Fiber-connected Massively Distributed Antenna Systems:Energy Efficiency and Interference ManagementbyHaoming LiB.Eng., Sichuan University, 1994M.Sc., Sichuan University, 1997M.A.Sc., Carleton University, 2007A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Electrical and Computer Engineering)The University Of British Columbia(Vancouver)October 2013? Haoming Li, 2013AbstractThe density of wireless access nodes keeps increasing to provide ubiquitous wireless access andmeet the ever-increasing traffic demand. However, the shrinking distance among neighboring ac-cess nodes causes excessive interference and the increasing number of access nodes incurs a higherpower consumption. A careful management of interference ensures a high system capacity. Animproved energy efficiency in wireless access network prevents the fast growth of wireless com-munication systems from aggravating the global energy crisis. In this thesis, we propose a novelarchitecture, Fiber-connected Massively Distributed Antennas (FMDA), to address the challengesof managing interference and improving energy efficiency in wireless access networks.A FMDA system is composed of a centralized processing system connected to a large numberof antennas via optical cables. The centralized processing system processes all the radio signals andallocates all the radio resources to better manage interference; each antenna contains much simplercircuits than conventional access nodes and therefore allows a massive deployment and reducesthe antenna power consumption. We first propose a novel multi-cell wireless local area network(WLAN) system based on our proposed FMDA architecture, where the centralized processingsystem can see the entire spectrum usage across the coverage area and control the radio signalsto be sent to each antenna, thus allowing a better management of inter-cell interference. We thenpropose an antenna scheduling scheme in a novel cellular system composed of fiber-connectedfemto access nodes to manage the excessive inter-femtocell interference and reduce the energiesconsumed by non-sleeping access nodes, thus simultaneously improving the spectral and energyefficiency.iiWhen the number of cooperating antennas increases, the power consumption of signal pro-cessing spikes, thus drastically degrading the overall energy efficiency due to much smaller radiotransmission power levels. Focusing on two typical indoor environments, office buildings and largepublic venues, we propose two low-complexity downlink transmission schemes to address theseenergy efficiency challenges.iiiPrefaceThis thesis is based on the following publications. Dr. Victor C. M. Leung, my supervisor, co-authored all the papers and supervised all the research.Journal papers published/submitted:1. H. Li and V. C. M. Leung, ?Low complexity zero-forcing beamforming for distributed mas-sive MIMO systems in large public venues,? Journal of Communications and Networks, vol.15, no. 4, pp. 370-382, 2013. The material is incorporated in Chapter 5.2. H. Li and V. C. M. Leung, ?Energy-efficient low-complexity zero-forcing beamforming viabanded matrix inversion in indoor massively distributed antenna systems,? Submitted, underthe second round of review. The material is incorporated in Chapter 4.3. H. Li, A. Attar, and V. C. M. Leung, ?Energy conservation via antenna scheduling in fiber-connected femto base stations,? Mobile Networks and Applications, vol. 17, no. 5, pp.685-694, 2012. The material is incorporated in Chapter 3.4. H. Li, J. Hajipour, A. Attar, and V. C. M. Leung, ?Efficient HetNet implementation usingbroadband wireless access with fibre-connected massively distributed antennas architecture,?IEEE Commun. Mag., vol. 18, pp. 72-78, 2011. The material is incorporated in Chapter 3.5. A. Attar, H. Li, and V. C. M. Leung, ?Green last mile: How fiber-connected massivelydistributed antenna systems can save energy,? IEEE Commun. Mag., vol. 18, pp. 66-74,iv2011. The material is incorporated in Chapter 3.6. H. Li, A. Attar, V. C. M. Leung, and Q. Pang, ?Collision reduction in cognitive wireless localarea network over fibre,? International Journal on Advances in Internet Technology, vol. 3,no. 1-2, pp. 1-12, 2010. The material is incorporated in Chapter 2.Conference papers published:1. H. Li, A. Attar, Q. Pang, and V. C. M. Leung, ?Collision avoidance and mitigation in cogni-tive wireless local area network over fibre,? in Proc. IEEE INTERNET?09, Cannes, France,2009. The material is incorporated in Chapter 2.2. H. Li, Q. Pang, and V. C. M. Leung, ?Cognitive access points for dynamic radio resourcemanagement in wireless LAN over fiber,? in Proc. WWRF 20th meeting, Ottawa, Canada,Apr. 2008. The material is incorporated in Chapter 2.The following explains the co-authorship of each paper:? Journal paper 3 was co-authored with Dr. Alireza Attar. I proposed the scheduling scheme,established the power consumption model, analyzed energy efficiency and conducted simu-lations. Dr. Attar provided inputs to the system architecture and comments on performanceevaluation.? Journal paper 4 was co-authored with Mr. Javad Hajipour and Dr. Alireza Attar. I estab-lished the system model and evaluated the system performance. Mr. Hajipour providedchannel configurations and frequency-selective fading channel models. Dr. Attar proposedwhere Fiber-connected Massively Distributed Antennas fit in a heterogeneous network andorganized the structure of the paper.? Journal paper 5 was co-authored with Dr. Alireza Attar. I established the power consump-tion model, conducted simulations and wrote the simulation description and performancevevaluation in the paper. Dr. Attar organized the structure of the paper and surveyed greencommunication techniques in cellular networks.? Journal paper 6 was co-authored with Dr. Alireza Attar and Dr. Qixiang Pang. I reviewedprevious research in radio over fibre, proposed two interference management schemes andevaluated the system performance. Dr. Attar provided inputs to the performance evaluation.Dr. Pang provided inputs to the comparison method.? Conference paper 1 were co-authored with Dr. Alireza Attar and Dr. Qixiang Pang. I re-viewed previous research in radio over fibre, proposed two interference management schemesand evaluated the system performance. Dr. Attar provided inputs to the performance evalua-tion. Dr. Pang provided inputs to the comparison method and how to evaluate wireless localarea network performance.? Conference paper 2 were co-authored with Dr. Qixiang Pang. I proposed the wireless localarea network over fibre architecture and described the functions of the cognitive access point.Dr. Pang provided inputs to interference scenarios in the 2.4 GHz band.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview of Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1 Distributed Antenna System . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Radio over Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.3 Massive MIMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.4 Heterogeneous Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4vii1.1.5 Green Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Motivation of Fiber-connected Massively Distributed Antennas . . . . . . . . . . 91.2.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.2 Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 Summary of Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.4.1 Interference Management in Cognitive WLAN over Fiber . . . . . . . . . 141.4.2 Energy Conservation in Fiber-connected Femto Base Stations . . . . . . . 151.4.3 Low-complexity Beamforming in Office Buildings . . . . . . . . . . . . . 161.4.4 Low-complexity Beamforming in Large Public Venues . . . . . . . . . . 171.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Interference Management in Cognitive Wireless Local Area Network over Fiber 202.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2 Related Work on WLAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3 Collision Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3.1 Load Balancing Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3.2 Transmitter and Receiver Diversity Method . . . . . . . . . . . . . . . . . 272.4 Performance Evaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.4.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.4.2 Effects of Receiver Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . 312.4.3 Spatially Uniformly Distributed Traffic . . . . . . . . . . . . . . . . . . . . 322.4.4 Spatially Non-uniformly Distributed Traffic . . . . . . . . . . . . . . . . . 422.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Energy Conservation via Antenna Scheduling in Fiber-connected Femto Base Sta-tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48viii3.2 Power Consumption in Fiber-connected Massively Distributed Antennas . . . . . 503.2.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.2 Power Consumption Model . . . . . . . . . . . . . . . . . . . . . . . . . . 513.3 Energy Efficiency in Single Femto-CoMP . . . . . . . . . . . . . . . . . . . . . . . 553.3.1 Approximate Spectral Efficiency . . . . . . . . . . . . . . . . . . . . . . . 553.3.2 Maximize Energy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4 Energy Efficiency in Multiple Femto-CoMPs . . . . . . . . . . . . . . . . . . . . . 593.4.1 Motivation of Antenna Scheduling . . . . . . . . . . . . . . . . . . . . . . 593.4.2 Antenna Scheduling Based on Two-user MIMO . . . . . . . . . . . . . . . 603.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.5.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.5.2 Spectral Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.5.3 Energy Efficiency vs. Spectral Efficiency . . . . . . . . . . . . . . . . . . 663.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674 Energy-efficient Low-complexity Zero-forcing Beamforming via BandedMatrix In-version in Indoor Fiber-connected Massively Distributed Antenna Systems . . . . 694.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.1.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.2.1 Channel Matrix H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.2.2 Precoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.2.3 Stream Power Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.3 Banded Inversion of Matrices with Compositely Decayed Off-Diagonals . . . . . 754.3.1 Banded Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.3.2 Striped Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77ix4.4 SINR Loss Using Dense W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.4.1 Path Loss Matrix ED?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4.2 Path Loss Matrix EP?,? ,? . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.4.3 Random Matrices EZ?and EPRZ?,? . . . . . . . . . . . . . . . . . . . . 804.5 SINR Loss Using Sparse W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.5.1 SINR Loss in EZ?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.5.2 SINR Loss in EPRZ?,? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.6 Downlink Energy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.6.1 Power Consumption of Radio-over-Fiber and Downlink Baseband Process-ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.6.2 Floating-point Operation Count of Beamforming . . . . . . . . . . . . . . 874.7 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.7.1 SINR Loss in EZ?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.7.2 SINR Loss in EPRZ?,? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.7.3 Downlink Energy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 924.7.4 Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965 Low Complexity Zero-forcing Beamforming for Massively Distributed AntennaSystems in Large Public Venues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.2.1 Channel Matrix H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.2.2 Compositely Decayed Multi-banded Path Loss Matrix . . . . . . . . . . . 1035.2.3 Precoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.2.4 Stream Power Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.3 Multi-banded Matrix Inversion in Two-dimensional Networks . . . . . . . . . . . 106x5.3.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.3.2 Computation Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.4 Residual Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.4.1 Deterministic Channel Matrix . . . . . . . . . . . . . . . . . . . . . . . . . 1105.4.2 Stochastic Channel Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.1 Summary of Work Accomplished . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137A Derivation of lg(I?i) for H ? EP?,? ,? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150B Inverse of EZ?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152C Inverse of EPRZ?,? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157D Derivation of (?p+1??p) for H ? EZ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161E Inverse of ED?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163F Derivation of E{ln[max1?i?N(? fi/gi?2)]} . . . . . . . . . . . . . . . . . . . . . . . . . . 164xiList of TablesTable 2.1 Simulation parameters in cognitive WLAN over fiber systems . . . . . . . . . 30Table 3.1 Power consumption coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Table 3.2 Floating-point operation count of scheduling: f (Nc,NU) . . . . . . . . . . . . 55Table 4.1 Algorithm: Banded forward/backward substitution . . . . . . . . . . . . . . . . 76Table 4.2 Algorithm: Striped LU factorization of H . . . . . . . . . . . . . . . . . . . . . 78Table 4.3 Types of channel matrix H (0 < ? < 1,2 ? ? ? 4) . . . . . . . . . . . . . . . . . 79Table 4.4 Floating-point operation count of banded matrix inversion and stream powerallocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88Table 4.5 Simulation parameters in office buildings . . . . . . . . . . . . . . . . . . . . . 91Table 5.1 Algorithm: Multi-banded LU factorization . . . . . . . . . . . . . . . . . . . . 108Table 5.2 Algorithm: Multi-banded forward/backward substitution . . . . . . . . . . . . 109Table 5.3 Complexity comparison of the proposed and conventional ZFBF (2 ? p ??N) 110Table 5.4 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Table 5.5 Simulation parameters of SDU, SDC and SAC. SDU: under-floor-mounted dis-tributed antennas; SDC: ceiling-mounted distributed antennas; SAC: ceiling-mounted array antennas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Table C.1 Constants used in the analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160xiiList of FiguresFigure 1.1 Motivation of Fiber-connected Massively Distributed Antennas. WLAN: wire-less local area network. ISM band: the industrial, scientific, and medical band.LTE: Long-Term Evolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 2.1 A cognitive WLAN over fiber system and the structure of the cognitive accesspoint (CogAP). ISM band: the industrial, scientific, and medical band. E/O:electrical-optical converter. O/E: optical-electrical converter. . . . . . . . . . 22Figure 2.2 Collision reduction: Diversity and two-channel-operation. BSS: Basic ServiceSet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 2.3 Frequency plan in simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 2.4 Outage probabilities in a WLAN Extended Service Set. Two antennas (or ac-cess points) are located at (15,15) and (45,15). Carrier-sensing threshold =-70 dBm. Conv: conventional WLAN. . . . . . . . . . . . . . . . . . . . . . . 33Figure 2.5 Reduction in outage probability withMRC and EGC. Carrier-sensing threshold= -70 dBm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Figure 2.6 Outage probabilities in a WLAN Extended Service Set. Each sub-figure showsthe outage probability of a station when it is placed on a cross section (indicatedby a fixed y value). Carrier-sensing threshold = -70 dBm. Conv: conventionalWLAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34xiiiFigure 2.7 Reduction in outage probability withMRC and EGC. Carrier-sensing threshold= -70 dBm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 2.8 TCP throughput and average packet error rate of CBR downlink vs. Numberof stations. CBR: constant bit-rate traffic. PER: packet error rate. Traffic: VoIPuplink/downlink + FTP downlink. MRC-up: MRC is used for uplink diversity.EGC-down: EGC is used for downlink diversity. Conv. WLAN: conventionalWLAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 2.9 TCP throughput and average packet error rate of CBR traffic vs. Number ofstations. Traffic: IPTV downlink + FTP downlink. MRC-down: MRC is usedfor downlink diversity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 2.10 TCP throughput and average packet error rate of CBR traffic vs. Number ofstations. Traffic: VoIP uplink/downlink + FTP uplink/downlink. . . . . . . . 39Figure 2.11 TCP throughput degradation of two-channel-operation method in heavily loadednetworks. Traffic: VoIP uplink/downlink + FTP uplink/downlink. . . . . . . . 40Figure 2.12 Packet error rate degradation of CBR traffic (two-channel-operation in lightlyloaded networks). Traffic: IPTV downlink + FTP downlink. . . . . . . . . . . 40Figure 2.13 Effects of synchronization interval (SI). . . . . . . . . . . . . . . . . . . . . . . 42Figure 2.14 Spatially non-uniformly distributed traffic. Hotspot locations are numberedfrom 1 to 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 2.15 TCP throughput and average packet error rate of CBR downlink vs. Hotspotlocation. Traffic: VoIP uplink/downlink + FTP downlink. Antenna-distance =30 m. Shadowing standard deviation = 3.5 dB. . . . . . . . . . . . . . . . . . . 44Figure 2.16 TCP throughput and average packet error rate of CBR downlink vs. Hotspotlocation. Traffic: VoIP uplink/downlink + FTP downlink. Antenna-distance =30 m. Shadowing standard deviation = 10 dB. . . . . . . . . . . . . . . . . . . 46Figure 2.17 Effects of antenna-distance. Traffic: VoIP uplink/downlink + FTP downlink.Antenna-distance ?{45m, 60m}. Shadowing standard deviation = 10 dB. . . 47xivFigure 3.1 Fiber-connected femto base stations with two service providers. . . . . . . . 50Figure 3.2 Simulation scenarios for femtocell and FMDA. Antennas of FMDA-Nr-Nc-Ntsare scheduled in up to four time slots. . . . . . . . . . . . . . . . . . . . . . . . 62Figure 3.3 Spectral and energy efficiency vs. Transmission power per antenna. . . . . . 65Figure 3.4 Energy efficiency vs. Spectral efficiency under different Ptx (10?3 ?102 mW/MHz).Mbits/joule: 106 bits/joule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 4.1 A Fiber-connected Massively Distributed Antennas system. CPS: centralizedprocessing system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 4.2 LU factorization of banded and striped matrices. Blank areas are zeros. . . . 77Figure 4.3 Entries of Wp. H ? EZ? . ? ? {0.1,0.2,0.3,0.4,0.5}. N=50. p=40. . . . . . . 89Figure 4.4 SINR using dense and sparse W. H ? EZ?. ? ? {0.82,0.45,0.20,0.09}. N=50. 90Figure 4.5 The ?p slowly increases with p. H ? EZ? . N=50. Sim(recur): Simulation basedon recursive equations. Analy(log-normal): Asymptotic analysis based on log-normal assumption. Sim(? ? {0.01,0.1,0.45,0.62,0.82,1}): Simulation of ?p. 90Figure 4.6 Entries of Wp. H ? EPRZ?,? . ? ? {2,3,4}. ? ? {0.1,0.5,0.9,1}. N=50.p=40. 1-term: LW (1)k . 3-term: LW(3)k . All-term: the simulations based on{c0,c1,?,ck?2} (See Appendix C for details). As the effect of ? is alreadydeducted from the Y-axis, all ? values produce the same curve for a given ?value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Figure 4.7 SINR using dense and sparse W. H ? EPRZ?,? . sim: simulation; analy: anal-ysis. ? = 3. ? ? {1,0.82,0.67,0.45,0.20,0.09}. N=50. . . . . . . . . . . . . . 92Figure 4.8 Energy efficiency ?e vs. Spectral efficiency ?s (Ns = 7). H ? EPRZ?,? . ? = 3.? = 0.45. N=50. The width p ranges from 2 to 26. Mbits/joule: 106 bits/joule. 94Figure 4.9 Power consumption contributed by radio-over-fiber and beamforming (Ns = 7).RoF: radio-over-fiber. The sparse scheme is used. H ? EPRZ? ,? . ? = 3.? = 0.45. N=50. The width p ranges from 2 to 26. . . . . . . . . . . . . . . . 94xvFigure 4.10 Energy efficiency ?e vs. Spectral efficiency ?s (Ns = 1). H ? EPRZ?,? . ? = 3.? = 0.45. N=50. The width p ranges from 2 to 26. . . . . . . . . . . . . . . . 95Figure 5.1 A large public venue with M2 under-floor mounted antennas uniformly de-ployed over an M?M grid. CPS: centralized processing system. . . . . . . . 101Figure 5.2 Log-scale contour of path loss matrix. Parameters: N=100, M=10, ?=0.3dB/m, ?=2, ?=10. Black pattern: the mask to obtain V3. . . . . . . . . . . . . 104Figure 5.3 Multi-banded LU factorization. Blank areas are zeros. . . . . . . . . . . . . . 107Figure 5.4 Outband drop estimation. Red dash line: the main diagonal containing dom-inating entries. O0: outband drop in the main band. Ol: outband drop in thel-th side band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Figure 5.5 Differential decay of H and W. ? ? {0.3,1.2,2.4}. The decay is defined asE[lg(?hk,k+b/hk,k+b?1?2)] for H and E[lg(?wk+b,k/wk+b?1,k?2)] for W. . . . . . 117Figure 5.6 Energy efficiency ?e vs. Spectral efficiency ?s. SDU: under-floor-mounted dis-tributed antennas; SDC: ceiling-mounted distributed antennas; SAC: ceiling-mounted array antennas. The width p increases from 2 to 11 for SDU; p=11for SDC. ?=2. Ns=7. Parameters for SDU: {?=0.3, ?=6, Gt=5 dB}. . . . . 123Figure 5.7 SDU: Power consumption contributed by radio-over-fiber and beamforming.RoF: radio-over-fiber. ?=2. ?=0.3. ?=6. Gt=5 dB. Ns=7. . . . . . . . . . . . 123Figure 5.8 Average SINR vs. Width in SDU, SDC and SAC. 10 user-drops. 100 fadingsamples per user-drop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure 5.9 CDF of SINR in SDU, SDC and SAC. 1 user-drop. 1000 fading samples. p=11for SDU and SDC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure 5.10 SDU: CDF of antenna transmission power. . . . . . . . . . . . . . . . . . . . . 125Figure 5.11 SDU: Bounds of average SINR. ?=2. ? ? {0.1,0.3,0.5}. ?=6. Gt=5 dB. . . 126Figure 5.12 SDU: Average SINR vs. Width. ?=2. ? ? {0.1,0.2,0.3}. ?=6. Gt=5 dB. . . 126xviFigure 5.13 SDU: Gt effect on SINRs in dense and sparse scheme. ?=2. ?=0.3. ?=6.Gt ? {0,1,?,5} dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Figure 5.14 SDU: Dense scheme vs. Krylov subspace method (L=6). ?=2. ?=0.1. ?=6.Gt ? {0,5} dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129xviiList of Symbols? Per-wall penetration loss in linear scale, i.e., ? = 10?L/20. 74? Linear attenuation coefficient in the unit of dB/meter 98B Channel bandwidth 55Bp The set of banded matrices with width p 72?k The distance between the k-th user and the k-th antenna 74?SINR SINR loss from using sparse precoding, defined as SINRdw?SINRsw. 82dk,b The distance between the k-th user and the b-th antenna in meters 102D Inter-antenna distance in the unit of meter in a large public venue 116Dp The difference between the true channel matrix and the banded channelmatrix, given by H?Hp.75? Path loss exponent 74?e Energy efficiency in the unit of bit/joule 55?s Average spectral efficiency per user in the unit of bps/Hz/User 55Ep The difference between the sparse precoding matrix and the dense pre-coding matrix, given by Sp?Wp.83ED?The Toeplitz matrix with exponentially decayed off-diagonal entries atrate ? , i.e., entry (i, j) is given by ? ?i? j?.79EP?,? ,? EPR? ,? with fixed ? , representing a Toeplitz matrix H where hi j = ?i?j???/2? ?i? j? for i ? j and ?? ???/2?0 for i = j (?? ? < 0.5).79xviiiEPR? ,? The set of random matrices whose off-diagonal entries decay both expo-nentially at rate ? and polynomially at rate ? , i.e., entry (i, j) is given by?i? j+?i???/2? ?i? j?, where ?i is the normalized distance between the i-thuser and the i-th antenna, subject to U(?0.5,0.5).79EPRZ?,? The Hadamard product of a ZMCSCG matrix and an EPR?,? matrix. 79EZ?The Hadamard product of a ZMCSCG matrix and an ED?matrix. 79fk,b The small-scale fading between the k-th user and the b-th antenna 115F Small-scale fading matrix 74Gr Receiver antenna gain in dB 116Gt Transmitter antenna gain in dB 116hk,b The channel gain between the k-th user and the b-th antenna 115H Full channel matrix 16Hp Banded channel matrix in Chapter 4, or multi-banded channel matrix inChapter 5.72Ii Linear-scale residual interference power of the i-th stream 78I?i Linear-scale residual interference power of the i-th stream assuming equalstream power allocation79I?i Log-scale residual interference power of the i-th stream averaged overuser location and fading.80I?(D)i Log-scale residual interference power of the i-th stream averaged overuser location and fading when dense precoding is used.83I?(S)i Log-scale residual interference power of the i-th stream averaged overuser location and fading when sparse precoding is used.83? Rician K-factor in linear scale 121L Per-wall penetration loss in dB 74xixM The number of lanes/files in an antenna grid that is deployed in a largepublic venue.98MBM,p The set of multi-banded matrices with inter-band distance M and width p,in which entry (k,b) is zero for max(?k%M?b%M?, ??k/M???b/M??) ? p.100MEPRM,?,? The set of multi-banded matrices defined in the context of large publicvenues. The matrices have exponentially and polynomially decayed off-diagonal entries and uniformly distributed user-antenna locations.103MEPRZM,?,? The Hadamard product of anMEPRM,?,? matrix and a ZMCSCGmatrix 103Nc The number of antennas in a femto-CoMP cluster 49NCoMP Total number of femto-CoMP clusters 51Nr Total number of distributed antennas 49Ns The number of OFDM symbols per scheduling interval 87Nsc The number of subcarriers per resource block in LTE 53Nts Total number of time slot sets in a FMDA system composed of multiplefemto-CoMP clusters49NU Total number of active users in a femto-CoMP cluster 51NUtotal Total number of active users in a FMDA system 51Op Outband drop at width p, which is defined as the log-ratio of the acceler-ated and the normal decay in Wp.81p The width of a banded matrix where entry (k,b) is zero for ?k?b? ? p. 72P Per-antenna transmission power constraint 75PRF Power consumption contributed by radio-over-fiber components 51Psp Power consumption contributed by signal processing components 51PspB Power consumption contributed by base amount 51Pspc Sum transmission power constraint 75xxPspMS Power consumption contributed by zero-forcing beamforming and userscheduling51Ptot Total power consumption of a FMDA system 51Ptx Transmission power per antenna 54Sp Sparse precoding matrix 75SINRdw SINR measured in dB when dense precoding is used. 82SINRsw SINR measured in dB when sparse precoding is used. 82SIRdw SIR measured in dB when dense precoding is used. 112SIRsw SIR measured in dB when sparse precoding is used. 114V Path loss matrix 74W Precoding matrix 16Wp Dense precoding matrix 75xxiGlossaryAP access pointBS base stationBSS Basic Service SetCBR constant bit-rateCDF cumulative distribution functionCogAP cognitive access pointCoMP coordinated multi-point transmissionsCPS centralized processing systemCPRI common public radio interfaceC-RAN cloud-based radio access networkCSI channel state informationDAS distributed antenna systemEGC equal-gain combingESS Extended Service SetxxiiFDD frequency division duplexflop floating-point operationFMDA Fiber-connected Massively Distributed AntennasFTP File Transfer ProtocolGOPS giga-operation-per-secondHetNet Heterogeneous Networksi.i.d. independent and identically distributedIPTV IP televisionISM industrial, scientific, and medicalLTE Long-Term EvolutionMAC medium access controlMIMO multiple-input multiple-outputMRC maximum-ratio combiningOFDM orthogonal frequency-division multiplexingPAPC per-antenna power constraintPER packet error ratePF proportional fairnessPF-SUS proportional fairness scheduler based on semi-orthogonal user selectionRoF radio over fiberxxiiiRRH remote radio headRR-SUS round-robin scheduler based on semi-orthogonal user selectionSI synchronization intervalSIR signal-to-interference-ratioSINR signal-to-interference-noise-ratioSNR signal-to-noise-ratioSPC sum power constraintTCP Transmission Control ProtocolTDD time division duplexVoIP Voice over Internet ProtocolWF waterfillingWLAN wireless local area networkZFBF zero-forcing beamformingZMCSCG zero-mean circularly symmetric complex GaussianxxivAcknowledgmentsMy greatest thanks go to my supervisor, Dr. Victor C. M. Leung, for his guidance on my researchdirections, knowledge and insights in my research areas, valuable advice on my research methods,continuous encouragements to my research findings, and consistent supports on my study andresearch during all these years. Without his guidance and supports, this thesis would have beenimpossible.I would like to thank my supervisory committee members, Dr. Lukas Chrostowski and Dr. LutzLampe, for their valuable advice on radio-over-fiber techniques, energy-efficiency, and user-trafficconsiderations. I would like to thank Dr. Vikram Krishnamurthy for his valuable comments onthe analysis. I would like to thank Dr. Peyman Servati for chairing my PhD department exam. Iam grateful of Dr. Claude Desset (IMEC) for clarifying the power consumption model in EARTHproject D4.3.I thank my colleagues, Dr. Alireza Attar, Dr. Qixiang Pang and Dr. Shengchun Huang, for theirknowledge and wisdom that ensured the quality of our numerous research collaborations. I thankDr. Jun-bae Seo for his insights that greatly helped my studies during my first two years in UBC.I thank Mr. SeyedAli Hosseininezhad for helps on NS-2 simulator and Linux environments, Mr.Javad Hajipour for helps on frequency-selective channel modeling, Mr. Liming Chen for sharinghis knowledge on Cloud-RAN, and Dr. Hu Jin for organizing our biweekly seminars. I thankDr. Arghavan Emami and Mr. Robert White (Radio Science Lab of UBC) for their kind helps onWireless InSite? 3D ray-tracing simulation tool.I would like to thank Mr. Saad Mohaboob, Mr. Chinmaya Mahapatra and Dr. Roberto Rosales,xxvfor their knowledge and helps during the preparation of an MIMO-OFDM testbed. I thank Mr.Sebastien Maury and Mr. Maxime Dumas for many discussions over radio front-ends and digi-tal signal processing platforms that have deepened my understanding in wireless communicationsystems.Lastly, I would like to thank my father-in-law (who passed away) for his encouragement andoptimism, and my mother-in-law and my wife who had to face the very difficult time while stillgiving me tremendous amount of supports during my last two years of PhD study. Without theirsupports, it would have been very difficult for me to complete this thesis.The research in this thesis were supported in part by a grant from Bell Canada through theBell University Laboratories program, the Canadian Natural Sciences and Engineering ResearchCouncil through grant CRDPJ 320552-04 and STPGP 396756, The University of British ColumbiaFour-Year-Fellowship (4YF), and The University of British Columbia PhD Tuition Scholarship.xxviDedicationTo my parentsxxviiChapter 1IntroductionWireless communications systems need to provide a wide coverage and a large system capacityto address the ever-increasing need of ubiquitous wireless access, to support the growing traffic-intense applications including multimedia streaming and file storage in Internet, and to cater theincreasing number of people on Earth. Wireless communication systems also need to accomplishthese tasks in a cost-effective and energy-efficient way to meet the expectation of industries andfollow the increasing global consciousness in energy crisis. Given finite radio frequency resources,techniques in the areas of radio over fiber (RoF), distributed antenna system (DAS), multiple-inputmultiple-output (MIMO) systems and Heterogeneous Networks (HetNet) have been developed toenhance system coverage and to increase system capacity through efficient frequency reuse andMIMO techniques. The area of green communications has also drawn attentions from telecom-munication operators in reducing the infrastructure energy cost and from mobile terminal manu-facturers in extending battery life. However, each of these research areas has its own challengeson achieving their goals. This motivates us to propose a novel wireless access architecture, Fiber-connected Massively Distributed Antennas (FMDA), which combines the techniques that havebeen developed in these research areas to increase system capacity in an energy-efficient manner.In the following we survey the advances in the aforementioned research areas, present the archi-tecture of FMDA, state our research questions, and then summarize our main contributions. In theend of this chapter, we state the organization of this thesis.11.1 Overview of Related Work1.1.1 Distributed Antenna SystemDAS were proposed to provide more reliable coverage by splitting the transmission power amongspatially distributed antennas [1]. DAS is needed in rural areas where it is expensive to installbase stations (BSs), in large buildings that wireless signals are hard to penetrate from outside (e.g.,government buildings and hospitals), and in crowded large public venues where a large number ofantennas are needed to provide a sufficient system capacity (e.g., stadiums and convention centers).The DAS in the setting of outdoor cellular communication systems has evolved into coordi-nated multi-point transmission [2], cooperative base station [3], or multi-cell processing [4] bycombining MIMO technique, which has been adopted in Long-Term Evolution (LTE) networks[5, 6]. Researchers in coordinated multi-point transmissions are investigating how BSs exchangeinformation to smoothly handle handover and increase both uplink and downlink throughput [4, 7?14]. These studies are focused on cellular systems that use licensed bands to serve large numberof users per cell through intelligent BSs. In practice, however, the cooperating BSs often com-municate through a backhaul link with a finite capacity and a non-negligible delay. Therefore,many research efforts have been put into how to improve system performance under a backhaulcapacity constraint [15, 16]. There are also research in deploying distributed antennas in largebuildings to improve the throughput of single user through single-user MIMO techniques [17?24],or use multi-user MIMO techniques to simultaneously transmit multiple packets to multiple users[25, 26].In hyper-dense venues such as stadiums and convention centers, wireless local area network(WLAN) operators are deploying a large number of distributed access point (AP)s to meet theincreasing demand of Internet access and content delivery during live events. To mitigate the inter-AP interference that increases with the AP density, designers rely on orthogonal channels, thoroughradio frequency planning and careful tuning of directional antennas. However, these measures are2limited by the number of channels available to the operator, and the time and the cost to conduct arealistic radio frequency survey. Therefore, there has been a trend of mounting the APs under-seat[27] or under-floor [28] to be closer to the mobile terminals and achieve higher inter-AP isolationsby taking advantage of the heavy human body penetration loss, thus allowing more APs beingdeployed to provide a very-high system capacity. Under-seat or under-floor mounting also hasadvantages in aesthetics and ease of installation [29]. Femtocells [30] follow a similar path toimprove indoor wireless coverage by locating the antennas closer to users, which will be reviewedin Section 1.1.4.1.1.2 Radio over FiberA RoF system [31], composed of a central controller unit and multiple fiber-connected antennas,was originally proposed to extend system coverage by simulcasting messages through antennas.It is transparent to traffic being carried and therefore future-proof since only baseband processingunits in the central controller unit need an update when wireless technology evolves. Studies in[32?35] investigated the feasibility of carrying a wide-band signal through RoF systems, specifi-cally, multiple WLAN channels over low-cost multi-mode optical fibers. And it was shown thatWLAN medium access control mechanism in RoF systems are not affected by the optical delay[36?38]. Commercial fiber-based indoor wireless networks have been deployed to deliver bothWLAN and cellular communication signals inside large civil structures such as stadiums [39, 40],subways [41], hospitals [42], business buildings and shopping malls [43]. RoF has also been usedin high-altitude balloons to provide radio communication and video surveillance in battlefields dueto the light weight and high bandwidth of optical fibers [44]. However, most of these studies areconcentrated on the design of optical-electric converter components and most of applications areonly using simulcasting mode to improve coverage in hard-to-reach areas. Thus far, two abilitiesof the central controller unit in a RoF system have not been explored. One is to see the completepicture of radio spectrum usage in the coverage area. Another is to intelligently combine signalstransmitted through antennas to make use of MIMO technique.31.1.3 Massive MIMOMassive array-MIMO addresses ever-increasing traffic demand by densifying radio access net-works. The spectral efficiency advantages of massive array-MIMO systems have been shown inanalysis under match filter precoding [45], zero-forcing beamforming [46], and demonstrated inexperiments [47]. Compared with array MIMO systems, distributed MIMO systems improve linkreliability by locating antennas closer to users and therefore improve spectral efficiency both in-doors [1, 14, 48] and outdoors [4, 49] while requiring less transmission power. When the number ofusers being served, K, is smaller than the coverage radius measured in the number of wavelengthsof the carrier signal, a distributed MIMO system achieves a capacity linear in K [50], demonstrat-ing its potential to satisfy high traffic demands in large public venues such as stadiums, arenas andconvention centers. While many research in the area of massively distributed MIMO systems arefocused on asymptotic analysis when the number of antennas N grows to infinity, few research areconducted to reduce the demanding signal processing complexity when N is large.1.1.4 Heterogeneous NetworksAs the demand for indoor wireless connectivity increases, shrinking the cell sizes through installa-tion of more macro-BSs is no more a sustainable solution to handle the traffic load. An emergingsolution to address the increased network capacity demand is to deploy smaller scale access nodeswhich can form femtocells or picocells and facilitate a higher level of reuse of available spectrum,thereby shifting the cell planning model in future wireless networks towards universal frequencyreuse pattern. The creation of femtocells and picocells within a macro cell shortens the commu-nication link, especially for indoor users, which in turn reduces the co-channel interference levelin the network. As the capacity of most packet-based wireless communication technologies isinterference-limited, such a reduction in network interference level is directly translated into ca-pacity enhancement of the system. On the other hand new forms of interference, mainly the mutualinterference between femtocell or picocell access nodes and macro cell users arise in this new net-4work architecture paradigm. The research community in academia and industry has started to morecarefully address such coexistence problems under the umbrella term HetNet. While HetNet pre-viously refers to cooperation of different wireless technologies, e.g., a complementary operationof a WLAN in conjunction with a cellular network, in this section we limit our discussions HetNetbased on a single wireless standard. Note that in the context of HetNet, the prefixes macro-, micro-,pico- and femto- are used to indicate the relative sizes of the cell coverage areas and do not implyany exact ratio of their coverage areas. For example, a pico-cell does not cover exactly 103 timeslarger area than a femto-cell.HetNet aims to improve the network performance via coordinating the resource allocation andservice delivery using nodes with different transmission capabilities within a given cell. In June2009, HetNet became a study item for LTE-Advanced networks [51]. A HetNet in LTE-Advancedcontext is comprised of a macro cell associated with a macro-BS, and a random distribution oflower power BSs, such as micro-, pico- and femto-BSs, which form their own closed subscribergroups [51]. Thus, HetNet will not be a specific technology but will represents a network of aspecific radio access technology where BSs might have different radio capabilities, ranging frommacro- and micro- to femto- and pico-cell scales. As subscriber groups are closed, a user can onlyassociate with its own BS even when nearby BSs have stronger signal strengths. The resultingindependent operations among neighboring cells incur the following interference scenarios [52].In the downlink, a given macro cell user will be interfered by nearby users that associate withmicro-, pico- or femto-cells. Further, a neighboring femto-BS will interfere with users associatedwith another femto-BS. In the uplink, on the other hand, macro cell users will create significantinterference to neighboring femto-BSs, especially when the macro cell users are near the cell edgesand therefore are transmitting at the largest power level. The interference scenarios become morecomplicated in LTE time division duplex systems [53], where eight scenarios are described andfive of them are given a high priority. Note that in the context of LTE, the above interferencescenarios need to be considered in both data and control channels, and in many cases it is more im-portant to mitigate interference in control channels, which carry synchronization and broadcasting5information that allow a user to successfully attach to the network.The coexistence challenge in LTE has ignited the research in more intelligent BSs that self-organize and negotiate resources with neighboring BSs, termed Self-Organizing Networks [54,55]. The coexistence between a macro cell and femtocells ignited both data and control channelprotection schemes, which are being considered in inter-cell interference coordination schemein LTE release 8/9 [56], enhanced inter-cell interference coordination scheme in LTE release 10[53, 57, 58] and enhanced interference management and traffic adaptation scheme in LTE release11/12 [59, 60]. However, these inter-cell interference management schemes are still limited bythe inefficient communications between the macro-BS and the femto-BSs, which have to cross X2interface that is implemented on a data packet network and is often susceptible to capacity bottleneck and delay.1.1.5 Green CommunicationsThe growing concern over the power consumption aspect of wireless and cellular networks hastriggered a new research initiative in academia and industry, referred to as green communication[61]. A surge in wireless network power consumption can be directly translated into increasingCO2 emission. Vodafone estimates the total gross CO2 emissions of this firm at 1,676,949 tonnesby BSs and 615,612 tonnes by its other network equipment as compared with 251,358 tonnes byoffices and 40,446 tonnes by retail stores for 2012/2013 [62], indicating that the access network isthe main source of power consumption and power inefficiency.To address the power efficiency of cellular/broadband systems, one can target component, linkand/or network level power efficiency solutions [63]. Component power efficiency addresses per-formance enhancements of the electrical and electronic components in the system, such as poweramplifiers, while sustaining power conservation. Link level power efficiency aims at deliveringhigher throughput to end users while maintaining or even decreasing the transmit power budgetat the link level. Finally, network level solutions address the effects of static/dynamic networktopologies, among other factors, on the power consumption of the network.6The main components of a typical macro cell site include a power supply unit and a coolingsystem, and the BS units including base band processing units and radio frequency units (poweramplifier, low noise amplifier and antenna feed). The authors in [61] estimate that of the totalpower consumption of a typical macro cell site, 43% is consumed by the cooling system followedby 41% by the BS itself. Within the BS, the shares of the main power sinks are the feeder at 44%,radio frequency conversion and power amplifier at 15% and signal processors at 9%.In [64] the authors present a link level power efficiency analysis of cellular networks, by de-veloping a framework to study the effect of BS cooperation, such as coordinated multi-point trans-mission techniques. Further, an early deliverable in EARTH project [65, 66] develops power con-sumption models of various types of cellular BSs, from a component energy-efficiency point ofview, in order to analyze network level green solutions based on deployment strategies in hetero-geneous cellular systems. A recent deliverable of EARTH project [67, 68] presented a scalablepower consumption model based on measurements in realistic LTE frequency division duplex sys-tems including macro-BS, micro-BS, pico-BS and femto-BS. The comprehensive model scaleswith the number of antennas, the channel bandwidth, the coding rate, the modulation type, andthe semiconductor process used in digital signal processors. The model is separately modeled foruplink and downlink. These power consumption models reveal that in femto- and pico-BSs whereradio transmission power is largely reduced and active cooling units are removed, signal processingis contributing more in total power consumption.In massive array-MIMO systems, two recent contributions analyzed the energy efficiency inthe uplink [69] and downlink [70]. From the path loss aspect, however, it would be more energy-efficient to locate the antennas closer to the users, which motivates the use of a large number ofantennas. In such systems, the feeder loss disappears due to the collocation of a power amplifierand the corresponding antenna. The power amplifier contribution also shrinks because a muchsmaller transmission power is used, which consequently allows the use of passive cooling at thedistributed antennas. As a result, signal processing algorithms have a higher impact on the energyefficiency of access networks. Since the cooling is now only needed at the central unit where7signal processing units consume the most part of energies, a simpler signal processing algorithmalso reduces the power consumption of cooling.Another direction in green communication is to shut down devices when there is no traffic.Traffic-aware sleeping techniques have been proposed in femto-BSs [71] and WLAN APs [72] totake advantage of temporal and spatial traffic load variations. However, when the device wakesup, the mobile terminals have to wait for the device to boot and then synchronize to the network,thus reducing the user responsiveness. Therefore, the demand to provide anywhere connectivity ata high data rate as well as seamless mobility at any time requires that almost all BSs within thetraditional last-mile networks should continue to operate regardless of temporal and spatial trafficload variations. The recently proposed cloud-based radio access network (C-RAN) [73, 74] isable to resolve the conflict between reducing power consumption and maintaining anywhere andanytime connectivity. In C-RAN, baseband processing of all the BSs are concentrated at a centrallocation, termed baseband unit. The rest of each BS, termed remote radio head, only containsa power amplifier, a low-noise-amplifier, a set of analog-digital/digital-analog converter, and anoptical transceiver that supports common public radio interface, open base station architectureinitiative, or other communication protocols that vendors of baseband unit and remote radio headagree on. Compared with traditional HetNets, the energy efficiency of C-RAN is improved becauseof two facts. First, the power consumption of remote radio head is reduced due to its simplifieddesign. If desired, remote radio heads can be swiftly switched on and off to adapt to temporaland spatial traffic load variations, which is possible due to the centralized processing in C-RAN.Second, the power consumption of signal processing can be reduced by the increasing utilizationratio of baseband processing units at the baseband unit. When a C-RAN covers both residentialareas and business districts, the overall traffic becomes stable over day and night and thereforerequires less number of baseband processing units.The trend of C-RAN is apparent considering recent advances from major wireless equipmentvendors, e.g., lightRadio from Alcatel-Lucent in 2011, Antenna Integrated Radio from Ericsson in2011, Liquid Radio from Nokia Siemens Networks in 2011, AtomCell from Huawei in 2012 and8a successful lightRadio trial in Telefonica in 2012. Since C-RAN heavily depends on the base-band unit to accomplish the baseband processing, reducing signal processing power consumptionbecomes more important.1.2 Motivation of Fiber-connected Massively DistributedAntennasWe first combine the innovations in DAS and RoF to form a fiber-connected DAS that is ableto address the backhaul capacity challenge from coordinated multi-point transmission technique,exploit the centralized processing and sensing opportunities in RoF systems, and reduce the in-terference management difficulty in HetNets. We then employs massive MIMO technique inthe fiber-connected DAS to deliver high-throughput wireless access to end users. The resultingnetworking paradigm is termed Fiber-connected Massively Distributed Antennas, which providesa high-capacity low-delay backhaul, enables centralized processing and sensing capabilities andharnesses the advantages of distributed networking architecture, thus facilitating interference man-agement solutions and achieving a high energy efficiency. Because of the wide-band nature ofoptical cables and technology-transparent RoF technique, systems built on the FMDA architecturecan support single wireless technology such as WLAN, LTE or any other future wireless tech-nology, as well as HetNet which contains many combinations of existing wireless technologies.We summarized in Fig. 1.1 the motivations of FMDA architecture and the challenges that needto be addressed, in which we focus on mitigating interference to improve spectral efficiency andreducing signal processing complexity to improve energy efficiency.1.2.1 ArchitectureA FMDA system is comprised of three main components, antennas, fiber-connection medium andthe centralized processing system (CPS).9Anywhere access Growing wireless trafficIncrease spectral efficiencyWiden the coverageGreen communicationsIncrease infrastructureenergy efficiencyPassivecoolingLowtransmissionpowerUniversal frequency reuseShorter antenna-user distance(femtocell, dense WLAN)MIMOCoordinatedtransmissionBackhaulcapacityInterferencemanagementSignalprocessingcomplexitySpectrumusagein ISM bandSitesurveyMultipleradio access technologies(LTE+WLAN)Fiber-connected Massively Distributed Antennas:Energy efficiency + Interference managementIncrease access network energy efficiencyChallengesFigure 1.1: Motivation of Fiber-connected Massively Distributed Antennas. WLAN: wire-less local area network. ISM band: the industrial, scientific, and medical band. LTE:Long-Term Evolution.Antennas Antennas provide a convenient means of delivering blanket coverage for a targeted lo-cale, while avoiding the time consuming and costly cell planning phases. Each antenna is onlyequipped with radio frequency components and optical-electrical converters, whereas the process-ing functionalities are transferred to the CPS. Each antenna forms a cell to provide wireless cov-erage to nearby users. Given the fast and reliable fiber-connection medium to/from the CPS, theFMDA system has the potential of scaling from a few antennas, covering tens of meters of space,to hundreds of antennas, covering a few kilometers of the targeted area. The location arrangementof individual antennas in this massive DAS is quite arbitrary, providing ease of deployment.Centralized processing system All the processing functionalities are concentrated in the CPSwhich provides an opportunity to enhance the system performance from several perspectives. First,the inter-antenna interference can be easily managed as the CPS has the ability to detect the spec-10trum usage across the entire area, owing to the widely distributed antennas. Second, the signalingoverhead associated with coordinated transmission and reception of data, such as through em-ploying coordinated multi-point transmission mode in LTE context, reduces significantly as all theprocessing will be performed centrally. Therefore, a distributed MIMO system can be formed toincrease system capacity. Third, not all antennas need to be activated at the same time. Thus, theFMDA system achieves a higher utilization ratio of processing units, which reduces the systemcost and the energies consumed by signal processing.Fiber-connection medium The backbone of FMDA is a network of optic cables connecting theCPS to each antenna. The wide-band nature and very low attenuation of optical cables allow reli-able and energy-efficient delivery of wireless signals and therefore contribute to the advantages ofFMDA over wireless-only solutions. The key in wide-spread deployment of FMDA is an efficientbut inexpensive optical fiber backhaul, which itself is composed of two parts. First, an electrical-to-optical and optical-to-electrical converter transforms the communicated signal between optical andradio frequency domain. Second, the optical links will form a network, which can utilize passive oractive optical networking protocols. If multiple antennas are fed via a shared pair of optical fibers,wavelength division multiplexing techniques can be exploited to reduce optical cable deploymentcost. While the nonlinearity of the electrical-to-optical and optical-to-electrical converters incursdistortions to radio frequency signals, the resulting error vector magnitude had been shown to be assmall as 1% in 16-, 64-, and 256-quadrature-amplitude-modulation signals if the input power to thefiber is smaller than 4 dBm [75]. In this thesis, we assume that radio frequency signals experienceno distortions when they are transmitted over fibers.The fiber-connection medium interconnecting the CPS and an antenna can also carry digi-tal baseband signals in the form of high-rate in-phase/quadrature samples [76, 77], thus com-pletely eliminating the signal distortions caused by nonlinearity while directly transmitting radiofrequency signals over optical cables. In such case, however, an antenna needs a very-high-rate dig-ital transceiver and high-speed analog/digital and digital/analog converters, which incur a higher11component cost and a higher power consumption when compared with radio frequency signaling.A comparison of radio frequency signaling and digital baseband signaling is presented in [75].The existence of abundant optical cables inside buildings and large public venues is the keyassumption we made in this thesis, which is based on the ever-decreasing cost of optical fibersand wavelength-division multiplexing components as well as the increasing fiber-to-the-homeand fiber-to-the-building penetration rates. According to the European 2011-2016 forecast [78],the fiber-to-the-home/building maturity, defined as 20% household penetration of fiber-to-the-home/building, will be achieved by 2016 in eight countries in Europe and Asia. Currently, UnitedArab Emirates, Japan, Korea, Qatar had already achieved the maturity [79]. While the assumptionis reasonable, requiring a large number of optical cables does increase the infrastructure cost ofa FMDA system when compared with wireless-only solutions, and slows down the deploymentspeed when the required cables are not in place. In Section 6.2, we discuss how to reduce systemcost by choosing different optical backbone topologies.1.2.2 ConfigurationsA FMDA system can be flexibly configured as different types of communication systems, e.g., aWLAN Extended Service Set, an LTE system comprised of a large number of cooperating fem-tocells, a DAS that consists of a large number of antennas to cover an office building or a largepublic venue, or a HetNet that provisions different radio access networks over a metropolitan area.To configure FMDA as a WLAN Extended Service Set, we replace the existing APs with the an-tennas and convert the existing WLAN controller to the CPS by adding more functionalities. Theresulting network, termed cognitive WLAN over fiber system, will be elaborated in Chapter 2. Toconfigure FMDA as an LTE system, we replace femto-BSs with the antennas in FMDA and addthe component CPS. The resulting network becomes a set of fiber-connected femto-BSs, whichwill be elaborated in Chapter 3. The last step of the WLAN and LTE configurations is to replacethe electrical cables with optical cables. Chapter 4 and 5 elaborate the DAS configurations to coveroffice buildings and large public venues.121.3 Research QuestionsIn each of the above configurations, there are research questions to be answered. In a cognitiveWLAN over fiber system, antennas can either cooperate to improve WLAN sensing capability andreduce packet error rate, or independently operate multiple WLAN channels to form co-locatedWLAN Extended Service Sets. The question is which strategy brings a higher throughput andproduces a lower packet error rate. We are also concerned with how the answer varies with appli-cation types, spatial traffic distribution and other network parameters. We answer these questionsin Chapter 2 by considering realistic network settings and typical WLAN applications (includingfile transfer, Internet television, and audio streaming over Internet).When a FMDA system is configured as an LTE system comprised of a large number of cooper-ating femtocells, compared with standalone femtocells, there arise one new dimension that we canexplore to improve spectral and energy efficiency: each antenna can be activated or deactivatedat per-slot-level, thus allowing the possibility of antenna scheduling. The sets of antennas beingactivated in each slot has a direct impact on spectral efficiency and signal processing complexity.Increasing the cooperation set size increases the spectral efficiency but incurs a higher power con-sumption in baseband processing. The question is whether it is possible to simultaneously improvespectral and energy efficiency. We answer this question in Chapter 3.In view of the signal processing complexity challenge in massive MIMO systems and the in-creasing importance of low-complexity signal processing algorithms in green communications andC-RAN, we study low-complexity baseband processing schemes in our proposed FMDA architec-ture. As a FMDA system is equipped with a powerful, centralized signal processing capability,with traditional processing algorithms, the energy efficiency will drastically decrease when thenumber of cooperating antennas becomes very large. The question is to what extent the antennasshould cooperate to satisfy a required system capacity. In Chapter 4 and 5, we answer this questionby exploiting the distributed nature of antennas in two different network topologies.131.4 Summary of Main ContributionsIn this thesis, we propose a novel wireless access architecture, namely, FMDA, which addressesthe finite-capacity backhaul challenge in the areas of DAS and HetNet, explores the opportu-nity of combining massive MIMO and RoF techniques, and allows the development of low-complexity beamforming schemes that are often not possible in massive array-MIMO systems. Wedemonstrate the advantages of FMDA in managing interference and improving energy-efficiencyin both WLAN and LTE. When FMDA is employed to cover office buildings and large publicvenues, we carefully model the resulting channel matrix and propose two low-complexity zero-forcing beamforming (ZFBF) schemes to significantly reduce the baseband processing complexityin downlink, thus substantially improving the downlink energy efficiency. More importantly, theenergy saving from our proposed ZFBF schemes increases with the network size, thus offering agreat potential in future access networks. Detailed contributions are listed below.1.4.1 Interference Management in Cognitive WLAN over FiberTo increase the system capacity of a traditional WLAN system that is composed of a WLAN con-troller and multiple WLAN APs, previous research are focused on channel assignment strategies,user association schemes (or load balancing), and AP transmission power control [17]-[21]. Thepurpose of these strategies is to reduce co-channel and adjacent-channel interference among theAPs and therefore increase the system capacity. However, as each AP typically supports onlyone channel, these algorithms have limited abilities to handle dynamic traffic, and become ex-tremely complicated when channel allocation, load balancing and AP transmission power controlare jointly considered.In Chapter 2, we configure our proposed FMDA architecture as a novel WLAN Extended Ser-vice Set, where the CPS serves as a cognitive access point that is able to see the entire spectrumusage across the coverage area and control the radio frequency signals to be sent to each antenna.As a result of the wide bandwidth of optical cables, each antenna can operate multiple channels.14The antennas can also cooperate with the help of the centralized baseband signal processing at theCPS. The proposed WLAN system can exploit additional frequency channels to reduce the load ineach channel and consequently the packet collisions, thus providing a much higher system capacitythan the traditional WLAN system. The ability to cooperate among antennas also improved thesensing capability of the CPS, thus reducing the collisions between downlink and uplink transmis-sions. The two added abilities, which are only made possible by the proposed FMDA architecture,can also be combined to better accommodate dynamic traffic. Specifically, we achieve up to 62%Transmission Control Protocol throughput gain in hotspots.This is a simulation-based research and our simulation model is based on an accurate WLANsimulation model that combines NS-2.33 simulator [80] with its dei80211mr WLAN rate adapterpackage [81]. The interference-recorded channel model incorporated in the package greatly en-hances the accuracy of simulations involving channel capturing. Parts of this chapter have beenincluded in one published journal article [82], and two published conference papers [83, 84].1.4.2 Energy Conservation in Fiber-connected Femto Base StationsFemtocell addresses the challenge on indoor wireless connectivity by pulling BS closer to user. Thecell planning is shifted towards universal frequency reuse pattern largely due to the advantages onarea spectral efficiency previously reported in cellular networks [85]. However, in very dense ur-ban areas with a high concentration of residential and business users, inter-cell interference amongfemtocells using universal frequency reuse may drastically decrease system capacity. Coopera-tive communications among neighboring femtocells can eliminate the interference by frequencyallocation, which, however, decreases the capacity gain from the use of universal frequency reuse.Meanwhile, in such hyper-dense deployments a large number of active femtocells are constantlyconsuming a large amount of energies even when some of them have no active users attached.While femtocell sleeping techniques can help reduce the energy waste, the wake-up time preventsanytime wireless access and therefore harms user experience.To address these two challenges in densely deployed femtocell network, in Chapter 3 we con-15figure our proposed FMDA architecture as fiber-connected femto-BSs, where each antenna formsone femtocell. For all femtocells being formed, the CPS schedules all the attached users, allocatesthe frequency channel(s) in each cell, adjusts the transmission power at each antenna, and processesall the baseband signals to allow per-slot-level cooperations among the femtocells. In the formedsystem, we propose an antenna scheduling scheme to activate and deactivate the antennas to si-multaneously improve spectral and energy efficiency. Compared with standalone femtocells, theproposed scheme is shown in a typical office building to increase energy efficiency by 64%?160%and spectral efficiency by 2%?36%.The proposed antenna scheduling strategy relies on a large number of antennas that are able tosleep on demand while incurring negligible wake-up delay. This capability is only possible in thearchitecture of FMDA due to its centralized processing unit and the reduced antenna complexity.The idea of antenna scheduling also enriches network configurations on howmany antennas shouldcooperate and how much separation distance should be kept among cooperating antenna clusters,thus offering service providers a greater flexibility on choosing different balance points betweenspectral and energy efficiency. Parts of this chapter have been included in three published journalarticles [86?88].1.4.3 Low-complexity Beamforming in Office BuildingsDAS have been widely used in indoor environments such as office buildings and stadiums to pro-vide reliable coverage and a higher system capacity while using a lower radio transmission powerat antennas. In Chapter 4 we consider a FMDA system that is configured as a typical DAS coveringan office building. Our focus is to design a multi-user downlink transmission scheme that allowsuniversal frequency reuse and thus provides a high system capacity.We consider a single channel matrix H that includes the whole set of antennas in the entirenetwork, and based on H , we devise a ZFBF scheme to support multi-user transmission. When thenumber of antennas is large, however, it is challenging to determine the entire channel matrixH andpower-consuming to generate the precoding matrix W and precode the symbols, especially when16these operations are required in each subcarrier if orthogonal frequency-division multiplexing isused. Our idea is to treat the channel matrix as a banded matrix, thus allowing a low-complexitybeamforming scheme. Previously Wyner model [89] had been used to approximate a channelmatrix of an one-dimensional outdoor cellular system as a banded matrix [90, 91]. However, theaccuracy of Wyner model is established on a sufficiently large number of simultaneous users [92].Banded matrices had also been applied to electromagnetic wave simulation [93], inversion of tri-diagonal matrices [94], and equalization [95]. However, in the area of distributed MIMO systems,the only literature exploiting the banded path loss structure is [96], where the authors focused onoptimal allocation of channel state information rather than a low-complexity beamforming scheme.In Chapter 4, we discover that the existence of indoor wall penetration loss allows us to discardless important off-diagonal elements inH and then form a banded, sparse matrix, Hp, where p con-trols the sparsity of H . The precoding W is then generated based on Hp. The scheme is evaluatedby applying it to a DAS that covers a dual-stripe office building floor. Compared with traditionalZFBF, our analysis and numerical evaluations show that the low-complexity beamforming schemeincurs negligible loss in signal-to-interference-noise-ratio (SINR), while offering 45%?79% gainin energy efficiency.To the best of our knowledge, our work is the first to consider the inversion of random matriceswith exponentially decayed off-diagonals or compositely decayed off-diagonals. Previously stud-ied Wyner model, full channel matrix model and standalone femtocell model are special cases ofthe proposed model. In practice, the introduced parameter p can be used by system operators toobtain a fine control over the tradeoff between spectral and energy efficiency. Parts of this chapterhas been included in one journal article under review [97].1.4.4 Low-complexity Beamforming in Large Public VenuesA single outdoor micro- or macro-BS cannot provide enough capacity in large public venues suchas stadiums and convention centers because of the increasing demand of Internet access and con-tent delivery during live events. WLAN and DAS operators have been deploying a large number of17distributed antennas to offer a higher system capacity in these venues. To mitigate the interferencearising from the dense deployment, the system operators still rely on a thorough radio frequencyplanning and careful tuning of directional antennas, which support channel allocation and trans-mission power control decisions. However, these measures are limited by the number of channelsavailable to the operator; a realistic radio frequency survey is also time-consuming and very expen-sive (in some cases the presence of audience is even required to ensure human effects are includedin the survey).To simplify the frequency allocation difficulty and eliminate the need of a RF survey, in Chapter5 we propose a FMDA system to cover a large public venue. Similar to Chapter 4, we design aZFBF scheme by considering a single channel matrix H that includes the whole set of antennasin the venue. However, unlike an office building, the absence of walls in the venue invalidates thechannel model developed in Chapter 4 and would incur a large throughput loss were our previouslyproposed scheme applied. To reestablish the decays in H , we follow the under-floor antennamounting strategy that had been adopted in hyper-dense WLAN industries [27?29] such that theheavy human body penetration loss can help increase the propagation loss among antennas. Wethen develop a new channel model and propose a multi-banded matrix inversion algorithm thatsubstantially reduces the computation cost of ZFBF while incurring a negligible throughput loss.Compared with a massive array-MIMO system located in the center of the venue, our proposedscheme provides 19 times higher energy efficiency while only incurring 6% spectral efficiencyloss. We also discover that although massive array-MIMO can deliver a very high system capac-ity, its co-located antennas disallow a low-complexity matrix inversion. Therefore, a massivelydistributed MIMO system equipped with our proposed low-complexity ZFBF scheme can offer ahigher energy efficiency than a massive array-MIMO system. This chapter has been included inone published journal article [98].181.5 Thesis OrganizationThe rest of the thesis is organized as follows. In Chapter 2, we propose two methods that utilizethe specialized capabilities of the cognitive WLAN over fiber architecture to improve system ca-pacity by reducing packet collisions through load balancing and employing diversity to reduce theeffects of packet collisions. In Chapter 3, we present how antenna scheduling can improve theenergy efficiency when a FMDA system is used to form fiber-connected femto-BSs, and show itssubstantial advantages when compared with standalone femtocells. In Chapter 4, we present thelow-complexity ZFBF scheme in a FMDA system covering an office building, analyze the resid-ual interference due to the use of a simplified matrix inversion and then demonstrate its energy-efficiency advantage when compared with conventional ZFBF. In Chapter 5, we consider the low-complexity ZFBF scheme in a two-dimensional network and propose the use of floor-mounteddirectional antennas to enable the possibility of simplified matrix inversion. The main results andpotential research topics are summarized in Chapter 6. Chapter 2, 3, 4 and 5 are self-containedand have been included in separate journal articles and conference papers. Each of these chaptersincludes its own literature survey that reviews previous solutions to the corresponding researchproblem.19Chapter 2Interference Management in CognitiveWireless Local Area Network over Fiber 12.1 IntroductionWireless local area networks (WLANs) are widely used for connecting computing equipment inhomes and offices to the Internet. However, WLANs share the industrial, scientific, and medical(ISM) band with other independently-operated license-free devices such as Bluetooth radios andmicrowave ovens; therefore, they must tolerate interference from these devices. Cognitive radiotechniques have been proposed for secondary users to exploit spectrum holes left unused in li-censed frequency bands by primary users of the allocated spectrum. In this chapter, we employFiber-connected Massively Distributed Antennas (FMDA) in WLANs and propose a novel archi-tecture, cognitive WLAN over fiber, which applies advanced cognitive radio [99] and broadbandradio-over-fiber [31] technologies to an infrastructure-based IEEE 802.11 WLAN Extended Ser-vice Set (ESS) comprised of multiple access point (AP)s, each forming its own Basic ServiceSet (BSS). Successful simultaneous transmissions of multiple WLAN channels over low-costmulti-mode optical fibers [32?35] and clarification of WLAN medium access control (MAC) op-1This chapter is based on [82, 84] co-authored with Dr. A. Attar, Dr. V. Leung and Dr. Q. Pang, and [83]co-authored with Dr. Q. Pang and Dr. V. Leung.20eration in radio-over-fiber structures [36?38] also support the proposal of cognitive WLAN overfiber as an architecture that offers huge potentials to increase system capacity and improve quality-of-service.The ever-decreasing cost of optical fibers and wavelength-division multiplexing componentshas resulted in commercial fiber-based indoor wireless networks being deployed to penetrate largebuildings such as stadiums [39], hospitals [42], business buildings and shopping malls [43]. Itwould be expensive to cover these buildings with cable-based networks due to the ever-increasingcable cost. It is also difficult to monitor and manage the radio environment within such largebuildings if antennas cannot be efficiently coordinated. The success of these commercial indoorwireless networks further demonstrated potential markets for cognitiveWLAN over fiber networks.In a conventional WLAN, each AP performs carrier sensing independently and only over thechannel it operates on. In contrast, a cognitive WLAN over fiber system applies cognitive radiotechniques to more efficiently utilize the ISM band. The centralized architecture enables coopera-tive sensing and consequently reduces the interference detection time while improving the detec-tion accuracy. Moreover, the multi-channel carrying capability of advanced broadband radio-over-fiber systems can significantly increase available radio resources at each AP. By implementingdynamic radio resource management based on accurate spectrum sensing, interference avoidanceor mitigation can be easily accomplished. Effectively, the cognitive WLAN over fiber architectureenables the new concept of applying cognitive radio techniques for equal spectrum access in theISM band.Each AP in a conventional WLAN has an 802.11 radio modem and is digitally bridged to adistribution system, usually an 802.3 Ethernet. In a cognitive WLAN over fiber system, radiomodems and bridges in the APs are moved to a centralized unit referred to as the cognitive accesspoint (CogAP); the resulting simplified APs become antennas, which are connected to the CogAPvia optical fibers that carry analog radio frequency signals. By centrally processing broadbandradio frequency signals received from the antennas, the CogAP has a complete picture of the radiospectrum usage in the coverage area of the WLAN ESS. The Distributed Coordinated Function21of 802.11 MAC, which employs carrier sensing with collision avoidance, is carried out at theCogAP instead of at individual APs as in a conventional WLAN. These changes enable a cognitiveWLAN over fiber system to more effectively combat packet collisions that inevitably occur over arandom-access channel. A cognitive WLAN over fiber system and the structure of the CogAP areillustrated in Fig. 2.1.In this chapter, we focus on how to reduce access collisions in a WLAN through methods madepossible by the cognitive WLAN over fiber architecture, which would be difficult if not impossibleto realize in a conventional WLAN. The chapter is organized as follows. In Section 2.2, we reviewrelated work on how to improve WLAN system capacity. In Section 2.3, two methods are proposedto reduce collisions among WLAN stations: load balancing to reduce collisions caused by heavytraffic, and transmitter and receiver diversity to reduce the effects of collisions. The performanceof proposed methods is evaluated through Monte-Carlo simulations in Section 2.4. We summarythe chapter in Section 2.5.AntennaCognitiveaccess pointEthernet8 fibersOptical Interface(E/O and O/E)Radio / BasebandOptical Interface(E/O and O/E)Radio / Baseband?Bridge to 802.3 EthernetControllerFrom/toAntenna 1From/toAntenna N802.11 carrier sensingAnalog/digital converterDigital signal processorSpectrum Usage AssessmentTransmit / Receivediversity processingISMband devices?Figure 2.1: A cognitive WLAN over fiber system and the structure of the cognitive accesspoint (CogAP). ISM band: the industrial, scientific, and medical band. E/O: electrical-optical converter. O/E: optical-electrical converter.222.2 Related Work on WLANMuch recent research on WLANs aims to increase system capacity of individual WLAN BSSs,and reduce co-channel and adjacent-channel interference among BSSs in a WLAN ESS.The system capacity of a WLAN BSS can be increased through three methods: enhancingexisting MAC protocols by either adjusting parameters or adding new MAC flavors to achieve ahigher MAC efficiency, exploiting capture effects, and introducing multiple-input multiple-output(MIMO) to exploit spatial multiplexing. Enhancing the WLAN MAC protocol usually requires anupdate of station hardware or firmware. We therefore mainly review recent advances on exploitingcapture effects and employing MIMO in WLAN.The capture effect has been initially studied within the context of an ALOHA network [100].It refers to the fact that when two packets arrive at one station at the same time, the packet withstronger signal strength will be synchronized and ?captured? by the station. Luo and Ephremides[101] showed that with the capture effect, system throughput is maximized when all nodes trans-mit at maximum power. This conclusion, however, is based on an optimistic assumption that anypacket can be successfully received as long as it has the highest power level at the receiver, re-gardless of how many overlapping packets are being received at lower power levels. After takinginterference into account, Hadzi-Velkov and Spasenovski investigated the capture effect and itsinteraction with request-to-send/clear-to-send in 802.11b networks [102]. Kochut et al. studiedthe capture effect by comparing system throughput at the physical and transport layers in 802.11bnetworks [103]. Their comparisons showed that capture effect is magnified through variations ofcontention window size in the MAC layer and congestion window size in the Transmission ControlProtocol (TCP) layer. Based on Bianchi?s model [104], WLAN performance was derived in [105]after considering the capture effect. Capture effect and successive interference cancellation werelater studied in a ZigBee network that is based on direct-sequence spread spectrum [106].Capture effect in 802.11a networks was studied in [107, 108] through real-world experimentsusing commercial WLAN devices. It was shown that with an arrival time difference of up to 50 ?s,23the stronger 802.11a packet can still be captured. Different from previous 802.11b capture effectstudies where the stronger frame has to arrive within the preamble time of the weaker frame, thisobservation suggests that even when the arrival time difference of two packets is larger than thepreamble length of the first packet, the stronger packet could still be captured. Such phenomenahave been observed in commercial 802.11a/b/g adapters working in either direct-sequence spreadspectrum mode or orthogonal frequency-division multiplexing mode.The capture effect was further exploited in the form of ?message-in-message? to increase sys-tem throughput [109, 110]. An AP sends the message with smaller channel gain first and themessage with larger channel gain later such that the weaker packet?s preamble can be successfullylocked by one recipient and the stronger packet can also be locked by another recipient. The APabuses carrier-sensed multiple access rule and stations use delayed ACKs. Using ?message-in-message? requires the AP to update the system interference map periodically.Exploiting diversity in WLAN is classified into micro-diversity and macro-diversity. The IEEE802.11n standard is developed to enable micro-diversity in WLANs using MIMO. Previous workon macro-diversity includes the concept of distributed radio bridges proposed in [24] and theirsubsequent applications in WLAN [111, 112].A WLAN ESS is a multi-cell WLAN system in which the WLAN controller assigns channelsand sets maximum AP transmit power to different BSSs to reduce co-channel and adjacent-channelinterference among them. Sub-optimal radio resource management algorithms have been exten-sively studied for this purpose. These algorithms address three basic problems: channel allocation[113], user association (or load balancing) [114], and transmit power control [115]. The conflictset coloring method jointly optimizes channel allocation and load balancing [116]. Measurement-driven guidelines in [117] provide a heuristic method to jointly address the three basic problems.However, due to the limited number (usually one) of channels that each BSS can support, these al-gorithms have limited abilities to handle dynamic traffic, and become extremely complicated whenchannel allocation, load balancing and transmit power control are jointly considered. Authors of[118] investigated how to coordinate medium access across multiple APs in an ESS by switching24from contention-based access to time-slotted access when the ESS is heavily loaded with audio andvideo streams. The switching reduces packet collisions and thus provides better quality-of-servicefor multimedia streams. However, the signaling protocol required by the AP coordination was notgiven in [33].2.3 Collision ReductionA collision happens when two stations access the channel at the same time, or when one stationfails to sense an on-going packet transmission due to fading or hidden terminal problem and startsa new transmission. Based on the cognitive WLAN over fiber architecture, in this chapter wepropose a load-balancing method to reduce collisions caused by heavy traffic, and a transmitterand receiver diversity method to reduce the impact of packet collisions by increasing the chanceof successful reception. The two methods used to reduce collisions in cognitive WLAN over fiberare illustrated in Fig. 2.2.WLAN stationsAntennasTwo-channel operatingco-channel interferenceDiversity methodPacket 1 Packet 2Packet 1 Packet 1BSS 1 BSS 2BSS 1Figure 2.2: Collision reduction: Diversity and two-channel-operation. BSS: Basic ServiceSet.252.3.1 Load Balancing MethodA practical load balancing technique facilitated by the cognitive WLAN over fiber architecture isto distribute the total traffic load in the frequency domain. The broadband radio-over-fiber connec-tion between each antenna and the CogAP allows multiple channels to be allocated to any antenna.Consider the case of two antennas covering a given area: antenna A1 operates on the channel f1and antenna A2 operates on f2. When the collision rate on f1 is higher than a target threshold, theCogAP can use the ?disassociation? process to force some of the stations to be dissociated fromthis channel, while simultaneously sending beacons on a different channel f3. Stations dissociatedfrom f1 will then have two options. If a dissociated station receives beacons on channel f2 fromA2, it can request to associate with A2 on this channel. This effectively transfers a portion of thetraffic load of A1 to A2, creating a distributed load balancing solution among antennas. Alternately,a dissociated station will receive beacons on channel f3 from A1, and request to associate with A1over this channel. In this case, load balancing occurs over the frequency domain within the sameantenna, where a portion of the traffic at A1 is switched from overloaded channel f1 to channel f3.The second case is particularly made possible by the broadband radio-over-fiber connections be-tween antennas and the CogAP. In contrast, conventional WLAN APs are generally not equippedfor multi-channel operations.The gain in system throughput in the above example is two-fold: one from increased mediumaccess efficiency due to decreased contention among stations accessing the same channel, andanother from the use of three channels instead of two. We are more interested in the latter owingto its potential of linearly increasing system throughput. However, to fairly compare a cognitiveWLAN over fiber with a conventional WLAN, we investigate the worst case where the new channelassigned to A1 is the same as that assigned to A2, i.e., f2. We shall examine the throughput gainthat can be achieved in the presence of co-channel-interference on f2.WLAN operations on f1 and f2 can be independent and as such we refer to this load-balancingmethod as multiple-independent-channel-operation. Let us compare a two-AP conventionalWLAN,26where AP1 operates on f1 and AP2 operates on f2, with a two-antenna cognitive WLAN over fibersystem, where A1 operates on f1 and f2 and A2 operates on f2. We can certainly focus on thethroughput on f2. It is clear that the cognitiveWLAN over fiber system provides the worst through-put on f2 when all stations associated on f2 can perfectly hear each other. We now argue that evenin such a situation, the cognitive WLAN over fiber system could provide a higher throughout thana conventional WLAN. In the conventional WLAN, AP2 can only send one data packet at a time.In the cognitive WLAN over fiber system with A1 and A2 independently operated, they might si-multaneously send two data packets on f2. Owing to capture effects, the two packets may bothsurvive from the collision, thus generating a throughput gain.2.3.2 Transmitter and Receiver Diversity MethodBesides operating channels independently, the CogAP can also manage channels to exploit macro-diversity since signals received from widely separated antennas tend to be uncorrelated. If eachantenna is also equipped with multiple antenna elements, we can further implement micro-diversityin conjunction with macro-diversity. However, as only two fibers are used to connect each antennato the CogAP (one to transmit and one to receive), wavelength division multiplexing would thenbe required to deliver radio frequency signals from/to different antenna elements attached to thesame antenna. Here we focus on macro-diversity enabled by distributed antennas.Receiver diversityConsider an area covered with two antennas, using the same set of frequencies to serve a groupof stations. When maximum-ratio combining (MRC) is used at the CogAP for uplink signals, notonly do we achieve an array gain of 3 dB due to the coherent combining at the receiver, but alsoobtain a diversity order of 2 if the two signal paths from the station to the two antennas experienceindependent fading. The array gain and the diversity order reduce the effects of packet collisions,resulting in increased throughput and reduced packet error rate (PER). When the number of an-tennas increases to four, we expect a higher performance improvement due to 3 dB more in array27gain and a larger diversity order.An immediate effect of receiver diversity is an improvement in sensing capability at the CogAP,and hence a reduction in WLAN packet collisions between downlink and uplink packets. Anothereffect of diversity gain is to reduce unfairness among stations in terms of their chances to accessthe channel due to their different distances from the antennas.Transmitter diversityFor the downlink, we can use transmitter diversity to improve signal-to-noise-ratio at the stationswithout requiring them to have additional capabilities. Multiple copies of each packet are dis-tributed to antennas and then to the destination such that when some copies are largely attenuateddue to poor channel conditions, other copies can still reach the destination; hence, transmitter di-versity. By reciprocity of the channel, transmitter diversity at the CogAP through multiple antennasachieves the same signal-to-noise-ratio gain as receiver diversity, subject to a total transmit powerconstraint on all antennas.We investigate equal-gain combing (EGC) and MRC using transmitter diversity. In EGCscheme, each antenna is subject to a given per-antenna transmit power constraint, which reducesdistortions due to the nonlinearity at optical-electrical converters. In MRC scheme, antennas areonly subject to a total transmission power constraint, and therefore have a larger freedom on trans-mission power allocation across antennas, providing a larger signal-to-noise-ratio gain than EGC.Both EGC and MRC require that signals from different antennas can be added coherently atthe receiving station. Therefore, the CogAP must have exact channel state information from allparticipating antennas to the receiving station right before a packet is sent, such that signal phasescan be properly shifted at the different antennas. This makes estimating channel state informationfor transmitter diversity more difficult than receiver diversity, where the CogAP can always rely onthe physical-layer header of WLAN packets to estimate channel state information.282.4 Performance EvaluationsWe utilize the NS-2.33 simulator [80] with its dei80211mr WLAN rate adapter package [81] toevaluate the performance of the proposed methods based onMonte-Carlo method. The interference-recorded channel model incorporated in this package is used to accurately simulate capture effect.2.4.1 Simulation ModelThe simulation model includes two antennas connected to one CogAP, which is then connected toa fixed host computer. Single-antenna stations are either uniformly or non-uniformly placed in a60?30m2 area. Two antennas (or APs in the conventional WLAN) are fixed at locations (15, 15)and (45, 15) in units of meters. When no diversity is used, the CogAP communicates with stationsthrough their closest antennas. Traffic streams only flow between stations and the fixed host. Thewireless propagation model is a simplified path loss model [119] with shadowing and Rayleighfading.WLAN parameters follow IEEE 802.11g and two non-overlapping channels are used. EachAP in the baseline conventional WLAN operates on one channel only, while the CogAP in thecognitive WLAN over fiber system operates on both channels through the two antennas either co-operatively for macro-diversity or independently. Data mode used by each station and the CogAPis determined by the signal-to-noise-ratio-based dynamic rate adaptor in dei80211mr package. Norequest-to-send/clear-to-send is used. Perfect channel state information is assumed to be availableat the CogAP.The frequency plan used in the simulations is shown in Fig. 2.3 and simulation parameters arelisted in Table 2.1. The synchronization interval (SI) is used to model the capture effect. When thearrival time difference of two packets is smaller than the SI, it is assumed that the receiver is ableto synchronize to the packet with the stronger received power.The simulations employ two types of traffic that represent increasingly popular Internet appli-cations: File Transfer Protocol (FTP) over TCP in downlink representing traffic from file down-29loading applications, and constant bit-rate (CBR) traffic in both uplink and downlink representingVoice over Internet Protocol (VoIP) and IP television (IPTV). FTP over TCP traffic is saturated,i.e., stations always have packets to send. VoIP and IPTV, as multimedia traffic, have the samefixed packet interval yet different packet length due to different amount of information containedin their packets. We are mainly interested in file downloading speed and voice and video quality;thus, throughput of TCP downlink traffic and packet error rate of CBR traffic are chosen as ourmain performance evaluation criteria. To evaluate proposed methods for file sharing applications,we also evaluate TCP uplink throughput in some simulation scenarios. Detailed traffic parametersare listed in Table 2.1.f1 f2ConventionalWLANf1f2f1f2Two-channelf1f2f1f2Transmitter andReceiver diversityCognitive WLAN over fiber systemsFigure 2.3: Frequency plan in simulations.Table 2.1: Simulation parameters in cognitive WLAN over fiber systemsPropagationPath loss exponent = 2.5Reference distance, d0 = 2 mStandard deviation of shadowing = 3.5 dBPhysical layer Transmission power, Pt = 10 mWCarrier-sensing threshold = -70 dBmMAC layerSynchronization interval = 5 ?saSlotTime = 20 ?sCWMin = 31CWMax = 1023FTP traffic TCP/Reno. Packet size = 1000 bytes.CBR traffic Packet interval 20 ms. 1000-byte packets for IPTV; 40-bytepackets for VoIP.302.4.2 Effects of Receiver DiversityWe first investigate the effect of receiver diversity, i.e., using multiple antennas to receive a packettransmitted by a single-antenna station. Assuming the channel gain of each path is Rayleigh dis-tributed, we know that the received signal power at the i-th antenna, P(i)r (x,y), is an exponentiallydistributed random variable with the probability density functionfi,x,y(P(i)r ) =1P(i)avg(x,y)?e? P(i)rP(i)avg(x,y) , (2.1)where P(i)avg(x,y) is the averaged power of signals received by antenna Ai from a station located at(x,y) and reflects the path loss between them. Thus, at the CogAP that receives the signals fromboth Ai and Ak, the p.d.f. of the total received signal power is given byfcap,x,y(P(cap)r ) =e? P(cap)rP(i)avg(x,y) ?e? P(cap)rP(k)avg (x,y)P(i)avg(x,y)?P(k)avg(x,y), (2.2)where P(cap)r is the received signal power at the CogAP after coherently combining signals fromAi and Ak and the notation fcap,x,y(P(cap)r ) implies that the p.d.f. of P(cap)r is a function of (x,y),the geographical coordinate of the transmitter. When the station has the same average path loss tothe two antennas, fcap,x,y(P(cap)r ) becomes an Erlang distribution with the shape factor N = 2.Given different locations of stations, the CogAP and individual antennas exhibit different out-age probabilities over the whole coverage area, as shown in Fig. 2.4, where Prob(Pr ?threshold)represents the probability of the received signal power being smaller than or equal to the carrier-sensing threshold, commonly set at -70 dBm in WLANs. Denote the location at x = x0 and y = y0 by(x0,y0). The location (15,15) and (45,15) correspond to the locations of two antennas (or APs).Four edges of the coverage area correspond to x = 0, x = 60, y = 0 and y = 30. Fig. 2.5 shows thereduction on the outage probability when MRC or EGC is used, compared with the case wherediversity is not employed. In both figures the dotted blue surfaces correspond to EGC and the dash31red ones correspond to MRC. The solid black surface corresponds to conventional WLAN in Fig.2.4 and serves as the zero-reference plane in Fig. 2.5.We observe from Fig. 2.4 and 2.5 that MRC always reduces outage probabilities more thanEGC, especially for stations at corner areas where the path losses to the two antennas largely differ.To have a clearer observation, we plotted four cross sections of Fig. 2.4 and 2.5 respectively inFig. 2.6 and 2.7, where each sub-figure shows the outage probability of a station when it is placedon a cross section (indicated by a fixed y value). For symmetry, we only plotted cross sections aty=0, 5, 10 and 15. In Fig. 2.6 and 2.7, the locations (0,0) and (60,0) correspond to two cornersand a smaller y value indicates that the station is closer to the edge y = 0. We clearly observe thatMRC reduces outage probabilities more than EGC, especially for stations at corner areas.From Fig. 2.4 and 2.6, we also observe that compared with EGC, MRC has a flatter distributionof outage probabilities across the area, so that stations located farther away from the antennas willstill be heard by the CogAP. Therefore, their uplink packets will less likely collide with downlinkpackets, and consequently their contention windows will not suffer as much from exponentialincreases. With receiver diversity at the CogAP, stations farther away from the antennas still havegood chances to access the channel compared with those closer to the antennas.2.4.3 Spatially Uniformly Distributed TrafficWe place stations uniformly over the whole area to represent spatially uniformly distributed traffic.For a given number of active stations, 20 different sets of station locations are randomly generated.Simulated results under these scenarios are then averaged for evaluations. From Fig. 2.8 andFig. 2.9, we observe that under two types of spatially uniformly distributed traffic, operating twochannels in both antennas increases TCP throughput by 14%?18% when only 8 stations are active.When the number of active stations increases, the TCP throughput gain also increases, reaching36% for VoIP uplink/downlink plus FTP downlink traffic and 20% for IPTV downlink plus FTPdownlink traffic when the number of active stations is 32. The packet error rate of CBR downlinktraffic is also reduced by 50%. The packet error rate of CBR uplink is zero and thus not presented320153045600510153000.050.10.15x (meter)y (meter)Prob(Pr <= ?70 dBm)ConvEGCMRCcross sections aty=0, 5, 10, 15meterFigure 2.4: Outage probabilities in a WLAN Extended Service Set. Two antennas (or ac-cess points) are located at (15,15) and (45,15). Carrier-sensing threshold = -70 dBm.Conv: conventional WLAN.01530456005101530?0.0500.050.10.15x (meter)y (meter)Reduction of Prob(Pr <= ?70 dBm)MRCEGCcross sections aty=0, 5, 10, 15meterFigure 2.5: Reduction in outage probability with MRC and EGC. Carrier-sensing threshold= -70 dBm.here. The reason is that uplink is not heavily loaded without the presence of saturated FTP/TCPtraffic. The performance gain of two-channel-operation can be attributed to channel capture effectson downlink data packets in the cognitive WLAN over fiber system (See Section 2.3.1).330 20 40 6000.050.1y=15 (meter)x (meter)Prob(Pr <= ?70 dBm)ConvEGCMRC0 20 40 6000.050.1y=10 (meter)x (meter)0 20 40 6000.050.10.15 y=5 (meter)x (meter) 0 20 40 6000.050.10.15 y=0 (meter)x (meter)Figure 2.6: Outage probabilities in a WLAN Extended Service Set. Each sub-figure showsthe outage probability of a station when it is placed on a cross section (indicated by afixed y value). Carrier-sensing threshold = -70 dBm. Conv: conventional WLAN.0 20 40 60?0.0500.050.10.15 y=15 (meter)x (meter)Reduction of Prob(Pr <= ?70 dBm)MRCEGC0 20 40 60?0.0500.050.10.15 y=10 (meter)x (meter)0 20 40 60?0.0500.050.10.15 y=5 (meter)x (meter) 0 20 40 60?0.0500.050.10.15 y=0 (meter)x (meter)Figure 2.7: Reduction in outage probability with MRC and EGC. Carrier-sensing threshold= -70 dBm.Note that we use the number of stations to indicate the intensity of traffic since all of stationshave always-on CBR and FTP/TCP traffic.The confidence interval of obtained average packet error rates can be estimated by berconfint345 10 15 20 25 30 353456789TCP throughput (Mbps)Number of StationsConv. WLANMRC?upMRC?up/EGC?downMRC?up/MRC?down2?channel?operation(a)5 10 15 20 25 30 350246810Average PER of CBR downlink (%)Number of StationsConv. WLANMRC?upMRC?up/EGC?downMRC?up/MRC?down2?channel?operation(b)Figure 2.8: TCP throughput and average packet error rate of CBR downlink vs. Number ofstations. CBR: constant bit-rate traffic. PER: packet error rate. Traffic: VoIP uplink/-downlink + FTP downlink. MRC-up: MRC is used for uplink diversity. EGC-down:EGC is used for downlink diversity. Conv. WLAN: conventional WLAN.355 10 15 20 25 30 35345678910TCP throughput (Mbps)Number of StationsConv. WLANMRC?upMRC?up/EGC?downMRC?up/MRC?down2?channel?operation(a)5 10 15 20 25 30 350246810Average PER of CBR downlink (%)Number of StationsConv. WLANMRC?upMRC?up/EGC?downMRC?up/MRC?down2?channel?operation(b)Figure 2.9: TCP throughput and average packet error rate of CBR traffic vs. Number ofstations. Traffic: IPTV downlink + FTP downlink. MRC-down: MRC is used fordownlink diversity.36function in MATLAB, provided that the number of packet errors follows binomial distribution.Each simulation run lasts 120 seconds with 20 ms packet interval. Therefore, in 12-station case,36,000 downlink and 36,000 uplink packets are generated, resulting the following 95% confidenceintervals: [0.93%, 1.08%] at 1% average error rate and [0.08%, 0.13%] at 0.1% average error rate.A higher number of stations or a higher average packet error rate generates a tighter confidenceinterval. To avoid clutter, we do not superpose the confidence intervals on the figures of packeterror rates.Comparing the diversity methods we have investigated, using only MRC for uplink diversityslightly increases TCP throughput and reduces downlink packet error rate for CBR traffic, whileengaging additionally downlink EGC or MRC transmit diversity further improves performanceby providing a higher TCP throughput gain and lower packet error rate for CBR traffic. The re-sults also show that two-channel-operation always outperforms the diversity methods in both TCPthroughout and downlink packet error rate for CBR traffic. The advantage of multi-channel oper-ation originates from additional operation channels, which can linearly increase system capacity(assuming no co-channel interference), while diversity methods we investigate here only logarith-mically increase system capacity. When the always-on VoIP traffic is not present, our simula-tion results showed similar TCP throughput gains from both multi-channel operation and diversitymethods. The results are not presented here to avoid repetition.As shown in Fig. 2.10, heavy traffic streams like VoIP uplink/downlink and FTP uplink/down-link largely increase the packet error rate of VoIP traffic. We observe that diversity methods stillconsistently improve TCP throughput at different number of active stations. The packet error rateof VoIP traffic, however, is only slightly affected, and we regard the small difference of the packeterror rate between conventional WLAN and diversity methods as random effects in the simula-tions. In fact, our simulations show little difference among diversity methods; therefore, onlyMRC-uplink/MRC-downlink method is plotted in the packet error rate figure to avoid clutter. Thetwo-channel-operation method improves TCP throughput and outperforms diversity methods whenthe number of active stations is less than 10. When the network contains more than 10 active sta-37tions, TCP throughput of two-channel-operation method decreases and even becomes worse thanconventional WLAN when there are 24 active stations.To identify the reason of TCP throughput degradation of two-channel-operation, we plottedthe TCP uplink and downlink throughput separately in Fig. 2.11. We observe that two-channel-operation generates the highest TCP downlink throughput but the lowest TCP uplink throughput,which taken together causes the lowest total TCP throughput. To explain the reason of TCP uplinkthroughput degradation, we notice that when two-channel-operation method is used, stations beingserved in one channel are found in areas twice as large as those in the conventional WLAN, andtherefore suffer more packet collisions due to the hidden terminal problem. The above observationsuggests that when there are too many active stations in the ESS formed by the cognitive WLANover fiber system, enough number of channels should be operated to ensure proper file sharingefficiency.Compared with diversity methods and conventional WLAN, the two-channel-operation methodgenerates the highest packet error rate of CBR traffic when the number of active stations is lessthan 12, and the lowest packet error rate when the number of active stations is larger than 12. Thisphenomenon is not easy to see in scenarios under VoIP traffic. To see it more clearly, observescenarios under IPTV downlink and FTP downlink traffic, enlarged in Fig. 2.12. When two-channel-operation method is used in lightly loaded networks, the packet error rate of CBR trafficis increased because capturing a new packet causes a loss of previously being received packet; inheavily loaded networks, however, the reduced packet collisions due to extra channels outweighsthe disadvantage of CBR packet loss due to channel capture effect, causing a lower overall packeterror rate of CBR traffic than diversity methods and conventional WLAN. Although two-channel-operation caused a bit higher packet error rate for uplink CBR traffic, the packet error rate in CBRdownlink is largely decreased. For VoIP application, such balanced packet error rates provided bytwo-channel-operation would be very useful.380 5 10 15 20 25345678910TCP throughput (Mbps)Number of StationsConv. WLANMRC?upMRC?up/EGC?downMRC?up/MRC?down2?channel?operation(a)0 5 10 15 20 2501020304050Average PER of CBR (%)Number of StationsConv. WLAN (uplink)MRC?up/MRC?down (uplink)2?channel?operation (uplink)Conv. WLAN (downlink)MRC?up/MRC?down (downlink)2?channel?operation (downlink)(b)Figure 2.10: TCP throughput and average packet error rate of CBR traffic vs. Number ofstations. Traffic: VoIP uplink/downlink + FTP uplink/downlink.Explanations on the performance improvementIn diversity-based cognitive WLAN over fiber systems, the TCP throughput gains and the packeterror rate reductions come from independent channel fading and more antennas being involved at3910 15 20 2505101520TCP throughput (Mbps)Number of StationsConv. WLAN (uplink)MRC?up/MRC?down (uplink)2?channel?operation (uplink)Conv. WLAN (downlink)MRC?up/MRC?down (downlink)2?channel?operation (downlink)Figure 2.11: TCP throughput degradation of two-channel-operation method in heavily loadednetworks. Traffic: VoIP uplink/downlink + FTP uplink/downlink.8 10 12 14 1600.511.522.5Average PER of CBR downlink (%)Number of StationsConv. WLANMRC?upMRC?up/EGC?downMRC?up/MRC?down2?channel?operationFigure 2.12: Packet error rate degradation of CBR traffic (two-channel-operation in lightlyloaded networks). Traffic: IPTV downlink + FTP downlink.the receiver or transmitter. Gains of two-channel-operation in cognitive WLAN over fiber systemscome from channel capture and channel fading effects. We now further explain where these gainscome from.40Suppose a conventional WLAN ESS serves 10 stations on channel 1 of AP1 and another 10stations on channel 2 of AP2. Assume these stations are associated to the AP closer to them.Two-channel-operation actually splits the 20 stations into 4 groups, each assigned to one chan-nel through one antenna. The resulting cognitive WLAN over fiber system can be viewed asfour independently-operated conventional BSSs. Although co-channel interferences exist betweenthese BSSs, we still gain system capacity due to the linearly increased bandwidth while the signal-to-interference-noise ratio is only logarithmically degraded. On the other hand, a diversity-basedcognitive WLAN over fiber system controls antennas and forms BSSs with distributed antennas,serving stations that spread out in the whole area.An intuitive example can observed from Fig. 2.2. Apparently, stations located in the middleof the area will favor diversity technique since they have similar average path losses to the twoantennas, while stations at corner areas will favor multiple-independent-channel-operation methodsince there will be less co-channel interferences between corners. This observation reminds usthat when the location information of stations is available at the CogAP, advanced location-awarechannel management techniques can provide even higher system capacity.Effects of synchronization intervalWe examine effects of different SI values on TCP throughput under three types of traffic, as shownin Fig. 2.13. Effects of SI on the packet error rate of CBR traffic is very small and thus omitted.Since different SI values only affect two-channel-operation; only one diversity method (MRC inuplink and downlink) is plotted for comparison purpose.We observe that by using SI=1432 ?s, TCP throughput can be increased by 5.6%?10% whencompared with SI = 5 ?s, owning to the fact that larger SI values cause more packet capturing thansmaller SI values. However, we also notice that there is little difference between SI=1432 ?s andSI=100 ?s, indicating that by only looking for the strongest signal during SI=100 ?s, a WLANreceiver can achieve most of the throughput gains due to capture effect. For the rest of this chapter,100 ?s is used as the SI value.415 10 15 20 25 30 350246810TCP throughput (Mbps)Number of StationsConv. WLANMRC?up/MRC?down2?channel (SI=5 us)2?channel (SI=100 us)2?channel (SI=1432 us)(a) Traffic: VoIP uplink/downlink + FTP downlink0 5 10 15 20 25345678910TCP throughput (Mbps)Number of StationsConv. WLANMRC?up/MRC?down2?channel (SI=5 us)2?channel (SI=100 us)2?channel (SI=1432 us)(b) Traffic: VoIP uplink/downlink + FTP uplink/downlinkFigure 2.13: Effects of synchronization interval (SI).2.4.4 Spatially Non-uniformly Distributed TrafficWhen a hotspot area has much larger traffic demand than other areas, we face a spatially non-uniformly distributed traffic. We split the 60?30m2 area into 6?3 sub-areas and place the hotspot42WLAN stations for background trafficWLAN stations in a hotspot locationAntennas1 2 34 5 6Figure 2.14: Spatially non-uniformly distributed traffic. Hotspot locations are numberedfrom 1 to 6.into one of these sub-areas to simulate non-uniformly distributed traffic. Totally 8 stations are usedfor background traffic and 4 other stations are placed in certain hotspot location, as shown in Fig.2.14. By geometric symmetry, we only need study hotspot locations from 1 to 6. To concentrateon studying the effects of dynamic traffic, we fix the locations of background-traffic stations at thecenters of sub-areas 2, 4, 6, etc. Stations that generate hotspot traffic are also fixed in the centerpart of their respective sub-area. Only one set of station locations is used for simulations followed.As shown in Fig. 2.15 and Fig. 2.16, compared with conventional WLAN, diversity methodsin the cognitive WLAN over fiber system achieve 10%?62% higher TCP throughput and two-channel-operation achieves 17%?48% higher TCP throughput, whereas only 14%?36% gain isachieved when the traffic is spatially uniformly distributed (comparing Fig. 2.8 to Fig. 2.10).The packet error rate of CBR downlink is also largely reduced. This demonstrates the enhancedcapability of handling dynamic traffic in cognitive WLAN over fiber systems. Not surprisingly,two-channel-operation achieves a larger throughput gain when the hotspot is in the corners (e.g.,location 1), while diversity methods achieve larger gains when the hotspot is in the overlappingarea of antenna A1 and A2 (e.g., location 3 and 6). In fact in such areas, MRC in both uplink anddownlink achieves higher TCP throughput than two-channel-operation when the standard deviationof shadowing increases to 10 dB.When the hotspot moves to location 5, stations at the hotspot are closer to A1. Therefore, co-channel interference from stations in BSS2 to those in BSS1 is less likely due to the capture effect.Thus, we observe a larger TCP throughput gain in the two-channel-operation method, as shown in431 2 3 4 5 602468101214TCP throughput (Mbps)Hotspot location2?channel?operationConv. WLANMRC?upMRC?up/MRC?downMRC?up/EGC?down(a)1 2 3 4 5 600.511.522.533.5Average PER of CBR downlink (%)Hotspot location2?channel?operationConv. WLANMRC?upMRC?up/MRC?downMRC?up/EGC?down(b)Figure 2.15: TCP throughput and average packet error rate of CBR downlink vs. Hotspotlocation. Traffic: VoIP uplink/downlink + FTP downlink. Antenna-distance = 30 m.Shadowing standard deviation = 3.5 dB.Fig. 2.15 and Fig. 2.16.We further study antenna-distance effects under spatially non-uniformly distributed traffic.44Effects of antenna-distanceThe antenna-distance is also the physical size of a BSS in our simulations. Comparing Fig.2.17 with Fig. 2.16, we observe that both diversity and two-channel-operation methods providelarger TCP throughput gains when the antenna-distance is increased to 45 or 60 meters. Signal-to-noise-ratio gains generated by diversity methods have larger effects on throughput due to theincreased antenna-distance and consequently increased path loss. Two-channel-operation methodprovides higher throughput gains due to the increased antenna-distance and consequently reducedco-channel interference, especially at hotspot location 5 where stations are less susceptible to co-channel interferences from stations being served by the neighboring antenna.2.5 SummaryA cognitive WLAN over fiber system, as an application scenario of FMDA systems, can provide acost-effective and efficient method for devices to equally share the ISM band by taking advantageof cognitive radio capabilities. In this chapter, we have proposed two methods that utilize thespecialized capabilities of the cognitive WLAN over fiber system to improve system capacity byreducing packet collisions through load balancing and employing diversity to reduce the effects ofpacket collisions.By exploiting the wide-band radio-over-fiber connections between antennas and the cognitiveaccess point, multiple-independent-channel-operation at each antenna has been proposed to reducethe collision probability in each channel by moving stations to different channels. By exploitingthe distributed antennas in a cognitive WLAN over fiber system, we have demonstrated the use ofmacro-diversity to increase the sensing capability of the cognitive access point. Simulation resultsshow that both methods can achieve 14%?18% TCP throughput gain and 10%?50% packet errorrate reduction in constant bit-rate traffic for spatially uniform traffic in an IEEE 802.11g network,and up to 62% TCP throughput gain when hotspots exist.We also studied effects of synchronization interval and antenna-distance of cooperating anten-nas. Similar TCP throughput gain and packet error rate reduction are observed in all scenarios.451 2 3 4 5 602468101214TCP throughput (Mbps)Hotspot location2?channel?operationMRC?up/EGC?downMRC?up/MRC?downMRC?upConv. WLAN(a)0 1 2 3 4 5 6 7012345Average PER of CBR downlink (%)Hotspot location2?channel?operationMRC?up/MRC?downMRC?up/EGC?downMRC?upConv. WLAN(b)Figure 2.16: TCP throughput and average packet error rate of CBR downlink vs. Hotspotlocation. Traffic: VoIP uplink/downlink + FTP downlink. Antenna-distance = 30 m.Shadowing standard deviation = 10 dB.461 2 3 4 5 6024681012TCP throughput (Mbps)Hotspot locationConv. WLANMRC?upMRC?up/EGC?downMRC?up/MRC?down2?channel?operation(a) Antenna-distance = 45 m.1 2 3 4 5 6024681012TCP throughput (Mbps)Hotspot locationConv. WLANMRC?upMRC?up/EGC?downMRC?up/MRC?down2?channel?operation(b) Antenna-distance = 60 m.Figure 2.17: Effects of antenna-distance. Traffic: VoIP uplink/downlink + FTP downlink.Antenna-distance ?{45m, 60m}. Shadowing standard deviation = 10 dB.47Chapter 3Energy Conservation via AntennaScheduling in Fiber-connected Femto BaseStations 13.1 IntroductionFemtocell addresses the challenge on indoor wireless connectivity by pulling base station (BS)closer to users. While the cell planning is shifted towards universal frequency reuse pattern largelydue to the advantages on area spectral efficiency previously reported in cellular networks [85],in very dense urban areas with a high concentration of residential and business users, inter-cellinterference among femtocells using universal frequency reuse may drastically decrease systemcapacity. Cooperative communications among femtocells are therefore needed to eliminate theinterference in the expense of decreasing femtocells? backhaul capacity. To reduce the coopera-tion expense, motivated by advances in radio over fiber (RoF) technique [31] that improve indoorcoverage of wireless local area network [32, 33] and cellular networks [120], in this chapter wepropose to configure Fiber-connected Massively Distributed Antennas (FMDA) to form localized1This chapter is based on [86] co-authored with Dr. A. Attar and Dr. V. Leung, [87] co-authored with Mr. J.Hajipour, Dr. A. Attar and Dr. V. Leung, and [88] co-authored with Dr. A. Attar and Dr. V. Leung.48cooperation among femtocells. Focusing on coordinated multi-point transmissions (CoMP) forfemtocells in Long-Term Evolution (LTE), to which we referred as femto-CoMP, we demonstrateits considerable spectral and energy efficiency enhancement over standalone femtocells.We first formulate the power consumption under a generalized framework that takes into ac-count various contributing factors including orthogonal frequency-division multiplexing (OFDM),error control coding, and different packet schedulers that consider user fairness. After analyzing thecomputation cost of both user scheduling and multiple-input multiple-output (MIMO) linear beam-forming, we developed an optimization tool in a single femto-CoMP cluster for service providersto maximize energy conservation by adjusting the number of transmission antennas and controllingwireless transmission power in linear beamforming. Based on the analysis results, we use 2-MIMOand 3-MIMO femto-CoMPs as building blocks in a new group of network configurations, whichemploys antenna scheduling to simultaneously improve spectral and energy efficiency.The proposed configurations are denoted as FMDA-Nr-Nc-Nts: Nr ceiling-mounted fiber-connectedantennas are deployed to provide wireless access in a building, every Nc of which form one femto-CoMP cluster that serves Nc single-antenna users at a time. All antennas are equally split into Ntssets, each being chosen in its assigned time slot while other antennas are left unused. The idea ofantenna scheduling is to selectively use a large number of antennas which are only made possiblein FMDA systems such that downlink throughput can be enhanced due to reduced interference andenergy efficiency can be improved due to the reduced amount of calculations in collecting channelstate information (CSI) and linear beamforming. Antenna scheduling also enables a broad rangeof network configuration choices which offers LTE service providers the flexibility of choosingdifferent balance points between spectral and energy efficiency.The rest of the chapter is organized as follows. We first briefly review the architecture ofFMDA and present the power consumption framework. The optimization tool in single femto-CoMP network is then developed. Based on the analysis results, we propose a group of fixedantenna scheduling strategies and verify its performance improvement in Section 3.5. In the endwe summary the chapter.493.2 Power Consumption in Fiber-connected MassivelyDistributed Antennas3.2.1 ArchitectureThe architecture of FMDA is depicted in Fig. 3.1, composed of three components, namely theantennas, the fiber-connection medium and the centralized processing system. The antennas inFMDA transmit and receive radio frequency signals over the air. There is no processing capa-bility embedded in the antennas, except for radio frequency signal amplification and electrical-optical/optical-electrical conversion. The antennas will be excited from the optical link, whichcan be OM2 or laser-optimized-OM3 multi-mode fibers for low deployment costs, or single-modefibers for larger scale deployments. Owing to low propagation loss of optical fibers, the distancebetween the antennas and the centralized processing system, with off-the-shelf RoF equipment, canreach hundreds of meters, which suffice to cover most buildings in practice. FMDA integrates thecapabilities of a distributed network, based on its massively distributed antenna topology and thecentralized processing capability at the centralized processing system. Digital signal processors arepooled in the centralized processing system, which acts as femto-BS gateway in LTE-Advanced, toprovide an unparalleled throughput delivery performance in an energy efficient manner.Radio over fiber equipmentGateway of provider AGateway of provider BOptical connection boxBackbone/InternetofficefiberantennaFigure 3.1: Fiber-connected femto base stations with two service providers.50In this chapter we consider a FMDA system with Nr antennas. The number of active users isNUtotal . Every Nc antennas form a femto-CoMP cluster to serve NU users. Within each femto-CoMP, a user scheduler chooses Nc users at a time to serve through Nc ?Nc multi-user MIMOdownlink transmission. In particular, we use zero-forcing beamforming for its simplicity and near-optimal performance at high SNRs. If each femto-CoMP contains an equal number of users, thenumber of femto-CoMPs, denoted by NCoMP, can be given by NCoMP=NUtotal/NU .3.2.2 Power Consumption ModelThe total power consumption of a FMDA network, denoted by Ptot , is given byPtot = Psp+PRF , (3.1)where Psp is the signal processing component and PRF is the transmission power component con-tributed by RoF links. In this chapter we focus on downlink as downlink traffic are much heavierthan uplink traffic and thus dominate the total power consumption.Signal processing component PspConsider a BS with Nc antennas serves Nc users through Nc ?Nc zero-forcing beamforming. Wenow present a general power consumption model of signal processing component, which incorpo-rates user scheduling overhead into the micro-BS model in [121] and the cooperative BS model in[64]:Psp = PspB?B+PspB?FONCoMPNc+PspB?ENCoMPN2c +PspMS, (3.2)PspMS = PspB?MS [NCoMP(8N3c3+2N2c +Nc log2Nc+5Nc+f (Nc,NU)Nsc)] . (3.3)The PspB represents the power consumption contributed by base amount, which does not dependon Nc; PspMS represents the power consumption contributed by zero-forcing beamforming anduser scheduling. The ?B, ?FO, ?E and ?MS are positive coefficients that had been measured in51Table 3.1: Power consumption coefficientsCoefficients ?B ?E ?FO+?MSValues 0.87 0.10 0.03[64, 66] to quantify the power consumption amount attributed to the base amount, forward errorcorrection and OFDM, channel estimation, and zero-forcing beamforming and user scheduling,respectively. Each coefficient establishes the relation between the floating-point operation (flop)count and the power consumption in its corresponding component; therefore, its value dependson particular signal processing hardware and channel bandwidth configuration. Table 3.1 lists thecoefficients measured in the 10-MHz MIMO-OFDM reference system in [64, 66], which will beused throughout this chapter.We explain the formulation of (3.2) as follows. The flop count of forward error correction,OFDM, channel estimation, zero-forcing beamforming and user scheduling scales linearly withNCoMP. The flop count of forward error correction and OFDM modulation scales linearly with Nc.The flop count of channel estimation is proportional to the number of links and thus incurs O(N2c )flops. The zero-forcing beamforming is dominated by matrix inversion to generate beamformingdirections and one round of water-filling among Nc users to allocate power. Generating beam-forming directions via matrix inversion involves 8N3c /3 flops, provided Gaussian elimination withpartial pivoting is used [122]; water-filling includes calculating Nc vector 2-norms (each requires2Nc-1 flops), sorting the norms requiring O(Nc log2Nc) flops, and determining the water level andpower allocation requiring 5Nc flops. When Nc is large, the dominating term in zero-forcing beam-forming is 8N3c /3. For Nc ? 3, however, the computation cost of matrix inversion can be reduced bytaking analytic form based on Cramer rule [123], which requires 8 flops for Nc=2 and 39 flops forNc=3. The power consumption of user scheduling is expressed as f (Nc,NU), where the functionf (?) can be exponential in exhaustive search or polynomial N?c N?U for schedulers with lower com-putation costs, where ? and ? vary with different schemes. When the channel bandwidth changes,we remark that the power consumption of forward error correction, OFDM, channel estimation52and beamforming scales linearly with the number of subcarriers while scheduling can be done ata coarser granularity, per resource block, which results in a discounting factor 1/Nsc (Nsc is thenumber of subcarriers per resource block in LTE).The Psp in (3.2) is decomposed according to two principles. One is to group Nc-terms and thusprovide the insights on how to choose Nc. Another is to group functions which are implementedin the same circuit or accomplished at the same time such that the corresponding coefficientscan be measured by profiling power consumption of real products. The forward error correctionand OFDM functions are usually conducted on dedicated chips; channel estimation is performedduring uplink transmission; scheduling and beamforming are usually performed at digital signalprocessors for flexible implementation.Computation cost of user scheduling f (Nc,NU)A proportional fairness (PF) exhaustive scheduler is extremely expensive because zero-forcingbeamforming is needed at each subcarrier to estimate the instantaneous rate and the estimation isrequired by each of (NUNc) trials. Without counting PF rate update, the flop count already amountsto (NUNc)8N3c3 .A proportional fairness scheduler based on semi-orthogonal user selection (PF-SUS) [124] hasthe flop count NU2 (N3c + 8N2c ? 10Nc + 4)?Nc3 (N3c + 5.5N2c ? 10Nc ? 2.5) and can be approximatedas NU2 (N3c +8N2c ?10Nc) when NU > Nc. A round-robin scheduler based on semi-orthogonal userselection (RR-SUS) has an approximate flop count NU4 (N3c +8N2c ?10Nc) when NU >Nc. Table 3.2lists the exact flop count of the schedulers as well as the asymptotic flop count, which only takesthe highest-order of Nc terms in the exact flop count.The simplest user scheduling to preserve fairness is round-robin. In this chapter we consider around-robin tournament scheduler, termed robinT. When the set of rooms being served in two con-secutive time slots is the same, the scheduler ensures that the set of users being scheduled differs.In the case that a user combination incurs a poor channel conditional number, the combination onlyappears once and thus has minor effects on the system throughput. Consider a typical multi-floor53office building where we deployed a FMDA system by mounting one antenna in each room. Wefirst make robinT work for Nc > 2 by setting up an initial grouping in which every possible com-bination is equally probable. To improve spectral efficiency of each combination, we then enforcea heuristic constraint: in each round of multi-user MIMO transmission, one and only one user isscheduled from each room. Take NU=12 and Nc=6 as an example. The constraint comes fromthe intuition that with only free-space path loss and wall penetration loss at present, the smallestconditional number of all possible 6?6 submatrices out of the 12?6 channel matrix results fromchoosing only one user per room.Transmission power component PRFBesides the signal processing component, another power consumption contributor is the transmis-sion power component, contributed by RoF links and given byPRF = PRoFD?NCoMP?Nc, (3.4)where PRoFD is the power per RoF downlink and NCoMP ?Nc represents the total number of RoFlinks. We adopt the model presented in [125] to estimate PRoFD:PRoFD = (PLDA+PLD+PPD)+PPA,PLDA = PLDAout/?LDA, PPA = Ptx/?PA, (3.5)PLD = 140 mW, PPD = 83 mW,where PLDA is the power consumption of one laser-diode amplifier and PLDAout is its output power,set at 5 dBm in [125]; PLD, PPD and PPA are power consumption contributed by a laser diode, aphotodiode, and a power amplifier, respectively; ?LDA and ?PA indicate the efficiency of the laser-diode amplifier and the power amplifier, both fixed at 2.2%; Ptx represents the transmission powerper antenna. From (3.5) we learn that when a RoF link is not excited, there still exists a fixed powerconsumption, PLDA+PLD+PPD.54Table 3.2: Floating-point operation count of scheduling: f (Nc,NU)Scheduler Granularity Exact flop count Asymptotic flopcountPF exhaustivesearchResourceblock(NUNc)8N3c383N3cNNUPF-SUS ResourceblockNU2 (N3c + 8N2c ? 10Nc + 4)?Nc3 (N3c +5.5N2c ?10Nc?2.5)0.5N3cNURR-SUS ResourceblockNU4 (N3c + 8N2c ? 10Nc + 2)?Nc12(N3c ?2N2c ?10Nc?4)+2N2cNU0.25N3cNUrobinT Resourceblock1 13.3 Energy Efficiency in Single Femto-CoMPDefine energy efficiency as?e ?System throughputTotal power consumption= B?NUtotal ??sPtot, (3.6)where B is the channel bandwidth, NUtotal = NU for single femto-CoMP, ?s is average spectralefficiency per user under a given user scheduler and Ptot is total power consumption, given by(3.1), (3.2), and (3.4). The use of ?average spectral efficiency per user?, although not precise, canbe viewed as per-user throughput averaged over channel bandwidth and collected during networkoperation. Our focus in this section is to find optimal Nc and Ptx to maximize energy efficiency insingle femto-CoMP.3.3.1 Approximate Spectral EfficiencyAverage spectral efficiency per user under a given user scheduler is ?s = 1NU ?NUi=1?s,i, where ?s,i isthe average spectral efficiency of the i-th user. The ?s can be approximated as a time-average overpossible channel variations (including user location changes, dynamic shadowing and fading):?s =1NslotNslot?t=1{ 1NUNU?i=1[I?t(i) log2(1+Ptx?hi,t?2Pnoise)]} , (3.7)55where Nslot is the number of time slots observed; ?t is the scheduled user set at the t-th timeslot; I?t(i) is an indicator function that takes value 1 when the i-th user belongs to ?t ; Ptx is totaltransmission power constraint per MHz averaged over all antennas; Pnoise is thermal noise powerper MHz, and ?hi,t? is the average frequency channel gain of the i-th user at the t-th time slot. Asthe system of interest is single femto-CoMP, there is no inter-CoMP interference. Note that the useof Gaussian signaling is assumed in (3.7).The ?s in (3.7) can be periodically monitored by service providers to track traffic patternchanges and channel variations. By ?NUi=1 I?t(i) = Nc, the ?s at high SNRs can be approximatedas a linear function of ln(Ptx):?s =NcNU ln2lnPtx+1NslotNUNslot?t=1NU?i=1(I?t(i) log2?hi,t?2Pnoise) , (3.8)where the second term can be viewed as an estimated expectation over user locations, shadowing,fading, user scheduling decisions and other random variables through Monte-Carlo simulations,provided that Nslot is large enough. Since the second term also scales linearly with Nc, we rewrite(3.8) as?s =Nc(c1 lnPtx+c2), (3.9)c1 =1NU ln2, c2 =1NslotNUNcNslot?t=1NU?i=1(I?t(i) log2?hi,t?2Pnoise) . (3.10)563.3.2 Maximize Energy EfficiencyCombining (3.1), (3.2), (3.4), , (3.9), (3.10) and dropping lower order Nc terms in PspMS, we have?e =BNU(c1 lnPtx+c2)BPtx?+c3, (3.11)c3 = PLDA+PLD+PspB ??FO+PspB ?g(Nc), (3.12)g(Nc) =?BNc+?ENc+?MS [8N2c3+ f (Nc,NU)NcNsc] , (3.13)where ?PA is replaced by ? for notation convenience. Since g(Nc) contains all the Nc terms butno Ptx terms, we propose to maximize ?e by first finding optimal Nc to minimize g(Nc) and thenfinding optimal Ptx under such Nc.Optimal NcFor PF-SUS and robinT schedulers, g(Nc) is given by:gPF-SUS =?BNc+?ENc+?MS [8N2c3+ NU2? N3c +8N2c ?10NcNcNsc] , (3.14)grobinT =?BNc+?ENc+?MS8N2c3. (3.15)Both gPF-SUS and grobinT are convex as their second-order derivatives are positive.Consider PF-SUS scheduler. AssumeNc continuous for analytical convenience. By argmaxNc ?e =argminNc g(Nc), we find the optimal Nc, denoted by N?c , by solvingdg(Nc)dNc= ?MS(163+ NUNsc)Nc+?E +?MS4NUNsc? ?BN2c= 0. (3.16)Apparently gPF-SUS(Nc) is strictly increasing when Nc > N?c and strictly decreasing when 2 ? Nc <N?c . Since the value of Nsc is 12 in LTE, eq. (3.16) is rewritten as?B = ?EN2c +?MS [(163+ NU12)N3c +NU3N2c ] , (3.17)57which suggests that to double N?c (thus doubling the spectral efficiency), system designers needto roughly quadruple channel estimation efficiency and octuple the efficiency of beamforming andscheduling. Instead of giving involved algebraic roots of a cubic function, we list requirements on?B, ?MS, ?E for some typical values of N?c :?B ? 4?E +?MS(43+2NU),for N?c = 2,?B ? 16?E +?MS(341+10.67NU),for N?c = 4, (3.18)?B ? 36?E +?MS(1152+30NU),for N?c = 6.When a robinT scheduler is used, similarly we have,?B ? 4?E +43?MS,for N?c = 2,?B ? 16?E +341?MS,for N?c = 4, (3.19)?B ? 36?E +1152?MS,for N?c = 6.Optimal Ptx under N?cLet ??e?Ptx = 0. The optimum P?tx is found by solvingc1c3? ?BPtx(c2?c1)?c1BPtx lnPtx = 0. (3.20)Note that Ptx in LTE indoor deployment is less than 1 watt/MHz. Therefore to have a solution in(3.20), we need c2 > c1; otherwise ?e would be monotonically increasing in Ptx. From (3.8) one canshow c2 > c1 if the SNR at Ptx=1 is larger than lge, i.e., 4.3 dB. This condition is certainly satisfiedat high SNRs.58To verify whether ?e reaches the global maximum at Ptx=P?, we evaluate?2?e?P2tx?Ptx=P? =??c1BNU(P?)2(BP?+c3?)< 0. (3.21)So ?e is strictly concave at Ptx = P?. From (3.20) one can show that ??e?Ptx < 0 when P? < Ptx < 1and ??e?Ptx > 0 when Ptx < P?, indicating P? is a global optimum and the convergence of a nonlinearequation solver is guaranteed.3.4 Energy Efficiency in Multiple Femto-CoMPsThe above optimization process is based on single-CoMP configuration. In multiple femto-CoMPs,however, the parameter c2 in (3.7) is affected by inter-CoMP interference and therefore dependson frequency reuse pattern and {NCoMP, Nc} configuration, making it difficult to have a reliableestimate on spectral efficiency. To optimize the overall system energy efficiency, one needs to findthe optimal transmission power and the optimal number of cooperating antennas for each femto-CoMP. This combinatorial optimization problem is generally difficult to be solved in real time. Inthis section, we propose an antenna scheduling approach to heuristically solve this problem.3.4.1 Motivation of Antenna SchedulingOur approach exploits one major advantage of FMDA architecture, abundant antennas available ina system. Compared with an outdoor cellular network, an indoor FMDA system typically has muchless users nearby each antenna; therefore, universal frequency reuse may not provide the largestsystem capacity. Instead of using all antennas and trying to reduce inter-CoMP interference, wecould selectively use antennas in time slots and as the result of less interference and less number offemto-CoMPs per slot, spectral and energy efficiency are expected to be concurrently improved.In this joint scheduling problem, we need to find an optimal user-antenna matching. To reducecomplexity, we decouple it into two scheduling problems: user scheduling and antenna scheduling.For user scheduling, we use round-robin tournament algorithm for its simplicity, fairness and good59performance in spectral efficiency when the number of users per femto-CoMP is small. Considera multi-floor office building where we deployed a FMDA system by mounting one antenna in eachroom. Once the user set is given, the antennas in corresponding rooms have to be chosen to ensurebeamforming performance. Therefore, our first problem is to determine the number of users beingscheduled for each time slot. Scheduling too many users causes excessive inter-CoMP interference;scheduling too few wastes transmission opportunities. Also, the users being scheduled should bespread in space to reduce inter-CoMP interference.Once the user set is determined, CSI should be collected to enable antenna scheduling andbeamforming. The second problem is to determine the amount of CSI needed for schedulingpurpose. Since CSI varies over space, time and frequency, its collection is an expensive operationin MIMO systems, as indicated in (3.2), and needs to be carefully planned.Given collected CSI, the third problem is finding the optimal clustering pattern to maximize anefficiency criterion subject to certain constraint, as required by the service provider. Examples ofsuch balance include maximizing spectral efficiency while maintaining minimal energy efficiencyin network peak hours, and maximizing the energy efficiency while maintaining minimal level ofservice at midnight.3.4.2 Antenna Scheduling Based on Two-user MIMOIn the energy efficiency analysis of single CoMP cluster, after plugging ?B = 0.87, ?E = 0.10 (asused in [64]) and ?MS = 0.02 into (3.19) to check the optimum condition of N?c =2, we found?B < 4?E +43?MS, indicating that two-user MIMO provides the best energy efficiency among allNc choices. By solving (3.20) we found that the optimal transmission power is 5.1 mW/MHz fora 10-MHz channel. The optimal transmission power is under the output power limit regulated inLTE, 100 mW per single-antenna home BS [126]. Note that we consider each antenna equivalent toone home BS (or femto-BS). Motivated by this finding, we attempt to solve the antenna schedulingproblem by posing two constraints: each femto-CoMP has the same Nc; Nc is fixed at 2. The Ptx isfixed as transmission power control is not the focus of this chapter.60To avoid expensive CSI collection, we base the scheduling strategy on geographical informa-tion that includes dual-stripe floor plan and the existence of wall/floor penetration loss. Specifi-cally, cooperation of two antennas only occur when they are located in neighbor rooms and whenpossible, the cooperation between two antennas on one side of corridor is preferred because thereis only one wall penetration and thus more signal energies can be harvested in two-user MIMOoperation.Under the above constraints, we denote possible configurations as FMDA-Nr-2-Nts, which in-dicates that the system is equipped with Nr ceiling-mounted antennas, every two of which formone femto-CoMP cluster, and all antennas are equally split into Nts sets. Each set of antennas isused in its assigned time slot while the rest of antennas are left unused. Apparently the energyconsumption of both signal processing and CSI collection is reduced by Nts times.In the ideal case, antenna scheduling should track channel variations on per-slot basis. How-ever, extra CSI between each scheduled user and its neighboring antennas are needed when wewant to reconfigure femto-CoMPs. To reduce the CSI collection overhead, we could increase thetime interval of scheduling update to the channel coherence time or even the shadowing coherencetime; the scheduling granularity in frequency can also be increased to the coherence bandwidthrather than one resource block. In this chapter, we propose multiple promising static antennascheduling and demonstrate their potentials to simultaneously improve energy and spectral effi-ciency.When standalone femtocells are operated, antenna scheduling in time is impossible as switch-ing off any femto-BS for a long time will affect short-term user fairness while a frequent switchingis impractical due to the required femto BS boot-up and network synchronization time.3.5 Numerical ResultsWe consider a four-floor office building with six rooms per floor. The rooms are divided into twostripes by a two-meter wide corridor. The dimension of each room is 12?6?3 m3. We assume twousers with fixed separation dU=12 meters, as depicted in Fig. 3.2, and focus on saturated down-61FMDA-Nc-Nc-1FMDA-24-2-1FMDA-24-3-1FMDA-24-2-2FMDA-2-2-1 FMDA-6-6-1FMDA-4-4-118m18mStandalonefemtocells12m36m6m14m 2mFloor layout: Dual-stripe. Room height: 3 meters.dUFMDA-24-3-2FMDA-24-2-3 roomfloorcorridorSlot 1LegendStandalone femtocellAntennaUserSlot 2Slot 3Slot 4Femtocell 1Femtocell 2FMDA-Nr-Nc-NtsFMDA-24-3-3 FMDA-24-3-4Figure 3.2: Simulation scenarios for femtocell and FMDA. Antennas of FMDA-Nr-Nc-Ntsare scheduled in up to four time slots.link traffic. To provide wireless access to users in the building, we have two options: standalonefemtocell and FMDA. The following describes antenna or femto-BS placement within each con-figuration. Antenna scheduling and clustering are detailed in corresponding FMDA configurations.3.5.1 Simulation ModelStandalone femtocell: Each femto-BS forms a closed subscriber group and therefore operates in-dependently. We assume that there exists one femto-BS, equipped with one antenna in each room.62In femtocell-1 configuration, all femto BS units transmit in each slot; in femtocell-2 configuration,all femto-BS units are equally split into two sets that transmit in alternate time slots to reduceinter-cell interference. As explained earlier, regardless the transmitting state of a femto-BS, itspower consumption is assumed constant at 18 watts, which is a typical power consumption valuein commercial femto-BS units.FMDA-Nc-Nc-1: Denotes a FMDA network that is equipped with Nc antennas, where Nc ?{2,4,6}. The antennas are placed on the ceiling of the corridors and form a single femto-CoMPcluster.FMDA-Nr-Nc-Nts: Denotes a FMDA network that is equipped with Nr ceiling-mounted anten-nas, every Nc of which forms one CoMP cluster. All antennas are equally split into Nts sets, eachset being active in its assigned time slot while other antennas are left unused. Besides Nc=2 config-uration, we also verified Nc=3 configuration as potential candidates for energy saving. As opposedto FMDA-Nc-Nc-1, the antennas are placed within the rooms. Water-filling was conducted withineach femto-CoMP as if there is no inter-CoMP interference.Following the air interface of LTE Release 8, we chose to use 10 MHz channel bandwidth with9 MHz allocated for data communications. Every device is attached to only one channel in the 2.5GHz band. The channel model of each link is composed of static path loss, spatially correlatedstatic shadowing, and time-varying frequency-selective fading.Shadowing and fading: While fading channels in the three studied access technologies aremodeled as tapped delay lines with parameters from ITU-R M.1225, path loss and shadowingmodels vary with systems and different antenna placements. Link path loss follows M.1225 withthe penetration loss model from COST231, i.e., 18.3 dB loss per floor and 6.9 dB loss per wall.In the femtocells, there are two links from two users in each room to their corresponding femto-BS. We model the shadowing in this case as spatially correlated with an exponential correlationfunction of the user separation. The shadowing is assumed to be independent for two users indifferent rooms. Given two links from two femto-BS units to one user, we always assume thatthese two links have independent shadowing due to the large femtocell separation distance.63Further in the FMDA network, when antennas are placed in corridors, the indoor hotzonemodel in M.2135-1 [127] is used to describe the path loss and shadowing. When an antenna isplaced in each room, as in FMDA-Nr-Nc-Nts, the path loss and shadowing models follow those instandalone femtocells. The noise figure at each user?s receiver is assumed to be 7 dB. All otherchannel propagation parameters follow M.2135-1 unless otherwise noted.User scheduling: A robinT scheduler is used in FMDA. For femtocells, robinT scheduling onlysuffers minor spectral efficiency loss when compared with computationally intensive PF exhaustivesearch. As such, only robinT is used to evaluate energy efficiency of femtocells.Antenna scheduling in FMDA-Nr-Nc-Nts: When Nts = 1, neighboring antennas on one floor areclustered into 2- or 3-MIMO setting, as shown in the bottom part of Fig. 3.2, and other floorsfollow the same configuration. When Nts > 2, femto-CoMPs assigned with the same time slot areplaced on alternating sides of the building to reduce inter-CoMP interference. In all configurationsin Fig. 3.2 except FMDA-24-3-3, only two neighboring floors are shown and other two floorsfollow the same pattern.Power consumption coefficients: The ?B is set as 0.87 and ?E=0.10, as listed in Table 3.1. The?FO, ?MS are chosen as 0.01 and 0.02, respectively; their sum matches the value 0.03 in Table 3.1.3.5.2 Spectral EfficiencyWe now demonstrate the advantages of the proposed FMDA antenna scheduling in both energyefficiency and spectral efficiency in comparison with standalone femtocells. The throughput ofa given user at a given time slot is the sum of Shannon capacities of all subcarriers used by thisuser. All packets are transmitted in a slotted manner, where each slot lasts 1 millisecond and eachsimulation lasts 5 seconds.In both FMDA-24-2-Nts and FMDA-24-3-Nts configurations, as shown in Fig. 3.3a, the systemgradually enters the interference-limited state when Ptx increases. Those configurations with alarger Nts enter the state at higher Ptx values due to the increased inter-CoMP separation distance.The ?s in interference-limited state increases when Nts increases from 1 to 2. Specifically, the6420% and 23% gain in ?s are achieved in FMDA-24-2-2 and FMDA-24-3-2, respectively. The ?s,however, drops when Nts further increases to 3 or larger due to wasted transmission opportunities.In fact, FMDA-24-2-4 and FMDA-24-3-4 did not even enter the interference-limited state.1e?3 1e?2 0.1 1 10 1000.811.21.41.61.822.22.42.6Transmission power per antenna (mW/MHz)Spectral efficiency (bps/Hz/User)FMDA?24?2?1FMDA?24?3?1FMDA?24?2?2FMDA?24?3?2FMDA?24?2?3FMDA?24?3?3FMDA?24?2?4FMDA?24?3?4femtocell1?1femtocell1?2(a) Spectral efficiency vs. Transmission power per antenna.0.001 0.01 0.1 1 10 10024487296 120144168192216240264Transmission power per antenna (mW/MHz)Energy efficiency (Mbits/joule) FMDA?24?2?1FMDA?24?3?1FMDA?24?2?2FMDA?24?3?2FMDA?24?2?3FMDA?24?3?3FMDA?24?2?4FMDA?24?3?4femtocell1?1femtocell1?2(b) Energy efficiency vs. Transmission power per antenna.Figure 3.3: Spectral and energy efficiency vs. Transmission power per antenna.653.5.3 Energy Efficiency vs. Spectral EfficiencyFig. 3.3b presents the energy efficiency ?e at different levels of Ptx, which range from 10?3 to100 mW/MHz. Driving Ptx up to 100 mW/MHz is to show a complete picture of energy efficiencyalthough the transmission power level is over the limit regulated in LTE [126]. As expected, theconfiguration group FMDA-24-2-Nts provides the best energy efficiency due to the use of two-userMIMO and they reach the optimal efficiency when Ptx ? 1 mW/MHz, approximately correspondingto the Ptx level when the systems become interference-limited. The phenomenon suggests whenPtx is less than 1 mW/MHz, energies consumed by wireless transmission are much less than thoseconsumed by signal processing. Therefore the best strategy to be energy efficient is increasing Ptxuntil the FMDA system becomes interference-limited.The tradeoff between energy and spectral efficiency is shown in Fig. 3.4. In all configurationswe observe the bell-shaped curves because, as we observed in Fig. 3.3b, the energy efficiencyfirst increases when the transmission power increases from a very low value to certain point wherethe system enters the interference-limited state. After the transmission power surpasses this point,much more energies are consumed by radio frequency power amplifiers but little throughput gainis achieved, thus causing a drop in energy efficiency. The drop is steep because of the extremelypoor power amplifier efficiency, 2.2%, as modeled in Section 3.2.2.The square area enclosed by gray dotted lines represents a preferable operation region whereany operating point has advantages over standalone femtocells in both spectral and energy effi-ciency. Among single femto-CoMP configurations, only FMDA-4-4-1 can enter the region whenPtx reaches 100 mW/MHz.In multiple femto-CoMPs, four configurations are able to simultaneously improve both en-ergy and spectral efficiency, demonstrating the potential of antenna scheduling in achieving a de-sired balance between spectral and energy efficiency. Compared with femtocell-2, FMDA-24-2-3improves energy efficiency by 160% and spectral efficiency by 2%; FMDA-24-3-2 improves en-ergy efficiency by 64% and spectral efficiency by 36%. Compared with FMDA-4-4-1 at Ptx=10660 1 2 3 4 50 4896144192240288Spectral efficiency (bps/Hz/User)Energy efficiency (Mbits/joule)femtocell1?2femtocell1?1FMDA?24?3?3FMDA?24?2?3FMDA?24?3?2FMDA?24?2?2FMDA?6?6?1FMDA?4?4?1FMDA?2?2?1Figure 3.4: Energy efficiency vs. Spectral efficiency under different Ptx (10?3 ? 102mW/MHz). Mbits/joule: 106 bits/joule.mW/MHz, FMDA-24-2-3 improves energy efficiency by 68% and spectral efficiency by 15%;FMDA-24-3-2 improves energy efficiency by 6% and spectral efficiency by 55%. However, oneshould also be aware of the higher infrastructure cost associated with FMDA-24-2-3 and FMDA-24-3-2 since a much higher number of ceiling-mounted antennas and more optical fibers need to beinstalled when compared with FMDA-4-4-1. Notice that since systems in multiple femto-CoMPsetting are able to reach interference-limited state, their optimal operation points are reached at aPtx level significantly lower than systems in single femto-CoMP setting.3.6 SummaryWe proposed a novel group of network configurations that employs antenna scheduling in anFMDA network to simultaneously improve both spectral and energy efficiency. Denoted as FMDA-Nr-Nc-Nts, the proposed scheme selects Nr/Nts antennas out of Nr ceiling-mounted fiber-connectedantenna in each time slot, every Nc neighboring antennas forming a femto-CoMP cluster that servesNc users at a time. Compared with standalone femtocells, the proposed scheme is shown in a typi-67cal office building to increase energy efficiency by 64%?160% and spectral efficiency by 2%?36%.The exact gain depends on network configurations and transmission power levels because a higherenergy efficiency gain implies a lower spectral efficiency gain.The proposed antenna scheduling strategy relies on a large number of antennas, which are onlymade possible in FMDA system. Downlink throughput is enhanced due to reduced interference;energy efficiency is improved as leaving antennas unused reduces energy consumed by collectingchannel state information and zero-forcing beamforming. Antenna scheduling enriches networkconfigurations on how many antennas should cooperate and how much separation distance shouldbe kept among cooperating clusters, thus offering service providers a greater flexibility on choosingdifferent balance points between spectral and energy efficiency.68Chapter 4Energy-efficient Low-complexityZero-forcing Beamforming via BandedMatrix Inversion in Indoor Fiber-connectedMassively Distributed Antenna Systems14.1 IntroductionMassive array multiple-input multiple-output (MIMO) addresses ever-increasing traffic demandby densifying radio access networks. The spectral efficiency advantages of massive array-MIMOsystems have been shown in analysis under match filter precoding [45], zero-forcing beamforming[46], and demonstrated in experiments [47]. Two recent contributions analyzed the energy effi-ciency of massive array-MIMO in the uplink [69] and downlink [70]. From the path loss aspect,however, it would be more energy-efficient to locate the antennas closer to the mobile terminals,which motivates the use of a large number of femtocells. While adopting universal frequency reusein such networks to enjoy the advantages on area spectral efficiency [85], one needs to mitigate1This chapter is based on [97] co-authored with Dr. V. Leung.69the resulting inter-cell interference. Multi-cell processing can mitigate the inter-cell interferencethrough multi-user MIMO, which however requires channel state information (CSI) from partici-pating femto base stations (BSs) and therefore decreases the backhaul capacity. Pooling basebandsignal processing at a centralized processing system (CPS) can reduce the cost of cooperation,in which case each BS is reduced to an antenna that contains a power amplifier and a low-noiseamplifier, and when a large number of such antennas are deployed, the system constitutes a Fiber-connected Massively Distributed Antennas (FMDA) system. The optical or coaxial wireline facil-ity interconnecting the CPS and an antenna can be analog or digital. An analog facility carries radiofrequency signals (e.g., by radio over fiber (RoF) technology in an optical facility), thus allowingantennas that are simpler and more transparent to standards (e.g., [87]). A digital facility carrieshigh-rate in-phase/quadrature samples, thus eliminating signal distortions caused by nonlinearitywhile transmitting analog signals [76]. In such case, however, an antenna needs a very-high-ratedigital transceiver and high-speed analog/digital and digital/analog converters.In this chapter we study how to improve the energy efficiency and reduce the computation costof FMDA systems. Locating antennas closer to mobile terminals cause the power consumptionof digital signal processing rather than radio frequency transmissions to be emphasized in theoverall energy consumption, which has not been widely considered in previous literature. Notethat baseband signal processing is a significant contributor of the overall energy consumption,especially in femtocells where the transmission power is low and no air conditioning is needed[63]. Our research question is how to make beamforming feasible for practical implementationand energy efficient in the presence of a large number of antennas. We consider an indoor officeenvironment where each room is equipped with one antenna. The antennas cooperate by zero-forcing beamforming (ZFBF) due to its simplicity and near-optimal performance at a high signal-to-noise-ratio (SNR) [128].We propose a low-complexity ZFBF algorithm via banded matrix inversion that aims to reducesignal processing complexity in indoor FMDA systems. The idea is motivated by the phenomenonthat in massively distributed antenna systems, only neighboring antennas need to cooperate. Large70wall-penetration losses in indoor environments strengthen such a phenomenon and allow the use ofbanded inversion, which offers a substantial reduction in the computation cost of matrix inversion,CSI collection, and MIMO precoding.4.1.1 Related WorkThe Wyner model [89] is a widely accepted inter-cell interference model that involves a tri-diagonal matrix, a special case of banded matrix. Specifically, BSs are linearly placed and theinterference between the k-th BS and b-th BS (denoted by vk,b) is 1 for k = b, ? for ?k?b? = 1, and 0otherwise. While convenient to analyze in multi-cell processing [90, 91, 96], the Wyner model isonly accurate with a sufficiently large number of simultaneous users and perfect BS power control[92]. Banded matrices had been applied to electromagnetic wave simulation [93], inversion oftri-diagonal matrices [94], and equalization [95]. Specifically, the equalization scenario resemblesdistributed MIMO in that a farther distance in the frequency domain implies less inter-carrier inter-ference. With regard to ZFBF in distributed MIMO systems, the only work to exploit banded pathloss structure is [96], where under a given backhaul constraint, unequal CSI in distributed antennasystems and optimal CSI allocation are discussed.Approximated matrix inversion have been used to find a suitable starting point for iterativeinversion of sparse matrices, such as Jacobi/Gauss-Siedel and conjugate-gradient methods. Givena finite banded matrix V, Demko showed in [129] that the inverse V?1 has exponentially decayedoff-diagonals (EDODs), i.e., v?1k,b ? K? ?k?b?, where K is a constant, 0 < ? < 1, and both K and ?depend on the width of V. It was later shown [130, 131] that given V with EDODs, V?1 alsohas EDODs yet at a higher rate, i.e., v?1k,b ? ? ?k?b?(0 < ? < ?). When V has polynomially decayedoff-diagonals, i.e., vk,b ? K(1+ ?k?b?)??(? > 1), Jaffard?s theorem [132] states that V?1 also haspolynomially decayed off-diagonals at the same decay rate, i.e., v?1k,b ? K(1+ ?k?b?)?? . A goodsummary of Demko and Jaffard?s work along with other findings can be found in [133]. The decayrate bound in [130] is for general banded matrices and increases with the width p. Such bound istoo loose when applied to estimate the signal-to-interference-noise-ratio (SINR). Besides, we are71more interested in random channel matrices with a path loss matrix having compositely decayedoff-diagonals (CDODs) that comprises both exponential and polynomial decays.4.1.2 ContributionsIn a massively distributed antenna system, it is challenging to determine the entire channel ma-trix H and power-consuming to both generate the precoding matrix W and precode the symbols,especially when these operations are required in each subcarrier if orthogonal frequency-divisionmultiplexing (OFDM) is used. Our proposed low-complexity ZFBF scheme meets these chal-lenges by discarding less important off-diagonal elements in H to form a banded, sparse matrix,Hp, where p controls the sparsity of H. The precoding W is then generated based on Hp. Thescheme is evaluated by applying it to a distributed antenna system that covers a dual-stripe officebuilding floor. Compared with traditional ZFBF, the proposed scheme significantly reduces theamount of signal processing and hence improves the energy efficiency due to the reduced com-plexities in CSI collection, matrix inversion and precoding.The proposed scheme contains two versions: denseW and sparseW. The denseW version usesthe full inversion of Hp as the precoding matrix, incurring quadratic computation cost, relative tothe number of antennas. The sparse W version further bands W to achieve linear computationcost of precoding. We analyze the performance impact of banding random channel matrices, inwhich the variances of the entries have EDODs or CDODs. Both the SINR analysis and numericalevaluations indicate that compared with a dense W, a sparse W incurs a negligible SINR lossunder CDOD but significant loss under EDOD. To the best of our knowledge, our work is the firstto consider the inversion of random matrices with EDODs or CDODs.Notations: A bold capital A indicates a matrix A; a bold lowercase a indicates a column vectora. The l2-norm of a is ?a?. The entry on the i-th row and j-th column of H is denoted by H(i, j) orhi, j; Ha?b,c?d denotes the submatrix of H formed by rows [a,a+1,?,b] and columns [c,c+1,?,d].Bp denotes the set of banded matrices with width p, i.e., entry (k,b) is zero for ?k?b? ? p. Weconsider banded matrices with equal upper- and lower-width p?1, which is the number of non-72zero sub-diagonals above and below the main diagonal, respectively. Given a matrix H, the bandedH with width p is obtained by keeping the main diagonal and p?1 off-diagonals on both sides,denoted by Hp. HT , HH , H?1, ?H? denote the transpose, Hermitian transpose, inversion, anddeterminant of matrix H, respectively. A diagonal matrix D is denoted by diag[d1,1,d2,2, ...,dn,n].The operator ? denotes the Hadamard product. I denotes identity matrix. The largest integer notlarger than x is denoted by ?x?. The variance of a random variable x is denoted by var(x). zero-meancircularly symmetric complex Gaussian (ZMCSCG) distribution with variance ?2 is denoted byCN (0,?2). The uniform distribution between a and b is denoted by U(a,b). The functions ln(?)and lg(?) represent natural and base-10 logarithm, respectively. RHS means ?right hand side?.EX[?] denotes the expectation over the random variable X.The rest of this chapter is organized as follows. We introduce the system model in Section 4.2and propose the banded inversion algorithms in Section 4.3. The SINR loss from using a denseand sparse precoding matrix is analyzed in Sections 4.4 and 4.5, respectively. The downlink energyefficiency is modeled and analyzed in Section 4.6. We evaluate the performance in Section 4.7 andsummary this chapter in Section 4.8.4.2 System ModelConsider a massively distributed antennas system deployed on one floor of an office building withN rooms arranged in a single-stripe topology as depicted in Fig. 4.1. The system is composed ofthree components, namely the antennas, the optical cables and the CPS. Each room has one userand one ceiling-mounted fiber-connected antenna, which transmits and receives radio frequencysignals over the air while all the baseband signal processing is concentrated at the CPS. Opticalfibers have a low propagation loss and high bandwidth, and are well-suited to carry radio frequencysignals between antennas and the CPS. The fiber runs can reach hundreds of meters, thus it isfeasible to implement a massive array of distributed antennas to cover most buildings in practice.73??2p-1 roomsantennauserroom1st room Nth roomCPSfiberFigure 4.1: A Fiber-connected Massively Distributed Antennas system. CPS: centralizedprocessing system.4.2.1 Channel Matrix HThe N?N channel matrix H is given by V?F, where V is the path loss matrix and F is a frequency-flat block-fading matrix, modeled as independent and identically distributed (i.i.d.) ZMCSCG. Inthis chapter, we ignored static and dynamic shadowing for analytic convenience.Let the k-th room enclose the k-th user and the k-th antenna. The path loss between the k-thuser and the b-th antenna (1 ? k,b ? N) is modeled as the free space propagation loss with pathloss exponent ? , plus the wall penetration loss which is given by L(k?b) dB, where L is 6.9 dBfor concrete walls and 3.4 dB for plasterboard walls according to the COST231 indoor path lossmodel in ITU M.1225 [127]. The (k,b) entry in V is then given byvk,b = (?k?b???k)??/2? ?k?b? ? (?k?b?)??/2? ?k?b?, (4.1)where ?k is the distance between the k-th user and the k-th antenna and ? = 10?L/20 (?=0.45 forL=6.9 dB). The term ? ?k?b? indicates exponentially decayed off-diagonals in V, attributed to thewall-penetration loss. The term (?k?b?)??/2 indicates polynomially decayed off-diagonals, whichare caused by free space propagation losses. The inter-antenna distance is normalized to 1.4.2.2 PrecodingAssume perfect CSI at the transmitter [134] and perfect synchronization [135, 136]. We considerN?1?N downlink transmissions: N pre-scheduled single-antenna users are simultaneously served74by N antennas through N?N multi-user MIMO downlink transmissions. After precoding, thereceived signal vector is y =HWs+n, where y is the N?1 received symbols, H = [hT1 ;hT2 ;?;hTN],W = [w1w2?wN] is the N?N precoding matrix, s = [s1s2?sN]T is the N?1 transmitted symbolvector, and n is the N?1 i.i.d. additive Gaussian noise vector in which each component has zeromean and variance ?2. Considering ZFBF, we have W = H?1. Given a stream power allocation{Pk}(1 ? k ?N), we assume s ? CN (0,diag[P1,?,PN]).4.2.3 Stream Power AllocationStream power allocation employs waterfilling (WF) algorithm under sum power constraint (SPC),denoted by Pspc, or per-antenna power constraint (PAPC), denoted by P. WF-SPC establishesan analytic solution of the convex optimization problem [128]. WF-PAPC uses the interior pointmethod to iteratively solve the problem [137]; however, the average number of iterations is hardto predict. To control nonlinearity in each RoF link while maintaining a low complexity, we use arelaxed version of WF-SPC, termed ?WF-SPCr?, which first achieves a lower bound of WF-PAPCby running WF with Pspc = P, as proposed in [138]. Once an initial allocation {Pk}(1 ? k ? N) isobtained, the second step is to tighten the lower bound by scaling up all streams? power with asingle scaling factor until P is first reached at one antenna. The scaling factor is found by firstlocating the antenna being assigned with the maximal power and then dividing its output power byP. Our benchmark is conventional WF-SPC subject to Pspc = NP with the precoding matrix beingWp, termed ?WF-SPC-dW?.4.3 Banded Inversion of Matrices with Compositely DecayedOff-DiagonalsWe now develop banded matrix inversion algorithms for matrices with CDODs. Consider an N?Nmatrix H. Let H = Hp +Dp where Dp is the difference between the banded H and the true H.Denote by W the full inversion of H; Wp the full inversion of Hp, also referred to as dense W; Spthe banded inversion of Hp, also referred to as sparse W.754.3.1 Banded InversionConsider a nonsingularH ?Bp and assumeH can be factorized intoLUwhereL is lower-triangular,U is upper-triangular, and L,U ? Bp [27]. Therefore, as depicted in Fig. 4.2, we can obtain Wpby factorizing Hp into LpUp via Gaussian-elimination without pivoting, followed by conventionalforward and backward substitution as Lp and Up, although banded, still have dense inverses. Dis-abling pivoting does not cause numerical instability if Hp is strictly diagonally dominated, i.e., themagnitude of the diagonal entry in a row is larger than or equal to the magnitude sum of other en-tries in the same row. Owing to the fast decaying off-diagonals in V, we expect that most instancesof Hp possess this property.To avoid the expensive multiplication U?1p L?1p , we truncate L?1p and U?1p during forward andbackward substitution to obtain Sp. For each column of L?1p and U?1p , we keep only 2p-1 entriesthat are closest to the main diagonal. The resulting algorithm consists of a banded LU factorizationto factorizeHp intoLp andUp [139], and a banded forward/backward substitution to solveLpx=biandUpy=x, where bi is the i-th column of I. The banded forward/backward substitution algorithmsare listed in Table 4.1.Table 4.1: Algorithm: Banded forward/backward substitutionDense-W Sparse-WBandedForwardSubstitutionfor r=i+1:Nidx=max(i,r-p+1):r-1b(r)=b(r)-L(r,idx)*b(idx)endfor r=i+1: min(i+p-1,N)idx=max(i,r-p+1):r-1b(r)=b(r)-L(r,idx)*b(idx)endBandedBackwardSubstitutionb(N)=b(N)/U(N,N)for r=N-1:-1:1idx=r+1:min(r+p-1,N)b(r)=(b(r)-U(r,idx)*b(idx))/U(r,r)endes=min(i+p-1,N)ee=max(1,i-p+1)b(es)=b(es)/U(es,es)for r=es-1:-1:eeidx=r+1:min(r+p-1,es)b(r)=(b(r)-U(r,idx)*b(idx))/U(r,r)end761 p N-p+2 N1 p 1 pp-1 N-2p+1 pp-1N-2p+1pBandedLUStripedLUFigure 4.2: LU factorization of banded and striped matrices. Blank areas are zeros.4.3.2 Striped InversionWrapping around the topology in Fig. 4.1 leads to a circular topology that corresponds to a stripedchannel matrix, named after two stripes formed by the zero entries in the upper-right and the lower-left area, as shown in the bottom part of Fig. 4.2. Unlike the banded inversion, the striped inversionneeds to generate the lower-left and upper-right corner areas in the inverse. However, the increasedindexing complexity is negligible when p ? N. Note that the valid range of p is 1 ? p ? N in thebanded inversion and 1 ? p ? ?(N +1)/2? in the striped inversion.The striped LU factorization, as listed in Table 4.2, still uses vector-matrix operations for thefirst and last p-1 rows, which densify the last (p-1) rows in L and the last (p-1) columns in U,shown as the dark areas in Fig. 4.2. Those entries, however, are not accessed by the stripedforward/backward substitution and thus, equivalently, zeros.77Table 4.2: Algorithm: Striped LU factorization of HStriped LU for k=1:N-1if k<p; rl=[k+1:k+p-1 N-p+k+1:N]else rl=k+1:min(k+p-1,N)endH(rl,k) = H(rl,k)/H(k,k)H(rl,rl) = H(rl,rl) - H(rl,k)*H(k,rl)end4.4 SINR Loss Using Dense WTo analyze the residual interference when the dense precoding matrix Wp is used, we start withpath loss matrices with CDODs and then move on to random matrices.Given an instantaneous full channel matrix H and the dense precoding matrix Wp, the receivedsignal y is given by:y =HWps+n = (Hp+Dp)Wps+n = (I+DpWp)s+n ? Is+DpWps, (4.2)where the last approximation is possible under the high SNR assumption. Let A =DpWp, whichrepresents the residual interference after the banded inversion. Although the main diagonal of Astill contributes to the signal power, they are relatively small when being added by the identity ma-trix I. Thus we redefine A as DpWp with the main diagonal cleared. By E[ssH] = diag[P1,?,PN],the residual interference power of the i-th stream, denoted by Ii, is given by:Ii =N?j=1, j?i[?ai, j?2Pj] ? PN?j=1, j?i[?ai, j?2], (4.3)where P is the sum power constraint divided by N and Pj is the power of the j-th stream. Theapproximation is to decouple the analysis of residual interference from stream power allocation.Notice that the RHS in (4.3), denoted by I?i, is reached under equal stream power allocation.In the following, we analyze I?i for different types ofH, as listed in Table 4.3.78Table 4.3: Types of channel matrix H (0 < ? < 1,2 ? ? ? 4)ED?The Toeplitz matrix H with exponentially decayed off-diagonal entriesat rate ? , i.e., hi j = ? ?i? j?.EPR?,? The set of random matrices whose off-diagonal entries decay bothexponentially at rate ? and polynomially at rate ? , i.e., hi j = ?i? j +?i???/2? ?i? j?, where ?i is the normalized distance between the i-th userand the i-th antenna, subject to U(?0.5,0.5).EP? ,? ,? EPR?,? with fixed ? , representing a Toeplitz matrix H where hi j =?i? j???/2? ?i? j? for i ? j and ?? ???/2?0 for i = j (?? ? < 0.5).EZ?The Hadamard product of a ZMCSCG matrix and an ED?matrix.EPRZ?,? The Hadamard product of a ZMCSCG matrix and an EPR?,? matrix.4.4.1 Path Loss Matrix ED?Given H ? ED?, we now develop how lg(I?i) varies with p. Let H = Hp +Dp and A = DpWp.Consider p+ 1 ? i ? N ? p. The transpose of the i-th row of Dp, denoted by di, is composed ofthree sections: [? i?1;?;? p], [0;?;0] and [? p;?;?N?i]. Each entry in the j-th column of Wpis bounded by the corresponding entry in w j = [? j?1;?;?N? j] (1 ? j ? N), according to Wp ?ED?(? < ? < 1) which we learn from [130]. All of the multiplicative constants are dropped as ourinterest is to examine how I?i varies with p. By ai, j = dTi w j, the ai, j reaches its maximum when ? pin di meets 1 in w j. When the entry ?1? in w j falls in one of three sections in di, there is one rulingitem for each j:ai, j ???????????????????????????????i? j(??)p, j ? i? p?p(? j?i+p+? i? j+p)1??? , i? p < j < i+ p?1?????j?i(??)p, j ? i+ p?1(4.4)After some algebraic manipulations, the I?i is approximated byI?i ?2P?2p1?? 2( ?? ??)2? ?2p, (4.5)79where i ? [p+ 1,N ? p] and p ? 2. For i ? [1, p] and i ? [N ? p+ 1,N], there is only one side ofinterference; hence, I?i ??2p. By ? = 10?L/20, we have lg(I?i) decreases linearly with p (1< p?N).4.4.2 Path Loss Matrix EP?,? ,?Given H ? EP?,? ,? , we can show that the interference term lg(I?i) approximately decreases byL+10? lg(1+1/p) when the width increases from p to p+1 (1 < p?N). The derivation process issimilar to the case of ED?, except we encounter power series rather than geometric series. Detailscan be found in Appendix A.4.4.3 Random Matrices EZ?and EPRZ?,?Consider H ? EPRZ?,? . Let H =V?F, where V ? EPR?,? and entries of F are i.i.d. ZMCSCG.Assume F as frequency flat and block-fading. Our interest is the long-term time-average of in-stantaneous capacity, termed ?throughput capacity of slow-fading? in [140] and defined as thetime-average of mutual information under block-fading channels, provided that an infinite numberof blocks are transmitted. Given high SNRs and equal stream power allocation, the throughputcapacity of the i-th stream, denoted by C?i, can be approximated by c0?EF,?[log2(P/I?i)], which isproportional to I?i, defined asI?i ?EF,???????lg??N?j=1, j?i?ai, j?2????????. (4.6)Following the procedure in Section 4.4.1, we know that ai, j is a sum of the series {? ?i?k? fi,kwk, j},where ?i?k? ? p, fi,k ? CN (0,1), and wk, j is the (k, j) entry in Wp. We now investigate the statisticalproperties of wk, j, in particular, EF,?[lg(?wi, j?2)] since from the perspective of channel capacity,we are more interested in the average of log-scale interference.Consider H ? EZ?in which hi, j is given by ? ?i? j? fi, j; fi, j ? CN (0,1). It can be shown thatEF[lg(?wk, j?2)] linearly decays with k (3 ? k ? p+1) and when ? approaches zero, the decay rateis approximated byrEZ = 2lg? + lge. (4.7)80The derivation details are given in Appendix B, where we also show that for k > p+1, EF[lg(?wk, j?2)]linearly decays with k at a rate smaller than (4.7). By symmetry of Hp, the decay rate in (4.7) alsoapplies to any row of Wp.Now consider H ? EPRZ?,? . We use E[?] instead of EF,?[?] when this causes no ambiguity. Itcan be shown that E[lg(?wk,1?2)](k ? p) linearly decays with k and the decay rate is approximatedbyrEPRZ = (2k?2) lg? ?? lg(k?1). (4.8)See Appendix C for the derivation details. We list below the important findings.The simplest estimate of E[lg(?wk,1?2)], denoted by LW(1)k , is given byLW (1)k = (2k?2) lg? ?? lg(k?1)?2? lg(2e)+?/ ln10. (4.9)A better estimate, denoted by LW (3)k , introduces an adjustment ?? (listed in Table C.1):LW (3)k = LW(1)k +??ln10(k?1k?2)?/2. (4.10)Comparing (4.8) (whereH ? EPRZ?,? ) with (4.7) (whereH ? EZ? ), we notice that the lge penaltyin the decay rate disappears due to the presence of the polynomial decay, which indicates that forH ? EPRZ?,? , E[lg(?wk, j?2)] has the same decay rate as E[lg(?hi,k?2)].We are also interested in E[lg(?wp+1,1?2)] as it is the largest term being dropped when Spis used. Unlike EZ?case, E[lg(?wp+1,1?2)] in EPRZ?,? drops significantly. To quantify thebehavior, we define the outband drop as the log-ratio of the accelerated and the normal decay, i.e.,Op ? lg(?Wp(p+1,1)/Wp+1(p+1,1)?). It is shown in Appendix C that Op is negligible in EZ? ,and is given by ?/ ln10+??in EPRZ? ,? , where ?? is listed in Table C.1. As will be shown later,it is the outband drop that justifies the use of Sp for H ? EPRZ? ,? .We now analyze I?i based on the statistics of Wp. Applying Jensen?s inequality on (4.6) pro-duces an upper-bound of I?i: 2lg(?Nj=1, j?iEF[?ai, j?]). However, the exponential decay in Dp and81Wp, as revealed in (4.7) and (4.8), suggests highly dynamic values among ?ai, j? and therefore, atighter estimation of I?i shall be possible by considering only the dominating terms in ?ai, j?.Consider p ? i ?N ? p. By (4.7) and (4.8), we approximate ai, j = dTi w j byai, j ??????????????????????????? j?1k=0 [?i? j+k fi, j?kw j?k, j(i? j+k)?/2 ]+?i? j?pk=1 [?i? j?k fi, j+kw j+k, j(i? j?k)?/2 ] , 1 ? j ? i? p?i?1k=p [?k fi,i?kwi?k, jk?/2 ]+?N?ik=p [?k fi,i+kwi+k, jk?/2 ] , i? p+1 ? j ? i+ p?2, j ? i?N? jk=0 [?j?i+k fi, j+kw j+k, j( j?i+k)?/2 ]+?j?i?pk=1 [?j?i?k fi, j?kw j?k, j( j?i?k)?/2 ] . i+ p?1 ? j ?N(4.11)Inspecting (4.11) reveals that the variance of ai, j is tightly upper-bounded by that of ?(1+1/p)??/2ai, j+1for 1 ? j ? i? p. From (4.8) we know the dominating term corresponds to ai,i?p. Similarly, we ob-tain dominating terms in other intervals of j: ai,i?p+1 for i? p+1 ? j < i; ai,i+p for i+1 ? j ? i+ p?2;ai,i+p?1 for i+ p?1 ? j ? N. Since the variance of each of the four terms decreases by the ratio?(1+1/p)??/2 when p increases by 1, we estimate I?i by recursion:I?i?p=p? ? lg[?2(1+1/p)??]+ I?i?p=p??1 =? = ?pL/10?? lg p+ I?i?p=1, (4.12)which also applies to 1 ? i ? p?1 and N ? p+1 ? i ? N. The above equation indicates that givenH ? EPRZ?,? , the I?i decreases by L+10? lg(1+1/p) dB when the width increases from p to p+1(1 < p ? N). Denote by SINRdw the SINR measured in dB when dense precoding matrices areused. It immediately follows that SINRdw increases by L+ 10? lg(1+ 1/p) dB when the widthincreases from p to p+1 (1 < p?N).4.5 SINR Loss Using Sparse WDenote by SINRsw the SINR measured in dB when sparse precoding matrices are used. We nowinvestigate the SINR loss from using Sp, defined as ?SINR ? SINRdw?SINRsw.824.5.1 SINR Loss in EZ?Let H =Hp+Dp. Decompose Sp by Sp =Wp+Ep. Rewrite (4.2) asy ? Is+(DpWp+HpEp+DpEp)s. (4.13)Let A =DpWp and B =HpEp. We omit DpEp as its dominating term?s variance is much smallerthan those in A or B. Consider p ? i ?N ? p. Denote by I?(S)i the residual interference power of thei-th stream when Sp is used, and by I?(D)i when Wp is used. We haveI?(S)i =EF??????lg??N?j=1, j?i?ai, j +bi, j?2????????, (4.14)I?(D)i =EF??????lg??N?j=1, j?i?ai, j?2????????, (4.15)where ai, j = dTi w j and bi, j = hTi e j. The dTi and hTi are the i-th row of Dp and Hp, respectively; w jand e j are the j-th column of Wp and Ep, respectively. By ? ? 0, we invoke (4.7) to take only theterms that have the maximal variance. The (4.14) and (4.15) are then simplified asI?(S)i =EF[lg(?A11?A22?2+?A12?A21?2)], (4.16)I?(D)i =EF[lg(?A11?2+?A12?2)], (4.17)where A11 = ? p fi,i?p/ fi?p,i?p and A12 = ? p fi,i+p/ fi+p,i+p, representing the residual interferencefrom usingWp; A21 =?0 fi,iwi,i?p and A22 =?0 fi,iwi,i+p, representing the residual interference fromusing Sp. We consider {A21,A22} dominate {A11,A12} sinceEF[lg(?? i?k fi,k?)]<EF[lg(??0wi,k?)].The SINR loss of the i-th stream is then given by?SINR ?EF[10lg(?wi,i?p?2)]+10?p?? ?20p lg? ?EF[10lg(? fi,i?p?2+? fi,i+p?2)], (4.18)where ?p =EF[lg(1+?wi,i+p/wi,i?p?2)].83We now show that (?p+1 ? ?p) approaches 0 as p? +? and ? ? 0. Details can be found inAppendix D. We only list below an outline of the derivation. We first derive a set of recursiveequations:np =p?1?k=0[(?1)k fi+k,i+pnk]/ fi+p,i+p, dp =p?1?k=0[(?1)k fi?k,i?pdk]/ fi?p,i?p, (4.19)zp ? ?wi,i+p/wi,i?p?2 ? ?np/dp?2. (4.20)We can then evaluate ?p in a closed-form,?p ? lge?ppi12[1+ 32pi2p]+0.2826, (4.21)from which we establish that as p? +? and ? ? 0, the term (?p+1??p) approaches 0.Considering EF[ln(? fi,i?p?2 + ? fi,i+p?2)] = 1? ? and EF[lg(?wi,i?p?2)] ? p(2lg? + lge) from(4.7), we obtain the approximate rate at which the ?SINR linearly increases with p: 10lge.The above process also applies to 1 ? i ? p?1 and N? p+1 ? i ?N, where only one dominatingterm is present in I?(S)i . For H ? ED? , however, there is no similar conclusion. Its inverse can beshown as a tri-diagonal matrix, where the main diagonal entry is 11??2 at the first and last rows, and1+?21??2 at other rows. The off-diagonal entries of H?1 take the same value: ??1??2 . See Appendix Efor details.4.5.2 SINR Loss in EPRZ?,?Given H ? EPRZ? ,? . The four terms in (4.16) and (4.17) become:A11 = ? pp??/2 fi,i?p/wi?p,i?p, A12 = ? pp??/2 fi,i+p/wi+p,i+p, (4.22)A21 = ?0?i??/2 fi,i/wi,i?p, A22 = ?0?i??/2 fi,i/wi,i+p. (4.23)84During the derivation of (4.8), we learn that unlike EZ?case, an EPRZ?,? matrix has a significantdrop in E[lg(?wi,i?p?2)] and E[lg(?wi,i+p?2)]. Therefore, {A11,A12} dominates {A21,A22} for? > 2 and {A21,A22} dominates {A11,A12} for ? < 2. We now rewrite (4.16) and (4.17) as:I?(S)i ????????????????E[lg(?A11?A21?2)]+E[lg(1+?A12/A11?2)], ? > 2,E[lg(?A11?A21?2)]+E[lg(1+?A22/A21?2)], ? < 2,(4.24)I?(D)i ?E[lg(?A11?2)]+E[lg(1+?A12/A11?2)]. (4.25)Consider ? > 2. We have?SINR/10 =E[lg(1??A21/A11?2)]. (4.26)Plugging into (4.26) the estimations of wi,i?p and wi?p,i?p, we have?SINR/10 ?E???????lg???XXXXXXXXXXXX1?(?1)pi?1?m=i?p+1((m? i+ p+?m)(i?m+?i)?p+?i???m?)??/2?fm,i?p fi,mfi,i?p fm,mXXXXXXXXXXXX2??????????. (4.27)Eq. (4.27) coincides with the inband estimation error of LW (1)k at k = p+1, defined asE[lg(?wk,1?2)]?LW (1)k . It can be therefore estimated by the difference of LW(1)p+1 and LW(3)p+1:?SINR/10 ???ln10( pp?1)?/2. (4.28)4.6 Downlink Energy EfficiencyWe study the downlink energy efficiency in a FMDA system with N antennas serving N pre-scheduled users through ZFBF. Radio frequency signaling is adopted to simplify the antenna de-sign and reduce the amount of energy consumed in backhaul signalling between the antennas andthe CPS. Smaller antenna-user distances and low attenuations of optical fibers allow a smaller85transmission power being used at antennas. Consequently, baseband processing contributes morein the total power consumption.Define the energy efficiency as:?e ?System throughputTotal power consumption= B?N ??sPRoF+PBB, (4.29)where B is the channel bandwidth; ?s is per-user spectral efficiency given by SINR/3; PRoF is thepower consumption of RoF components; PBB is the power consumption contributed by basebandprocessing.4.6.1 Power Consumption of Radio-over-Fiber and Downlink BasebandProcessingThe PRoF is decomposed as [125]:PRoF =N(PLDAout?LDA+ Ptx?PA+0.083+0.140) , (4.30)where PLDAout is the output power of the laser-diode amplifier, set at 5 dBm in [125]; Ptx is the out-put power of the power amplifier; the efficiency of the laser-diode amplifier and the power amplifierare denoted by ?LDA and ?PA and set at 2.2% and 4.4% [141], respectively; the constants 0.083 and0.140 represent the power consumption of the laser diode and the photodiode, respectively.The model of PBB follows [68], where measurements in a Long-Term Evolution (LTE) fre-quency division duplex system establish the relationship between the computation cost and thepower consumption. The system operates in a 20-MHz channel, using 64-quadrature-amplitude-modulation. The PBB is translated from the computation cost of four major downlink operations,namely, OFDM, encoding of forward error correction, mapping and beamforming, denoted byGofdm, Gfec, Gmap and Gbf, respectively:PBB = (Gofdm+Gfec+Gmap+Gbf)(1+?oh)/cgops. (4.31)86According to [68], Gofdm and Gmap, measured in the unit of giga-operation-per-second (GOPS),scales linearly with N; Gfec scales linearly with both N and ?s; ?oh is 39.76%, representing theoverhead due to leakage current, power conversion and active cooling at the CPS; cgops is assumed40 GOPS per watt. The Gbf is obtained by converting the floating-point operation (flop) count ofbeamforming into GOPS:Gbf = 14000 ?1200 ? [(Fcsi+Fmi+Fspa)/Ns+Fpre], (4.32)where Fcsi, Fmi, Fspa, Fpre represent the flop count of CSI collection, matrix inversion, stream powerallocation and precoding, respectively; 14000 is the number of OFDM symbols per second in thedownlink of an LTE frequency division duplex system; 1200 is the number of subcarriers in a20-MHz channel. The down-scaling factor Ns is the number of OFDM symbols per schedulinginterval, which is introduced because CSI collection, matrix inversion and stream power allo-cation only occur when the set of users changes, while precoding is required for each symbol.The Gofdm is estimated by the computation cost of 2048-point inverse fast Fourier transform, i.e.,Gofdm = N ?14000 ?2400 ? log2(2400). Based on Gofdm and its relations to Gmap and Gfec that weremeasured in [68], we have Gmap =Gofdm/3 and Gfec =Gofdm/3?(?s/5.04), where the constant 5.04is the baseline when the modulation is 64-quadrature-amplitude-modulation and the coding rate offorward error correction is close to 1.4.6.2 Floating-point Operation Count of BeamformingWe consider four components: CSI collection, matrix inversion, stream power allocation and pre-coding. Two versions of the proposed scheme have the same flop count in CSI collection butdifferent ones in matrix inversion and precoding. The flop count of CSI collection is linearly pro-portional to the number ofH entries being used to calculateWp: N2 for fullH, 2Np? p2 for bandedH, and 2Np for striped H. The exact flop count of matrix inversion is determined by enumeratingnon-zero entries that participate in the calculation, as summarized in Table 4.4.87Table 4.4: Floating-point operation count of banded matrix inversion and stream power allo-cationComponents Banded (2 ? p ?N) Striped (2 ? p ?N)LU factorization 2Np2? 43 p3 2Np2+43 p3Forward substitution(dense W)N2p?Np2+ 13 p3 N2p?Np2+23 p3Backward substitution(dense W)2N2p?Np2 2N2pForward substitution(sparse W)Np2? 23 p3 Np2+23 p3Backward substitution(sparse W)3Np2?2p3 3Np2+2p3WF-SPC-dW 2N2+Nlog2N +5 2N2+Nlog2N +5NWF-SPCr 4Np+Nlog2N+5N?2p2+2p N(4p+ log2N +5)The flop count of precoding is linearly proportional to the number of non-zero entries in W,each requiring one multiplication and one addition. Thus the flop count is 2N2 for dense W,4Np?2p2 for the banded version of sparse W, and 4Np for the striped version of sparse W.4.7 Numerical ResultsWe first examine the decaying behaviors of Wp and then numerically evaluate SINR, where twoschemes are considered. Scheme ?Dense? uses Wp for precoding and WF-SPC for power al-location, subject to the sum power constraint NP. Scheme ?Sparse? uses Sp for precoding andWF-SPCr for power allocation, subject to per-antenna power constraint P. To allow a clearerobservation on how SINR varies with p, we lower the noise floor to -154 dBm/MHz.Lastly, we evaluate the downlink energy efficiency in an LTE system that operates in a 20-MHz channel. The noise floor is restored to the normal value, -114 dBm/MHz. Throughout thissection, the banded matrix inversion is used to evaluate the decay behavior of Wp; the stripedmatrix inversion is used to simulate SINR for its homogeneous property.880 10 20 30 40?80?60?40?20020kE[lg(||w k,1||2 )]simulationestimation? from 0.1 to 0.5Figure 4.3: Entries of Wp. H ? EZ? . ? ? {0.1,0.2,0.3,0.4,0.5}. N=50. p=40.4.7.1 SINR Loss in EZ?We first observe the normal decay for H ? EZ?. 20000 independent fading samples are generatedaccording to the definition of EZ?in Table 4.3. From Fig. 4.3 we observe that the decay rate givenin (4.7) is accurate when ? ? 0.3 and becomes an upper-bound when ? > 0.3.Fig. 4.4 shows SINR and ?SINR for ? ? {0.82,0.45,0.20,0.09}, which correspond to a quarter,one, two and three walls, respectively. The SINR loss from using Sp linearly increases with puntil p reaches a threshold, at which point the system transits from the interference-limited stateto the noise-limited state. As stated in Section 4.5.1, the increment rate approaches 10p lge when? decreases and p increases. Fig. 4.5 shows that compared with 10p lge, the ?p is becomingnegligible when p increases. At small ? values, (4.19) and (4.20) match simulations and (4.21)well tracks the variation of ?p. We also observed that ?p decreases with ? .4.7.2 SINR Loss in EPRZ?,?We simulate SINR in the network shown in Fig. 4.1 with parameters listed in Table 4.5. In eachsimulation scenario, 20000 independent user-location drops and fading samples are generated. Wefirst observe normal decay and the outband drop. In Fig. 4.6, we plotted E[lg(?wk,1?2)] minus890 10 20 30 40 50020406080100120140160width (p)SINR (dB)0 10 20050100150width (p)? SINRDenseSparse?=0.45?=0.20?=0.0910p?lg(e)?=0.82?=0.45?=0.20?=0.09Figure 4.4: SINR using dense and sparse W. H ? EZ?. ? ? {0.82,0.45,0.20,0.09}. N=50.0 2 4 6 8 10 12 14 160.40.50.60.70.80.911.11.21.31.4width (p)? psim(recur)analy(log?normal)sim(?=0.01)sim(?=0.1)sim(?=0.45)sim(?=0.67)sim(?=0.82)sim(?=1)? decreases from 1 to0.01Figure 4.5: The ?p slowly increases with p. H ? EZ? . N=50. Sim(recur): Simulation basedon recursive equations. Analy(log-normal): Asymptotic analysis based on log-normalassumption. Sim(? ? {0.01,0.1,0.45,0.62,0.82,1}): Simulation of ?p.(2k?2) lg? to remove the effect of ? . It can be observed that both LW (1)k in (4.9) and LW(3)k in(4.10) fit the simulation for ? ? {2,3,4} and ? ? {0.1,0.5,0.9,1}. The gap between the analysisand the simulation decreases with ? because when ? becomes smaller than 2, the channel matrix90Table 4.5: Simulation parameters in office buildingsFrequency 2.5 GHz P (per-antenna powerconstraint)10 dBm/MHzWall penetra-tion loss6.9 dB Thermal noise floor -114,-154 dBm/MHzD (inter-officedistance)3 meters Noise figure at user 7 dBAntenna gain 0 dB ? (path loss exponent) {2,3,4}0 10 20 30 40 50?18?16?14?12?10?8?6?4?20E[lg(||wk,1||2 )] ? (2k?2)lg(?)ksimulationall?term1?term3?term?=2,3,4Figure 4.6: Entries of Wp. H ? EPRZ?,? . ? ? {2,3,4}. ? ? {0.1,0.5,0.9,1}. N=50. p=40.1-term: LW (1)k . 3-term: LW(3)k . All-term: the simulations based on {c0,c1,?,ck?2}(See Appendix C for details). As the effect of ? is already deducted from the Y-axis,all ? values produce the same curve for a given ? value.H is shifting towards EZ?, which makes the estimations given by (4.8) less accurate.We observe that using Sp causes less than 4 dB SINR loss in Fig. 4.7, where to avoid cluttering,only ?SINR at ? ? {0.45,0.20,0.09} are shown. Simulated SINRs match the SINRdw analysis inSection 4.4, except at ? =1, in which caseH has only polynomial decay that invalidates the analysisbased on dominating terms. One can notice that the existence of exponential decay is important tothe proposed scheme.910 5 10 15 20 250102030405060708090100width (p)SINR (dB)0 5 10 15024? SINRsim(Dense)sim(Sparse)analy(Dense)analy(Sparse)?=0.45, 0.20, 0.09? decreases from 1 to 0.09Figure 4.7: SINR using dense and sparseW.H ?EPRZ? ,? . sim: simulation; analy: analysis.? = 3. ? ? {1,0.82,0.67,0.45,0.20,0.09}. N=50.4.7.3 Downlink Energy EfficiencyWe compare the energy efficiency of the dense and sparse schemes at three per-antenna powerconstraint levels, P ? {0.1,1,10} mW/MHz, in the same LTE system as in [68]. The transmissionpower of all antennas in each transmission is recorded to calculate the RoF power consumption.The energy efficiency is obtained from (4.29), (4.30), (4.31), (4.32) and Table 4.4. Although thesystem operates in a 20-MHz frequency-selective fading channel that consists of 1200 subcarriers,we obtain the spectral efficiency by simulating a single subcarrier through 20000 independent user-location drops and fading samples. As our purpose is to compare the spectral efficiency obtainedfrom the traditional beamforming and the proposed one, the difference evaluated at one subcarriercan represent the results evaluated in the 20-MHz channel. This choice is also made to greatlyincrease the simulation speed. In practical LTE systems, the proposed beamforming ought to beperformed at each subcarrier. However, not each subcarrier or time slot is allocated with trainingsymbols. So there is an opportunity to jointly design the proposed beamforming scheme and theinterpolation-based channel estimation, which are often used in practical systems like LTE. Thistopic is further discussed in Chapter 6.92Fig. 4.8 shows how energy and spectral efficiency change when p increases, where the schedul-ing interval is assumed to be seven OFDM symbols. At each power level, there exists an optimalvalue p = p? that maximizes the energy efficiency in both dense and sparse precoding schemes. Atthese optimal operation points, the sparse scheme offers 22%?59% higher energy efficiency thanthe dense scheme due to the use of sparse precoding, only with small loss in the spectral efficiencyafter the system becomes noise-limited. When p reaches its maximum (equal to 26 for N=50),both schemes converge to the full inversion that degrades energy efficiency. When the power levelbecomes lower, such degradations worsen because the beamforming contributes more in the totalpower consumption. Fig. 4.9 shows the power consumption contributed by RoF and beamform-ing in the sparse scheme, where the RoF contribution is calculated by (4.30) and the beamform-ing contribution is translated from (4.32). When the transmission power level drops, the powerconsumption contributed by RoF drops significantly, whereas the power consumption contributedby beamforming remains the same. The observation indicates the importance of low-complexitybeamforming scheme when lower transmission power levels are used.We observe in Fig. 4.8 that the sparse scheme maximizes energy efficiency at p? = 4,5,6 for thepower level 0.1, 1 and 10 mW/MHz, respectively. The p? is reached when the residual interferencebecomes commensurate with the noise floor, in which case further increasing p produces few gainsin spectral efficiency but decreases the energy efficiency. Therefore, it is expected that a higherpower level leads to a larger p?.Fig. 4.10 shows Ns = 1 case, where we observe similar behaviors as in Ns = 7. The sparsescheme is more attractive in energy efficiency because the energies consumed by beamforming aremore significant at a lower Ns value, which may happen in uplink zero-forcing equalization in fast-fading channels. In such cases, the equalizer needs to track the channel variations by extracting thereference symbols that are regularly inserted by users.9310 12 14 16 18 20 220100200300400500600Spectral efficiency ?s (bps/Hz/User)Energy efficiency ? e (Mbits/joule) 10mW/MHz 1mW/MHz 0.1mW/MHzDenseSparseNs=7+79%+22%+45%+35%+59%Figure 4.8: Energy efficiency ?e vs. Spectral efficiency ?s (Ns = 7). H ? EPRZ?,? . ? = 3.? = 0.45. N=50. The width p ranges from 2 to 26. Mbits/joule: 106 bits/joule.0 5 10 15 20 25 30050100150Power consumption (watt)width (p)RoF: 10 mW/MHzRoF: 1 mW/MHzRoF: 0.1 mW/MHzBeamformingFigure 4.9: Power consumption contributed by radio-over-fiber and beamforming (Ns = 7).RoF: radio-over-fiber. The sparse scheme is used. H ? EPRZ?,? . ? = 3. ? = 0.45.N=50. The width p ranges from 2 to 26.4.7.4 Practical ConsiderationsIn this subsection, we briefly discuss how to apply the proposed scheme in practice. In a typicaldual-stripe office environment, users residing on two sides of the stripe are scheduled alternatively9410 12 14 16 18 20 220100200300400500600Spectral efficiency ?s (bps/Hz/User)Energy efficiency ? e (Mbits/joule) 10mW/MHz 1mW/MHz 0.1mW/MHzDenseSparse Ns=1+355%+72%+73%+223%+68%Figure 4.10: Energy efficiency ?e vs. Spectral efficiency ?s (Ns = 1). H ? EPRZ?,? . ? = 3.? = 0.45. N=50. The width p ranges from 2 to 26.to form a one-dimensional network for each transmission. In each room, only one user is scheduledper transmission such that the resulting channel matrix has desired CDODs. If a room has multipleactive users, the system serves the users one at a time because each room is only equipped with oneantenna. If a room has no active users, the corresponding antenna does not join the beamformingand the resulting channel matrix still has CDODs.In ensuring the desired CDOD structure, another practical issue is the corridor propagationpath. Unlike the direct path crossing multiple walls, the corridor path crosses only two walls andreflects upon one wall. To attenuate this passage, the antennas can be side-mounted on the corridor-side wall such that the front-back ratio of the antennas (typically 10 dB in a directional antenna)can further attenuate the corridor path. Another benefit of such antenna mounting is to increase theisolation between neighboring rooms by taking advantage of the antenna directionality.In a two-dimensional hyper-dense network (e.g., those deployed in stadiums and airports),the extension of the proposed scheme will be addressed in the next chapter where we study thestructure of multi-banded channel matrix with the help of floor-mounted directional antennas. Ina three-dimensional network (e.g., a highrise apartment), the concrete floor typically introduces9518.3 dB penetration loss [127] and therefore largely increases the off-diagonal decays when thescheduled users are distributed across multiple floors. However, one should caution to enumerateantenna/user pairs to form a channel matrix that has the desired CDOD structure.4.8 SummaryWe have proposed a low-complexity zero-forcing beamforming scheme in an indoor massivelydistributed antenna system, where the channel matrix can be modeled to have exponentially andpolynomially decayed off-diagonals. Since only neighboring antennas need to cooperate, we bandthe channel matrix to reduce the computation cost of CSI collection, matrix inversion and precod-ing. Two versions of the scheme are presented: the dense precoding version provides quadraticcomputation cost in matrix inversion and precoding; the sparse precoding version provides linearcomputation cost. The resulting SINRs in both versions are analyzed for random channel matri-ces. Compared with beamforming based on the full matrix inversion, our analysis and numericalevaluations show that both versions incur negligible loss in SINR, while offering 45%?79% gainin energy efficiency at lower transmission power levels. At a higher transmission power level,although the energy saving from the proposed scheme is less noticeable due to the dominance ofthe radio transmission power consumption, the sparse precoding scheme still provides 22%?59%higher downlink energy efficiency than the dense precoding scheme. While this chapter is focusedon beamforming, the proposed scheme can be easily extended to uplink equalization, where matrixinversion may occur more frequently than in downlink as the receiver can track the channel fromregularly transmitted reference symbols by the users. Therefore in uplink scenarios, the energysaving from the proposed scheme would be more significant.96Chapter 5Low Complexity Zero-forcing Beamformingfor Massively Distributed Antenna Systemsin Large Public Venues15.1 IntroductionThe spectral efficiency advantages of massive array multiple-input multiple-output (MIMO) sys-tems have been shown in analysis [46] and demonstrated in experiments [47]. Compared with arrayMIMO systems, distributed MIMO systems improve link reliability by locating antennas closer tousers and therefore improve spectral efficiency both indoors [1, 14, 48] and outdoors [4, 49] whilerequiring less transmission power. When the number of users being served, K, is smaller thanthe coverage radius measured in the number of wavelengths of the carrier signal, a distributedMIMO system achieves a capacity linear in K [50], demonstrating its potential to satisfy high traf-fic demands in large public venues such as stadiums, arenas and convention centers. In practice,operators are also deploying a large number of distributed antennas or access points to cover thehyper-dense venues. Particularly in hyper-dense wireless local area networks, access points are1This chapter is based on [98] co-authored with Dr. V. Leung.97preferably mounted under-seat [27] or under-floor [28] to be closer to users and achieve higherinter-access-point isolations by taking advantage of heavy human body penetration loss, thus al-lowing more access points being deployed to provide a very-high system capacity. Under-seat orunder-floor mounting also has advantages in aesthetics and ease of installation [29].When antennas are mounted under-floor in a distributed massive MIMO system, the channelgain matrix H can be modeled as a multi-banded matrix with off-diagonal entries that decay bothexponentially due to heavy human body penetration loss and polynomially due to free space prop-agation loss. The human body penetration loss in an antenna-user link is characterized as ?d(? > 0) by following the widely used linear attenuation model [142, 143], where the unit of thelinear attenuation coefficient ? is dB/meter and d represents the antenna-user distance in meters.Realizing that entries in the matrix are not equally important, we propose a simpler zero-forcingbeamforming (ZFBF) scheme based on sparse matrix inversion. Specifically, to send a symbol to agiven user, only the channel gains from its nearby antennas matter the most in calculating its beam-forming vector, as also observed in [96]. While ignoring other entries causes residual inter-streaminterference, the resulting throughput loss is small if the residual interference is commensuratewith the inaccuracy of channel estimation, the external interference, or the interference tolerablefor the highest level modulation and coding scheme.The proposed low-complexity ZFBF scheme is designed in a two-dimensional network wherea large number of antennas are uniformly deployed in an M?M grid to cover a large public venue.We study how to relate the residual interference level to the number of channel entries participatingin the matrix inversion. To the best of our knowledge, these issues had only recently been addressedin [144, 145].In [144], the matrix inversion in a linear minimummean-square-error detector, (HHH +?2I)?1,was expanded as a sum of polynomials, ?L?1l=0 wl(HHH)l , where (HHH)l forms the l-th base ofKrylov subspace, wl is the corresponding coefficient, ?2 is the noise power and I is an identitymatrix. When the dimension ofH grows to infinity, the coefficient set {wl} converges and thereforecan be pre-calculated. Thus, the polynomial expansion renders quadratic computation cost, relative98to the size of H. Note that a larger L leads to a better approximation at the expense of morematrix multiplications to find the bases. The Krylov subspace method was also explored in low-complexity code division multiple access receivers [146, 147]. In [145], a general approximatesparse matrix inverter was used to reduce the computation cost of minimum mean-square-errorbeamforming. In Chapter 4 of this thesis, a banded matrix inverter was proposed to enable a low-complexity ZFBF scheme by targeting a one-dimensional network that contains a stripe of indooroffices.Approximated matrix inversion had also been extensively studied to find a suitable startingpoint for iterative inversion of sparse matrices. Given a finite banded matrix V, Demko showedin [129] that the inverse V?1 has exponentially decayed off-diagonals (EDOD), i.e., v?1k,b ?K? ?k?b?,where K is a constant, 0 < ? < 1, and both K and ? depend on the width of V. It was later shown[130, 131] that given V with EDOD, V?1 also has EDOD yet at a higher rate, i.e., v?1k,b ? ? ?k?b?(0 <? < ?). In Chapter 4 of this thesis, the decay rate increment was obtained in the inversion ofV?Z, where the elements of Z are independent and identically distributed (i.i.d.) zero-mean cir-cularly symmetric complex Gaussian (ZMCSCG) random variables and the operator ? denotes theHadamard product.Banded matrices had been used in electromagnetic wave simulations [93], inversion of tri-diagonal matrices [94], equalization [95] and circuit design [148]. Multi-banded matrices hadonly been studied in graphics where neighboring pixels are more relevant [149], in inter-carrier-interference mitigation [150] and in circuit design [151].The contribution of this chapter is that given a large public venue deployed with a distributedmassive MIMO system with M?M antennas mounted under-floor, we propose a multi-banded ma-trix inversion algorithm that substantially reduces the computation cost of ZFBF while incurring anegligible throughput loss by keeping the most significant entries in H and the precoding matrixW. By introducing a parameter p to control the sparsity of H and W, we can control the compu-tation cost and establish the relationship between the residual interference level and p. A larger pvalue requires more channel entries to be collected and more calculations in inverting H yet offer-99ing a higher throughput. The proposed algorithm includes dense and sparse precoding versions,providing quadratic and linear computation cost in M2, respectively. The difference between thischapter and Chapter 4 lies in the network dimension and channel propagation environment: Thischapter considers a two-dimensional network without inner walls, while Chapter 4 considers aone-dimensional network with inner walls which can strengthen inter-antenna isolation.We also show that polynomially decayed off-diagonals are not enough to offer the opportunityof reducing the computation cost of matrix inversion. Instead, EDOD is needed. However, thedistance-based exponential decay model (which will be made clear in Section II.A) weakens themain diagonal dominance of H and therefore causes the off-diagonal entries in W to decay slowerthanH, regardless of how large ? is. This phenomenon drastically reduces the throughput in sparseprecoding and motivates us to examine the benefit of using directional antennas. As demonstratedby both analysis and simulations, when the directional antenna gain increases, the resulting signal-to-interference-ratio (SIR) increment in sparse precoding increases linearly with p, while the SIRof dense precoding is much less sensitive to p.Notations: A bold capital A indicates a matrix A; a bold lowercase a indicates a vector a. Thel2-norm of a is ?a?. HT , HH , H?1, ?H? denote the transpose, Hermitian transpose, inversion, anddeterminant of matrix H, respectively. The entry on the i-th row and j-th column of H is denotedby H(i, j) or hi, j; the i-th row or column of H is hi; Ha?b,c?d denotes the submatrix of H formed byrows [a,a+1,?,b] and columns [c,c+1,?,d]. The smallest integer not less than x is denoted by?x?; the largest integer not larger than x is denoted by ?x?; the remainder of a/b is denoted by a%b.Bp denotes the set of banded matrices with width p, i.e., entry (k,b) is zero for ?k?b? ? p. MBM,pdenotes the set of multi-banded matrices with inter-band distance M and width p, in which entry(k,b) is zero for max(?k%M?b%M?, ??k/M???b/M??)? p. A diagonal matrix with the diagonal a isdenoted by diag[a]. ZMCSCG distribution is denoted by CN (0,?2), where ?2 is the variance andthe mean is zero. The uniform distribution between a and b is denoted by U(a,b). The functionsln(?) and lg(?) represent natural and base-10 logarithm, respectively. EX[?] denotes the expectationover the random variable X; E[?] is used when this causes no ambiguity.100The rest of this chapter is organized as follows. The system model is introduced in Section 5.2.Section 5.3 presents the proposed multi-banded inversion algorithm. We analyze the SIR in denseand sparse precoding in Section 5.4 and present the numerical results in Section 5.5. Section 5.6concludes this chapter.5.2 System ModelConsider an occupied large public venue uniformly deployed with M2 under-floor mounted anten-nas arranged in an M?M grid, as shown in Fig. 5.1. Each of the M2 squares in the grid has onepre-scheduled user and one centrally located antenna, which transmits and receives radio frequencysignals over the air while all the baseband signal processing is concentrated at the centralized pro-cessing system through optical cables. Under-floor propagation paths are blocked by concrete andsteel structures, which are often present in large public venues [28]. Blocking under-floor propaga-tion paths is to force inter-antenna interference to be attenuated by heavy human body penetrationloss, thus allowing the channel matrix to be modeled as a sparse matrix.? lane 1lane 2lane Mfile 1AntennaUserCPS optical cables???file 2 file MFloorConcrete and steel structureAntenna (pointing upwards)Figure 5.1: A large public venue with M2 under-floor mounted antennas uniformly deployedover an M?M grid. CPS: centralized processing system.1015.2.1 Channel Matrix HEnumerating the antennas and users lane by lane and letting N =M2, we obtain an N ?N channelmatrix H, given by V ?F = V ? (Z+K), where V is the path loss matrix, F is the fading matrix(frequency-flat block-fading is assumed), Z is i.i.d. ZMCSCG and K is the matrix of Rician K-factors representing the ratios of the energy in the specular path to the energy in the scattered pathsin the corresponding links. The antenna-user pair at the i-th lane across the j-th file is labeled as(i?1)M+ j (1 ? i, j ?M) and the corresponding link is called home antenna-user link. Equivalently,the coordinate of the k-th antenna-user (1 ? k ?N) is given byik = ?k/M?, jk = (k?1)%M+1. (5.1)To enhance clarity of this section, we reserve (i, j) to index physical coordinates, while (k,b) isused to index rows and columns of H, which correspond to users and antennas, respectively. Weignored shadowing for analytic convenience. Only the home antenna-user links are assumed toexperience Rician fading; therefore, K is a diagonal matrix with each diagonal element fixed at? .The path loss between the k-th user and the b-th antenna is modeled as the free space propa-gation loss with the path loss exponent ? (? ? 2) plus the linear attenuation loss, given by ?dk,b(? > 0), which had been widely used in the previous literature [142, 143] and is used here tocharacterize heavy loss induced by human body penetrations. The unit of ? is dB/meter and dk,brepresents the distance between the k-th user and the b-th antenna in meters. The (k,b) entry in Vis then given byvk,b = d??/2k,b 10??dk,b/20 = d??/2k,b ?dk,b,? = 10??/20 (5.2)dk,b =?(ik? ib+xk)2+( jk? jb+yk)2+h2 (5.3)where (xk,yk) determines the distance between the k-th user and the k-th antenna; h is the height102of all users. The inter-antenna distance is normalized to 1; xk,yk ? U(?0.5,0.5). We assumeh ? 1 such that dk,b in (3) can be simplified as the Euclidean distance on a plane rather than ina three-dimensional space. The set of matrices that possess the properties (5.1)?(5.3) is denotedby MEPRM,?,? , which has a multi-banded structure, exponentially and polynomially decayedoff-diagonal entries, and uniformly distributed xk and yk. We further denote byMEPRZM,?,? theHadamard product of an MEPRM,?,? matrix and a ZMCSCG matrix.V can be viewed as an M ?M block matrix, where the (i, j)-block, denoted by Bi, j, containsthe path loss information between the users at the i-th lane and the antennas at the j-th lane. Theblock-diagonal that contains Bi,i (1 ? i ?M), Bi,i+l (1 ? i ?M? l), Bi?l,i (l+1 ? i ?M) are called themain band (or 0-th band), the l-th sideband and the (-l)-th sideband, respectively (0 ? l ? M ?1).The way we enumerate the antenna-users determines that each band resembles a ridge that has apeak with both sides gradually decaying, as shown by the contour pattern in Fig. 5.2. The mainband has the highest peak and the sharpest decay; a sideband has a smaller peak and a slowerdecay when it is farther away from the main band. The term ?dk,b in (5.2) indicates exponentiallydecayed off-diagonals within each band and also across the peaks of sidebands; the terms d??/2k,bindicate polynomially decayed off-diagonals. The value of ? depends on the crowdedness of thevenue, ranging from 0.1 to 0.3 dB/meter in previous measurements [142, 143].5.2.2 Compositely Decayed Multi-banded Path Loss MatrixThe composite decay within each sideband and across the peaks of sidebands in V motivates us toform a sparser V, denoted by Vp, by keeping only the main band and p-1 sidebands on both sides,each block in these bands being a banded matrix with width p. An example is shown for p=3in Fig. 5.2. Define the p-multi-banded H by Hp = Vp ?F . The particular structure in Vp allowsa simple approximate matrix inversion that delivers a desired spectral efficiency at a much lowercomputation cost than a full inversion.The choice of p is determined by the throughput demanded by users and the highest levelmodulation and coding scheme in practical systems. Therefore, values of p of interest to us would1030 50 10002040608010020 40 60 80 100102030405060708090100 ?5?4.5?4?3.5?3?2.5?2?1.5?1?0.50Figure 5.2: Log-scale contour of path loss matrix. Parameters: N=100, M=10, ?=0.3 dB/m,?=2, ?=10. Black pattern: the mask to obtain V3.be much smaller than M when the distributed massive MIMO system covers a very large area.And in such cases, obtaining Hp requires much less training than obtaining H. Since links beingestimated are grouped locally, it is now possible for antennas that are far away from each other touse non-orthogonal (or to reuse) training sequences, thus mitigating the system capacity reductioncaused by the use of long globally orthogonal training sequences.5.2.3 PrecodingAssuming perfect channel state information (CSI) at the transmitter and perfectly synchronizedcommunications, we consider N ? 1?N downlink transmissions: N pre-scheduled users are si-multaneously served by N antennas through ZFBF, which is adopted for simplicity and near-optimal performance at high signal-to-noise-ratio (SNR)s [128]. The N ? 1 received symbol is104given by y =HWs+n, where H = [hH1 hH2 ?hHN ]H , W = [w1w2?wN] is the N ?N precoding matrix,s = [s1s2?sN]T is the N ?1 transmitted symbol vector, and n is the N ?1 i.i.d. additive Gaussiannoise vector in which each component has zero mean and variance ?2. Thus, W =H?1. Given astream power allocation {Pk}(1 ? k ?N), we assume s ? CN (0,diag[P1;?;PN]).Our focus in this chapter is hyper-dense deployment scenarios where there will always beactive users. Therefore, we consider N ?N channel matrices. If some users are inactive, we havea Q?N channel matrix H (Q < N). In this case, calculating the right inverse of H destroys theparticular structure of H while the proposed algorithm is built on that very structure to achieve alow computation cost. A simple adaptation is to first calculate H?1 using the proposed algorithmand then remove the columns that correspond to inactive users. This adaption is suboptimal in thatstream power levels should be adjusted after removing the columns. When Q ? N, it is possibleto devise a proper user scheduling scheme that forms a single-band channel matrix, thus furtherreducing computation cost.5.2.4 Stream Power AllocationStream power allocation is accomplished through the waterfilling (WF) algorithm under sum powerconstraint (SPC), denoted as Pspc, or per-antenna power constraint (PAPC), denoted as Ppapc andsimplified as P for notation convenience. WF-PAPC uses the interior point method to iterativelysolve the problem [137]; however, the average number of iterations is hard to predict. To maintaina low computation cost, in this chapter we continue to use the relaxed version of WF-SPC, termed?WF-SPCr? in Chapter 4, which first achieves a lower bound of WF-PAPC by running WF withPspc =P. Once an initial allocation {Pk}(1 ? k ?N) is obtained, all streams? power is scaled up withthe same factor until any antenna?s output power reaches P. In practice, satisfying the per-antennapower constraint reduces the dynamic rage of output signals at antennas and therefore the cost ofpower amplifiers.1055.3 Multi-banded Matrix Inversion in Two-dimensionalNetworksIn this section we present an approximate inversion to an N ?N matrix H ?MEPRZM,?,? . LetH =Hp+Dp, whereDp is the difference betweenHp and the trueH. Denote byW the full inversionof H; Wp, or dense W, is the full inversion of Hp; Sp, or sparse W, is the p-multi-banded inversionof Hp.The approximate solution can be obtained directly or iteratively. Since an iterative solver usu-ally converges slower than a direct one [152], we choose a direct solver and in particular, focuson sequential methods for lower computation cost. Parallel methods in direct solvers are mostlybased on the divide-and-conquer strategy, offering higher levels of parallelism while incurringhigher complexities [153]. When orthogonal frequency division multiplexing is used, differentsubcarriers or sub-bands can be distributed to the baseband processing cores, thus achieving paral-lelism without suffering the overhead usually associated with divide-and-conquer methods. Sincethe sparsity pattern of H is known beforehand, we are able to design an efficient multi-bandedmatrix inversion algorithm by following the idea of incomplete LU factorization and incompleteforward/backward substitution, as used in Chapter 4.5.3.1 AlgorithmConsider a nonsingularH ?MBM,p and assume thatH can be factorized into LUwhere L is lower-triangular and U is upper-triangular. By MBM,p ? B(p?1)M+p, we have L ? B(p?1)M+p and U ?B(p?1)M+p [139]. Thus Sp can be obtained by an incomplete LU factorization followed by bandedforward/backward substitution, which however incurs a floating-point operation (flop) count inthe order of Np2M2. Considering M ? p in massive MIMO systems, we further simplify thisalgorithm.Although L,U ?MBM,p due to the ?fill-in? during LU factorization (i.e., some zero entries inHbecome non-zero), the most significant entries in L andU still reside in 2p?1 sidebands. Therefore106we propose a multi-banded LU factorization based on Gauss elimination without pivoting, wherefor each pivot we eliminate p?1 sidebands independently and in parallel. And in each sideband,only 2p?1 entries are eliminated. The process is illustrated in Fig. 5.3 and the pseudo codes arelisted in Table 5.1.The multi-banded forward and backward substitution algorithms are similarly devised, as de-tailed in Table 5.2. The process to find Sp is equivalent to maskingWp by keeping only 2p?1 blockdiagonals, including the main band and 2p?2 sidebands, and keeping only 2p?1 side-diagonalswithin each band. The algorithm can be easily extended to topologies with unequal number oflanes and files.M???????pMp????????sidebandssidebandsmain bandFigure 5.3: Multi-banded LU factorization. Blank areas are zeros.5.3.2 Computation CostWe consider four components: CSI collection, matrix inversion, power allocation, and precoding.The flop count of CSI collection is linearly proportional to the number of non-zero entries in thechannel matrix: N2 for a full H, N(2?Np? p2) for a p-multi-banded H. The flop count of matrixinversion is determined by enumerating non-zero entries that participate in the calculation andlisted in Table 5.3, along with the flop count of stream power allocation schemes. The flop count107Table 5.1: Algorithm: Multi-banded LU factorizationInput H,M, p(p <M)Output H: L and U are stored as its lower and upper triangular part, respectively.Algorithm for k from 1 until N-1 doimb? ?k/M?r? [k+1 ?min(k+ p?1, imbM)]km? (k?1)%M+1rs?max(1,km? p+1) ?min(km+ p?1,M)for isb from imb+1 until min(imb+ p?1,M) dor? [r rs+(isb?1)M]end (isb-loop)H(r,k)?H(r,k)/H(k,k)H(r,r)?H(r,r)?H(r,k)H(k,r)end (k-loop)of precoding is linearly proportional to the number of non-zero entries in W, each requiring onemultiplication and one addition. Thus the flop count is 2N2 for using Wp and 2N(2?Np? p2) forusing Sp.As summarized in Table 5.3, the total flop counts of using W, Wp and Sp are in the order of2N3, 3N2p2 ? p6 and 6Np4 ?4p6, respectively, which show significant reduction in computationcost from using the proposed multi-banded inversion algorithm.5.4 Residual InterferenceIn this section we analyze the residual interference when Wp and Sp are used for precoding. Westart with a simple analysis on a path loss matrix where all antenna-user distances are fixed at asmall constant and fading is absent. Once the matrix structure is understood, we move on to theanalysis of stochastic H.Given an instantaneous full channel matrix H and the precoding matrix Wp, the received signaly is:y =HWps+n = (Hp+Dp)Wps+n = (I+DpWp)s+n ? Is+DpWps (5.4)108Table 5.2: Algorithm: Multi-banded forward/backward substitutionForward BackwardInput: L,M, p(p <M), ei(the i-th column of I) Input: U,b,M, p(p <M)Output: b ?L?1ei Output: b ?U?1bb? eiBs? ?i/M??1i0? (i?1)%M+1rm? i0+1 ?min(i0+ p?1,M)rs?max(1, i0? p+1) ?min(i0+ p?1,M)for Bt from Bs until min(Bs+ p?1,M?1) doif Bt = Bs:r? rm+MBsfor k in rc? i ? k?1bk ? bk?L(k,c)b(c)end (k-loop)cp? [i r]else:r? rs+MBtfor k in rif k is the first element in r:c? cpelse: c? [c k?1]endifbk ? bk?L(k,c)b(c)end(k-loop)cp? [cp r]endifend (Bt-loop)t ?min(i0+ p?1,M)rm? t ?1 ? ?1 ?max(1, i0? p+1)rs? [t rm]Bts?min(Bs+ p?1,M?1)Bte?max(Bs? p+1,0)for Bt from Bts, step size -1, until Bte doif Bt = Bts:a? t +MBtsba? ba/Ua,ar? rm+MBtfor k in rc? k+1 ?min(k+ p?1,a)bk ? [bk?U(k,c)b(c)]/Uk,kend (k-loop)cp? [a r]else:r? rs+MBtfor k in rif k is the first element in r:c? cpelse: c? [c k+1]endifbk ? bk?U(k,c)b(c)/Uk,kend(k-loop)cp? [cp r]endifend (Bt-loop)where DpWp is the residual interference after the multi-banded inversion. The last approximationis due to the high SNR assumption in our network of interest, where antennas are densely deployedto increase the system capacity; therefore, dramatically reduced antenna-user distances allow thesystem to operate in the high SNR regions. Although the main diagonal of DpWp still contributesto the signal power, the contribution is much smaller when added by the identity matrix I in theterm I+DpWp. We thus define A as DpWp with the main diagonal set to zeros. By E[ssH] =109Table 5.3: Complexity comparison of the proposed and conventional ZFBF (2 ? p ??N)Components Proposed ZFBF(dense W version)Proposed ZFBF(sparse W version)ConventionalZFBFLU factorization 2Np4? 43 p6 2Np4?43 p623N3Forward substitution N2p2?Np4+ 13 p6 Np4?23 p613N3Backward substitution 2N2p2?Np4 3Np4?2p6 N3CSI collection N(2?Np? p2) N(2?Np? p2) N2Precoding 2N2 2N(2?Np? p2) 2N2Stream power allocation: WF-SPC 2N2+N log2N / 2N2+N log2NStream power allocation: WF-SPCr / 2Np2+N log2N /Total 3N2p2? p6 6Np4?4p6 2N3diag[P1;?;PN], the residual interference power of the k-th user, denoted by I(D)k , is given by:I(D)k =N?b=1,b?k[?ak,b?2Pb] ? PN?b=1,b?k?ak,b?2 (5.5)where ak,b is entry (k,b) in A, P is the sum power constraint divided by N and Pb is the power ofthe b-th stream. The approximation is to decouple the analysis of residual interference from powerallocation by invoking equal stream power allocation. In this section, we consider k = (N ?M)/2,which points to the middle row that has interference coming from both sides of the k-th column.5.4.1 Deterministic Channel MatrixGiven H ?MEPRM,?,? , we fix xk and yk at a small constant c/?2(c? 1), simplify dk,b as?(ik? ib)2+( jk? jb)2 for k ? b, and then multiply H by c to normalize its main diagonal entries.The resulting matrix becomes deterministic, denoted by MEPDM,? ,? .Lemma 1: Given H ?MEPDM,?,? . (a) HT =H. (b) H = PpiHPpi , where Ppi is a permutationmatrix according to pi = (pi1pi2?piM) and pii is given by?????M(i?1)+1 M(i?1)+2 M(i?1)+3 ? iMi i+M i+2M ? i+M(M?1)?????. (5.6)110Proof: (a) and (b) immediately follow from the construction process of H. ?The first row of pii corresponds to antennas in the i-th lane while the second row correspondsto those in the i-th file. Thus, the result of applying Ppiis enumerating antennas file by file insteadof lane by lane.Lemma 2: Given Hp as the p-multi-banded version ofMEPDM,?,? . The following propertieshold:(a) Decays within the main band: The ?Wp(k,k+b)? decays at the same rate as ?hk,k+b? when ?b?increases from 1 to p?1, provided that ? ? 0.(b) Decays within sidebands: The ?Wp(k,k+mM +b)? decays at the same rate as ?hk,k+mM+b?when ?b? increases from 1 to p?1, provided that ? ? 0; this holds for 1 ? ?m? ? p?1.(c) Peaks in sidebands: The ?Wp(k,k+mM)? = ?Wp(k,k+m)? for 0 ? ?m? ? (M+1)/2.Proof: (a) and (b) Consider 1 ? b ? p?1. We have ?Wp(k,k+b)? = (?1)bMk+b,k/?Hp?, whereMk+b,k is the (k + b,k) minor of Hp. Viewing Hp as an M ?M block matrix and denoting the(i, j)-block by Bi, j, we obtain the block index of hk+b,k as i = j = ?k/M?. By p ? M and ? ? 0,Mk+b,k approaches the product of three determinants: ?H1?l,1?l ?? ?Hl+1?r?1,l+1?r?1?? ?Hr?N,r?N ?, wherel = (i?1)M and r = (i+1)M. We notice that only ?Hl+1?r?1,l+1?r?1? varies with b and when ? ? 0, itapproaches ?Hl+1?k?1,l+1?k?1?? ?Hk?k+b?1,k+1?k+b?? ?Hk+b+1?r?1,k+b+1?r?1?. Since the first and third termapproach 1 when ? ? 0, the b?b matrix Hk?k+b?1,k+1?k+b, denoted by J, is of our main interest.When ? ? 0, ?J? approaches c?bb??/2. It follows that ?Wp(k,k+ b)?? c?bb??/2. By HT = H,we complete the proof of (a). The above process also holds for 1? p ? b ? ?1. The proof of (b)similarly follows.(c) By H =PpiHPpi, we have Hp =PpiHpPpi . So the (k,k+m)-minor of Hp is the (k,k+m)-minorof PpiHpPpi , which is the (k,k+mM)-minor of Hp by (5.6). Thus, ?Wp(k,k+mM)? = ?Wp(k,k+m)?for 0 ? ?m? ? (M+1)/2. ?111SIR when using WpFrom Lemma 2 we know Wp decays at the same rate as H and the main diagonal of Wp is con-stantly 1. The residual interference is therefore governed by the dominating entries in A, eachbeing generated when Wp(b,b) meets a non-zero entry in Dp. Considering that each non-zero en-try in the l-th sideband of Dp (?p+1 ? l ? p?1) has a counterpart outside of the 2p?1 sidebands,we rewrite (5.5) as:I(D)k ? 2Pp?1?l=?p+1[M?k/M??k?b=p?hk,k+lM+b?2+M?k/M??k+1?b=p?hk,k+lM?b?2] ? P(8p?4)?2p/p2. (5.7)The residual interference given in (5.7) is mainly contributed by 8p-4 interfering antennas thatgeographically form a square around the k-th user, 2p-1 interfering antennas residing at each side.The SIR in dB when using Wp, denoted by SIRdw, is then given bySIRdw ? ?20p lg(?)+10lg(p)?9 (5.8)which increases by ?20lg(?)+10lg(1+1/p) dB when the width increases from p to p+1 (1 < p?M).Outband dropLemma 2 indicates that Wp decays at the same rate as Hp. However, once ?b? passes p?1, thecurrent dominating term in ?J? disappears due to the multi-banding of H, which would acceleratethe decay of ?Wp(k,k+b)?. To quantify the behavior, we define the outband drop of Wp, denotedby Ol , as the log-ratio of the accelerated and the normal decay in the l-th sideband:Ol = lg(?Wp(k,k+ lM+ p)/Wp+1(k,k+ lM+ p)?) (5.9)112where 0 ? l < p. We first evaluate O0, the outband drop in the main band. The p? p matrix J isgiven byJ = cp??????????????????? ?1??/2 ?22??/2 ? ? p?1(p?1)??/2 01/c ? ?1??/2 ? ? ? p?1(p?1)??/2? ? ? ? ??p?3(p?3)??/2 ? ? ? ?1??/2 ?22??/2?p?2(p?2)??/2 ? p?3(p?3)??/2 ? 1/c ? ?1??/2??????????????????. (5.10)Considering that 1/c is much larger than other entries in J, we approximate ?J? by taking as many1/c-entries as possible. Specifically, we can have p?1 terms in the Leibniz expansion of ?J?, whereeach term has p-2 1/c-entries with the pair {J(b+1,b),0} being replaced by {J(1,b+1),J(b+1,1)}(2 ? b ? p). Note that each term is only one exchange away from the permutation {p,1,2,?,p-1}and therefore has the same sign. So we have?J? ? c2p?1?b=1[? pb??/2(p?b)??/2] ? c2[2ln(p?1)+1]? p/p (5.11)where the second approximation is from setting ? = 2 and applying Euler-Maclaurin formula.Therefore, O0 ? lg(2c ln p).Now consider l > 0. The ?J? in the l-th sideband is approximated by ?lm=0?p?1b=1 ?m,b, where?m,b = ??b2+m2+?(p?b)2+(l?m)2?b2+m2??(p?b)2+(l?m)2. This summation is visualized in Fig. 5.4. To estimate ?J?, we firstexamine how ?m,b varies with m and b. According to Minkowski inequality, the exponent part in?m,b,?b2+m2 +?(p?b)2+(l?m)2, has the minimum?p2+ l2, which can be shown achievedat b? = pm/l. The denominator of ?m,b, however, reaches its minimum at b = 1 for 0 ?m ? l/2 andat b = p?1 for l/2 ? m ? l. Therefore, ?m,b reaches its maximum at ?0,1 and ?l,p?1. For 0 < m <l, exponential decay dominates polynomial decay; therefore, other dominating elements of ?m,breside at {m,?pm/l?} and {m,?pm/l?}. In fact, ?m,b can be visualized as a saddle with the central113line connecting two peaks ?0,1 and ?l,p?1. Approximating ?J? by ?0,1+?l,p?1+2?l?1m=1?m,pm/l , wehaveOl = lg(2??p2+l2?(p?1)2+ l2/c??p2+l2?p2+ l2) ? lg(2c) (5.12)which also holds for the (-l)-th sideband. And when Ol in (5.9) is defined at another side of thesideband, i.e., lg(?Wp(k,k+lM? p)/Wp+1(k,k+lM? p)?), (5.11) and (5.12) also hold. For notationsimplicity, we only invoke the definition in (5.9). By the same argument in proving Lemma 2(c),the accelerated decay at the peak of the p-th sideband of Wp, given by lg(?Wp+1(k,k+ pM)???Wp(k,k+ pM)?) can be also represented by O0. Note that by symmetry of Hp, the above resultsalso hold for any column of Wp.SIR when using SpAfter learning the structure of Wp, we can now evaluate the SIR in dB when using Sp, denoted bySIRsw. First, decompose Sp by Sp =Wp+Ep and rewrite (5.4) asy = (Hp+Dp)(Wp+Ep)s+n ? Is+(DpWp+HpEp+DpEp)s. (5.13)?M-2p+1?2p-12p-1p-1p+12p-1M-2p+1?? 02p-2??O0 Ol0 0 1 2 l-2 l-1 l0 l l-1 l-2 2 1 0Figure 5.4: Outband drop estimation. Red dash line: the main diagonal containing domi-nating entries. O0: outband drop in the main band. Ol: outband drop in the l-th sideband.114Let A =DpWp and B =HpEp. We omit DpEp in estimating the residual interference. Denoting byI(S)k the residual interference power of the k-th user, we haveI(S)k ? PN?b=1,b?k?ak,b+bk,b?2. (5.14)From Lemma 2 we know that Wp decays at the same rate as H and from Section 5.4.1 we learnthat the outband drop in Wp is significant. Therefore, ?bk,b? is much smaller than ?ak,b?, from whichwe conclude that I(S)k ? I(D)k and SIRsw ? SIRdw.5.4.2 Stochastic Channel MatrixConsider H ?MEPRZM,?,? (0 < ? < 1,? = 2), in which hk,b = fk,b?dk,b/dk,b.Structure of WpIn an indoor office environment where each room is equipped with one antenna and has one user,we have shown in Chapter 4 that in the presence of both exponential and polynomial decay, theoff-diagonal entries in Wp has the same decay rate as in H and there exists a noticeable outbanddrop in Wp, which is why by using Sp we were able to achieve similar performance as using Wp.The reason of having equal decay rates in Wp is the use of discrete exponential decay model, inwhich the attenuation between a user and an antenna depends on the number of walls separatingthem rather than the distance. The main diagonal dominance is therefore strengthened by officewalls that enclose an antenna-user pair and provide isolation from its neighboring antenna-userpairs.In a large open space, however, the exponential decay depends on the antenna-user distanceand the decay model becomes continuous. When H is deterministic, the home antenna-user linkdistance is set at a small constant c to ensure the main diagonal dominance in H and thereforeallows the proof of Lemma 2. When H is stochastic, however, the dominance is disrupted byrandomized antenna-user distance and particularly, weakened by the two diagonals next to the115main diagonal in the main band. The first upper and lower sideband may also be comparableto the main diagonal, according to Lemma 1(b). We term this dominance structure as tri-bandtri-diagonal dominance.Fig. 5.5 presents simulation results for the differential decay in the main band, defined asE[lg(?hk,k+b/hk,k+b?1?2)] for H and E[lg(?wk+b,k/wk+b?1,k?2)] for W to signify how much decay isincurred when an entry is moving away from the main diagonal. Following the setting in Table 5.4,we compare two systems: M?M lanes and M?1 lanes. The differential decay of W in the M?1system, which has only one band, can be obtained by following the same procedure in Section5.4.1 and numerically evaluating the determinant of the random matrix Hk+1?k+b,k?k+b?1, denotedby J, at two consecutive b values. Although among b! terms of ?J?, the termx0 = ?dk+b,kdk+b,k fk+b,k?b?1m=1(?dk+m,k+mdk+m,k+m fk+m,k+m) is the largest contributor, the evaluation should also in-clude the main diagonal and the second upper diagonal in J as they are comparable to the firstupper diagonal. In the M?M system, the presence of tri-band dominance further complicates theprocess and only evaluating ?J? is not enough to accurately estimate E[lg(?wk+b,k?2)]. Simulationresults in Fig. 5.5 show that the tri-band dominance further decelerates the decays in W even after? reaches 2.4 dB/m.Table 5.4: Simulation parametersParameter ValueFrequency 2.5 GHzD (inter-antenna distance) 20 metersVenue size 400?400m2N (number of antennas) 400? (path loss exponent) 2? (linear attenuation factor) 0.3 dB/meterP (per-antenna power constraint) 0 dBm/MHzGt (transmitter antenna gain) 0 ? 5 dBGr (receiver antenna gain) 0 dBThermal noise floor -114 dBm/MHzUser noise figure 7 dB1161 2 3 4 5 6 7 8 9?7?6?5?4?3?2?10Differential decaybW (MxM lanes)W (Mx1 lanes)H (MxM lanes)?=0.3?=1.2?=2.4Figure 5.5: Differential decay of H and W. ? ? {0.3,1.2,2.4}. The decay is defined asE[lg(?hk,k+b/hk,k+b?1?2)] for H and E[lg(?wk+b,k/wk+b?1,k?2)] for W.SIR when using WpAlthough off-diagonal entries of Wp decay more slowly than H, the main diagonal entries in Wpare still dominating and can be expressed as:? 1wk,k? = ?hk,k+?b?khk,b(?1)k+bMk,bMk,k?? ?hk,k? ?l=?1hk,k+lMk,k+lMk,k+ ?i=?M?l=?1(?1)i+lhk,k+i+lMk,k+i+lMk,k? (5.15)where the approximation follows from the tri-band tri-diagonal dominance. When directional an-tennas are used, we are able to boost the dominance of the main diagonal and then simplify ?wk,k?as 1/?hk,k?. In such cases, the residual interference is still governed by the dominating entries inA = DpWp, each being generated when wk+b,k+b meets hk,k+b in Dp. As revealed in (5.7), weconsider the 8p-4 major interfering antennas and denote each resulting interference term by re,i(1 ? e ? 4, ?p+1 ? i ? p?1), where e is the index of the direction of the interfering antenna (corre-117sponding to east, west, north and south, respectively). Rewrite (5.5) as:I(D)k /P ?E??????lg??4?e=1p?1?i=?p+1re,i????????. (5.16)The evaluation of (5.16) depends on the distribution of hk,k. For hk,k subject to ZMCSCG, re,iis subject to a ratio distribution, i.e., re,i = ?2?p2+i2p2+i2 ??e,i fe,ige,i ?2, where fe,i,ge,i ? CN (0,1) and ?e,i ?U(?0.5,0.5). Since each of 8p?4 major interfering terms involves a different entry in Dp and adifferent main diagonal entry in Wp, and we have simplified ?wk,k? as 1/?hk,k?, the independenceamong fe,i, ge,i and ?e,i can be established.As ratio distributions have infinite variance, we set re,i by ?2pp2 ??e,i fe,ige,i ?2 to approximate a lowerbound of SIRdw. For hk,k without fading (due to a strong Rician K-factor and the use of di-rectional antennas), re,i is subject to a product distribution that has a finite variance, i.e., re,i =?2?p2+i2p2+i2 ??e,i fe,i?2, which generates an upper bound of SIRdw. Both bounds are given as follows:?10E??????lg??e=4?e=1p?1?i=?p+1?2pp2??e,i fe,ige,i?2????????? SIRdw ? ?10E??????lg??e=4?e=1p?1?i=?p+1?2?p2+i2p2+ i2??e,i fe,i?2????????. (5.17)In evaluating the upper bound, the Central Limit Theorem (CLT) can be applied to model?4e=1?p?1i=?p+1 re,i as a real Gaussian random variable. However, its mean and variance have to beevaluated numerically because the close-form of ?p?1i=?p+1?2?p2+i2p2+i2 is unknown. The expectationof the logarithm of positive samples of a real Gaussian random variable also requires a numericalevaluation. To avoid numerical evaluation and gain some insights on how SIR varies with p, wepropose an approximation of (5.16) by using the median of ?e,i to approximate re,i as ?2pp2 ?14 ?fe,ige,i ?2such that ?e,i is decoupled from fe,i/ge,i. The decoupling is motivated by the infinite varianceof fe,i/ge,i versus the finite variance of ?e,i; another reason of decoupling is that the cumulativedistribution function (CDF) of Xe,i ? ??e,i fe,i/ge,i?2 can be shown as FXe,i(x) = 2?x tan?1(?0.25/x),118which complicates subsequent derivations. We now rewrite (5.16) as:I(D)k /P ?E??????lg???2p16p2e=4?e=1p?1?i=?p+1?fe,ige,i?2?????????E??????lg???2p16p2maxe,i?fe,ige,i?2????????(5.18)where the second approximation is from ln(ea+eb) = ln[ea(1+eb?a)] = a+ ln(1+eb?a) ? a (0 < b <a). Such an approximation is reasonable because of the infinite variance of ? fe,ige,i ?. By showing thatE{ln[max1?i?N(? fi/gi?2)]} is the (N-1)-th harmonic number for N > 1 (See Appendix F for details),we estimate SIRdw as:SIRdw ? ?10lg(?2p16p2)?10lge8p?5?b=1(1b) = ?20p lg? +10lg( 16p28p?5)?5lge. (5.19)Eq. (5.19) suggests that in the case of stochasticH, SIRdw still increases by ?20lg?+10lg(1+1/p)dB when the width increases from p to p+1 (1 < p?M).SIR when using SpThere are two factors increasing the SIR loss due to Sp, when compared with Chapter 4. One is amuch smaller outband drop in Wp due to the tri-band tri-diagonal dominance structure. Anotherfactor is that entries in Wp cannot decay as fast as those in H; therefore, banding Wp would incura larger loss of information, or equivalently, the contribution from EpHp will be much larger thanfrom DpWp. In this section we show that with the use of directional antennas, the main diagonaldominance can be re-established and the SIR loss from using Sp can be largely reduced.In practice, the under-floor or under-seat mounted antennas are reversed downtilt antennas thatare omni-directional in the horizontal plane and directional in the vertical plane with typically 5dB gain variation between 0 and 180 degree, as shown in Fig. 5.1. We use a simplified directionalantenna model by assuming the channel gains of home antenna-user links are multiplied by 10Gt/20while other links remain the same, where Gt is the transmitter antenna gain in dB. Consequently,the transmission power should be reduced by Gt to comply with radio regulations. The combined119effect is all entries in H being suppressed by Gt except those in the main diagonal, while thetransmission power constraint remains the same.When p= 1, using directional antennas has no effect on SIRsw. When p> 1, the decrement in ?J?due to Gt increases with b (the size of J) in that approximately, we have ?J?Gt=x = ?J?Gt=0/10bGt/20.This indicates the effect of Gt on suppressing Wp off-diagonal growth is amplified by width p.Since SIRsw is governed by B = EpHp, a system operating at a larger p would benefit more fromGt , e.g., when Gt increases from 0 to 1 dB, SIRsw would roughly increase by pGt . But when Gtincreases, the x0 term in ?J? is becoming more significant, causing a tapering SIR increment whenGt becomes higher.Compared with SIRsw, the increment of SIRdw from a higher Gt is expected to be much lesssensitive to changes in p because the governing residual interference term, A = DpWp, is moresensitive to the main diagonal of Wp rather than its off-diagonal entries.5.5 Numerical ResultsWe evaluate the signal-to-interference-noise-ratio (SINR) in a 400? 400m2 public venue with auniformly deployed 20?20 antenna grid, i.e., N=400 and M=20. The height of all users is set athd=0.7 meters. We compare the proposed system, denoted by SDU (?D? stands for distributedMIMO and ?U? for under-floor mounted), with two other forms of massive MIMO systems: SDCand SAC (?A? for array-MIMO and ?C? for ceiling-mounted). SDC is a distributed MIMO systemwith its antennas evenly spread on the ceiling to benefit from the line-of-sight propagation to allusers; SAC is a massive array-MIMO system with its antennas mounted in the center of the ceiling.The ceiling height, hc, is set at 14 meters such that the edge-center distance ratio, 200/hc, is thesame as the one in SDU, given by 10/hd . The per-antenna transmission power constraint of SDUis set at 1 mW/MHz. For a fair comparison, the per-antenna power constraint of SAC is raisedby 26 dB such that its edge SNR is equal to the one in SDU; the per-antenna transmission powerconstraint of SDC is raised by the same amount.In this section we consider two schemes. Scheme ?Dense? uses Wp for precoding and WF-120Table 5.5: Simulation parameters of SDU, SDC and SAC. SDU: under-floor-mounted dis-tributed antennas; SDC: ceiling-mounted distributed antennas; SAC: ceiling-mountedarray antennas.Parameters SDU SDC SACZFBF Dense and sparseschemes.Dense scheme. ConventionalZFBF.D (inter-antenna distance) 20 meters 20 meters 0.06 meterGt (transmitter antenna gain) 5 dB 0 dB 0 dB? (path loss exponent) 2 2 2? (linear attenuation factor) 0.3 dB/meter not present not present? (Rician K-factor in linearscale)6 for homeantenna-userlinks; 0 other-wise.10 for all links 10 for all linksSPC for power allocation, subject to the sum power constraint NP. Scheme ?Sparse? uses Spfor precoding and WF-SPCr for power allocation, subject to per-antenna power constraint P. ForSDU, we present both schemes; SDC employs the dense scheme; SAC employs conventionalZFBF, which corresponds to the dense scheme at the maximal p value. The path loss exponent isset at ?=2 as it is the case when the venue is outdoor, or indoor and occupied [154]. The range of? is set between 0.1 and 0.3 dB/meter. Common parameters are listed in Table 5.4 and differentialparameters in Table 5.5. Simulation results are averaged over 10 independent user-drops, eachhaving 100 independent fading samples. Channel matrices are wrapped around to remove edgeeffects; therefore, the maximal value of p is 11.To show the computation cost reduction of SDU, we denote per-user spectral efficiency by ?s(approximated by SINR/3) and define energy efficiency as?e ?System throughputTotal power consumption= B?N ??sPRoF+PBB, (5.20)where B is the channel bandwidth; PRoF and PBB represent the power consumption contributed byradio over fiber (RoF) components and baseband processing, respectively. We consider the same20-MHz frequency division duplex system as in Section 4.6 and also assume Ns = 7, which was121explained in (4.32). After calculating PRoF and PBB by (4.30) and (4.31), we examine the tradeoffbetween energy and spectral efficiency in Fig. 5.6. One can notice that p=6 is a good balance pointfor both dense and sparse schemes in SDU, where the most of inter-stream interference had beenremoved and the energy efficiency is still considerably higher than when p reaches its maximum.We now use p=6 as the reference point for SDU. Although the spectral efficiency provided by SDUsparse scheme is 6% lower than of SAC and 21% lower than of SDC, the energy efficiency of SDUis 19 times higher than SAC and 18 times higher than SDC. While offering the substantial energyefficiency improvement, the sparse scheme in SDU only incurs a small loss in spectral efficiencywhen compared with the dense scheme.Fig. 5.7 shows the power consumption contributed by RoF and beamforming in both denseand sparse schemes in SDU, where the beamforming contribution is translated from (4.32). Weobserve that even at small p values, beamforming in both versions is consuming much more ener-gies than RoF. Compared with what we observed in Fig. 4.9, the power consumption dominanceof beamforming over RoF in Fig. 5.7 is more significant because the number of antennas here is400 while only 50 antennas were considered in Fig. 4.9. These observations indicate the necessityof developing a low-complexity beamforming scheme in a massively distributed MIMO system.We also notice that at small p values, the beamforming power consumption in the sparse schemeis substantially lower than in the dense scheme, which explains the energy efficiency gain whenmoving from the dense to the sparse scheme, as we have observed in Fig. 5.6. Note that the sparsescheme is subject to a smaller sum power constraint than the dense scheme, thus causing a smallerRoF power consumption.In Fig. 5.8, we observe that SINR in SDU steadily increases with p while SDC requires afull matrix inversion due to its line-of-sight propagation in all links, indicating the importance ofexponentially decayed off-diagonals. Although SAC and SDC generate a slightly higher SINRthan SDU, the expenses include a 26 dB higher transmission power and the inability to controlthe tradeoff between the computation cost and the throughput. The use of ?WF-SPCr? powerallocation scheme causes at most 5 dB penalty in SDU, suggesting the SINR improvement from1224 6 8 10 12 14 16 18 200 20406080100120140160180200Spectral efficiency ?s (bps/Hz/User)Energy efficiency ? e (Mbits/joule)SDU(Dense)SDU(Sparse)SDCSACSAC: 4.1 Mbits/jouleSDC: 4.3 Mbits/jouleSDU(Dense):34 Mbits/jouleSDU(Sparse):82 Mbits/jouleFigure 5.6: Energy efficiency ?e vs. Spectral efficiency ?s. SDU: under-floor-mounted dis-tributed antennas; SDC: ceiling-mounted distributed antennas; SAC: ceiling-mountedarray antennas. The width p increases from 2 to 11 for SDU; p=11 for SDC. ?=2.Ns=7. Parameters for SDU: {?=0.3, ?=6, Gt=5 dB}.2 3 4 5 6 7 8 9 10 11020004000600080001000012000Power consumption (watt)width (p)RoF (Dense)Beamforming (Dense)RoF (Sparse)Beamforming (Sparse)310 watt190 wattFigure 5.7: SDU: Power consumption contributed by radio-over-fiber and beamforming.RoF: radio-over-fiber. ?=2. ?=0.3. ?=6. Gt=5 dB. Ns=7.any other schemes subject to a per-antenna power constraint is at most 5 dB and it shrinks with p.To compare user fairness, we plot the CDF of SINR in Fig. 5.9, where SDC demonstrates1232 4 6 8 10 120510152025303540455055width (p)Average SINR (dB)SDU(Dense)SDU(Sparse)SDCSACFigure 5.8: Average SINR vs. Width in SDU, SDC and SAC. 10 user-drops. 100 fadingsamples per user-drop.0 10 20 30 40 50 60 70 8000.10.20.30.40.50.60.70.80.91Average SINR (dB)CDFSDCSACSDU(Sparse)SDU(Dense)Figure 5.9: CDF of SINR in SDU, SDC and SAC. 1 user-drop. 1000 fading samples. p=11for SDU and SDC.the best user fairness, followed by SAC and SDU. Since SDC can be viewed as an SAC withantennas spread wider, its user fairness advantage is expected due to the better conditioned channel124matrices. The minor fairness disadvantage of SDU is attributed to the non-line-of-sight propagationcaused by under-floor antenna mounting, which is the price we paid for the significantly loweredcomputation cost and in practice, can be compensated by user-scheduling. At other choices of p,SDU shows similar user fairness and the curves are omitted here to avoid cluttering. The CDF ofantenna transmission power in SDU is presented in Fig. 5.10, where we observe that the ?WF-SPCr? power allocation scheme effectively compresses the transmission power to comply with theper-antenna power constraint.The bounds given by (5.17) are shown in Fig. 5.11, in comparison with simulated SINR whendense precoding is used. The bounds are tighter at ?=0.5 than at ?=0.1 because a more domi-nant main diagonal makes the approximations made in deriving (5.17) more accurate. The averageSINRs provided by three flavors of the proposed ZFBF scheme are shown in Fig. 5.12 under differ-ent ? values. The SINRs of dense and sparse precoding increase with p at a rate that is proportionalto ? until the system becomes noise-limited. One can observe that the SIRdw estimated by (5.19)tracks the actual SINR well.SDU converts to full matrix inversion at p=11. We observe that when Sp is used, the ?WF-?20 ?15 ?10 ?5 0 5 10 15 2000.10.20.30.40.50.60.70.80.91Antenna transmission power (dBm/MHz)CDFWF?SPCrWF?SPCper?antenna power constrait= 0 dBm/MHzFigure 5.10: SDU: CDF of antenna transmission power.1250 2 4 6 8 10 1205101520253035404550Width (p)Average SINR (dB)DenseUpper?boundLower?bound?=0.5?=0.3?=0.1Figure 5.11: SDU: Bounds of average SINR. ?=2. ? ? {0.1,0.3,0.5}. ?=6. Gt=5 dB.0 2 4 6 8 10 125101520253035404550Width (p)Average SINR (dB)Dense (sim)Sparse (WF?SPC)Sparse (WF?SPCr)Dense (analy)?=0.1?=0.2?=0.3Figure 5.12: SDU: Average SINR vs. Width. ?=2. ? ? {0.1,0.2,0.3}. ?=6. Gt=5 dB.SPCr? power allocation scheme only incurs minor throughput losses at a high SINR region, mak-ing it a better choice than the ?WF-SPC? scheme due to its simplicity of enforcing the per-antennapower constraint. We also observe that SINR sharply decreases when ? decreases to 0.1, suggest-ing that polynomial decay alone is not enough to offer the opportunity of reducing the computationcost of matrix inversion. Instead, exponential decay is needed, and preferably at a large attenuation126rate, to accelerate the off-diagonal decays in H.The effect of Gt is examined in Fig. 5.13, where ?=0.3 and ?=6. When Gt increases from 0to 5 dB, SINRs in both dense and sparse schemes increase, yet at a rate that decreases with Gt .At p=6, SINR in the sparse scheme increases by 4.6 dB when Gt increases from 0 to 1 dB, butonly 4 and 3.5 dB when Gt further increases to 2 and 3 dB, respectively. The diminishing benefitof Gt on the SINR increment in the sparse scheme can be better observed in Fig. 5.13b, wherethe five curves correspond to the SINR increment by increasing Gt from 0 dB to 1, 2, 3, 4 and 5dB, respectively. We also observe in Fig. 5.13b that at all Gt values, SINR in the sparse schemelinearly increases with p for p < 7 whereas SINR in the dense scheme remains relatively constantwhen p increases.In Fig. 5.14, we compare the performance of the proposed dense scheme with Krylov subspacemethod [144, 146], where we set L=6 and calculate the coefficient set {wl} for each individual Hp.Two different network sizes are considered: 120?120 and 400?400m2, corresponding to 36?36and 400?400 channel matrices, respectively. At ?=0.1 and Gt=0 dB, Krylov method outperformsthe dense precoding scheme. At a higher ? or a larger Gt , the proposed dense precoding schemeoutperforms Krylov method as the latter encounters extremely ill-conditioned matrices while solv-ing {wl}. The curves at higher ? are omitted to avoid cluttering in the figure. The SINR of Krylovmethod drops for 400? 400 channel matrices. The reason could be related to accumulating er-rors while multiplying matrices to obtain the subspace bases. We remark that although the abovecomparison favors the dense scheme, one should be aware that Krylov method is a general matrixinversion solver that does not depend on particular matrix structures.5.6 SummaryLarge public venues can be deployed with a distributed massive MIMO system with M?M anten-nas mounted under-floor, which makes the antennas closer to the users and provides a very highsystem capacity. Under such network configurations, the channel matrix H can be modeled as amulti-banded matrix with off-diagonal entries decaying both exponentially due to heavy human1272 4 6 8 10 12510152025303540455055Average SINR (dB)Width (p)DenseSparseGt=0,1,2,3,4,5 dB(a) Average SINR vs. Width.1 2 3 4 5 6 7 802468101214161820SINR gain (dB) compared with G t = 0 dBWidth (p)DenseSparseGt=1,2,3,4,5 dB(b) Average SINR gain when compared with Gt=0 dB.Figure 5.13: SDU: Gt effect on SINRs in dense and sparse scheme. ?=2. ?=0.3. ?=6.Gt ? {0,1,?,5} dB.penetration loss and polynomially due to free space propagation loss. The composite decays mo-tivate us to devise a multi-banded matrix inversion algorithm that, by keeping the most significant1280 2 4 6 8 10 1205101520253035404550Width (p)Average SINR (dB)Dense (Gt=0)Krylov (Gt=0)Dense (Gt=5)Krylov (Gt=5)400x400 m2120x120 m2Figure 5.14: SDU: Dense scheme vs. Krylov subspace method (L=6). ?=2. ?=0.1. ?=6.Gt ? {0,5} dB.entries inH and the precoding matrixW, substantially reduces the computation cost of ZFBF whileonly incurring a small throughput loss. Note that the very-high system capacity is only possiblewhen per-antenna power constraint remains fixed while the antenna density increases, in whichcase the signal strength at users can increase with the antenna density, thus increasing the systemcapacity.The proposed algorithm includes dense and sparse precoding versions, providing quadratic andlinear computation cost in M2, respectively. We have introduced a parameter p to control the spar-sity of H and W and thus achieve the tradeoff between computation cost and system throughput.We have shown both analytically and numerically how the SIR linearly increases with p in denseprecoding. In sparse precoding, we have demonstrated the necessity of using directional antennasby both the analysis and simulations. When the directional antenna gain increases, the resultingSIR increment in sparse precoding linearly increases with p, while the SIR of dense precoding ismuch less sensitive to p.129Chapter 6Conclusions and Future WorkIn this chapter, we conclude this thesis by summarizing the main findings and point out somepotential research topics.6.1 Summary of Work AccomplishedWe have proposed a novel wireless access architecture, Fiber-connected Massively DistributedAntennas (FMDA), in Chapter 1. In Chapter 2, we have demonstrated its capability to mitigateinterference that often arises in wireless local area networks (WLANs) and shown its flexibility tohandle spatially non-uniformly distributed traffic. The energy-efficiency of the proposed FMDAhas been compared with standalone femtocells in Chapter 3, where an antenna scheduling schemehas been proposed to simultaneously improve spectral and energy efficiency in FMDA systems.When FMDA are deployed in office buildings and large public venues, we have proposed twolow-complexity zero-forcing beamforming (ZFBF) schemes that significantly reduce the basebandprocessing complexity in downlink and therefore substantially improve the energy efficiency.? In Chapter 2, we have applied FMDA in WLANs to form a cognitive WLAN over fibersystem. The system can provide a cost-effective and efficient architecture for devices toequally share the industrial, scientific, and medical band by taking advantage of cognitiveradio capabilities. In the formed system, we have proposed two methods to reduce collisions130among stations, with multiple independent channels operating at each antenna, and transmit-ter and receiver diversity through cooperation of adjacent antennas. Multi-channel-operationmethod is enabled by wide-band optical fibers and diversity method is enabled by distributedantennas in the cognitive WLAN over fiber architecture. Extensive simulations have shownsubstantial improvements in Transmission Control Protocol throughput and packet error ratereduction of constant-bit-rate traffic streams, especially under dynamic traffic conditions.? In Chapter 3, we have proposed fiber-connected femto base stations based on our proposedFMDA architecture. After establishing a power consumption model of the proposed system,we have developed an optimization tool in a femtocell cluster based on coordinated multi-point transmissions to maximize energy efficiency by adjusting the number of transmissionantennas and controlling transmission power in ZFBF. Based on the analysis results, wehave proposed an antenna scheduling scheme to simultaneously improve spectral and energyefficiency. Compared with standalone femtocells, the proposed scheme has been shown in atypical office building to increase energy efficiency by 64%?160% and spectral efficiency by2%?36%. The exact gain depends on network configurations and transmission power levels.? In Chapter 4, we have considered a FMDA system that covers an office building and dis-covered that channel matrices in such environment can be modeled with exponentially andpolynomially decayed off-diagonals. Based on this analytic channel model, we have pro-posed an energy-efficient low-complexity ZFBF scheme, which reduces the computationcost of channel state information collection, matrix inversion and precoding by banding thechannel matrix. We have proposed two versions of the scheme. The dense precoding ver-sion provides quadratic computation cost and the sparse precoding version provides linearcomputation cost, relative to the number of antennas. The resulting signal-to-interference-plus-noise ratios (SINRs) in both versions have been analyzed for random channel matrices.Compared with beamforming via full matrix inversion, our analysis and numerical evalua-tions have shown that both versions incur negligible loss in SINR, while offering 45%?79%131gain in energy efficiency at lower transmission power levels. The sparse precoding versionprovides 22%?59% higher downlink energy efficiency than the dense version. We have alsointroduced a parameter p to control the sparsity of the channel matrix and the precoding ma-trix, and thus achieved a flexible control over the tradeoff between the system capacity andthe energy efficiency.? In Chapter 5, we have considered a FMDA system that covers large public venues. Asthe absence of wall penetrations invalidates the channel model developed in Chapter 4 andwould incur a large throughput loss were our previously proposed scheme applied, we haveemployed the under-floor antenna mounting strategy to increase the propagation loss amongantennas with the help of the heavy human body penetration loss. With this strategy, we havedeveloped a new channel model and proposed a multi-banded matrix inversion scheme thatsubstantially reduces the computation cost of ZFBF while incurring a negligible throughputloss. Compared with a massive array multiple-input multiple-output (MIMO) system locatedin the center of the venue, our proposed scheme has been shown to provide 19 times higherenergy efficiency while only incurring 6% spectral efficiency loss. Our proposed schemeincludes dense and sparse precoding versions, providing quadratic and linear computationcost, respectively, relative to the number of antennas. By introducing a parameter p to controlthe sparsity of the channel matrix, we have presented analysis and numerical evaluations toshow that the signal-to-interference-ratio increases linearly with p in dense precoding. Insparse precoding, we have demonstrated the necessity of using directional antennas by bothanalysis and simulations. When the directional antenna gain increases, the resulting signal-to-interference-ratio increment in sparse precoding has been shown to increase linearly withp, while the signal-to-interference-ratio of dense precoding is much less sensitive to changesin p. We have also discovered that although massive array-MIMO can deliver a very highsystem capacity, its co-located antennas disallow a low-complexity matrix inversion.1326.2 Future WorkWe list below potential research topics in how to apply the proposed FMDA architecture to manageinterference and improve energy efficiency in access networks:Interference management of time division duplex systems in Long-Term Evolution Long-TermEvolution (LTE) time division duplex (TDD) systems has many advantages over LTE frequencydivision duplex (FDD) systems because: (1) FDD spectrums have to allocated in pairs while TDDspectrums can be allocated one chunk at a time; (2) TDD supports asymmetric traffic often seen inaccess networks; (3) Reciprocated channels in TDD make it easier to have channel state informa-tion at the transmitter. However, the use of the same frequency in uplink and downlink complicatesthe interference scenarios in TDD systems and calls for more delicate control over timing and trans-mission power at both users and base stations. This topic, termed as ?traffic adaptation? [59, 60],is only at the starting stage in the Third Generation Partnership Project. Considering that the cen-tralized processing system (CPS) in a FMDA system is able to see the spectrum usage in the entirenetwork and each antenna can be arbitrarily configured by the CPS in transmitting or receivingstate, we expect to see that a rich set of interference management problems in LTE TDD trafficadaptation can be easier solved when the LTE system is built on our proposed FMDA architecture.It is also possible to extend the idea to the area of WLAN. An increasing number of devices areequipped with an 802.11ac network adaptor to support giga-bit-per-second throughput, which is of-ten needed in ad-hoc multimedia streaming in practice. However, such ad-hoc applications mightinterfere with infrastructure-based WLAN operations. When the infrastructure-based WLAN isbuilt on FDMA, the cognitive function of the CPS can be exploited to detect the ad-hoc transmis-sion and accordingly adjust the transmission strategies of the antennas being affected.Joint design of channel estimation and approximated channel matrix inversion To achieve anoverall lower complexity and putting engineering efforts in the most important and effective areasthat improve energy efficiency, a joint design of interpolation-based channel estimation and a low-133complexity beamforming is a future direction. In this area, a potential research topic is to reduce thenumber of matrix inversion based on frequency and time coherence in channel state information.Previous studies have revealed linear beamforming can be interpolated in both frequency [155?157] and time [158]. Another potential topic is to investigate how the pilot contamination affectsthe proposed low-complexity ZFBF scheme.In fact, a system designer can consider the overall system power consumption as a cross-layerconcept, which involves many components such as pilot design, channel estimation, carrier andtime synchronization, and forward error correction. Each component of practical systems oftenhas limits that incur a SINR loss. In such cases, a perfect solution in signal processing is often notneeded. The problem of improving energy efficiency then becomes a system-wide optimizationproblem.Extension of the proposed low-complexity zero-forcing beamforming scheme We considered ZFBFin Chapter 4 and 5. When minimum mean-square-error beamforming is used, two matrix multi-plications occur in calculating the precoding matrix. Since the width of the product of two bandedmatrices is the sum of their widths, the multiplications would triple the width of the precodingmatrix and therefore largely increase the computation cost. How to extend the proposed scheme tominimum mean-square-error beamforming is a potential research topic.We have only considered downlink due to its dominance in access networks. It is worth study-ing the extension of the proposed low-complexity scheme to uplink, where the sparse scheme ismore attractive in increasing energy efficiency because matrix inversion happens more frequentlyin uplink zero-forcing equalization, especially in fast-fading channels. In such cases, the equalizerneeds to track the channel variations by extracting the reference symbols that are regularly insertedby users.It is also interesting to study how the presence of shadowing affects the low-complexity ZFBFschemes proposed in Chapter 4 and 5. Once the shadowing is introduced, the proposed bandedand multi-banded channel matrix structures would not be good approximations due to the largely134increased variance of channel entries. The transmitter thus needs to track the most significantentries and either apply a general sparse matrix inversion solver or permute the matrix to putsignificant entries closer to the main diagonal. However, more entries in H need to be collected tomake an informative decision, thus increasing the overhead of collecting channel state information.Reduce system cost by choosing different optical backbone topologies We have proposed to con-nect all antennas to the CPS via point-to-multi-point optical links; therefore, each antenna con-sumes one strand of fiber. This choice of optical backbone largely increases the system cost inplaces where deploying optical cables are expensive. An alternate optical backbone is a time-division multiplexing optical ring, as used in current stages of cloud-based radio access networks,where each remote radio head (RRH) takes turns to communicate with the baseband unit. Suchtopology is already supported in the latest common public radio interface (CPRI) specification.Without a large buffer at RRHs, a full-scale downlink beamforming or uplink equalization wouldnot be possible since at any time, only one RRH per ring is transmitting/receiving baseband signalsamples to/from the baseband unit. Compared with a point-to-multi-point topology, a ring topol-ogy will leads to different antenna cooperation strategies. It would be also interesting to considerthe impact of bit-interleaved passive optical network [159], a novel passive optical network archi-tecture recently proposed by Alcatel-Lucent to significantly reduce the sampling rate of opticalnetwork units, thus reducing their component cost and power consumption.Flexible configuration of RRH in cloud-based radio access networks To support a CPRI interface,commercially available chips consume 0.5 watt in serialization/deserialization [160] and 1 watt atthe optical transceiver [161], which is significantly higher than what is needed to support a radio-over-fiber interface. If the design of RRH is flexible enough to support both radio-over-fiber andCPRI interface, the baseband unit can remotely configure RRHs to operate in either interface.When the traffic demand is low, radio-over-fiber signaling is advantageous because we avoidedthe more power-consuming signal path, which involves high-speed analog-digital/digital-analog135converters and digital transceivers. When the traffic demand is high, the system operator may wantto configure the RRH as CPRI-mode to ensure a very-high order of signal modulation can be usedto provide very-high-rate wireless links. Further, the CPRI circuits in a RRH should be able to beremotely turned off when there is no active user located nearby this RRH. Since a RRH is alreadyequipped with a micro controller to support CPRI, adding the above flexibilities should not causemuch increase in the RRH cost.136Bibliography[1] A. Saleh, A. Rustako, and R. Roman, ?Distributed antennas for indoor radiocommunications,? IEEE Trans. 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By ai, j = dTi w j, the ai, j reaches its maximum when p??/2? p in dimeets 1 in w j. When the entry ?1? in w j falls in each of three sections in di, the correspondingai, j involves a summation of power series, ?bk=a k??/2?k, where 1 < a < b. By approximating thesummation by a??/2 ?a1?? , we have:ai, j ??????????????????????????p??/2 ?????i? j(??)p, j ? i? pp??/2?p(? j?i+p+? i? j+p)1??? , i? p < j < i+ p?1p??/2 ?????j?i(??)p, j ? i+ p?1(A.1)After some algebraic manipulations, the I?i is approximated byI?i ?2Pp???2p1?? 2( ?? ??)2? p???2p, (A.2)150where p+ 1 ? i ? N ? p and p ? 2. For 1 ? i ? p and N ? p+ 1 ? i ? N, there is only one side ofinterference; hence, I?i ? p???2p. When the width increases from p to p+1 (1 < p? N), we havelg(I?i) approximately decreases by L+10? lg(1+1/p).151Appendix BInverse of EZ?Suppose j=1. By Cramer rule, wk,1 =C1,k/?Hp? = (?1)k+1M1,k/?Hp?, whereC1,k is the (1,k) cofactorof Hp and M1,k is the (1,k) minor of Hp. It is difficult to work with wk,1 as it is subject to certainratio distribution and has a heavy tail. The correlation between M1,k and ?Hp? also makes theanalysis intractable. However, the problem can be simplified by only counting dominating termsin M1,k and ?Hp? since the variance of off-diagonal entries in Hp are exponentially decayed. Hereby ?x dominates y?, we mean var(x)?var(y). Therefore, among N! terms in the Leibniz expansionof ?Hp?, the term h11h22?hNN is dominating. As for M1,k, there will be multiple dominating terms.Take p = 5 and k ? {2,3,4,5} as an example. Given H ? EZ?, where hi, j = ? ?i? j? fi, j and fi, j ?CN (0,1), we observe that the variance of dominating terms in M1,k should have ?k?1. Therefore,the number of dominating terms in M1,2, M1,3, M1,4, M1,5 is 20, 21, 22 and 23, respectively. We nowconjecture the number of dominating terms in M1,k is 2k?2 (2 ? k ? p) and prove it by induction.Assume there are 2k?2 dominating terms in M1,k. We approximate M1,k by ?Ak??Nm=k+1 fm,m,152where Ak is a (k-1)?(k-1) matrix given byAk =??????????????????????? f21 f22 ? ?k?4 f2,k?2 ?k?3 f2,k?1?2 f31 ? f32 ? ?k?5 f3,k?2 ?k?4 f3,k?1?3 f41 ?2 f42 ? ?k?6 f4,k?2 ?k?5 f4,k?1? ? ? ? ??k?2 fk?1,1 ?k?3 fk?1,2 ? ? fk?1,k?2 fk?1,k?1?k?1 fk,1 ?k?2 fk,2 ? ?2 fk,k?2 ? fk,k?1??????????????????????. (B.1)The M1,k+1 is then given byM1,k+1 ? ?Ak+1?N?m=k+2fm,m =RRRRRRRRRRRRRRRRRAk bTc ? fk+1,kRRRRRRRRRRRRRRRRRN?m=k+2fm,m,b = [?k?2 f2,k,?,?1 fk?1,k,?0 fk,k], (B.2)c = [?k fk+1,1,?,?3 fk+1,k?2,?2 fk+1,k?1].By Laplace formula, we expand ?Ak+1? along the last column, [b,? fk+1,k]T . Our purpose is to findterms with variance equal to ?k. One can notice that among the k terms in the last column, onlytwo terms expand dominating terms: ? fk+1,k and ?0 fk,k. Thus, the number of dominating terms inM1,k+1 is 2k?1. By induction, we proved that the number of dominating terms in M1,k is 2k?2.We now focus on evaluating EF[lg(?wk,1?2)], denoted by mk. After introducing ?k?1zk torepresent the sum of 2k?2 terms in ?Ak? where each term has a variance equal to ?k?1, we canapproximate ?wk,1? as ??k?1zk?/?km=1 ? fm,m?. Thus,m1 = ?/ ln10,m2 = 2lg? +?/ ln10, (B.3)mk = (2k?2) lg? +E[lg(?zk?2)]?k?m=1E[lg(? fm,m?2)],k ? 3. (B.4)153The ? in (B.3) is Euler constant - it comes from calculating the mean of Gumbel distribution.Note that we used E[?] instead of EF[?] when this causes no ambiguity. We now apply a recursivemethod to evaluate E[lg(?zk?2)] in (B.4). Let dk =mk?mk?1:dk = 2lg? +?/ ln10+E[lg(?zk/zk=1?2)]/ ln10. (B.5)Since half of 2k?2 terms in zk are expanded by ? fk,k?1 and another half by fk?1,k?1, we write?k?2zk?1 =k?3?m=1[?k?1?mNk?2,m(?1)m( fk?2,m fk?1,k?2? fk?1,m fk?2,k?2)], (B.6)?k?1zk = ?k?2zk?1 ?? fk,k?1+k?2?m=1[?k?mNk?1,m(?1)m( fk,m fk?1,k?1)], (B.7)where Nk?1,m is the (k-1,m) minor of Ak?1, Nk?2,m is the (k-2,m) minor of Ak?2, and the term (?1)mis obtained by examining the signature of permutation for each term. Dividing (B.7) over (B.6)produces:?zk/zk?1 = ?( fk,k?1+x fk?1,k?1), (B.8)where x = ?k?2m=1[?k?mNk?1,m fk,m]?k?2m=1[?k?mNk?1,m fk?1,m]. Owing to the group independence among fk,k?1, fk?1,k?1, fk,m,fk?1,m and Nk?1,m(1 ?m ? k?2), for each instance of Nk?1,m, the numerator in x is a linear combi-nation of independent and identically distributed (i.i.d.) complex Gaussian random variables fk,m(1 ?m ? k?2) and the denominator in x is a linear combination of i.i.d. complex Gaussian randomvariables fk?1,m with an equal set of coefficients. The distribution of x therefore does not depend onthe instances of Nk?1,m. In fact, x? g1/g2, where g1 and g2 are i.i.d. zero-mean circularly symmetriccomplex Gaussian (ZMCSCG) subject to CN (0,1). We further conclude that zk/zk?1 (3 ? k ? p) hasthe same distribution as g3+g4g1/g2, where gi(1 ? i ? 4) are i.i.d. ZMCSCG subject to CN (0,1).We applied two-sample Kolmogorov-Smirnov test to compare 106 samples from ?zk/zk?1?(k ?{4,5}) and from ?g3+g4g1/g2?. The P-value, defined in [162], is 0.54 for k=4 and 0.63 for k=5,154indicating that the null hypothesis, i.e., two sets of samples being consistent, cannot be rejectedeven at 50% significance level.To evaluate E[ln(?zk/zk?1?2)] in (B.5), we writeE[ln(?zk/zk?1?2)] =E[ln(?g4?2)]+E[ln(?g3/g4+g1/g2?2)]. (B.9)The second expectation in the RHS of (B.9) can be evaluated as 1 by applying the followingfacts: circular symmetry of gi; E?[ln(m+ncos?)] = 2[ln(?m?n+?m+n)? ln2](m > n > 0); thecumulative distribution function (CDF) of a Rayleigh ratio is FR0(r0) = r20/(r20 +1)(r0 > 0) [163].Combine (B.9) and (B.4):mk =???????????????(2k?2) lg? +?/ ln10, k = 1,2(2k?2) lg? +?/ ln10+(k?2) lge, 3 ? k ? p. (B.10)For other values of j, there are only minor variations in the above process. Thus, we have shownthat EF[lg(?wk, j?2)] linearly decays with k for 3? k ? p. The above analysis is based on dominatingterms. Therefore when ? approaches zero, the decay rate is approximated byrEZ = 2lg? + lge. (B.11)For k > p+1, the structure of M1,k can be similarly analyzed to show that zk/zk?1 has the samedistribution as g3+c0g4g1/g2, where gi(1? i? 4) are i.i.d. and subject to CN (0,1). The c0(0< c0 < 1)is a constant depending on p. Thus, for k > p, EF[lg(?wk,1?2)] also linearly decays with k yet witha rate smaller than 2lg? + lge.At k = p+1, the bottom-left entry ofM1,p+1 becomes zero, so we expectE[lg(?wp+1,1?2)] decayfaster.To quantify the behavior, we define the outband drop as the log-ratio of the accelerated and the155normal decay, i.e., Op ? lg(?Wp(p+1,1)/Wp+1(p+1,1)?). Owing to the exponential number ofdominating components in M1,p+1, the lost component in M1,p+1 does not affect the overall valuewhile p grows. Therefore, (B.10) also holds for k = p+1.156Appendix CInverse of EPRZ?,?Consider H ? EPRZ?,? (0 < ? < 1,? ? 2) and hi, j is given by ?i? j+?i???/2? ?i? j? fi, j, where fi, j ?CN (0,1) and ?i ?U(-0.5,0.5). We only show the case of j = 1; the derivation process at other valuesof j follows similarly.While the variance of dominating terms in M1,k should still be ?k?1 according to the samearguments in Appendix B, introducing polynomial decay reduces the number of dominating termsin M1,k. By inspection, at k ? 3 we have two choices:M(1)1,k ? (?1)k?k?1 ?x0(1?k?2?m=1[amxm]) ?N?m=k+1[??m???/2 fm,m], (C.1)M(2)1,k ? ?k?1 ? z0(1?k?2?m=1[bmzm]) ?N?m=k+1[??m???/2 fm,m], (C.2)wherex0 = (k?1+?k)??/2 fk,1k?1?m=2(??m???/2 fm,m), z0 =k?1?m=1[(1+?m+1)??/2 fm+1,m], (C.3)am = ((m+?m+1)(k?m?1+?k)(k?1+?k)??m+1?)??/2, xm =fm+1,1 fk,m+1fk,1 fm+1,m+1, (C.4)bm = ((2+?m+2)??m+1?(1+?m+1)(1+?m+2))??/2, zm =fm+2,m fm+1,m+1fm+1,m fm+2,m+1. (C.5)157The signs in (C.1) and (C.2) are determined by the signatures of corresponding permutations; thesummation ?k?2m=1[amxm] is formed by replacing the product hk,1hm+1,m+1 in x0 with hm+1,1hk,m+1one at a time. Comparing EF,?[ln?x0?] with EF,?[ln?z0?] reveals that M(1)1,k dominates over M(2)1,k .After approximating ?Hp? as the product of its main diagonal, we write?wk,1? ? ?k?1?(k?1+?k)??/2 fk,1??1???/2??k???/2 f1,1 fk,k?(1?k?2?m=1[amxm])? , (C.6)E[lg(?wk,1?2)] = (2k?2) lg? +?E[lg ??1?k?]+2?/ ln10+Bk. (C.7)The Bk in (C.7) is defined asBk ?E[lg?c0 fk,1?k?2?m=1[cmgm]?2] , (C.8)where gm =fm+1,1 fk,m+1fm+1,m+1 ,c0 = (k?1+?k)??/2 and cm = ((m+?m+1)(k?m+1+?k)??m+1? )??/2. Since Central LimitTheorem (CLT) cannot be applied to Bk as gm has infinite variance, we obtain two estimations ofBk by taking only c0-term, and taking three most significant terms, respectively:B(1)k =E[lg?c0 fk,1?2], (C.9)B(3)k =E[lg?c0 fk,1?c1g1?ck?2gk?2?2]. (C.10)Based on B(1)k , we estimate E[lg(?wk,1?2)] with LW(1)k (3 ? k ? p):LW (1)k = (2k?2) lg? ?? lg(k?1)?2? lg(2e)+?/ ln10. (C.11)At k=1 and 2, LW (1)1 = ?? lg(2e)+?/ ln(10) and LW(1)2 = LW(1)1 +2lg? ?1.5? lg3.To estimate E[lg(?wk,1?2)] based on B(3)k , we first conjectureBk ?E?[lg?c0?2]+E? [EF [lg? fk,1?afx fyfz?2]] , (C.12)158where a =?c21+c2k?2/c0; fx, fy, fz are i.i.d. and subject to CN (0,1). Given i.i.d. zi(1 ? i ? 4) subjectto CN (0,1), we know E[lg?z1/z2 +az3/z4?2] = 2a2 lgaa2?1 , which is tightly upper-bounded by a/ ln10for 0 < a < 1. We also know, for ?i ? U(-0.5,0.5) and at k > 3,E[lg(k?1+?k)] ? lg(k?1),E[lg ??1?] =E[lg ??k?] = ? lg(2e). (C.13)Combining (C.7), (C.12) and (C.13), we obtain the estimation of E[lg(?wk,1?2)] based on B(3)k (3 <k ? p):LW (3)k = (2k?2) lg? ?? lg(k?1)?2? lg(2e)+?/ ln10+E?[a]/ ln10. (C.14)To evaluate E?[a] in (C.14), we consider the following:E[?c21+c2k?2] ? (k?2)??/2E[?(1+?2??2?)?? +(1+?k??k?1?)??], (C.15)where the expectation in the RHS, denoted by ??, can be evaluated through Monte-Carlo methodat different ? values without depending on particular values of k (See Table C.1). Thus for k > 3,LW (3)k ? (2k?2) lg? ?? lg(k?1)?2? lg(2e)+?/ ln10+??ln10(k?1k?2)?/2. (C.16)For k ? {1,2,3}, LW (3)k can be explicitly calculated.Unlike EZ?case, (C.11) does not hold at k = p+1 because with the bottom-left entry of M1,kbeing zero, the Bk lost the most significant component, c0. In that case we rewrite (C.7):E[lg(?wp+1,1?2)] ? 2p lg? ?2? lg(2e)+2?/ ln10?? lg(p?1)+?? . (C.17)When we choose {c1,c2,ck?2,ck?1} to estimate Bk, the ?? can be evaluated through Monte-Carlomethod, as listed in Table C.1. The outband drop is then given by the difference between (C.17)and (C.11), i.e., ?/ ln10+??.159Table C.1: Constants used in the analysis? ?????/ ln10+??? ?????/ ln10+??0.5 0.9789 0.3389 n/a 2 0.4393 -0.6533 -0.40261 0.7220 -0.0222 n/a 3 0.2949 -1.2118 -0.96111.5 0.5548 -0.3498 n/a 4 0.2125 -1.7318 -1.4811160Appendix DDerivation of (?p+1??p) for H ? EZ?Define zp ? ?wi,i+p/wi,i?p?2. By ? ? 0, we can follow the procedure in Appendix B to establishwi,i+p/wi,i+p?1 ? ( fi+p?1,i+p+ fi+p?1,i+p?1g1/g2)/ fi+p,i+p, and then obtainzpzp?1?XXXXXXXXXXXfi+p?1,i+p+ fi+p?1,i+p?1 g1g2fi?p+1,i?p+ fi?p+1,i?p+1 g3g4?fi?p,i?pfi+p,i+pXXXXXXXXXXX2. (D.1)A suitable model is needed to remove the correlation between g1/g2 and fi+p,i+p, and betweeng3/g4 and fi?p,i?p. First we inspect (D.1) and establish the following recursive relationship (whichcan be proved by induction):np =?p?1k=0 [(?1)k fi+k,i+pnk]fi+p,i+p, dp =?p?1k=0 [(?1)k fi?k,i?pdk]fi?p,i?p, (D.2)zp ? ?wi,i+pwi,i?p?2? ?npdp?2, (D.3)where n0 = p0 = 1. Observing the sequence of np and dp reveals that their tails become heavierwhen p grows. So,?p =E[lg(1+ zp)] ? ?+?1lg(1+ z) fzp(z)dz ? lge?+?1(lnz+1/z) fzp(z)dz, (D.4)161where the first approximation is from the heavy tail of zp and the second is from the first orderTaylor expansion. For zp > 1, we model zp = zp?1?p?1, where ?p?1 = ?fi+p?1,i+p fi?p,i?pfi?p+1,i?p fi+p,i+p ?2 for ?p?1 > 1.By CLT, lnzp can then be modeled as N (0,2?g?p), where ?g = pi/?6. Applying the asymptoticexpansion of the complementary error function and Pr(?p?1 > 1) = 0.5 to (D.4), we write ?p ?lge?2pi[?g?p+ 14?g?p], from which we establish that as p? +? and ? ? 0, the term (?p+1 ? ?p)approaches 0.162Appendix EInverse of ED?Denote by T(N) an N ?N matrix that belongs to ED?. Denote the inverse of T(N) by W(N). Wehave?T(N)? = (1??2)?T(N?1)? =? = (1??2)N?1, (E.1)from which we obtain the main diagonal entries of W(N), w(N)i,i =11??2 for i = 1,N and w(N)i,i =1+?21??2otherwise.Nowwe consider off-diagonal entries ofW(N). We havew(N)i, j =C(N)j,i /?T(N)?= (?1)i+ jM(N)j,i /?T(N)?,where C(N)j,i is the ( j,i) cofactor of T(N) and M(N)j,i is the ( j,i) minor of T(N). For ?i? j? = 1, we haveM(N)j,i = (1??2)i?1(? ??3)?T(N?i?1)? =? = ?(1??2)N?2, (E.2)from which we establish that the off-diagonal entries of W(N) take the same value: ??1??2 .For ?i? j? > 1, it is easy to show the existence of two linearly dependent rows in the submatrixformed by deleting the j-th row and i-th column of T(N). Therefore, the inverse of T(N) is tri-diagonal.163Appendix FDerivation of E{ln[max1?i?N(? fi/gi?2)]}Theorem: Given i.i.d. fi,gi ? CN (0,1) (1 ? i ? N). E{ln[max1?i?N(? fi/gi?2)]} is equal to the (N-1)-th harmonic number (N > 1).Proof: Let Xi ? ? fi/gi?2, which is a ratio of two i.i.d. exponentially distributed random variables.By fXi(x) = 1/(x+1)2 and FXi(x) = x/(x+1), the CDF of maxiXi is given by F(x) = [x/(x+1)]N .Denoting E{ln[max1?i?N(? fi/gi?2)]} by SN , we haveSN = ?+?0lnx dF(x) = ( xx+1)N lnx?+?0 ??+?0xN?1(x+1)Ndx (F.1)from which we have SN ?SN?1 = 1/(N ?1). ?164
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Fiber-connected massively distributed antenna systems : energy efficiency and interference management Li, Haoming 2013
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Title | Fiber-connected massively distributed antenna systems : energy efficiency and interference management |
Creator |
Li, Haoming |
Publisher | University of British Columbia |
Date Issued | 2013 |
Description | The density of wireless access nodes keeps increasing to provide ubiquitous wireless access and meet the ever-increasing traffic demand. However, the shrinking distance among neighboring access nodes causes excessive interference and the increasing number of access nodes incurs a higher power consumption. A careful management of interference ensures a high system capacity. An improved energy efficiency in wireless access network prevents the fast growth of wireless communication systems from aggravating the global energy crisis. In this thesis, we propose a novel architecture, Fiber-connected Massively Distributed Antennas (FMDA), to address the challenges of managing interference and improving energy efficiency in wireless access networks. A FMDA system is composed of a centralized processing system connected to a large number of antennas via optical cables. The centralized processing system processes all the radio signals and allocates all the radio resources to better manage interference; each antenna contains much simpler circuits than conventional access nodes and therefore allows a massive deployment and reduces the antenna power consumption. We first propose a novel multi-cell wireless local area network (WLAN) system based on our proposed FMDA architecture, where the centralized processing system can see the entire spectrum usage across the coverage area and control the radio signals to be sent to each antenna, thus allowing a better management of inter-cell interference. We then propose an antenna scheduling scheme in a novel cellular system composed of fiber-connected femto access nodes to manage the excessive inter-femtocell interference and reduce the energies consumed by non-sleeping access nodes, thus simultaneously improving the spectral and energy efficiency. When the number of cooperating antennas increases, the power consumption of signal processing spikes, thus drastically degrading the overall energy efficiency due to much smaller radio transmission power levels. Focusing on two typical indoor environments, office buildings and large public venues, we propose two low-complexity downlink transmission schemes to address these energy efficiency challenges. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2013-10-03 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
DOI | 10.14288/1.0103296 |
URI | http://hdl.handle.net/2429/45199 |
Degree |
Doctor of Philosophy - PhD |
Program |
Electrical and Computer Engineering |
Affiliation |
Applied Science, Faculty of Electrical and Computer Engineering, Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 2013-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Aggregated Source Repository | DSpace |
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