.1(b),and Fig. E.1(c), respectively. Further, we have the voltage drop at the stand-alonereceiver,VRX = −I3ZRX. (E.5)By solving the three equations (E.2), (E.3), and (E.4) for three unknowns I1, I2, andI3, and by using (E.5), we obtain the CI transfer function from the first transmitterto the stand-alone receiver asVRXVTX,1=−2ZRX(δ31 + δ21δ32)(Zhyb + Z11) + Z12δ32 + Z13, (E.6)whereδ31 = −ZRX + Z33Z31(E.7)δ21 = −Z32Z31(E.8)δ32 = − Z23 + Z21δ31Zhyb + Z22 + δ21Z21. (E.9)Next, we represent this transfer function in terms of the reflection co-efficient atthe line-hybrid interface. The transceiver impedance matrix, ZTR, as seen from the204Appendix E. Interference Channel Transfer Functions at the Stand-alone Receiverline can be written asZTR =Zhyb 0 00 Zhyb 00 0 ZRX . (E.10)We then have the reflection co-efficient matrix at the line-hybrid interface asΓPLC =Γ11 Γ12 Γ13Γ21 Γ22 Γ23Γ31 Γ32 Γ33= (ZPLC − ZTR)(ZPLC + ZTR)−1. (E.11)Simplifying (E.11) using (E.1) and (E.10) reveals that VRXVTX,1= Γ31. Similarly, we alsoobtain the interference channel transfer function from the second transmitter to thestand-alone receiver as VRXVTX,2= Γ32.205

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