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Massive MIMO for 5G wireless networks : an energy efficiency perspective Vara Prasad Koppisetti, Naga Raghavendra Surya 2015

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Massive MIMO for 5G WirelessNetworks: An Energy EfficiencyPerspectivebyNaga Raghavendra Surya Vara Prasad KoppisettiB.Tech., Indian Institute of Technology Bhubaneswar, India, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdocotoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)January 2016c© Naga Raghavendra Surya Vara Prasad Koppisetti 2015AbstractAs we progress towards the fifth generation (5G) of wireless networks, the bit-per-jouleenergy efficiency (EE) metric becomes an important design criterion because it allows foroperation at practically affordable energy consumption levels. In this regard, one of the keytechnology enablers for 5G is the recently proposed massive multiple-input multiple-output(MIMO) technology, which is a special case of multiuser MIMO with an excess of base station(BS) antennas. However, techniques for extracting large EE gains from massive MIMO (MM)networks have not been actively investigated so far. We seek to address the above limitationin this thesis by (i) reviewing MM technology from an EE perspective, (ii) critically analyzingthe state-of-the-art and proposing new research directions for EE-maximization in “hybridMM” networks, where massive MIMO operates alongside other emerging 5G technologies,and (iii) proposing a novel resource allocation scheme for EE-maximization in MM networks.The thesis consists of three main parts.In the first part, we motivate the need for EE and explain why massive MIMO is promisingas an energy-efficient technology enabler for 5G networks. In the second part, we criticallyanalyze opportunities for EE-maximization in three types of hybrid MM networks, namely,millimeter wave based MM networks, MM-based heterogeneous networks, and energy har-vesting based MM networks. We analyze limitations in the state-of-the-art and proposeseveral promising research directions which, if pursued, will immensely help network opera-tors in designing hybrid MM networks.In the third part, we propose a novel EE-maximization scheme which optimizes resourceallocation in an MM network. Three communication resources, namely, the number of BSiiAbstractantennas, pilot power, and data power are optimized for EE. Since the optimization problemis difficult to solve in its original form, we propose a novel solution approach where eachiteration solves a sequence of difference of convex programming subproblems. Simulationresults render few interesting guidelines for network designers. For example, using higherpilot power than data power can improve the system EE, particularly when SNR is high.Also, the number of BS antennas should be optimized with the available power budget toensure operation at peak EE.iiiPrefaceThe following publications have resulted from the research presented in this thesis:• K. N. R. Surya Vara Prasad and V. K. Bhargava, “Resource Optimization for EnergyEfficiency in Multi-cell Massive MIMO with MRC Detectors,” accepted for presentationat 2016 IEEE Wireless Commun. Networking Conf. (WCNC). (Linked to Chapter 4)Statement of AuthorshipI am the primary author for the publication listed above. I have been responsible to developoriginal ideas, derive mathematical solutions, and generate simulation results for these publi-cations. Prof. Vijay K. Bhargava, who is my research supervisor, provided valuable guidanceand directions in identifying the research problems, developing solution methodologies, anddocumenting the results. Some of the simulation results were obtained using the disciplinedconvex optimization software CVX developed by Grant, Boyd & Ye [1].One research contribution which is not presented in the thesis, but has been publishedduring my MASc program at UBC is listed below.• K. N. R. Surya Vara Prasad, S. Mallick, V. K. Bhargava, “Design of adaptive antennasystems for LTE using Genetic Algorithm and Particle Swarm Optimization,” in IEEECCECE, 2015, pp. 1054-1059.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xMathematical Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Expectations from 5G Cellular Networks . . . . . . . . . . . . . . . . . . . . 11.2 Need for Energy-Efficient Systems . . . . . . . . . . . . . . . . . . . . . . . 11.3 Background on MIMO and Massive MIMO . . . . . . . . . . . . . . . . . . 41.4 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Introduction to Massive MIMO . . . . . . . . . . . . . . . . . . . . . . . . . 82.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8vTable of Contents2.2 Objectives and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Massive MIMO: A Multiuser MIMO Technology . . . . . . . . . . . . . . . 92.3.1 Linear Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.2 Low-complexity User Scheduling . . . . . . . . . . . . . . . . . . . . 122.4 Linear Detection Methods for Massive MIMO . . . . . . . . . . . . . . . . . 132.4.1 Maximum-ratio Combining (MRC) . . . . . . . . . . . . . . . . . . . 152.4.2 Zero-forcing (ZF) Detection . . . . . . . . . . . . . . . . . . . . . . . 162.4.3 Minimum Mean Squared Error (MMSE) Detection . . . . . . . . . . 172.4.4 Performance Comparison . . . . . . . . . . . . . . . . . . . . . . . . 182.5 Modelling Power Consumption in Massive MIMO . . . . . . . . . . . . . . . 192.6 Practicality of Massive MIMO . . . . . . . . . . . . . . . . . . . . . . . . . 202.7 Major Challenges in Massive MIMO . . . . . . . . . . . . . . . . . . . . . . 212.7.1 Pilot Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.7.2 Frequency Division Duplexing (FDD) Systems . . . . . . . . . . . . 232.7.3 Non-orthogonal Waveform Design . . . . . . . . . . . . . . . . . . . 252.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Hybrid Massive MIMO Systems: Opportunities and Challenges for Energy-Efficient Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2 Background and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 293.3 Methods to Improve Energy Efficiency in Massive MIMO Systems . . . . . . 313.3.1 Low-complexity BS operations . . . . . . . . . . . . . . . . . . . . . 313.3.2 Minimize Power Amplifier (PA) Losses . . . . . . . . . . . . . . . . . 333.3.3 Minimize RF Chain Requirements at the BS . . . . . . . . . . . . . 353.4 Millimeter Wave (mmWave)-based massive MIMO Systems . . . . . . . . . 373.4.1 Unique Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37viTable of Contents3.4.2 Benefits from Co-existence . . . . . . . . . . . . . . . . . . . . . . . 383.4.3 Existing Works on Energy-Efficient Design: Key Ideas . . . . . . . . 383.4.4 Proposed Research Directions for future work . . . . . . . . . . . . . 423.5 Massive MIMO-based Heterogenous Networks . . . . . . . . . . . . . . . . . 443.5.1 Unique Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.5.2 Benefits from Co-existence . . . . . . . . . . . . . . . . . . . . . . . 453.5.3 Existing Works on Energy-Efficient Design: Key ideas . . . . . . . . 453.5.4 Proposed Research Directions for Future Work . . . . . . . . . . . . 493.6 Energy Harvesting (EH)-based massive MIMO Networks . . . . . . . . . . . 523.6.1 Unique Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.6.2 Benefits from Co-existence . . . . . . . . . . . . . . . . . . . . . . . 523.6.3 Existing Works on Energy-Efficient Design: Key Ideas . . . . . . . . 533.6.4 Proposed Research Directions for Future Work . . . . . . . . . . . . 553.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564 Energy Efficiency Maximization for Uplink Data Transmissions in a Multi-cell Massive MIMO System with MRC Detectors . . . . . . . . . . . . . . 584.1 Research Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.3.1 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.3.2 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.3.3 Multi-user Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.3.4 Achievable Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.4 Realistic Model for Power Consumption . . . . . . . . . . . . . . . . . . . . 674.4.1 Power Expenditure at PAs (PPA) . . . . . . . . . . . . . . . . . . . . 674.4.2 Circuit Power (PC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67viiTable of Contents4.4.3 Site-specific Power (Psite) . . . . . . . . . . . . . . . . . . . . . . . . 684.5 Maximizing Energy Efficiency of Uplink Data Transmissions . . . . . . . . . 694.6 Solution Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.7 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 88Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92AppendixA Proof of results in Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 103A.1 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103A.2 Effect of Channel Estimation Error of Known Variance on Achievable Rates 104A.3 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108A.4 Proof of Proposition 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111viiiList of Tables3.1 Existing EE-maximization Methods for mmWave Massive MIMO Systems . 393.2 Proposed Research Directions for Designing Energy-efficient mmWave MassiveMIMO Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.3 Existing EE-maximization Methods for Massive MIMO-based HetNets . . . 463.4 Proposed Research Directions for Designing Energy-efficient Massive MIMO-based HetNets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.1 Power Expenditure on Different Circuit Operations for Uplink Transmissionsin a Massive MIMO System . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.2 Simulation Parameters for Resource Allocation . . . . . . . . . . . . . . . . 76ixList of Figures1.1 Overview of services expected in future 5G networks [2] . . . . . . . . . . . 21.2 Trends and forecast for greenhouse gas emissions by the mobile ICT sector [2] 32.1 Massive MIMO: a multi-user MIMO technology where K single-antenna UEsare served by a BS with M >> K antennas. . . . . . . . . . . . . . . . . . . 102.2 Throughput comparison for different linear detection methods. . . . . . . . . 182.3 Pilot contamination in massive MIMO: since pilot sequences are reused acrossthe network, channel estimates at the BSs may be inaccurate. . . . . . . . . 222.4 Possible range of (M,K) values in TDD and FDD for a coherence interval of300 symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1 Overview of standard EE-maximization techniques for massive MIMO systems. 323.2 Antenna selection methods for massive MIMO: circuit power consumption isreduced by operating with N < M RF chains at the BS. . . . . . . . . . . . 363.3 Large bandwidths of the order of GHz are available in the mmWave Spectrum 383.4 Hybrid analog-digital precoding with reduced RF chain requirements for mmWavemassive MIMO systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.5 Two-stage digital precoding with reduced training overhead for mmWave mas-sive MIMO systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.6 Co-channel TDD and co-channel reverse TDD deployment modes for massiveMIMO HetNets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.7 Massive MIMO with energy harvesting capability. . . . . . . . . . . . . . . . 53xList of Figures4.1 Simulation setup under study: assuming that the same frequency band andthe same set of pilot sequences are reused in all the cells, we investigate thebenefits of RA in the center cell. . . . . . . . . . . . . . . . . . . . . . . . . 754.2 Proof of convergence of the proposed solution methodology . . . . . . . . . 784.3 EE vs SNR budget Pmax for different RA schemes when M = 50, 100. . . . 794.4 Pilot and data SNR vs SNR budget Pmax for different RA schemes whenM = 50, 100. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.5 EE vs SNR budget Pmax for different RA schemes when (M, pp, pu) are opti-mized. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.6 Pilot SNR, data SNR, and budget utilization vs Pmax for different RA schemeswhen (M, pp, pu) are optimized. . . . . . . . . . . . . . . . . . . . . . . . . . 824.7 Optimal number of BS antennas M vs SNR budget Pmax when (M, pp, pu) areoptimized. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.8 EE vs SNR budget Pmax under different pilot reuse scenarios for K = 5. . . 854.9 EE vs SNR budget Pmax under different pilot reuse scenarios for K = 10. . 85xiMathematical NotationsWe represent matrices using boldface capital letters (e.g. A), vectors using boldfacesmall letters (e.g. a), and scalars using small letters (e.g. a). The transpose of a matrixA is represented as AT . The Hermitian transpose of a matrix A is represented as AH .An M ×M identity matrix is represented as IM and sometimes I when the dimensions areclear from the context. If a is a circularly-symmetric complex Gaussian vector with meanµ and covariance matrix Π, we represent its probability distribution as a ∼ CN (µ,Π). Afunction f in variables (x, y, z) is represented as f(x, y, z). When the variables (y, z) in fare assigned with values (y0, z0), the resulting function is represented as f(x; y0, z0). E{.}denotes expectation with respect to the random variable under context. The covariance ofa vector a is represented by cov(.). |A| and ||A|| respectively denote the determinant andthe vector 2-norm of the square matrix A.xiiList of Abbreviations5G : Fifth GenerationADC : Analog to Digital ConvertersBS : Base StationCCP : Convex Concave ProcedureCo-RTDD : Co-channel Reverse Time Division DuplexingCo-TDD : Co-channel Time Division DuplexingCMOS : Complementary Metal-oxide-semiconductorCQI : Channel Quality IndicatorCSI : Channel State InformationDoF : Degrees of FreedomDPC : Dirty Paper CodingeICIC : Enhanced Inter-cell Interference CoordinationEE : Energy EfficiencyEH : Energy HarvestingFDD : Frequency Division DuplexingGbps : Giga Bits Per SecondHetNet : Heterogenous NetworksICT : Information and Communication Technologyi.i.d : Independent and Identically DistributedIoT : Internet of ThingsLTE : Long Term EvolutionxiiiList of AbbreviationsMbps : Mega bits per secondMIMO : Multiple-input Multiple-outputML : Maximum LikelihoodMMSE : Minimum Mean Squared ErrormmWave : Millimeter WaveMRC : Maximal-ratio CombiningMRT : Maximal-ratio TransmissionMU-MIMO : Multi-user MIMOOFDM : Orthogonal Frequency Division MultiplexingPAPR : Peak-to-average-power RatioQoS : Quality of ServiceRA : Resource AllocationRBF : Random BeamformingRF : Radio FrequencyRSRP : Reference Signal Received PowerRSRQ : Reference Signal Received QualitySC : Small CellSCM : Single Carrier ModulationSIC : Successive Interference CancellationSINR : Signal to Interference Plus Noise RatioSIR : Signal to Interference RatioSNR : Signal to Noise RatioSUS : Semi-orthogonal User SelectionSWIPT : Simultaneous Wireless Information and Power TransferTDD : Time Division DuplexingUE : User EquipmentWET : Wireless Energy TransferxivAcknowledgementsFirstly, I would like to thank my supervisor Professor Vijay K. Bhargava for his patience,knowledge, and generous financial support. I thank him for providing me with an excellentresearch atmosphere in his lab. This thesis would not have been possible without his support,guidance, and encouragement.Secondly, I would like to sincerely thank Professor Lutz Lampe and Professor DavidMichelson for their valuable suggestions and critical comments on the thesis. Their excellentadvice has helped me in significantly improving the quality of the thesis.Thirdly, I am very fortunate and grateful to have excellent colleagues at the InformationTheory and Systems laboratory, who offered me genuine and friendly support and assur-ance to carry out my research. I should particularly thank Dr. Shankanaad Mallick forhis discussions, feedback and critical suggestions. I would also like to thank Buddhika Net-tasinghe, Lina Elmorshedy, Abdelmalik Nasser Aljalai, Reza Ramezan, and Sudha Lohanifor their friendship and support during my MASc research. I am also thankful to them forproofreading my thesis.Lastly, I am profoundly indebted to my parents, sister, and best friend in India for theirunconditional love and blessings. Without their continuous support and encouragement, Icould not have completed this thesis.xvDedicationTo my father Gopala Krishna Koppisetti, mother Surya Kumari Koppisetti, sister PavaniSindhura Koppisetti, and best friend Gayatri Bhavani.With gratitude for your inspiration, love, and support.xviChapter 1Motivation1.1 Expectations from 5G Cellular NetworksThe information and communication technology (ICT) industry currently connects and man-ages billions of devices across the globe. Currently, we are in the era of 4G and 4.5G networks,which are referred to as Long Term Evolution (LTE) and LTE-Advanced networks respec-tively by standardization bodies. Global trends suggest that future 5G networks shouldhandle up to a 1000-fold increase in the current traffic demands. In addition, a wide spec-trum of services should be supported. See Fig. 1.1 for an overview of 5G services envisionedby Huawei Technologies Co. Ltd. [2]. As we can observe from Fig. 1.1, the Internet ofThings (IoT), which promises to connect almost everything, is expected to be an integralpart of 5G networks. A host of emerging networks, such as, smart cities, vehicular networks,and augmented reality hubs will co-exist and operate simultaneously within 5G. In terms oftechnology demands, 5G networks should support latencies ranging from 1 millisecond (ms)to a few seconds, peak data rates up to 20 Giga bits per second (Gbps), average data ratesup to 100 Mega bits per second (Mbps), seamless connectivity for millions of IoT devicesper square kilometre, and signaling loads ranging from 1% to almost 100% [2].1.2 Need for Energy-Efficient SystemsWhen 5G networks are designed to meet such huge service expectations, energy consumptionbecomes a critical concern because mobile communication networks contribute towards a11.2. Need for Energy-Efficient SystemsFigure 1.1: Overview of services expected in future 5G networks [2]significant stake in the global carbon footprint. Trends [3] suggest that the mobile ICT sectorwould emit more than 300 million tonnes of greenhouse gases per annum by 2020. Observefrom Figure 1.2 that a majority of these emissions come from mobile access and mobiledevices, i.e., from powering the wireless communications between the base stations (BSs) andthe user equipments (UEs). Therefore, for a sustainable evolution into future 5G networks, itbecomes critically important for future wireless technologies to not only address the multifoldincrease in service expectations, but also to operate at reduced power consumption levels.A key design parameter in this regard is the bit-per-joule energy efficiency, defined asEnergy Efficiency (bits/Joule) =Throughput (bits/s)Power Consumption (Joule/s)(1.1)21.2. Need for Energy-Efficient SystemsFigure 1.2: Trends and forecast for greenhouse gas emissions by the mobile ICT sector [2]As we can observe from (1.1), the energy efficiency (EE) of a wireless communication systemcan be increased by using methods which maximize the system throughput or minimizepower consumption, or both. The focus of this thesis is on the massive multiple-inputmultiple-output (MIMO) technology, which offers higher EE levels than the current LTEand LTE-Advanced networks.31.3. Background on MIMO and Massive MIMO1.3 Background on MIMO and Massive MIMOOne standard technique to increase throughput in a wireless communication system is todeploy multiple transceiver antennas at the transmitters and the receivers. When multipleantennas are used at the transmitters and the receivers, throughput gains can be achievedbecause the transmitter can spatially multiplex parallel streams of data over the same time-frequency resource. Such multiple-input multiple-output (MIMO) systems have been underactive research investigation over the last decade and are currently being used in LTE andLTE-Advanced networks.Multiuser MIMO (MU-MIMO) systems [4], where a BS with multiple antennas can usescheduling algorithms to simultaneously serve multiple spatially-separated UEs over the sametime-frequency resource have gained prominence because (i) MU-MIMO systems offer mul-tiple access and broadcast capabilities and (ii) each UE in an MU-MIMO system can hosta single antenna and still achieve similar throughput gains as achieved in point-to-pointMIMO systems. In fact, the performance of point-to-point MIMO systems can be limitedby the physical size and cost constraints at the UEs because the UEs are generally low-costhandheld devices and are therefore, unable to host several antennas.Despite being practically more relevant than point-to-point MIMO systems, MU-MIMOsystems come with a significant increase in the system complexity. For example, the BSshould implement complex signal processing techniques, such as successive interference can-cellation (SIC) [5] on the uplink and dirty paper coding (DPC) [6] on the downlink, so asto mitigate interference among the UEs. This is inevitable because multiple UEs transmitor receive information simultaneously over the same time-frequency resource and are hencesubject to interference from each other. In addition, the BS should use complex schedulingalgorithms, such as random beamforming [7] and semi-orthogonal user selection [8], so as toselect the group of UEs for communication during each coherence interval. The computa-tional power requirements of these complex signal processing and complex user scheduling41.3. Background on MIMO and Massive MIMOtechniques are known to increase exponentially with the size of the system (for example,with the number of antennas at the BS) [5]-[8]. As a result, even if large throughput gainscan be achieved in an MU-MIMO system by increasing the number of antennas at the BS,we may not incur any EE gains (c.f. (1.1)). This limitation has prompted researchers toinvestigate methods which can extract large throughput gains from MU-MIMO systems atreduced levels of power expenditure.In this regard, a breakthrough contribution was provided by Marzetta in [9], where theconcept of massive MIMO was proposed. By definition, massive MIMO is an MU-MIMOtechnology, where the BS is equipped with an excessively large number of antennas whencompared to the number of UEs in the system. Deploying a large number of antennasat the BS results in an interesting propagation scenario, known as favourable propagation,where the wireless channels become near-deterministic because the BS-UE channel vectorsbecome near-orthogonal to each other. This is in turn because the effects of small-scalefading tend to disappear asymptotically when the number of antennas at the BS is increasedunboundedly [9]. Favorable propagation allows for some interesting design simplifications.Firstly, large multiplexing gains can be extracted using simple linear processing techniques,such as maximum-ratio combining (MRC) on the uplink and maximum-ratio transmission(MRT) precoding on the downlink. Secondly, large array gains can also be extracted, thusallowing for a substantial reduction in the radio frequency (RF) transmission power on boththe uplink and the downlink. Lastly, several operations at the BS, such as, user schedulingand power control, can be performed over the large-scale fading time scale because the effectsof small-scale fading are averaged out under favourable propagation, thanks to the near-deterministic channel vectors. Since massive MIMO offers large throughput gains, while alsoallowing for reductions in the transmission power and the computational power, multipleorders of EE gains can be achieved when compared to conventional MU-MIMO systems.Based on this motivation, this thesis studies how massive MIMO technology can be usedto design energy-efficient systems for future 5G deployments.51.4. Outline of the Thesis1.4 Outline of the ThesisIn Chapter 2, we introduce massive MIMO as an energy-efficient technology enabler forfuture 5G networks. The objective of this chapter is to build the necessary background forChapters 3 and Chapter 4. To achieve this, we first explain how massive MIMO deliversmultiple orders of EE gains by achieving large multiplexing and array gains at reduced powerconsumption levels. To support this discussion, we also evaluate few linear detection methodswhich achieve near-optimal throughput performance in massive MIMO systems. Later, sincethe EE metric includes a power consumption term, we present an insightful discussion onhow realistic power consumption models should be developed for massive MIMO systems.Critical comments are also provided on the practicality of massive MIMO and on some ofthe major roadblocks to its acceptance as a future technology.Chapter 3 presents a critical analysis on the state-of-the-art to identify new opportunitiesfor EE-maximization in massive MIMO systems. The objective of this chapter is to developa critical perspective on how EE-maximization can be attempted in massive MIMO systemsunder a 5G architecture. To achieve this, different phases in the design of massive MIMOsystems, ranging from computational operations at the BS to the hardware architecture, areinvestigated to identify opportunities for EE-maximization. We begin with an analysis onEE-maximization methods for conventional massive MIMO systems and proceed to study“hybrid massive MIMO” systems, where massive MIMO operates alongside other promising5G technologies, namely, millimeter wave (frequency bands beyond 30 GHz and up to 300GHz), heterogenous networks, and energy harvesting technologies. Each hybrid massiveMIMO system exhibits certain unique properties, which can be exploited to design novelEE-maximization techniques. To develop a comprehensive understanding on how this canbe done, we survey the state-of-the-art and identify prominent research directions pursuedfor EE-maximization in hybrid massive MIMO systems. We observe that most existingworks are streamlined in specific directions, leaving several new avenues unexplored. This61.4. Outline of the Thesisobservation leads us to identify few open research problems and to propose new researchdirections for future work. Open research problems identified in the process are of criticalconcern and would immensely benefit the network operators if addressed in an appropriatemanner. Also, given the number of opportunities observed, we believe that energy-efficienthybrid massive MIMO systems are very much promising for deployment in 5G.In Chapter 4, we solve a challenging resource allocation problem for maximizing EE ofcommunications in a massive MIMO system. Specifically, we investigate an EE-maximizationproblem for uplink data transmissions in a massive MIMO system, where the optimizationvariables are (i) the number of antennas per BS, (ii) the pilot signal power, and (iii) thedata signal power. Unlike most works on massive MIMO which assume equal pilot anddata signal powers, we treat pilot and data signal powers as separate optimization variables.Also, unlike most studies which model circuit power as a fixed component in the total powerexpenditure, we model circuit power as an increasing function in the number of BS antennasand the number of UEs. The resulting optimization problem has a fractional objectivefunction and is very difficult to solve in general. To address this concern, we use principlesfrom fractional programming and propose an iterative algorithm based on Jagannathan’stheorem [36], where each iteration uses an alternating optimization technique to decomposethe original problem into a sequence of solvable difference of convex (DC) programmingproblems. Through simulation results, we observe that higher EE levels can be achievedwhen the pilot and data signal powers are optimized separately. We also observe that higherEE levels can be achieved if the number of antennas at the BS is optimized with respect tothe available power budget.Finally, Chapter 5 provides few concluding remarks and topics for future work.7Chapter 2Introduction to Massive MIMO2.1 MotivationMassive multiple-input multiple-output (MIMO) is a promising technology enabler for future5G networks because it offers multiple orders of throughput and energy efficiency gainsover current LTE and LTE-Advanced networks. Currently, there is a dearth for referencebooks on massive MIMO which provide a detailed explanation on how massive MIMO offerslarge energy efficiency (EE) gains over current LTE networks. This is an important concernbecause massive MIMO is a promising technology enabler for 5G and it is not straightforwardto develop a critical understanding on how massive MIMO offers multiple orders of EE gains.We address this concern in the current chapter by laying specific focus on the objectivesoutlined in the next section.2.2 Objectives and OutlineFirstly, we intend to develop necessary background on massive MIMO for appreciating var-ious aspects of energy-efficient design discussed later in Chapters 3 and 4. Secondly, sincethe EE metric relies on the power expenditure in the system, we intend to provide importantguidelines on how mathematical models can be developed for power consumption in massiveMIMO systems. This is of prime importance because inaccurate power consumption modelsmay invalidate theoretical designs from being implemented in practice. Lastly, we intend toequip the reader with a critical understanding of the benefits as well as limitations associ-82.3. Massive MIMO: A Multiuser MIMO Technologyated with massive MIMO. To achieve the above mentioned objectives, we first provide anoverview of massive MIMO and develop a mathematical evaluation on how large EE gainscan be extracted from massive MIMO systems. Comparisons are drawn against conventionalmultiuser MIMO systems to illustrate how signal processing requirements are significantlysimplified in the large M regime. Important design guidelines are provided on how accuratepower consumption models can be developed for massive MIMO systems. Subsequently, crit-ical comments are provided on the practicality of massive MIMO and on some of the majorroadblocks in its acceptance as a future technology. The chapter is organized as follows.Section 2.3 introduces massive MIMO as a multiuser MIMO technology and explains howmassive MIMO offers multiple orders of energy efficiency gains over current LTE networks.Section 2.4 discusses few low-complexity linear detection methods which achieve near-optimalthroughput performance in massive MIMO systems. Section 2.5 provides few guidelines ondeveloping mathematical models for power consumption in massive MIMO systems. Section2.6 briefs upon the practicality of massive MIMO. Section 2.7 discusses major unresolvedchallenges in massive MIMO systems. Section 2.8 provides few concluding remarks.2.3 Massive MIMO: A Multiuser MIMO TechnologyMassive MIMO is a multi-user MIMO technology in which K single-antenna user equipments(UEs) are serviced simultaneously on the same time-frequency resource by a base station (BS)equipped with a relatively large number M of antennas, i.e., M >> K (c.f. Fig. 2.1). Ingeneral, the UEs in a massive MIMO system can be equipped with more than one antennas.However, to simplify our analysis, discussions in this thesis are limited to systems withsingle-antenna UEs.Deploying several antennas at the BS results in an interesting propagation scenario calledfavourable propagation, where the channel becomes near-deterministic because the radio linksbetween the BS and the UEs become nearly orthogonal to each other [9]. This is because92.3. Massive MIMO: A Multiuser MIMO TechnologyUE 11 2MUE 2UE 3UE 4UE 5UE KDownlinkUplinkFigure 2.1: Massive MIMO: a multi-user MIMO technology where K single-antenna UEs areserved by a BS with M >> K antennas.the effects of small-scale fading tend to disappear asymptotically in the large M regime.Significant EE gains can be achieved under favourable propagation because multiple ordersof multiplexing and array gains are realizable. For the purpose of illustration, let us considerthe uplink and downlink transmissions in a massive MIMO cell.The asymptotic Shannon capacities on the uplink (CUL) and the downlink (CDL) for amultiuser MIMO channel under favourable propagation are given by [42]CUL =K∑k=1log2(1 + pu,kMβk),CDL = max(ak≥0,∑ak≤1)K∑k=1log2(1 + pd,kMakβk),(2.1)where pu,k and pd,k are the uplink and downlink signal to noise ratios (SNRs) for the kthUE, βk represents the large-scale fading coefficient for the kth UE, and {ak, k = 1, 2, . . . , K},is an optimization vector to obtain CDL. For simplicity, if we neglect the effect of βk and102.3. Massive MIMO: A Multiuser MIMO Technologyassume that each UE transmits with an average signal to noise ratio pu, the uplink Shannoncapacity simplifies toCUL = K log2(1 +Mpu). (2.2)A similar argument can be made about downlink transmissions as well. The simplificationillustrated in (2.2) leads us to two important observations (i) the system throughput canbe improved by increasing K, i.e., by multiplexing parallel streams of data to more numberof UEs over the same time-frequency resource, and (ii) transmission power per UE can bedecreased by increasing M , i.e, the number of BS antennas, while still maintaining the samethroughput per UE. In other words, the simplification in (2.2) shows that we can achieveO(K) multiplexing gains and O(M) array gains under favourable propagation.While the large array gains are a straightforward opportunity to reduce UE transmissionpowers, massive MIMO also facilitates a drastic reduction in the circuit power consumedin the system. As discussed next, this is because the BS can implement (i) linear signalprocessing techniques and (ii) low-complexity user scheduling algorithms, and still achievenear-optimal throughput performance.2.3.1 Linear Signal ProcessingIn conventional multiuser MIMO systems, optimal capacities can be achieved if the BS im-plements complex signal processing techniques, such as, maximum-likelihood (ML) multiuserdetection on the uplink and dirty paper coding (DPC) [6] on the downlink. Unfortunately,such complex signal processing techniques incur large computational burdens which growexponentially with the size of the system, for example with the number of BS antennas M .As a result, when M and K are large, such techniques consume large amounts of circuitpower, thus becoming highly unsuitable for massive MIMO operations.Fortunately, in the large M regime, linear signal processing techniques, such as maximum-112.3. Massive MIMO: A Multiuser MIMO Technologyratio combining (MRC) on the uplink and maximum-ratio transmission (MRT) on the down-link, can achieve near-optimal throughput performance. See Section 2.4 for a detailed dis-cussion.2.3.2 Low-complexity User SchedulingIn conventional multiuser MIMO systems, simple linear precoding techniques, such as maximum-ratio transmission (MRT), do not achieve optimal capacities on the downlink. To reduce theperformance gap, the BSs generally implement certain user scheduling methods which exploitmulti-user diversity in the system. Basically, the BS selects few UEs during each transmis-sion interval and schedules them for simultaneous transmissions. Two seminal works on userscheduling are the random beamforming (RBF) [15] and the semi-orthogonal user selection(SUS) [8] methods. In the RBF method, the BS selects a group of UEs by matching themto a pre-determined set of orthogonal beams transmitted on the downlink. The matchingis based on feedback provided by each UE, in terms of a channel quality indicator (CQI),such as the signal to interference plus noise ratio (SINR), and the best beam index. In SUSmethod, the BS acquires full channel state information (CSI) from all the candidate UEsand selects a subset of UEs which have near-orthogonal channel vectors.Conventional user scheduling methods, such as RBF or SUS, may not be appropriate formassive MIMO systems due to a variety of reasons: (i) performance gains based on multi-user diversity may not be significant in the large M regime because the effects of small-scale fading are diminished (ii) such methods are computationally intensive and consumesignificant amounts of circuit power when M is large − SUS incurs O(M3K) computationalcomplexity [8], and (iii) such methods often suffer from practical limitations − RBF schemesdo not perform well in systems with finite number of UEs [15] and SUS schemes are unscalablebecause significant overhead is incurred when acquiring full CSI from all the candidate UEs.Fortunately, in the largeM regime, very simple user scheduling schemes, such as, selectinga subset of UEs randomly [16], selecting a subset of UEs in the descending order of their122.4. Linear Detection Methods for Massive MIMOlarge-scale fading coefficients [16], or selecting UEs in a round-robin fashion [55], are knownto achieve near-optimal throughput performance. This is because the channel vectors becomenear-orthogonal to each other and the effects of small-scale fading are diminished in the largeM regime.Since low-complexity signal processing and user scheduling algorithms achieve near-optimal throughput performance in massive MIMO systems, we observe that the circuitpower consumption is drastically reduced when compared to conventional multiuser MIMOsystems. Note that this reduction in circuit power consumption is in addition to the largearray gains, which allow for a significant reduction in the UE transmission powers. Conse-quently, by achieving near-optimal throughput performance at reduced power consumptionlevels, massive MIMO networks deliver multiple orders of EE gains over current LTE net-works.In the next section, we present a discussion on three prominent linear multiuser detectiontechniques for massive MIMO, namely maximum-ratio combining (MRC), zero-forcing (ZF)detection, and minimum mean squared error (MMSE) detection. We explain how theselinear detection techniques are derived and show that these techniques achieve near-optimalthroughput performance in the large M regime.2.4 Linear Detection Methods for Massive MIMOWhen linear multiuser detection techniques are used, the BS multiplies the received signalwith a linear detection matrix so as to decode the data streams transmitted by the K UEs onthe uplink. For the purpose of illustration, let us consider uplink transmissions in a massiveMIMO cell, where pu is the average transmission SNR on the uplink, s = [s1 s2 . . . sk]T ,such that E{|sk|2} = 1, is the vector of symbols transmitted by the K UEs, and H =[h1 h2 . . . hK ] is the channel matrix. The received signal vector at the BS y is given by132.4. Linear Detection Methods for Massive MIMOy =√puHs + n=√puK∑k=1hksk + n,(2.3)where n ∈ CM×1 is the additive noise vector. We assume that the elements of n are in-dependent and identically distributed Gaussian random variables with zero mean and unitvariance, i.e, n ∼ CN (0, IM). Now, if A ∈ CM×K is the linear detection matrix, the signalestimate yˆ = [yˆ1 yˆ2 . . . yˆk]T , which can be used to decode the original transmission vectors, is given byyˆ =√puAHHs + AHn (2.4)Based on (2.4), the signal estimate which is used to decode the symbol sk transmitted bythe kth UE is given byyˆk =desired signal︷ ︸︸ ︷√puaHk hksk +inter-user interference︷ ︸︸ ︷√puK∑j=1,j 6=kaHj hjsj +noise︷︸︸︷aHk n, (2.5)where ak is the kth column of A. Thereby, the received signal to interference plus noise ratio(SINR) is given bySINRk =pu|aHk hk|2∑Kj=1,j 6=k |aHk hj|2 + ||ak||2(2.6)As we can observe from (2.5), columns in the detection matrix A can be obtained by solvingan optimization problem which maximizes the “desired signal power” with respect to the“inter-user interference plus noise power” in the system. Since this can be computationallyintensive, the BS can choose to tradeoff performance by neglecting the effects of inter-userinterference or noise in the system. Based on this analogy, different multiuser detectiontechniques in the current literature choose to maximize different objective functions − MRC142.4. Linear Detection Methods for Massive MIMOdetection maximizes the signal to noise ratio (SNR) in the system, ZF detection maximizesthe signal to interference ratio (SIR) in the system, and MMSE detection maximizes thesignal to interference plus noise (SINR) in the system. Due to this fundamental difference inthe objective functions, the detection matrices used by these techniques are different fromeach other.2.4.1 Maximum-ratio Combining (MRC)When the BS employs MRC detection, it neglects the effects of inter-user interference andmaximizes the received signal to noise ratio (SNR). Therefore, using (2.5), the kth columnin the detection matrix A can be obtained as followsaMRCk = argmaxak∈CM×1desired signal powernoise power= argmaxak∈CM×1pu|aHk hk|2||ak||2= hk(because|aHk hk|2||ak||2 ≤||ak||2||hk||2||ak||2 , where equality holds when ak = hk)(2.7)As a result, the detection matrix for MRC is given byAMRC = H (2.8)Observe from (2.4) and (2.8) that MRC detection requires minimal signal processing becausethe BS should simply multiply the received signal with the conjugate-transpose of the channelmatrix H and proceed to decode each symbol independently. From an EE perspective, sucha low signal processing requirement is highly desirable in the large M regime because optimalsignal processing techniques, such as ML detection, consume prohibitively large amounts ofcircuit power when the size of the system is large. Note that MRC detection experiences152.4. Linear Detection Methods for Massive MIMOperformance degradation in interference-limited scenarios because the effects of inter userinterference are neglected.2.4.2 Zero-forcing (ZF) DetectionWhen the BS employs ZF detection, it neglects the effects of noise and maximizes thereceived signal to interference ratio (SIR). Therefore, using (2.5), the kth column in thedetection matrix A can be obtained as followsaZFk = argmaxak∈CM×1desired signal powerinter-user interference power= argmaxak∈CM×1pu|aHk hk|2pu|∑Kj=1,j 6=k akhj|2(2.9)To satisfy the requirement in (2.9), the columns {ak} in the ZF detection matrix can bechosen such thatakhk 6= 0,akhj = 0,∀j 6= k(2.10)In other words, the columns {ak} can be constructed by projecting the signal estimate ontothe orthogonal component of the inter-user interference in the system. This condition issatisfied if A is chosen as the pseudo-inverse of the channel matrix H, i.e.,AZF = H(HHH)−1 (2.11)Upon substituting (2.11) into (2.4), the signal estimate becomesyˆ = (HHH)−1HHy,=√pus + (HHH)−1HHn(2.12)Observe from (2.12) that the resulting signal estimate is free from inter-user interference inthe system. When compared to MRC, computational complexity is higher in ZF detection162.4. Linear Detection Methods for Massive MIMObecause it requires computation of the pseudo-inverse of the channel matrix. Nevertheless,since ZF detection is a linear signal processing technique, the computational requirementsare still lower than in optimal signal processing techniques, such as ML detection. Notethat ZF detection experiences performance degradation in noise-limited scenarios becauseit neglects the effects of noise in the system. Also, ZF detection may perform poorly if thechannel is not well-conditioned because matrix inversion may significantly amplify the noisein the system.2.4.3 Minimum Mean Squared Error (MMSE) DetectionWhen MMSE detection is employed, the BS attempts to maximize the received signal tointerference plus noise ratio (SINR). This can be achieved by minimizing the minimum meansquared error between the signal estimate yˆ and the transmitted symbol vector s. In otherwords, the MMSE detection matrix can be obtained as followsAMMSE = argminA∈CM×KE{||AHy − s||2}= argminA∈CM×KK∑k=1E{|aHk y − sk|2}= (HHH +1puIM)−1H [43](2.13)Since MMSE detection maximizes the received SINR, it performs better than MRC and ZFdetection techniques. However, it incurs higher computational complexity than the othertwo methods because it requires an increased number of matrix manipulations. In addition,similar to the case with ZF detection, MMSE may perform poorly for ill-conditioned channelsbecause matrix inversion significantly amplifies the noise in the system.172.4. Linear Detection Methods for Massive MIMOFigure 2.2: Throughput comparison for different linear detection methods.2.4.4 Performance ComparisonFig.2.2 plots the throughput performance of MRC, ZF, and MMSE detection methods whenthe number of BS antennas is increased up to 100. We assume K = 10, pu = −10 dB,and calculate the uplink sum-rates as∑Kk=1 E{log2(1 + SINRk)}, where SINRk values arecalculated for the three detectors by substituting the detection matrices in (2.8), (2.11),and (2.13) into the SINR expression in (2.6). When M is large, we observe that all thelinear detection methods achieve near-optimal throughput performance. The MRC detectionmethod does not perform as well as the other two linear detection methods because it neglectsthe effects of inter-user interference in the system. Nevertheless, the performance of MRCis comparable to the other two methods and is, in fact, the preferred choice for practicaldeployments because (i) MRC requires minimal number of computations and hence incurslow circuit power consumption and (ii) MRC does not suffer from noise amplification whenthe channels are ill-conditioned, as often experienced in practice.182.5. Modelling Power Consumption in Massive MIMOOn similar lines to our discussions for linear multiuser detection methods, linear pre-coders can also be derived for downlink transmissions in a massive MIMO system. Threeprominent linear precoders in the current literature, namely maximum-ratio transmission(MRT), zero-forcing (ZF), and minimum mean squared error (MMSE) precoders, have sim-ilar operational meanings and exhibit similar properties as MRC, ZF, and MMSE detectiontechniques respectively. Therefore, similar to the detection matrices given in (2.8), (2.11),and (2.13), the precoding matrices WMRC , WZF , and WMMSE for the three linear precodersmentioned above are given byWMRC = H,WZF = H(HHH)−1,WMMSE = (HHH +1pdIM)−1H,(2.14)where pd is the average transmission SNR on the downlink. Similar to the case with lineardetection methods, these linear precoders achieve near-optimal throughput performance inthe large M regime. This completes our discussion on how signal processing requirementsare simplified in massive MIMO systems.The next section presents a few guidelines on how realistic power consumption modelscan be developed for massive MIMO systems. This is important because the EE metric,defined in (1.1), relies on the accuracy of power consumption model used.2.5 Modelling Power Consumption in Massive MIMOThe sum power consumption P , aggregated over uplink and downlink transmissions in anmassive MIMO system, can be modelled asP = PPA + PC + Psys, (2.15)192.6. Practicality of Massive MIMOwhere PPA represents the total uplink and downlink power consumed by the power amplifiers(PAs) at the BS and the UEs, PC represents the total uplink and downlink circuit powerconsumed by different analog and digital signal processing circuits at the BS and the UEs,and Psys refers to the remaining system dependant component in P .While PPA accounts for the sum power expenditure on RF transmissions, PC includes thesum power consumption from RF chain components, such as, filters, mixers, and synthesizers,as well as baseband operations, such as, digital up/down conversion, precoding/receivercombining, channel coding/decoding, and channel estimation. Note that PC cannot bemodelled as per conventional practice as a constant term independent of (M,K) becausethe hardware requirements and the number of circuit operations in the system grow withM and K. For example, with the one RF chain per antenna design used in the currentLTE networks, the number of RF chains at the BS and the UEs grows affinely with Mand K, respectively. Additionally, the computational requirements for various basebandoperations are functions in M and K. For example [56], O(M,K2) operations are requiredfor ZF precoding, O(MK) for MRC detection, O(MK) for minimum mean squared error(MMSE) channel estimation, and O(K) for channel coding respectively. Therefore, realisticmodels should treat PC as a function in (M,K) and the variability of PC with (M , K)should be investigated during the design of energy-efficient massive MIMO networks. Lastly,Psys accounts for the power consumed by site-specific and architecture-specific factors, suchas, BS and UE architectures, power supply, cooling system, backhaul, and other controlequipment. Psys will play an important role in characterizing EE for 5G networks becauseseveral BS and UE types will co-exist in a multi-tier architecture with different cell sizes andpower consumption levels.2.6 Practicality of Massive MIMOFavorable propagation is derived in [9] as an asymptotic propagation scenario for independent202.7. Major Challenges in Massive MIMOand identically distributed (i.i.d) Rayleigh channels, achieved when M is increased unbound-edly. There is a general notion that massive MIMO may not be practical because some ofthe assumptions behind favourable propagation may not be valid in practice. For example, itmay not be feasible to increase M unboundedly. Also, due to rich scattering environments,practical channels are known to exhibit fundamentally different propagation characteristicswhen compared to theoretical i.i.d Rayleigh channels. Despite these concerns, recent fieldstudies [51] show that measured channels with large but finite M achieve a significant por-tion of the multiplexing and array gains derived under theoretical assumptions. This showsthat massive MIMO is indeed a practical technology.Nevertheless, several technological challenges continue to exist. For example, designingcompact massive MIMO antenna arrays is a challenge at the current sub-3GHz bands becausea minimum inter-antenna spacing of λ/2, where λ is the carrier wavelength, is required toavoid spatial correlation. Other important challenges include mitigating the role of pilotcontamination and reducing channel state information (CSI) overhead in frequency divisionduplexing (FDD) massive MIMO systems. Detailed discussions on these challenges arepresented in the next section.2.7 Major Challenges in Massive MIMO2.7.1 Pilot ContaminationAcquiring accurate CSI at the BS is very important in massive MIMO systems because theachievable throughput and EE gains depend directly on the accuracy of the CSI at the BS.This is because the performance of several BS operations, such as linear detection on theuplink and linear precoding on the downlink, is subject to the availability of accurate CSIat the BS. Due to moving UEs, the length of coherence intervals is generally limited andconsequently, only a finite number of orthogonal pilot sequences can be used within eachcoherence interval for channel estimation. This necessitates the reuse of a finite set of pilot212.7. Major Challenges in Massive MIMOP4P3P1P3P4P2P2P1Cell ICell IICell IIIPilot SignalPilot ContaminationP3P4P2P1Figure 2.3: Pilot contamination in massive MIMO: since pilot sequences are reused acrossthe network, channel estimates at the BSs may be inaccurate.sequences across the network during each coherence interval. When pilots are reused, thechannel estimates obtained in a given cell will be contaminated by pilot sequences transmittedby UEs in other cells. This effect, called “pilot contamination”, reduces the throughput andEE performance of the system. This is illustrated in Fig. 2.3, where the pilot sequences P1and P2 are re-used in cells I and II and the sequences P3 and P4 are reused in cells II andIII respectively. Each interfering pilot signal represents itself as the desired pilot signal at agiven BS, thus causing imperfections in the CSI estimated at the BS. CSI imperfections areknown to introduce upper bounds on the achievable throughput and EE gains in the systems[24].Since pilot reuse is inevitable, pilot contamination continues to be a performance bottle-neck in massive MIMO systems. Few researchers [10]-[13] have recently proposed methodsto reduce the effects of pilot contamination in massive MIMO but much of the research onthis topic is still ongoing.222.7. Major Challenges in Massive MIMO2.7.2 Frequency Division Duplexing (FDD) SystemsWorldwide, the number of licenses for the FDD mode of operation (> 400) is much more thanthat for the time division duplexing (TDD) mode of operation (< 30) [14]. Therefore, FDDsystems facilitate better hardware re-use, easier software upgrades, and a smoother transitioninto 5G when compared to TDD systems. Despite these advantages, most research workson massive MIMO have focused on the TDD mode of operation because TDD systems incurlower CSI overhead and offer better scalability than FDD systems. To make the argumentrigorous, let us compare the CSI acquisition overhead in TDD and FDD based massive MIMOsystems. The BS can implement very different channel estimation techniques, depending onwhether the system operates in TDD or in FDD.Channel estimation in TDD systemsFor channel estimation in the TDD mode, the K UEs transmit orthogonal pilot sequences onthe uplink. Since the pilot sequences are already known to the BS, it uses this knowledge toestimate uplink channels based on the received pilot signals. This process requires a minimumof K channel uses per coherence interval. Since the uplink and downlink transmissionsoccur over the same frequency resource, the BS can exploit channel reciprocity to precodetransmissions for the downlink. The UEs require information on the effective channel gainto detect desired signals on the downlink. To facilitate this, the BS can beamform pilotsignals on the downlink and the UEs can estimate the effective channel gains based onthe received pilot signals. This process also requires a minimum of K channel uses percoherence interval. Therefore, TDD systems incur a total CSI overhead of 2K channel usesper coherence interval. In other words, TDD systems are subject to the design constraint2K < T , where T is the channel coherence time in symbols.232.7. Major Challenges in Massive MIMOChannel estimation in FDD systemsWhen operating in the FDD mode, the uplink and downlink channels are not reciprocalbecause transmissions on the uplink and downlink occur over different frequency bands. Foruplink transmissions, the K UEs can transmit orthogonal pilot sequences and the BS canestimate uplink channels based on the received pilot signals. This requires K channel uses percoherence interval on the uplink. For precoding transmissions on the downlink, the BS needsto acquire channel state information by transmitting M orthogonal pilot sequences to theK UEs. The UEs estimate the M downlink channels based on the received pilot signals andfeedback the channel estimates to the BS on the uplink. This process requires a minimum ofM channel uses per coherence interval on the downlink and M channel uses per coherenceinterval on the uplink. Combining the channel uses required to obtain CSI for uplink anddownlink transmissions, we observe that FDD systems are subject to the constraint M+K <T on the uplink and the constraint M < T on the downlink. This makes M + K < T asthe universal design constraint for FDD systems. Since M is generally large in massiveMIMO systems, the CSI overheads are also generally large in FDD systems. Such largeCSI acquisition overheads can adversely affect the performance of the system, particularlyin high-mobility scenarios, because the CSI overhead consumes significant portions of therelatively smaller coherence intervals.Also, when compared to TDD systems, scalability can be severely curtailed in FDDsystems because the CSI overhead in FDD systems increases affinely with M . We illustratethis in Fig. 2.4 by comparing the feasible (M,K) in FDD and TDD systems. We assume acoherence interval of T = 300 symbols, corresponding to a coherence bandwidth of 200 kHzand a coherence time of 1.5 ms. Thereby, based on our previous discussions, TDD systemsare subject to the constraint 2K < 300 and FDD systems are subject to the constraintM + K < 300. We observe that the feasibility regions are much smaller in FDD systemsthan in TDD systems. Better scalability is offered by TDD systems because more antennascan be added at the BS without incurring any additional CSI overhead.242.7. Major Challenges in Massive MIMO0 50 100 150 200 250 30001002003004005006007008009001000Number of User Equipments (K)Number of antennas at the Base Station (M)TDDFDDFigure 2.4: Possible range of (M,K) values in TDD and FDD for a coherence interval of 300symbolsAs evident from the above discussions, large CSI overheads are a major bottleneck for thedesign of FDD massive MIMO systems. Although few recent studies [52] propose techniqueswhich exploit channel sparsity to reduce the CSI overhead in FDD massive MIMO systems,the validity of underlying channel sparsity assumptions can be questionable, particularlyin the low frequency regime. Therefore, designing FDD systems continues to be a majorresearch challenge for massive MIMO.2.7.3 Non-orthogonal Waveform DesignTo address issues such as non-contiguous spectrum and spectrum agility in 5G networks, mas-sive MIMO technology should be complimented with the use of appropriate non-orthogonalwaveforms. The strict synchronization and orthogonality constraints imposed by the widely-used OFDM waveforms are being viewed as a strong hindrance towards supporting servicessuch as low-latency tactile internet applications and highly sporadic machine-type commu-252.8. Summarynications (MTC). Other issues with OFDM such as the high peak to average power ratio(PAPR), sensitivity to phase noise, poor spectrum localization, and large out-of-band (OOB)emissions [17] are being viewed as potential drawbacks. Therefore, non-orthogonal waveformssuch as filter bank multi carrier (FBMC), single carrier modulation (SCM), bi-orthogonalfrequency division multiplexing (BFDM), and universal filtered multi carrier (UFMC) aregaining prominence [89]. Going by the state-of-the-art, there is no clear consensus on a par-ticular waveform combination with massive MIMO because each waveform comes with itsown share of advantages and disadvantages. For example, OFDM facilitates easier hardwareimplementation and backward compatibility but, as mentioned earlier, suffers from syn-chronization and orthogonality issues. SCM supports low-latency applications with reducedPAPR, but offers lower throughputs and requires computationally intensive equalizationtechniques. Similarly, FBMC offers flexible carrier aggregation, robustness against synchro-nization errors, and low OOB emissions, but suffers from implementation issues such as theuse of long filter lengths and complex multiuser receivers. As a result, there in no clear con-sensus on the choice of an appropriate non-orthogonal waveform for massive MIMO. This notonly offers huge scope for further research, but also reinforces the need for standardizationactivities.2.8 SummaryIn this chapter, we introduced massive MIMO as an energy-efficient technology enabler forfuture 5G networks. The chapter was organized as per the objectives outlined in Section2.2. Sections 2.3-2.4.4 laid focus on addressing the first objective, where massive MIMO wasintroduced as a special case of multiuser MIMO technology in which the base station (BS)is equipped with a large number M of antennas to serve a relatively small number of single-antenna user equipments (UEs). To analyze how massive MIMO achieves multiple ordersof EE gains over current LTE networks, mathematical explanations were presented on how262.8. Summarylarge multiplexing and array gains can be achieved at reduced power consumption levels inthe large M regime. To support this analysis, we compared massive MIMO against conven-tional multiuser systems and explained how massive MIMO facilitates a drastic reduction inthe computational requirements at the BS. Simple computer simulations were presented toillustrate that low-complexity linear detection methods, such as, maximum-ratio combining(MRC), zero-forcing (ZF), and minimum mean squared error (MMSE) detection, achievenear-optimal throughput performance in massive MIMO systems.Section 2.5 focused on addressing the second objective and has provided important guide-lines on modelling power consumption in the large M regime. A simple mathematical frame-work was developed by attributing power consumption in massive MIMO systems to threemajor operations, namely, power amplifier operations, circuit operations, and site-specificoperations. Special emphasis was laid on modelling circuit power as a function in the num-ber of antennas at the BS and the number of UEs in the system. As will be evident later inChapter 4, such a realistic model helps us in developing practical solutions to challenging re-source allocation problems in massive MIMO. The third and final objective was addressed inSection 2.7, where a detailed discussion was presented on the practicality of massive MIMOand on some of the major challenges to be overcome before accepting massive MIMO as afuture technology. Example scenarios were presented to develop a critical perspective onwhy pilot contamination and FDD mode of operation continue to be major roadblocks formassive MIMO. Since the intended objectives have been successfully achieved, we believethat the reader is now better equipped with the necessary background to appreciate thestudies presented in the next two chapters.27Chapter 3Hybrid Massive MIMO Systems:Opportunities and Challenges forEnergy-Efficient Design3.1 MotivationDue to spectrum crunch and ever increasing traffic demands, spectrum efficiency (SE) hasalways been the utmost design priority in our evolution over the last two decades from 1Gto 4G networks. While the data rates have significantly improved from kilobits per second(Kbps) in 2G to gigabits per second (Gbps) in 4G, operators have continued to overlook thepower expenditure in achieving these data rates. As a result, when compared to SE gains,energy efficiency (EE) gains have always lagged behind by several orders of magnitude inour evolution so far. As highlighted in the previous chapter, energy consumption trendssuggest that it is no longer a sustainable strategy to prioritize SE gains over EE gains inour evolution towards 5G. With this motivation, the current chapter critically analyzes howmassive MIMO technology can co-operate with other 5G technologies to realize multipleorders of EE gains over current LTE networks.283.2. Background and Contributions3.2 Background and ContributionsSeveral emerging technologies, such as massive MIMO, millimetre wave (mmWave), denseheterogenous networks (HetNets), energy harvesting, full duplex, and cloud based radio ac-cess, are currently being investigated as potential enablers for future 5G networks. Giventhe uniqueness of benefits offered, it is natural to expect that a subset of these technologieswill operate in unison under the 5G architecture. Despite growing evidence of such a coex-istence [61]-[86], limited literature is currently available on how the coexistence of multiple5G technology enablers can be exploited to design energy-efficient 5G networks.Particularly, there is no existing work which critically analyzes and develops a compre-hensive understanding on how the coexistence of massive MIMO with other promising 5Gtechnologies can be exploited to design energy-efficient 5G networks. While few studies havefocused on designing spectrally efficient hybrid massive MIMO systems [20]-[23], a compre-hensive study from an EE perspective is currently missing. This is an important shortcomingfrom a system designer’s perspective because massive MIMO, which offers multiple ordersof EE gains by itself, can mutually benefit from one or more of the above mentioned 5Gtechnologies. The current chapter addresses this shortcoming by critically analyzing thestate-of-the-art on designing energy-efficient “hybrid massive MIMO” systems. We coin theterm “hybrid massive MIMO” systems to refer to wireless networks where massive MIMOtechnology operates in conjunction with other emerging 5G technology enablers. The targetobjective is to develop a comprehensive understanding of the opportunities and challengeswhich arise when EE-maximization is attempted in hybrid massive MIMO systems. Ourcontributions in this chapter are summarized next.We take EE into perspective and critically analyze the potential of hybrid massive MIMOsystems in providing large EE gains over current LTE networks. The novelty of our work liesin analyzing the potential of hybrid massive MIMO systems from an EE perspective. Firstly,some of the most prominent EE-maximization techniques for massive MIMO systems, such293.2. Background and Contributionsas the use of low-complexity BS operations, minimizing power amplifier losses, redesigningtransceiver architecture and the use of antenna selection, are reviewed. For each technique,major limitations, which are not straightforward from an initial observation, are identified.We then critically analyze hybrid massive MIMO systems to identify new opportunitiesand challenges for EE-maximization. Detailed explanations are presented on how massiveMIMO benefits mutually from three promising 5G technologies, namely millimeter wave,heterogenous networks, and energy harvesting technologies. Some of the unique propertiesexhibited by each of these hybrid massive MIMO systems are studied so as to understandwhy new design constraints emerge from an EE perspective. Thereby, we critically reviewthe state-of-the-art on designing energy-efficient hybrid massive MIMO systems and observethat most research works are based on few key ideas. By critically analyzing these ideas andtheir impact on energy-efficient design, we are able to identify several shortcomings whichare not straightforward to observe. This allows us to highlight open research problems andto propose new research directions for future work. We believe that the insights developedin this chapter would be immensely helpful to both academic and industry researchers intouching unexplored avenues for energy-efficient design and in addressing few implementationconcerns thereof. The chapter is organized as follows.In Section 3.3, we analyze few standard EE-maximization techniques which can be ap-plied in general to any massive MIMO system. Major theoretical and practical limitationswith each of these techniques are highlighted so as to provide interested readers with poten-tial research directions. In Section 3.4, we critically analyze the coexistence of millimeterwave and massive MIMO technologies from an EE perspective. We explain how these tech-nologies benefit mutually from each other and how their co-existence gives rise to severalnew opportunities for the design of energy-efficient systems. We observe that most workson EE-maximization in mmWave massive MIMO systems have been streamlined in specificresearch directions with focus on few key ideas. This observation leads us to identify short-comings in the available literature and to propose new research directions for future work.303.3. Methods to Improve Energy Efficiency in Massive MIMO SystemsOn similar lines to Section 3.4, we analyze the coexistence of heterogenous networks andmassive MIMO in Section 3.5 and the coexistence of energy harvesting and massive MIMOin Section 3.6. Few concluding remarks are provided in Section 3.7.3.3 Methods to Improve Energy Efficiency in MassiveMIMO SystemsObserve, from (1.1), that the energy efficiency of a massive MIMO network can be maximizedby achieving optimal throughput performance while operating at minimum levels of powerconsumption. Based on this analogy, a number of research directions have been pursued forthe design of energy-efficient massive MIMO networks (see Fig 3.1 for a broad overview). Fewmethods devise low-complexity algorithms for BS operations, such as, multi-user detection,precoding, and user scheduling, so as to achieve near-optimal throughput performance at lowpower expenditure. Few other methods, such as, transceiver re-design, antenna selection,and power amplifier dimensioning, focus on improving resource utilization in the system so asto relax hardware requirements and thereby, the power expenditure in the system. Availableliterature also includes methods which minimize power losses in the system, such as, antennareservation and amplifier-aware design, and methods which relax hardware quality, i.e, byintroducing hardware imperfections, to reduce power expenditure in the system. In thissection, we study some of the techniques mentioned above and identify few open researchchallenges thereof.3.3.1 Low-complexity BS operationsDue to favourable propagation in the large M regime, simple linear processing techniques,such as Maximum-Ratio Combining (MRC) and Maximum-Ratio Transmission (MRT) pre-coding, and simple user scheduling algorithms, such as random and round robin scheduling,313.3. Methods to Improve Energy Efficiency in Massive MIMO SystemsEnergy Efficient Design for Massive MIMOLow-complex algorithms to achieve near-optimal throughputLinear Detectors Linear PrecodersSimple User SchedulingMinimize Power ExpenditureMinimize PA power (PPA)Minimize Circuit Power (PC)Minimize system-dependant power (Psys)PA aware designScale RF Transmit PowerMinimize PA lossesPA dimensioningAntenna ReservationConstant Envelope PrecodingAntenna SelectionRedesign Transceiver ArchitectureExploit Hardware ImperfectionsMinimize RF Chain requirementsHybrid Precoding TechniquesFigure 3.1: Overview of standard EE-maximization techniques for massive MIMO systems.achieve near-optimal throughput performance. These simplifications yield significant EEgains because the circuit power PC is drastically reduced when compared to conventionalsystems with computationally intensive signal processing schemes, such as ML detectionand successive interference cancellation (SIC), and complex scheduling algorithms, such asrandom beamforming and semi-orthogonal user selection.While channel reciprocity can be exploited in TDD systems to derive near-optimal low-complexity linear precoding schemes, precoders for FDD systems cannot exploit channelreciprocity because the UL and DL communications occur on separate frequency bands.FDD precoders cannot also rely on pilot signalling and feedback from the UEs because thisconsumes at least M +K symbols per coherence interval, making them impractical for highmobility scenarios. Few low overhead FDD precoders, which assume channel sparsity forchannel dimensionality reduction, have been proposed recently[52]. However, such precodersare limited to high frequency bands, such as mmWave, where channel sparsity assumptionsare valid. Consequently, low-complexity and low-overhead FDD precoding continues to be amajor research challenge for massive MIMO networks. Since there are many more licensesworldwide for FDD than for TDD, progress on low overhead FDD precoders will promote323.3. Methods to Improve Energy Efficiency in Massive MIMO Systemswider acceptance of massive MIMO as a future technology.3.3.2 Minimize Power Amplifier (PA) LossesSignificant energy efficiency gains can be achieved by minimizing power amplifier lossesbecause inefficient power amplifier operations in the current LTE networks discard as muchas 60% to 95% of the power input to the amplifiers [87]. Prominent research directions tominimize power amplifier losses include (i) dimensioning the power amplifier, (ii) use of lowpeak-to-average-power-ratio (PAPR) techniques, and (iii) PA-aware designPower amplifier dimensioningLosses at the power amplifiers can be minimized by operating the power amplifiers at pointsclose to the maximum allowed output. Unfortunately, most power amplifiers in current LTEdeployments are operated, on an average, at points much lower than the maximum allowedoutput because of the high linearity requirements imposed by high peak to average power(PAPR) waveforms such as OFDM. Power losses at linear power amplifiers can be reducedsignificantly by adaptively dimensioning, i.e., adjusting, the power amplifier’s maximumoutput power based on temporal variations in the traffic load in the system. Such load-adaptive power amplifier dimensioning techniques are known to enhance the energy efficiencyof massive MIMO systems by up to 30 % [88]. A major drawback for power amplifierdimensioning methods is that their performance is sensitive to the accuracy of availableinformation on temporal traffic variations in the system, which are generally very difficult topredict.Low PAPR techniquesAs an alternative to linear power amplifiers, the BS can deploy non-linear power amplifiers,which are known to be about 4-6 % more power efficient [91]. However, non-linear PAs requirelow PAPR input signals to avoid signal distortions. To address this concern, researchers have333.3. Methods to Improve Energy Efficiency in Massive MIMO Systemsbeen exploring different PAPR reduction methods. For example, few antenna reservationmethods have been recently proposed [93], wherein the signals sent to one set of antennasare deliberately clipped so as to achieve low PAPR, while correction signals are sent on theremaining set of reserved antennas so as to compensate for the clipping. In [93], the authorsassume M = 100 and reserve 25 % of the antennas so as to achieve a PAPR reduction of4 dB. A major drawback with antenna reservation methods is that they may not necessarilyincrease the system energy efficiency because reserving antennas results in reduced throughputand the reservation process increases signaling overhead in the system.Few low-PAPR non-orthogonal waveforms, such as single carrier modulation (SCM), havebeen proposed recently. However, designing appropriate non-orthogonal waveforms continuesto be a major research challenge because most of the recently proposed non-orthogonalwaveforms suffer from limitations, such as long filter lengths and complex receiver techniques[89]. Linearity requirements of power amplifiers can also be relaxed using constant envelopeinput signals. When appropriate precoding schemes are employed, constant envelope signalscan achieve similar throughputs as achieved by high-PAPR signals [92]. A major unresolvedchallenge concerning constant envelope signal studies is the generation of perfectly constantenvelope continuous-time signals.PA-Aware DesignA different approach to minimize power amplifier losses is the design of PA-aware mas-sive MIMO systems. This can be beneficial because conventional massive MIMO systems,designed with sum-power constraints per BS, do not impose constraints on the maximumoutput power and the power loss per PA. Recent studies on simple MIMO systems [94] [95]show that significant improvements in the throughput performance per UE can be achievedwhen PA-aware design is implemented with realistic constraints on both the PA output powerand the power losses per PA. We observe that the design of PA-aware systems is a relativelynew research field with no literature currently available for massive MIMO systems.343.3. Methods to Improve Energy Efficiency in Massive MIMO Systems3.3.3 Minimize RF Chain Requirements at the BSConventionally, MIMO precoding is performed digitally in the baseband. Since digital pro-cessing requires dedicated baseband and RF chain components for each antenna element,BS transceivers conventionally adopt a one RF chain per antenna design. Such a designcan result in significant circuit power consumption in the massive MIMO regime becausethe number of RF chains at the BS increases affinely with M . Therefore, minimizing RFchain requirements at the BS is an attractive strategy to improve energy efficiency in massiveMIMO networks. Prominent techniques which reduce RF chain requirements include hybridprecoding, antenna selection, and transceiver redesign. Hybrid precoding techniques aregenerally built on channel sparsity assumptions and are discussed in the context of mmWavesystems in Section 3.4.Antenna SelectionAntenna selection is a signal processing technique which reduces RF chain requirementsat the BS. As illustrated in Fig. 3.2, a subset comprising N out of the M BS antennas isselected based on a predefined selection criterion, such as maximizing the system throughputor energy efficiency. Antennas in the selected subset are then connected to RF chains forfurther processing. Since the number of RF chains is reduced from M to N , circuit powerconsumption in the system is reduced.353.3. Methods to Improve Energy Efficiency in Massive MIMO SystemsPrecodingData UE 1Data UE 2Data UE KRF Chain NRF Chain 2RF Chain 1RF Switch UE 1UE 2UE KSelection Criteria Channel Feedback12MAntenna Selection(N out of M)Figure 3.2: Antenna selection methods for massive MIMO: circuit power consumption isreduced by operating with N < M RF chains at the BS.Observe that, depending on the subset selection algorithms, such as, orthogonal match-ing pursuit and gradient descent, antenna selection methods may add to the computationalburden at the BS. As a result, energy efficiency maximization using antenna selection be-comes a non-trivial task. Current literature on antenna selection for massive MIMO ismostly confined to simple single cell scenarios [96] [97]. Performance tradeoffs introduced bydesign limitations, such as pilot contamination and antenna switching losses, have not beenevaluated so far.Redesign Transceiver ArchitectureAn alternative strategy to reduce RF chain requirements at the BS is to redesign the BStransceiver architecture. In this direction, few single RF chain transceivers have been re-cently designed, although at the cost of some serious practical limitations. For example,the electronically steerable parasitic antenna array proposed in [57] operates with a singleRF chain but supports a limited set of modulation schemes and requires almost twice thenumber of antennas than in conventional transceivers. Similarly, [58] proposes a single RF363.4. Millimeter Wave (mmWave)-based massive MIMO Systemschain transmitter based on a two-port matching network, but the transceiver performance issubject to power losses in the matching network and mutual coupling in the antenna array.Above mentioned examples show that, although transceiver redesign offers great promise toimprove energy efficiency in massive MIMO networks, existing works suffer from seriouspractical limitations.In the next few sections, we critically analyze state-of-the-art EE-maximization tech-niques for hybrid massive MIMO systems where massive MIMO operates in conjunctionwith other promising 5G technologies, namely, millimeter wave, heterogenous networks, andenergy harvesting networks.3.4 Millimeter Wave (mmWave)-based massiveMIMO Systems3.4.1 Unique PropertiesThe mmWave spectrum, which refers to spectrum in the 30-300 GHz band, is now being in-vestigated for 5G operations because the current sub-3GHz bands have become overcrowdedand there is a need for additional spectrum to accommodate future traffic demands. By mov-ing to the mmWave spectrum, significant throughput gains can be achieved because largebandwidths of the order of multiple GHz are available (c.f. Fig. 3.3). Typically, mmWavechannels exhibit huge reflection and absorption losses and poor diffraction characteristics.As a result, when compared to sub-3GHz bands, mmWave channels experience higher chan-nel correlation, signal attenuation, and sensitivity to blockage. mmWave channel estimationis still an active topic of research [62].373.4. Millimeter Wave (mmWave)-based massive MIMO Systems7"GHz"1.3"GHz" 2.1"GHz" 10"GHz"28"GHz" 37,42"GHz" 60"GHz" 71,76,"81,86"GHz""Figure 3.3: Large bandwidths of the order of GHz are available in the mmWave Spectrum3.4.2 Benefits from Co-existenceMassive MIMO implicitly offers the highly directional transmissions required to improvesignal strength and suppress interference in blockage-sensitive environments at mmWavebands. On the other hand, mmWave makes massive MIMO realizable because (i) the smallwavelengths at mmWave frequencies allow a large number of antennas to be fit into verysmall form factors - a 16 x 16 antenna array at 60 GHz can be fit into an 80 x 80 mm2area [60], and (ii) the near-LOS channels in mmWave massive MIMO networks can beestimated using direction of arrival (DoA) of the incident waves at the BS [63]. By replacingthe conventional pilot-based channel estimation techniques with such DoA-based channelestimation techniques, the need for pilot reuse can potentially be eliminated. Thereby, thepilot contamination effect, which is a major impediment for massive MIMO systems, maypotentially be overcome.3.4.3 Existing Works on Energy-Efficient Design: Key IdeasWe observe that the current literature on the design of energy-efficient mmWave massiveMIMO systems has mostly been streamlined in few specific research directions. In thissection, we present an outline on the fundamental ideas behind prominent research directionspursued so far. The observations we make in this section are summarized in Table 3.1 andexplained in detail here.FSparsity in mmWave channels has been exploited to design hybrid analog-digital beam-383.4. Millimeter Wave (mmWave)-based massive MIMO SystemsTable 3.1: Existing EE-maximization Methods for mmWave Massive MIMO SystemsMethod Key idea Impact(a) Hybrid analog-digital • Add an analog precoding phase • Reduced RF chain requirementsprecoding [62] • Exploit sparsity to reduce channeldimension(b) Multi-stage digital • Form UE groups with similar • FDD mode becomes realizableprecoding [52] covariance eigenspace• Exploit channel sparsity to reduceCSI overhead(c) Overlaid massive • Network densification • Higher throughputsMIMO macro tier [65] • Additional assistance to mmWave • Less frequent outagecells • Improved QoS(d) DoA-based channel • Use DoA to estimate channels • Potentially eliminate pilot reuseestimation [63](e) One-bit quantization • Use low-resolution ADC in • Reduced circuit power expenditure[64] RF chains • Simplified circuit complexityforming techniques which relax RF chain requirements in the system [62]. For example, thehybrid precoding technique shown in Fig. 3.4 reduces the number of RF chains from Mto NR, where S ≤ K, S ≤ NR ≤ M . The analog precoder applies phase-only control toreduce the channel dimensionality from M x K to NR x S. The digital precoder appliessimple linear precoding techniques on the effective NR × S channel to extract multiplexinggains. RF chain requirements are reduced because the digital precoders operate only on theeffective reduced dimensional channel.Sparsity in mmWave channels has also been exploited to derive low overhead multistageprecoding techniques, such as shown in Fig. 3.5. The two-stage digital precoding techniquesshown in Fig. 3.5 exploits channel sparsity to partition UEs into different groups, where eachgroup comprises UEs with approximately the same channel covariance eigenspace, such thatthe covariance eigenspaces of different UE groups are near-orthogonal to each other. Whensuch multistage digital precoding techniques are implemented, the FDD mode of operation,which incurs large CSI overhead and is therefore impractical at the sub-3GHz bands, becomesrealizable at mmWave bands because the CSI training overhead is significantly reduced. Tounderstand how the overhead is reduced, let us first denote r, r ≤ M , as the rank ofchannel covariance matrix and S, where (S ≤ K), as the number of independent streams393.4. Millimeter Wave (mmWave)-based massive MIMO SystemsDigital Precoder       Nx SSData StreamsRF ChainRF ChainRF ChainAnalog Precoder       M x  NUE 1UE 2UE K2MN RF Chains1Hybrid analog-digital precodingFigure 3.4: Hybrid analog-digital precoding with reduced RF chain requirements formmWave massive MIMO systemsto be transmitted to the UEs. Precoder I exploits the near-orthogonality of covarianceeigenspaces to reduce the channel dimensionality from M×K to B×S, where B (S ≤ B < r)is an optimization parameter to regulate intergroup interference in the system. A low-ratefeedback mechanism is sufficient to update Precoder I because it depends only on the channelcovariance, which typically varies very slowly when compared to the channel coherence time.Precoder II employs simple linear precoding techniques on the effective B × S channel so asto extract multiplexing gains within each UE group. To update precoder II, the BS shouldacquire instantaneous CSI of the effective B × S channel during each coherence interval.Observe that the CSI overhead will still be lower than in conventional FDD systems becausethe overhead comes predominantly from estimating reduced dimensional channels.Since the narrow directional beams and the near-LOS propagation eliminate much ofthe multipath in mmWave massive MIMO networks, few research works [65] have exploredthe use of mmWave massive MIMO BSs to support low power backhaul operations, thusbecoming an energy-efficient alternative to expensive fiber backhaul. Also, note that the cellradii in mmWave massive MIMO systems are expected to be of the order of 200m becauseatmospheric attenuation can be severe - it can go upto 20 dB/km [61]. This may be beneficial403.4. Millimeter Wave (mmWave)-based massive MIMO SystemsPrecoder II            Bx SRF ChainRF ChainRF Chain2MM RF Chains1Precoder I            M x B, B << MLow rate feedback on channel covarianceInstantaneous feedback on reduced channelsSData StreamsUE Group 1UE Group 2UE Group GLow overhead digital precodingFigure 3.5: Two-stage digital precoding with reduced training overhead for mmWave massiveMIMO systemsfrom an energy efficiency perspective because small cells offer considerable throughput gainsthrough extensive spatial frequency reuse.The near-LOS propagation in mmWave systems facilitate channel estimation based onthe direction-of-arrival (DoA) of information signals at the BS. Few research works [63]have exploited this new opportunity in mmWave systems to design energy-efficient systems.Improvements in EE arise from replacing conventional pilot-based, channel estimation withDoA-based estimation schemes. Since pilot contamination is known to adversely affect thethroughput rates in a system, improvements are observed in EE when pilot reuse is eliminatedthrough the use of DoA for channel estimation.The conventional one RF chain per antenna design cannot be attempted for mmWavemassive MIMO BSs because the large number of antennas and large bandwidth operationsrequire proportionately higher requirements, such as, the chip area to ensure sufficient sep-aration, local oscillator distribution, and power expenditure, particularly due to PAs andwideband analog-to-digital converters (ADCs). Particularly, wideband ADCs consume un-acceptably large amounts of power when operated at large bandwidths. Taking this intoperspective, few research works on conventional MIMO systems [64] demonstrate that ade-413.4. Millimeter Wave (mmWave)-based massive MIMO SystemsTable 3.2: Proposed Research Directions for Designing Energy-efficient mmWave MassiveMIMO SystemsMethod Limitations Proposed Research Directions(Table 3.1)(a) • Analog phase allows phase-only control Optimize EE subject to• Number of data streams limited • Limited precision of phase controlby number of RF chains • Limited number of phase shifts• Limited ADC resolution(b) • Rely on wide sense stationarity of channel • Optimize UE grouping for EEprocess • Develop low-complexity• Channel covariance is susceptible to mobility covariance tracking methods• Pilot contamination may affect performance • Optimize pilot sequence length and pilot(not studied so far) symbol placement to maximize EE(c) • Over densification may incur significant • Develop cell association, interferenceincrease in power expenditure coordination, and load balancing.methods to maximize EE(d) • Estimation is very sensitive to calibration • Develop DoA-based algorithms• Relies on computationally intensive algorithms which optionally use pilots for accuracy.(e) • Low-precision quantization introduces • Optimize ADC input distributionssevere non-linearity and thresholding to maximize EE• Performance loss is inevitablequate gains may still be achievable under the one RF chain per antenna design if appropriatelow-resolution ADCs are employed. This is because circuit power consumption at the RFchains is drastically reduced when low-resolution ADCs are employed.3.4.4 Proposed Research Directions for future workIn this section, we present a critical analysis on the key ideas on which most existing works onenergy-efficient mmWave massive MIMO systems are built. We identify limitations with eachapproach and propose new research directions which are not straightforward and obvious tomake. If addressed in an appropriate manner, we believe that the findings in this sectionwill immensely help network operators in planning for future mmWave massive MIMO de-ployments. Table 3.2 presents a summary of the major limitations which we identify forthe existing research directions shortlisted in Table 3.1. It also summarizes new researchdirections which we propose for future work. Details are presented next.Despite evidence that multi-stage precoding techniques, such as shown in Fig. 3.5, can bedesigned to reduce training overhead in mmWave massive MIMO systems, such techniques423.4. Millimeter Wave (mmWave)-based massive MIMO Systemshave only been studied to a limited degree of extent (see [52] for a recent example). Tradeoffsintroduced by pilot contamination should be evaluated to assess the true EE gains offeredby such multi-stage precoding techniques. Missing in the existing literature are studieswhich optimize the interference mitigation parameter B for energy efficiency. Other openproblems for future work include optimizing user grouping, covariance tracking, and intercell interference mitigation for energy efficiency. Similar is the situation with hybrid analog-digital precoding techniques which relax RF chain requirements at the BS. These techniquesare invaluable for mmWave operations because mixed signal components in the RF chain,particularly the high resolution ADCs, consume large amounts of power when operated atlarge bandwidths. Notice that the analog precoding phase introduces new constraints inthe transceiver design, such as limited precision for phase control, limited number of phaseshifts, and limited ADC resolution. Existing literature does not discuss the energy efficiencytradeoffs introduced by these new constraints, leaving scope for further research.Due to severe blockage in mmWave environments - brick and concrete can cause upto 80dB attenuation [61], small cell mmWave networks may experience frequent signal outages,thus enforcing service imbalance in terms of coverage, connectivity, and other quality of ser-vice (QoS) guarantees in the network. As a result, despite overlaying a massive MIMO macrotier, the blockage-sensitive mmWave environments may require additional assistance in theform of multi-hop relays and repeaters so as to achieve a network-wide service guarantee.Very limited literature is currently available on EE-maximization in two-tier mmWave mas-sive MIMO networks. Appropriate outage probability models ( see [66] for an example), cellassociation techniques, interference coordination methods, and load-balancing mechanismsshould be developed in order to evaluate the EE gains offered by such a multi-tier networkarchitecture.Although DoA-based channel estimation techniques are promising to eliminate pilot con-tamination, these techniques are generally very sensitive to calibration issues. In addi-tion, computational burden in DoA estimation may counterweigh the expected EE gains.433.5. Massive MIMO-based Heterogenous NetworksTherefore, future works should investigate hybrid channel estimation techniques, where sub-optimal and low-complexity DoA-based estimation algorithms receive optional assistancefrom additional pilot-based training so as to improve estimation accuracy. There is cur-rently no literature available on how one-bit quantization techniques can be used to improveEE in mmWave massive MIMO systems, although few results are available for simple MIMOsystems [64]. Associated design challenges to be addressed include the development of opti-mal input distributions and quantizer-thresholding techniques.Another major bottleneck in the realization of energy-efficient mmWave massive MIMOsystems is the hardware design. Silicon-based CMOS technologies provide a simple andcost-effective means to integrate several mmWave antennas with necessary analog and digitalcircuitry onto a single package. However, the high frequency and large bandwidth operationsin the mmWave regime impose constraints on the design of transceiver components. Forexample, high substrate absorption losses and high noise power levels become roadblocksto the design and integration of highly directional antennas into CMOS packages. On-chipADCs and power amplifiers should operate at a low supply voltage so as to avoid damagingother active on-chip components. In addition, improper isolation between active on-chipcomponents can result in mutual coupling, self-jamming, and signal distortion. Transceiverswhich address these design complications have not been fabricated till date.3.5 Massive MIMO-based Heterogenous Networks3.5.1 Unique PropertiesDense heterogenous networks (HetNets), where spectrum utilization is maximized by de-creasing the cell size and increasing the number of small cells (SCs) per unit area, offera promising approach to satisfy the traffic demands expected in 5G. In terms of energyefficiency, HetNets are a superior alternative to massive MIMO because (i) the power con-sumption per SC is generally low, (ii) BSs in SCs can be opportunistically turned on/off443.5. Massive MIMO-based Heterogenous Networksdepending on traffic demand, and (iii) high throughput gains can be achieved by offloadingtraffic between outdoor and indoor SCs. Moreover, when M SCs are deployed per unit areaand γ is the path loss exponent, O(Mγ2 ) array gains can be achieved because the averageBS-to-UE distance is reduced by M12 . These array gains are larger than the O(M) gainsoffered by massive MIMO because γ > 2 for most propagation conditions.3.5.2 Benefits from Co-existenceDue to smaller coverage areas, SCs fail to ensure seamless connectivity and quality of service(QoS) to UEs which are highly mobile. This limitation can be overcome by designing atwo-tier massive MIMO HetNet, wherein a macro cell tier formed by the massive MIMOBSs is overlaid with an SC tier formed by small cells, such as pico cells and femto cells. Themacro cell tier ensures uniform service coverage and supports highly mobile UEs, while thesmall cell tier caters to the local indoor and outdoor capacity requirements. Clearly, such anarchitecture can simultaneously extract the O(Mγ2 ) array gains offered by HetNets and theO(K) multiplexing gains offered by massive MIMO. In addition, since the macro tier hosts alarge number of antennas, few antennas can be reserved for low power wireless backhaul to theSC tier. Interference coordination in massive MIMO HetNets can be analyzed by using simpletools from random matrix theory. This is highly beneficial because tools from stochasticgeometry, which are used to study interference coordination in single antenna HetNets,cannot be easily applied to massive MIMO HetNets because beamforming introduces cross-tier statistical dependencies.3.5.3 Existing Works on Energy-Efficient Design: Key ideasResearchers have begun attempting standard EE-maximization techniques for HetNets, suchas, BS sleeping and cell zooming in the context of massive MIMO-based HetNets [53] [54][71]. Few other energy-efficiency maximization techniques have been designed by jointly453.5. Massive MIMO-based Heterogenous NetworksTable 3.3: Existing EE-maximization Methods for Massive MIMO-based HetNetsMethod Key idea Impact(a) Soft-cell coordination • Serve UEs jointly through • Significant reduction in circuit power[72] multiflow beamforming • Reduced hardware requirements(b) Spatial blanking • Blank out the dominating • Better resource utilization than eICIC.[67] [71] interference subspace spatially • Improved interference coordination• Eliminates need to orthogonalizetime-frequency resources(c) Co-channel TDD • Utilize spectrum fully in each • Significantly higher throughputsdeployments [68]-[70] network tier • In-band wireless backhaulto small cell tier(d) Decentralized cell • Asymptotic UE rates • Improved load balancingassociation [73]-[75] independent of each other’s • Simplified algorithm complexitycell association (NP-hard problem becomes decoupled)Table 3.4: Proposed Research Directions for Designing Energy-efficient Massive MIMO-basedHetNetsMethod Limitations Proposed Research Directions(Table 3.3)(a) • Rely on sharing control between • Attempt EE-maximizationnetwork tiers using sub-optimal schemes• Optimal beamforming can be • Investigate traffic-adaptivecomputationally intensive sleep modes(b) • Covariance-based blanking relies on • Optimize sacrificed degrees ofquasi-static channels freedom (DoFs) in each tier for EE• Very sensitive to pilot • Optimize pilot symbol placementcontamination for blanking• Develop low-complexitycovariance tracking algorithms(c) • Quality of interference estimation and • Dynamically switch betweenrejection varies significantly co-TDD and co-RTDDbetween co-TDD and co-RTDD with variations in traffic.• Requires tight timing synchronization • Implement interference-temperatureof all devices power control• Channel estimation suffers from • Design location-dependent schedulinginterference and pilot contamination(d) • Network management becomes • Develop QoS-aware antennacomplicated due to partitioning and allocation to aid decentralization.distributed control • Jointly optimize cell associationand traffic offloading463.5. Massive MIMO-based Heterogenous Networks(a) Co-channel TDD modeTime Slot 1, Desired SignalMM Macro BSSC BSSC UEMacrocell UE(b) Co-channel Reverse-TDD modeMM Macro BSSC BSSC UEMacrocell UETime Slot 1, Interfering SignalTime Slot 2, Desired SignalTime Slot 2, Interfering SignalFigure 3.6: Co-channel TDD and co-channel reverse TDD deployment modes for massiveMIMO HetNets.exploiting the properties of massive MIMO and HetNet technologies. For example, soft-cellcoordination techniques have been proposed for massive MIMO HetNets wherein BSs inthe macro and small cell tiers can jointly serve the UEs through low-complexity multiflowbeamforming. Such techniques offer high EE gains because they are known to drasticallyreduce hardware requirements at the massive MIMO BSs − [72] shows that the number ofmassive MIMO BS antennas can be reduced by more than 50% if a few single antenna SCsare overlaid on the massive MIMO cell.In addition, co-channel deployment modes, where the available spectrum is fully utilizedin both macro and SC tiers, have been recently attempted. To explain the underlying ideas,example scenarios are illustrated in Fig. 3.6 as the co-channel TDD (co-TDD) and the co-channel reverse TDD (co-RTDD) modes. In the co-TDD mode, the macro and SC tiersare time-synchronized to simultaneously transmit in the uplink or the downlink. In theco-RTDD mode, the order of uplink and downlink transmissions are reversed in one of thetiers, i.e., macro tier operates in the downlink when SC tier operates in the uplink and viceversa. Since the entire spectrum is utilized in both the tiers, simultaneous and uncoordinated473.5. Massive MIMO-based Heterogenous Networkstransmissions can introduce significant inter-tier and intra-tier interference when co-channeldeployment modes are practiced.Fortunately, the BSs in macro and SC tiers can not only estimate the channels to theirintended UEs, but also the covariance of interfering signals. As a result, few research workshave exploited channel reciprocity to design precoding vectors which sacrifice certain degreesof freedom (DoFs) on the downlink so as to blank out the strongest interference subspace.When such spatial blanking techniques are used and the number of sacrificed DoFs are opti-mized, throughput gains can be achieved in the SC tier at the cost of a negligible throughputloss in the macro tier [67]. Observe that spatial blanking techniques do not introduce ad-ditional overheads into the system because no explicit cross-tier information exchange isrequired. In addition, spatial blanking techniques are more resource-efficient than interfer-ence mitigation techniques, such as almost blank subframes and fractional frequency reuse,which are proposed under the enhanced Inter Cell Interference Coordination (eICIC) in thecurrent LTE standards [69]. This is because spatial blanking techniques avoid the need for or-thogonalizing time-frequency resources by spatially blanking out the dominating interferencesubspace during each time-frequency slot.Co-channel deployment modes have also been applied within each network tier by parti-tioning the network tier into groups of BSs and fully utilizing the available spectrum in eachBS group. For example, [70] studies a co-RTDD massive MIMO HetNet system where themassive MIMO BSs serve the UEs and also provide wireless backhaul to few BSs in the SCtier. co-RTDD mode is applied not only between the macro and SC tiers but also withinthe SC tier by partitioning the SC tier into BS groups. Power savings are observed whencompared to single-tier massive MIMO networks as well as massive MIMO HetNets withwired backhaul.EE-maximization has also been attempted when co-channel deployment modes are usedin propagation environments with highly directional channel vectors, such as observed atmmWave frequencies or when the UEs are concentrated at hotspots in certain areas (see [71]483.5. Massive MIMO-based Heterogenous Networksfor an example). The key idea has been to exploit directionality of the channel vectors so asto attempt spatial blanking based on low-overhead multi-stage precoding techniques, such asdiscussed earlier in Fig 3.5. Further enhancement in EE gains have been demonstrated byimplementing these precoding techniques alongside other EE-maximization techniques forHetNets, such as, dynamically turning on/off a few SCs, scheduling hotspots, and offloadingtraffic across network tiers [71].Lastly, EE-maximization in massive MIMO HetNets has also been attempted throughthe use of appropriate user association techniques. Conventional user association techniquesbased on reference signal received power (RSRP) or reference signal received quality (RSRQ)may not be suitable for massive MIMO HetNets because these techniques do not perform wellfor cells with asymmetric transmission powers, number of antennas, and load distributions.Additionally, biasing techniques, which artificially scale the RSRP by a bias term to offloadtraffic from macro-cells to SCs, may not be effective because these methods do not balancetraffic within each network tier and are generally based on average performance metrics.Generally, the joint optimization problem of user association, precoding design, and powerallocation is known to be non-deterministic polynomial-time hard (NP-hard). Fortunately,in the massive MIMO regime, this problem is decoupled because the asymptotic UE rates areindependent of each other’s cell association. Thanks to this simplification, studies such as[73]−[75] propose optimal user association algorithms which achieve efficient load balancing,both within and across network tiers.3.5.4 Proposed Research Directions for Future WorkIn this section, we explain some of the limitations associated with the key ideas which areexploited by most existing works on EE-maximization in massive MIMO HetNets. Thishas allowed us to propose interesting research directions for future work. Details on thelimitations and the proposed research directions are summarized in Table 3.4 and explainednext.493.5. Massive MIMO-based Heterogenous NetworksMultiflow beamforming techniques rely on sharing control information between networktiers. In addition, optimal beamforming, although beneficial in terms of reduction in cir-cuit power and hardware requirements, may incur significant computational complexity. Toaddress this concern, future studies should investigate designing suboptimal multi flow beam-forming techniques for EE-maximization. In addition, traffic adaptive sleep modes may beinvestigated to reduce computational burden and improve energy utilization in both thenetwork tiers. Most studies on spatial blanking attempt channel covariance estimation andprecoding based on a wide sense stationarity assumption on the channel process. Such anassumption is generally valid only locally and is susceptible to mobility in the system. Pilotcontamination may also affect the accuracy of channel covariance estimation and subse-quently the effectiveness of spatial blanking. Future studies should devise algorithms whichoptimize the sacrificed number of degrees of freedom (DoFs) for maximizing EE in both thetiers. Pilot symbol placement should be optimized to improve the effectiveness of spatialblanking. In addition, novel channel tracking algorithms should be developed to adaptivelylearn and update the estimated interference subspace according to the non-stationary time-varying effects in the system. Most studies on spatial blanking focus on simplistic UE distri-bution scenarios with either isolated UEs or hotspots. In contrast, realistic HetNets wouldexperience asymmetric traffic loads coming from a combination of hotspots and isolated UEs.Therefore, advanced low complexity interference coordination strategies should be designedto allow efficient spatial resource sharing between hotspots and isolated UEs.Note that the co-TDD and co-RTDD modes exhibit some conflicting properties, leadingto some interesting tradeoffs for the design of energy-efficient massive MIMO HetNets. Forexample, the quality of interference estimation and the ability to reject interference canbe considerably different because the interfering signals are different. Co-RTDD rendershigher interference estimation accuracy than co-TDD because the interferer channels arequasi-static in co-RTDD, due to fixed locations of the massive MIMO and SC BSs, but aredynamically varying in co-TDD, due to moving UEs. Consequently, when in the macro-tier503.5. Massive MIMO-based Heterogenous Networksuplink, co-RTDD can attempt spatial blanking to achieve large throughput gains in the SCtier (see [67] for an example), while this cannot be done in co-TDD. On the other hand, whenin the macro-tier downlink, co-RTDD offers lower throughput gains than co-TDD becauseco-RTDD renders lower interference rejection. This is in turn because the co-RTDD modecan only reject interference between massive MIMO and SC BSs.As a result, there is no clear winner among co-TDD and co-RTDD. This calls for thedesign of innovative co-channel deployment modes, which can simultaneously reap the ben-efits and overcome the limitations of co-TDD and co-RTDD. One example would be designco-channel deployment modes which dynamically switch between co-TDD and co-RTDDmodes with varying traffic conditions. Appropriate pilot assignment methods should bedeveloped to contain pilot contamination, which can be particularly severe in co-channeldeployments. Since co-channel deployment modes can incur significant increase in intra-tierand inter-tier interference, appropriate interference-temperature power control and location-dependent scheduling algorithms should be designed. To aid decentralization in cell associa-tion techniques for massive MIMO HetNets, future works should develop QoS-aware antennaallocation methods. Another unexplored subject in cell association for massive MIMO Het-Nets is to optimize cell association jointly with traffic offloading. Resource efficient inter-tieroffloading techniques based on load-adaptive cell zooming, dynamic antenna activation inthe macro tier, and mobility-aware handover policies, should be designed under practicalconstraints such as limited backhaul and load asymmetries.513.6. Energy Harvesting (EH)-based massive MIMO Networks3.6 Energy Harvesting (EH)-based massive MIMONetworks3.6.1 Unique PropertiesIncorporating energy harvesting capabilities at the BS and the UEs in a massive MIMOsystem introduces several new design constraints into the system. For example, unlike in grid-powered networks, the energy harvested from most renewable resources fluctuates randomly,although over a smaller range of magnitude and a larger timescale than the communicationchannel amplitudes. Also, the energy conversion efficiency is generally low - about 15%for solar [76]. Signal interference may not be desirable from a throughput perspective,but is desirable from an RF energy harvesting perspective. Also, power sensitivity levelsare radically different for RF energy harvesters (about −10 dBm) and information receivers(about−60 dBm) [81]. In addition, energy harvesting networks are subject to a new causalityconstraint: energy consumed until a given time cannot exceed the energy harvested untilthen. These new constraints in energy harvesting networks enforce the transmission policiesto depend not only on channel fading but also on the energy arrival and data backlog.3.6.2 Benefits from Co-existencePowering the BSs in massive MIMO networks with energy harvested from renewable re-sources, such as solar, wind, and thermal, can result in reduced carbon footprint and in-creased network lifetime. The UEs in a massive MIMO network can also benefit from energyharvesting capabilities because they are usually powered by limited-capacity batteries. Un-like at the BSs, energy harvesting rates at the UEs should be controllable because batterydrains can potentially lead to loss of network connectivity. To achieve this, the BSs cantransmit dedicated RF signals on the downlink and perform energy beamforming so as toprovide uninterrupted wireless energy transfer (WET) to the UEs. Alternatively, the BSs can523.6. Energy Harvesting (EH)-based massive MIMO Networksattempt simultaneous wireless information and power transfer (SWIPT), where the downlinkRF signals are used to simultaneously transport both energy and information to the UEs.Massive MIMO may be suitable more suitable than omnidirectional antenna systems for suchRF energy harvesting applications because the directional transmissions in massive MIMOsystems can increase the energy transfer efficiency of RF signals. This can be beneficialbecause the energy transfer efficiency of RF signals can be very low when the atmosphericattenuation is severe [82].UEUEInformation TransferEnergy TransferEnergy SharingUEUEBatteryEnergy SupplyRenewableEnergyPower GridEnergy SupplyEnergy SupplyEnergy SupplyFigure 3.7: Massive MIMO with energy harvesting capability.3.6.3 Existing Works on Energy-Efficient Design: Key IdeasEnergy harvesting (EH) is a natural option to improve energy efficiency in massive MIMOnetworks because it opens up several new opportunities for minimizing power consumptionfrom non-renewable resources, such as the power grid. Despite the well-known benefits ofincorporating EH capabilities into cellular wireless networks, limited literature is currently533.6. Energy Harvesting (EH)-based massive MIMO Networksavailable on EH massive MIMO networks. However, a number of works have investigatedthe benefits of incorporating EH capabilities in conventional MIMO networks. Therefore,we take inspiration from the vast amount of literature available on conventional EH MIMOnetworks to propose an EH architecture for future massive MIMO deployments, as illustratedin Fig. 3.7. Key ideas exploited in the current literature on conventional MIMO networkshave been summarized and included in the proposed architecture.In the EH massive MIMO network shown in Fig. 3.7, the massive MIMO BSs are poweredby energy supplies which can harvest and store renewable energy in a battery. Since theenergy harvested from renewable sources is generally sporadic, the energy supply at the BScan optionally draw power from the grid and can thereby, ensure network reliability. Inaddition, since the energy harvesting rates may be different for different BSs, the massiveMIMO network can employ an energy sharing architecture, which allows the energy harvestedlocally at each BS to be shared across the network. The BSs can attempt WET or SWIPTto enable RF energy harvesting at the UEs. Energy harvested from such RF transmissionscan be used by the UEs to recharge batteries or to power uplink transmissions.To improve the system energy efficiency, the BSs and the UEs can implement transmissionpolicies which optimally utilize the harvested energy. Example transmission policies includeoptimizing utility functions, such as maximizing the system throughput under a deadline anda constraint that the harvested energy is limited. Strategies to design transmission policiescan be categorized as offline or online strategies, depending on the availability of informationon statistical factors in the system. Offline strategies assume non-causal knowledge of energyarrival and channel state information (CSI) to provide an upper bound on the system per-formance. In contrast, online strategies assume causal knowledge of the channel and energyrealizations and use analytical models, such as Markov decision process (MDP) and queuingtheory, to derive near-optimal policies.543.6. Energy Harvesting (EH)-based massive MIMO Networks3.6.4 Proposed Research Directions for Future WorkDespite the well-known benefits of using a large number of antennas at the BS, limitedliterature is currently available on energy harvesting massive MIMO networks. One possiblereason is that the energy transfer and conversion efficiency values can be very low [84] [85].Even otherwise, most transmission policies available for conventional MIMO networks cannotbe generalized to the massive MIMO regime because these policies either assume zero circuitpower consumption or assume that the circuit power consumption (PC) is a constant termwhich is independent of (M,K). As discussed earlier in Section 2.5, such assumptions onPC are not valid in the massive MIMO regime. Very few studies, such as [78], use a realisticmodel for PC but make other unrealistic assumptions, such as, perfect CSI and full knowledgeof future energy arrival. This leaves scope for future work, particularly on the achievableenergy efficiency values under constraints, such as, battery imperfections, delay-sensitivetraffic, and lossy energy sharing architectures.RF energy harvesting capabilities have also not been thoroughly investigated in massiveMIMO networks. Few studies, such as [83], study energy beamforming for WET in massiveMIMO networks under practical constraints such as imperfect CSI and delay-sensitive traffic.However, tradeoffs introduced by other practical constraints, such as, finite battery capacity,energy leakages, and transceiver imperfections, are yet to be fully understood. Few otherstudies [86] discuss SWIPT-enabled massive MIMO networks, but several important concernsare yet to be addressed. For example, information leakage concerns, which arise whendownlink signals are amplified to improve RF energy harvesting rates at the UEs, have notbeen addressed so far. In addition, energy-aware medium access control (MAC) protocols,which optimize time resource allocation between channel access and energy harvesting, areyet to be designed.Several interesting research directions can be pursued in the future to realize the en-ergy efficiency gains offered by energy harvesting massive MIMO networks. Traffic-adaptivetransceiver activation methods should be designed to efficiently utilize the energy harvested553.7. Summaryat the BS. Reliability concerns in energy harvesting massive MIMO networks should be ad-dressed through the use of hybrid power supplies, cooperative relays, and energy cooperationtechniques. Another major research direction is to study optimal energy management poli-cies in the presence of uncertainties in the battery state information − circuit componentsare known to introduce uncertainty errors as high as 30 % [77]. In this context, partially-observed MDP frameworks may be utilized to arrive at trade-offs between the accuracy ofbattery state information and the amount of energy spent in acquiring it. Lastly, energyharvesting devices and communication protocols should be standardized so as to simplifynetwork planning and management.3.7 SummaryThis chapter analyzed the state-of-the-art on methods to improve energy efficiency in mas-sive MIMO systems. A brief discussion was initially presented on few EE-maximizationtechniques which are applicable to any massive MIMO system. The limitations identifiedin the process comprise both theoretical and practical issues, have been mostly longstand-ing, and are not straightforward to address. Therefore, we believe that significant effortsare required from both academia and industry in order to overcome the said limitations.We also analyzed the state-of-the-art on EE-maximization techniques for “hybrid massiveMIMO systems”, where massive MIMO operates alongside other 5G technologies, namely,millimeter wave, heterogenous networks, and energy harvesting networks.A detailed study on how massive MIMO benefits mutually from the abovementioned5G technologies allowed us to identify new opportunities and challenges for the design ofenergy-efficient systems. Our observations from the state-of-the-art reveal that the availableliterature on hybrid massive MIMO systems is streamlined in few specific directions. Byanalyzing the key ideas behind these specific research directions, we could identify few openresearch problems. We have categorically shortlisted a few ideas for future research, which,563.7. Summaryif addressed, will immensely help network operators in realistically extracting large EE gainsfrom hybrid massive MIMO systems. Given the number of opportunities identified in thischapter, we also believe that energy-efficient hybrid massive MIMO systems are very muchpromising for deployment in future 5G networks.57Chapter 4Energy Efficiency Maximization forUplink Data Transmissions in aMulti-cell Massive MIMO Systemwith MRC DetectorsAs with any general wireless communication system, the performance of a massive MIMOsystem is subject to constraints imposed by the wireless channel, such as, limited capacityand limited coherence interval. Therefore, the wireless channel should be taken into activeconsideration when designing massive MIMO systems. In this regard, one natural designstrategy is to intelligently allocate communication resources, such as, the number of antennas,and transmission power, based on any available channel information at the transmitter. Thischapter studies a challenging resource allocation problem in a massive MIMO system wherecommunication resources, namely, the pilot signal power, data signal power, and the numberof BS antennas, are optimized so as to maximize the energy efficiency (EE) of uplink datatransmissions.4.1 Research ContributionsWe investigate a challenging resource allocation (RA) problem for maximizing EE of uplinkdata transmissions in a pilot-contaminated multi-cell massive MIMO system. Assuming584.1. Research Contributionsthat the BSs employ maximum-ratio combining (MRC) technique for multiuser detection,we study the problem of maximizing EE of uplink data transmissions when the optimizationvariables are the number of antennas per BS, the pilot signal power, and the data signal powerand the constraints are in terms of the antenna budget and the power budget available in thesystem. Unlike most studies which discuss simplistic single-cell massive MIMO systems, westudy a practical multi-cell system where pilot reuse causes pilot contamination and thereby,results in reduced throughput rates.To develop the EE metric (c.f. (1.1)), we propose a realistic power consumption modelwhich incorporates the role of circuit power as an increasing function in the number of BSantennas and the number of UEs. Additionally, unlike most studies which assume equaltransmit power for pilot and data signals, we treat pilot and data signal powers as separatevariables and exploit this additional degree of freedom to achieve higher EE values. Incor-porating these features makes our optimization problem unique and different from existingworks. The problem under investigation has not been studied so far.The resulting optimization problem has a non-convex fractional objective function whichis difficult to solve in its original form, with no existing literature on possible solution method-ologies. To address this concern, we propose a novel solution approach which uses Jagan-nathan’s theorem [36] to first transform the fractional objective into an equivalent parametricform and then to derive an iterative RA algorithm. In each iteration of the proposed al-gorithm, an alternating optimization technique is used to solve the objective function bydecomposing it into a sequence of solvable difference of convex (D.C) programming sub-problems. Through simulation results, we observe that higher EE levels can be achievedby optimizing the pilot and data powers independently, particularly when operating in thehigh SNR regime. We also observe that the number of antennas per BS should be optimizedwith respect to the available power budget in order to operate at high EE levels. Pilotcontamination was observed to have an adverse effect on the achievable EE levels. Lastly,increasing the number of UEs in the system diminished the EE improvements achieved by594.2. Related Worksusing separate pilot and data signal powers.4.2 Related WorksSeveral recent studies have actively investigated resource allocation for the design of energy-efficient massive MIMO systems but most works have either ignored the dependence of circuitpower expenditure on the number of BS antennas in the system or have ignored the ideaof treating pilot and data signal powers separately. For example, the authors in [24] -[25]study resource allocation for energy efficiency in massive MIMO systems but use unrealisticpower consumption models, where the circuit power is either completely ignored or it ismodelled as a constant term independent of (M,K). Realistic power consumption modelshave been proposed in [26]−[28]. [26] studies how the system energy efficiency changes whenparameters in the power consumption model are varied. A similar analysis is performedin [27], in addition to optimizing the system energy efficiency with respect to (w.r.t) tothe system throughput. [28] proposes energy-efficient resource allocation algorithms fordownlink massive MIMO systems. However, the studies in [26] -[28] do not consider pilotreuse and therefore, neglect the impact of pilot contamination on the system design. Pilotcontamination in multi-cell massive MIMO systems has only been briefly investigated in [55],where a simplified special case of a multi-cell scenario with symmetric user distribution andpropagation conditions is studied.Lastly, although using different pilot and data powers lends an additional degree of free-dom in maximizing the system energy efficiency, this idea has not been fully explored for thedesign of energy-efficient massive MIMO systems. This is a bit surprising because currentLTE systems already employ pilot signal powers which are higher than data signal powersby upto 6 dB so as to achieve better channel estimation accuracy [29]. The authors in [30],[31] assume different pilot and data powers to study resource allocation in multi-cell massiveMIMO systems. Specifically, [30] investigates spectral efficiency maximization under power604.3. System Modelbudget constraints and [31] investigates energy efficiency maximization under per-user SINRand per-user power constraints. However, both [30] and [31] neglect the role of circuit powerconsumption in their analysis.This chapter is organized as follows. In Section 4.3, we present the system model andprovide a mathematical derivation for the achievable uplink rates in a pilot-contaminatedmulticell massive MIMO system. A realistic power consumption model for massive MIMO isproposed in Section 4.4. Thereby, an energy efficiency maximization problem is formulatedin Section 4.5 and a solution methodology is proposed in Section 4.6. Simulation results arepresented in Section 4.7, followed by some concluding remarks in Section 4.8.4.3 System ModelWe study uplink transmissions in a massive MIMO system comprising L cells, all operatingover the same frequency band of bandwidth B Hz. Each cell has K single-antenna UEswhich are serviced by a massive MIMO BS with M >> K antennas over the same time-frequency resource. To facilitate channel estimation at the BS, the K UEs in each celltransmit orthogonal pilot sequences of length τ symbols per coherence interval. Therefore,we have τ ≤ T , where T is the coherence interval in symbols. Since T is generally limited dueto moving users, we consider a scenario where the cells reuse pilot sequences, thus resultingin pilot contamination [9]. For simplicity, we assume that all the cells reuse the same set ofpilot sequences.4.3.1 Channel ModelLet Hli ∈ CM×K denote the flat-fading channel matrix between the K UEs in the ith cell andthe M BS antennas in the lth cell. The column hlik in Hli corresponds to the propagationvector for the kth UE, and can be written as614.3. System Modelhlik =√βlikqlik, (4.1)where βlik represents the path loss and large-scale fading coefficient and qlik ∈ CM×1,qlik ∼CN (0, IM) represents the small-scale fading coefficient vector comprising i.i.d complex Gaus-sian values. Accordingly, Hli can be written asHli = QliD1/2,D = diag{βlik}, k = 1 . . . K,(4.2)where Qli is the small-scale fading coefficient matrix with columns qlik, and D is the pathloss and large-scale fading coefficient matrix respectively. We assume that the βlik valuesremain constant over a given coherence interval. We also assume that βlik values are perfectlyknown to the lth BS.4.3.2 Channel EstimationThe BS employs minimum mean-squared error (MMSE) technique to estimate the channelmatrix Hli from the uplink pilot signals. Let pp be the average transmit power per pilotsymbol. We take the noise variance to be 1, to minimize notation, but without loss ofgenerality. Therefore, pp can also be interpreted as the normalized pilot transmit SNR andis therefore dimensionless. With this convention, the MMSE estimate matrix for the channelbetween the kth UE in the cell i and the lth BS is given by [43]hˆlik = (L∑q=1hlqk +1√τppwlk)[D′li]k,k,where, D′li = diag{d′lik}, d′lik = βlik(L∑q=1βlqk +1τpp)−1, k = 1 . . . K,wlk ∼ CN (0, IM),(4.3)In (4.3), D′li ∈ CK×K is a normalization matrix and wlk ∈ CM×1 represents additive white624.3. System ModelGaussian noise (AWGN). The channel estimate hˆlik follows Gaussian distribution with zeromean and covariance σ2hˆlikIM , where σ2hˆlikis given by Proposition 1. Also, by the propertyof MMSE technique, the channel estimation errors h˜lik corresponding to the channel hlik isgiven byh˜lik = hlik − hˆlik, (4.4)where h˜lik follows Gaussian distribution with zero mean and covariance σ2h˜likIM and σ2h˜likisgiven by Proposition 1.Proposition 1. If hˆlij ∈ CM×1 and h˜lij ∈ CM×1 are respectively the MMSE estimate andthe estimation error for the channel vector between the lth BS and the jth UE in cell i, theircovariance matrices are given byσ2hˆlijIM , d′lijβlijIM ,σ2h˜lijIM , (1− d′lij)βlijIM ,where, d′lij is given by (4.3)(4.5)Proof. See Appendix A.1From (4.3), the following mathematical relationship between hˆlik and hˆllk can be observedhˆlik =βlikβllkhˆllk. (4.6)Note that the BS l only needs to estimate hˆllk and the role of (4.6) is only to facilitate a math-ematical simplification in deriving the rate bound in Proposition 2. The above relationshipallows us to decompose the inter-cell interference into correlated terms, i.e., hˆlik, i = 1 . . . L,and uncorrelated terms, i.e., hˆlij, i = 1 . . . L, j = 1 . . . K, j 6= k, with respect to the desireduser’s channel estimate hˆllk, i = 1 . . . L.634.3. System Model4.3.3 Multi-user DetectionOnce the channel estimates are available, we assume that the BS employs maximum-ratiocombining (MRC) technique to detect the data symbols transmitted by the UEs. Let pube the average transmit power per data symbol. We take the noise variance to be 1, tominimize notation, but without loss of generality. Therefore, pu can also be interpreted asthe normalized data transmit SNR and is therefore dimensionless. With this convention, ifxi, such that√puxi ∈ CK×1 and E(xixHi ) = IK , is the vector of data symbols transmittedby the K UEs in the ith cell, the signal yl received at the lth BS is given byyl =√puL∑i=1Hlixi + nl, (4.7)where nl ∼ CN (0, IM) represents AWGN. When MRC technique is employed to detect thesymbol xlk transmitted by the kth UE, the BS multiplies the received signal yl with theconjugate transpose of the corresponding channel estimate hˆllk. Post this, we obtainhˆHllkyl =√puhˆHllkL∑i=1Hˆlixi +√puhˆHllkL∑i=1H˜lixi + hˆHllknl=√puhˆHllkhˆllkxlk +√puhˆHllkL∑i=1K∑j=1,j 6=khˆlijxij +√puhˆHllkL∑i=1K∑j=1h˜lijxij + hˆHllknl(4.8)The MMSE channel estimate hˆllk and the channel estimation error h˜llk are uncorrelated andindependent due to joint Gaussianity of both vectors, ∀j = 1 . . . K [43]. To obtain a lowerbound on the achievable uplink rates, we attempt the following procedure based on priorworks [44]-[47].Let us consider the achievable uplink rate between the kth UE and the BS in cell l.The BS knows the channel estimate hˆllk and treats it as the true channel. The BS alsoknows the variance of estimation error h˜llk (c.f. (4.5)) because we assume that the BS knowsthe large-scale fading coefficients, i.e, βlik. The interference-plus-noise term is modelled as644.3. System Modeladditive Gaussian noise independent of xlk. The channel estimation error h˜llk is also treatedas part of additive Gaussian noise (See Appendix A.2 for an illustrative example inspiredfrom [45] on why treating the channel estimation error as part of additive Gaussian noiseyields a lower bound on the achievable rates). Since Gaussian additive noise is the worst formutual information [48], we can obtain a lower bound on the achievable rate by treating theresulting additive noise, i.e., comprising both interference-plus-noise and channel estimationerrors, as a worst case Gaussian noise with the same variance. A similar analogy has beenused in [24] and [49] to derive lower bounds on achievable rates for single-cell scenario anda symmetric multi-cell scenario respectively.By following the procedure discussed above, the BS classifies the received signal vectorinto desired and interference-plus-noise components as followshˆHllkyl =√puhˆHllkhˆllkxlk︸ ︷︷ ︸desired+interference + noise︷ ︸︸ ︷√puL∑(i,j)6=K∑(l,k)hˆHllkhˆlijxij +√puL∑i=1K∑j=1hˆHllkh˜lijxij + hˆHllknl(4.9)4.3.4 Achievable RatesUsing (4.9), a lower bound on the uplink achievable rate for user k in the same cell is givenby [44]Rlk = B (1− τT) E{log2(1 + γlk)},where, γlk =pu||hˆllk||4pu∑Li=1∑Kj=1,(i,j)6=(l,k) |hˆHllkhˆlij|2 + pu||hˆllk||2∑Li=1∑Kj=1 σ2h˜lij+ ||hˆllk||2,(4.10)where E(.) is with respect to the channel estimates. Observe from (4.10) that we have (i)modelled the channel estimation errors with variance σ2h˜lij= (1 − d′lij)βlij given by (4.5) as654.3. System Modelpart of worst-case AWGN, and (ii) utilized the property that MMSE channel estimates andestimation errors are independent of each other. Since the expression for achievable rate Rlkin (4.10) is mathematically intractable, we obtain a lower bound R′lk on the achievable rateRlk as followsRlk ≥ R′lk , B (1−τT) log2(1 + (E{1γlk})−1), (4.11)where the bound R′lk is obtained by exploiting the convexity of log(1+1/x) and using Jensen’sinequality, i.e., E{log(1 + 1/x)} ≥ log(1 + 1/E{x}). Finally, as shown in Proposition 2, wecan express R′lk as a function in our design parameters (M, pp, pu) (c.f. (4.12)). The rateexpression R′lk in (4.12) is obtained by simplifying (4.10) using information on the statisticsof the channel estimates and channel estimation errors (c.f. (4.5)) (see Appendix A for adetailed derivation). The rate bound expression given in Proposition 2 can also be found in[30], but the derivation is not provided.Proposition 2. A lower bound on the achievable rate for uplink transmissions between thelth BS and the kth UE in the same cell, when the BS employs MMSE channel estimation andMRC multiuser detection, is given byR′lk(M, pp, pu) = B (1−τT) log2(1 +c1k(M − 1)pppuc2kpu + c3kpp + c4k(M − 1)pppu + c5kpppu + 1),where, c1k , τβ2llk, c2k ,L∑i=1L∑j=1βlij, c3k , τL∑i=1βlik,c4k , τL∑i=1,i 6=lβ2lik, c5k , c2kc3k − τL∑i=1β2lik(4.12)Proof. See Appendix A.3.Observe from (4.12) that our design parameters (M, pp, pu) are strongly coupled with eachother in the expression for R′lk.664.4. Realistic Model for Power Consumption4.4 Realistic Model for Power ConsumptionThe power expenditure Ptot for uplink transmissions in a massive MIMO cell can be at-tributed to three major operations, namely, (i) power amplifier (PA) operations at the UEs,(ii) circuit operations at the BS and the UEs, and (iii) site-specific operations, such as, BScooling, control, and backhaul. We derive an expression for Ptot by modeling the powerexpenditure for these major operations.4.4.1 Power Expenditure at PAs (PPA)If η is the power efficiency of the PAs embedded in the UEs, the average power spent by theK UEs at the PAs for pilot and data transmissions can be given asPPA =KηT(τpp + (T − τ)pu). (4.13)4.4.2 Circuit Power (PC)To model the power expenditure on circuit operations, we classify the circuit power PC intothree major components, namely, signal processing at the radio frequency (RF) transceiverchains, channel estimation and multiuser detection. As practiced in current LTE and LTE-Advanced networks, we assume that each antenna at the BS and the UE has a dedicatedRF chain. Also, let Ptb represent the power per RF chain at the BS, Ptu the power per RFchain at the UE, and F the computational efficiency at the BS (in flops/Watt). Then, basedon prior works [33]-[35], the abovementioned components in PC can be modelled as shownin Table 4.1. Thereby, PC can be accumulated from Table 4.1 asPC = MPtb +KPtu +2MKBF(4.14)Observe that, unlike most studies which assume PC to be a constant term independent of(M,K), we propose a realistic model where PC is an increasing function in (M,K). Such a674.4. Realistic Model for Power Consumption(a) Mathematical Model for Power Expenditure on Different Circuit OperationsIndex Circuit Operation Power Consumption ModelA RF chain operations M Ptb + K PtuA.1 RF chain operations at the BS M PtbA.2 RF chain operations at the UEs K PtuB MMSE estimation 2MKτBTFC MRC receiver combining 2MKBF(1− τT)(b) Explanation for Mathematical Models Proposed in Table 4.1aIndex DescriptionA A.1 + A.2A.1 M antennas, each consuming PtbA.2 K single-antenna UEs, each consuming PtuBMultiplication of M × τ matrix with τ ×K matrix(c.f. (4.3)), once per coherence intervalCMultiplication of K ×M matrix with M × 1 matrix,(c.f. (4.9)), for every channel useTable 4.1: Power Expenditure on Different Circuit Operations for Uplink Transmissions ina Massive MIMO Systemrealistic model is particularly important for our study because M is an optimization variablein our system design.4.4.3 Site-specific Power (Psite)Power spent on different site-specific factors, such as, power supply, active/passive cooling,AC/DC and DC/DC converters, switches, and backhaul operations, is accumulated intoPsite. For simplicity, we model Psite as a fixed component in Ptot.Finally, using (4.13) and (4.14), we obtain Ptot asPtot(M, pp, pu) =KηT(τpp + (T − τ)pu) +MPtb +KPtu + 2MKBF+ Psite. (4.15)Observe from (4.15) that Ptot is an increasing function in our design parameters (M, pp, pu).684.5. Maximizing Energy Efficiency of Uplink Data TransmissionsIn the next section, we utilize the expressions derived in Section 4.3 - 4.4 to formulatea resource allocation problem which maximizes the EE of uplink data transmissions in amassive MIMO cell.4.5 Maximizing Energy Efficiency of Uplink DataTransmissionsUsing the expressions for achievable rates and power consumption in (4.12) and (4.15), alower bound on the bit-per-joule energy efficiency (EE) for uplink data transmissions in thecell l is obtained asEE(M, pp, pu) =∑Kk=1R′lk(M, pp, pu)Ptot(M, pp, pu), (4.16)We now attempt to maximize the EE, given in (4.16), by optimizing (M, pp, pu) subject tobudget constraints on M and the transmission power per coherence interval. Mathematically,this EE maximization problem can be expressed as P1P1 =maximizeM,pp,puEE =∑Kk=1R′lk(M,pp,pu)Ptot(M,pp,pu)subject to :C1 : αK ≤M ≤Mmax,M ∈ R+C2 : τpp + (T − τ)pu ≤ TPmax,C3 : pu ≥ 0, pp ≥ 0,(4.17)where C1 is a budget constraint on M , α >> 1 ensures operation in the massive MIMOregime, Mmax is the maximum allowed number of antennas per BS, C2 is a power budgetconstraint, Pmax is an upper limit on the average transmission power per UE per transmissionsymbol, and C3 ensures non-negative pilot and data powers. If M in P1 is treated as an694.5. Maximizing Energy Efficiency of Uplink Data Transmissionsinteger variable, the solution approach incurs additional complexity because the feasibilityset takes both discrete and continuous forms. We avoid this complexity by assuming M tobe a continuous variable and later, rounding off the optimal M to the nearest integer value.The following observations can be made on P1.(i) The objective function has a fractional form where both the numerator and denomi-nator are non-linear in (M, pp, pu).(ii) P1 is non-convex because M, pp, and pu are strongly coupled with each other in boththe numerator and the denominator of the objective function.As a result of these features, the fractional programming problem P1 is very difficult tosolve under polynomial time complexity. Therefore, we use Jagannathan’s theorem[36] toderive an equivalent parametric form P2(θ), given byP2(θ) =maximizeM,pp,pu∑Kk=1R′lk − θPtotsubject to : C1 − C3,(4.18)where θ ∈ R is an auxiliary variable introduced to derive the parametric form. If C is theconvex feasibility set defined by C1−C3, Jagannathan’s theorem [36] states that the optimalsolution set (M∗, p∗p, p∗u, θ∗) satisfies Theorem 3.Theorem 3. θ∗ is the optimal EE obtained by solving P1, i.e.,θ∗ = EE(M∗, p∗p, p∗u) =∑Kk=1R′lk(M∗, p∗p, p∗u)Ptot(M∗, p∗p, p∗u)(4.19)if and only if P2(θ∗) = 0, i.e.,max(M,pp,pu)∈CK∑k=1R′lk(M, pp, pu)− θ∗Ptot(M, pp, pu)=K∑k=1R′lk(M∗, p∗p, p∗u)− θ∗Ptot(M∗, p∗p, p∗u) = 0.(4.20)704.6. Solution MethodologyTheorem 3 shows that we can solve P2(θ) to obtain an optimal solution for P1 if we candevelop an intelligent strategy to find θ = θ∗ which satisfies (4.19) - (4.20). In the nextsection, we use an alternating optimization technique [37] to solve P2(θ) and an iterativeupdate strategy based on Dinkelbach algorithm [38] to obtain θ∗.4.6 Solution MethodologySolving P2(θ): Alternating OptimizationFor a given θ, observe that the objective function∑Kk=1R′lk − θPtot in P2(θ) is still non-convexbecause our variables (M, pp, pu) are strongly coupled with each other in the expressions forR′lk and Ptot (c.f. (4.12), (4.15)). Therefore, to solve P2(θ), we propose an alternatingoptimization framework where M , pp, and pu are sequentially optimized as described inAlgorithm 1. Basically, we decompose P2(θ) into a sequence of sub-problems, formed bytreating one of the three design variables as the optimization variable and assigning pre-determined values to the other two design variables. This sequence is solved iterativelyuntil convergence is observed in our design variables. Observe that the energy efficiencyexpression in (4.16) has a finite upper bound because the rate expression, i.e., (4.12), andthe power consumption expression, i.e., (4.15), are positive and bounded. The proposedalternating optimization technique converges monotonically, at least to a local optimum, forany feasible starting point (M0, pp0 , pu0), because the iterative updates of (M0, pp0 , pu0) willeither increase or maintain the objective function, but will never decrease it. See [37] for adetailed proof of convergence.Upon close inspection, we realize that the sub-problems in steps 2−4 of Algorithm 1 aredifference of convex (DC) programming problems in their respective optimization variables.For the purpose of illustration, let us consider the subproblem in step 2 of Algorithm 1,where we assign (pp0 , pu0) to (pp, pu) and solve P2(θ) for M . This subproblem can be writtenas714.6. Solution MethodologyAlgorithm 1 Alternating Optimization TechniqueRequire: Inputs θ, initial set (M0, pp0 , pu0)1: while Convergence in (M,pp, pu) not observed do2: Given (pp0 , pu0), solve P2(θ) for M and update M0.M0 ← argmaxM{P2(θ; pp0 , pu0)}3: Given (M0, pu0), solve P2(θ) for pp and update pp0 .pp0 ← argmaxpp{P2(θ;M0, pu0)}4: Given (M0, pp0), solve P2(θ) for pu and update pu0 .pu0 ← argmaxpu{P2(θ;M0, pp0)}5: end while6: return (M0, pp0 , pu0)P3(θ) = P2(θ; pp0 , pu0)=maxM∈R∑Kk=1R′lk(M ; pp0 , pu0)− θPtot(M ; pp0 , pu0)subject to : C1,(4.21)where, R′lk(M ; pp0 , pu0) can be obtained by substituting (pp0 , pu0) into (4.12) as follows,R′lk(M ; pp0 , pu0) = B(1−τT)log2(1 +A1kM − A1kA2kM + A3k),where A1k , c1kpp0pu0 ,A2k , c4kpp0pu0 ,A3k , c2kpu0 + c3kpp0 + (c5k − c4k)pp0pu0 + 1(4.22)and Ptot(M ; pp0 , pu0) can be obtained by substituting (pp0 , pu0) into (4.15) as followsPtot(M ; pp0 , pu0) = D1M +D2,where D1 , Ptb +2KBF,D2 ,KηT(τpp + (T − τ)pu) +KPtu + Psite.(4.23)Using the expressions (4.22) and (4.23) to simplify P3(θ), we can make the following propo-sition.724.6. Solution MethodologyProposition 4. The subproblem P3(θ), given in (4.21), can be expressed as the followingdifference of convex (DC) programming problemP3(θ) =minM∈R+∑Kk=1 flk(M)− glk(M, θ)subject to : C1,(4.24)where flk(M) and glk(M, θ) are convex functions in M and are given byflk(M) = −B(1− τT) log2((A1k + A2k)M + (A3k − A1k)),glk(M, θ) = −B(1− τT) log2(A2kM + A3k) + θ(D1M +D2)(4.25)Proof. See Appendix A.4Proposition 4 shows that P3(θ), which is the subproblem in step 2 of Algorithm 1, is a DCprogramming problem. Following a similar discussion, it can be verified that the subproblemsin steps 3−4 of Algorithm 1 are also DC programming problems. Such problems are non-convex and are generally hard to solve [39]. We propose to use the convex-concave procedure(CCP) [40] − a powerful local heuristic technique which leverages the ability to efficientlysolve convex optimization problems.To illustrate how CCP works, let us again consider the subproblem in step 2 of Algorithm1, where we solve P3(θ) for M . The CCP technique for this subproblem is described inAlgorithm 2. During each iteration of the algorithm, we convexify the concave part of theobjective function. Thereby, upon replacing the concave part with its convexified form, weobtain the subproblem in step 3 of Algorithm 2, which is re-stated below.minM∈R+K∑k=1flk(M)− gˆlk(M, θ)subject to: C1(4.26)734.6. Solution MethodologyObserve that the optimization problem in (4.26) is convex in M , because the objective andconstraint functions are convex in M . Therefore (4.26) can be solved efficiently using stan-dard convex optimization techniques [41] and we use the convex optimization software cvxby Grant and Boyd [1]. See [40] for a detailed proof on the convergence of CCP techniques.Algorithm 2 CCP technique to Solve the DC Programming Problem P3(θ)Require: Inputs M0, M0: Initial feasible point > 0: convergence thresholdinitialize: n← 0 (Iteration index),1: repeat2: Convexify the concave part of the objective function:gˆlk(M, θ) , glk(θ;Mn) +∇M glk(θ;Mn)T (M −Mn)3: Solve P3(θ) after replacing glk(M, θ) in (4.24) with gˆlk(M, θ)Mn+1 ←argminM∈R+∑Kk=1 flk(M)− gˆlk(M, θ)subject to : C1,4: Update iterationn← n+ 1.5: until Stopping criterion is satisfied(flk(Mn)− glk(Mn)) - (flk(Mn+1)− glk(Mn+1)) < 6: return MnOn similar lines to Algorithm 2, CCP techniques can be used to solve the DC program-ming problems in steps 3-4 of Algorithm 1. This completes our discussion on solving P2(θ).Algorithm 3 Iterative Update Strategy to Obtain θ∗Require: Inputs δ, (M0, pp0 , pu0)δ > 0: tolerance for convergence in θ values(θ0,M0, pp0 , pu0): Feasible starting pointm← 0 (Iteration index),1: repeat2: m← m+ 13: Input (θm−1,Mm−1, ppm−1 , pum−1) to Algorithm 1(Mm, ppm , pum)← P2(θm−1)4: Update θm using (4.19) in Theorem 3θm =∑Kk=1R′lk(Mm,ppm ,pum )Ptot(Mm,ppm ,pum )5: until θm − θm−1 < δ6: return θm, (Mm, ppm , pum)744.6. Solution MethodologyObtaining optimal θ: Iterative Update StrategyTo obtain optimal θ, i.e., θ∗, we utilize the optimality condition in Theorem 3 and developan iterative update strategy based on Dinkelbach algorithm [38]. The proposed strategy isdescribed in Algorithm 3. During each iteration, we invoke Algorithm 1 with the (M, pp, pu)values from the previous iteration, so as to solve P2(θ) for the next solution set. The(M, pp, pu) returned by Algorithm 1 is substituted into (4.19), so as to generate a θ updatefor the next iteration. This is continued until convergence is observed in the θ values. Proofof convergence for this algorithm follows from the proof of Dinkelbach algorithm given in [38].Observe from Theorem 3 that the θ value returned by Algorithm 3 is the energy efficiencyvalue.−1000 −500 0 500 1000−1500−1000−500050010001500X coordinate in meters(with BS in the center cell as reference)Y coordinate in meters(with BS in the center cell as reference)  Base StationUser EquipmentCell under investigationFigure 4.1: Simulation setup under study: assuming that the same frequency band and thesame set of pilot sequences are reused in all the cells, we investigate the benefits of RA inthe center cell.754.7. Simulation ResultsTable 4.2: Simulation Parameters for Resource AllocationParameters ValuesPA efficiency (η) 0.3Circuit power per RF chain at the BS (Ptb) 1WCircuit power per RF chain at the UE (Ptu) 0.2WComputational efficiency at the BS F 5 ∗ 109 flops/WSite-specific power consumption (Psite) 5W4.7 Simulation ResultsIn this section, we present simulation results to verify if the proposed resource allocation (RA)method can yield better EE values than conventional RA schemes. For all the simulationresults, we consider two baseline scenarios for comparison (i) “no RA”, where no resourceallocation is attempted and full power budget is always utilized, and (ii) “RA with pp = pu,where RA is performed but with equal pilot and data powers.We study EE-maximization in a hexagonal cell that is uniformly surrounded by six otherhexagonal cells (c.f. Fig. 4.1). Monte Carlo simulations with random user locations andshadowing were used to optimize the system EE with respect to our design variables. Forthe simulations, we assume operation at the 2 GHz band with bandwidth B = 10 MHz. Allthe cells reuse the same frequency band and each cell has a coverage radius of 500m. Unlessstated explicitly, all the cells reuse the same set of pilot sequences in order, i.e., the kth UEin each cell reuses the same pilot sequence. The channel coherence interval is assumed to beT = 180 symbols, corresponding to a coherence bandwidth of 180 kHz and a coherence timeof 1 ms.Each BS is assumed to serve 5 UEs, i.e., K = 5, which are located uniformly within itscell area such that all the UEs are at least d0 = 100m away from the serving BS. We alsoassume a pilot sequence length of τ = K. The large-scale fading coefficients are obtainedas βlik = zlik/||dlik/d0||ν , where zlik is a log-normal random variable with standard deviationof 8 dB, dlik is the distance between the lth BS and the kth UE in cell i, and ν = 3.8is the path loss exponent. For the constraint C1, we assume α = 10 and Mmax = 300.764.7. Simulation ResultsThe convergence thresholds in Algorithms 2 and 3 are chosen as  = 0.01 and δ = 0.1respectively. Also, inspired by prior works [33] - [35], we choose simulation parameters forthe power consumption model as listed in Table 4.2. We refer to Pmax as the average transmitSNR budget because Pmax is the average power budget available per transmission symbolwhen we assume noise variance to be 1.We begin with the proof of convergence of the proposed solution methodology by plottingthe θ values returned by the outer algorithm, i.e., Algorithm 3, in Figure 4.2. The plotcorresponds to a particular snapshot of βlij values when K = 5 and we attempt to optimize(M, pp, pu) assuming that the same set of pilot sequences is reused in all the cells. In thefigure, we choose Pmax ranging from −15 dB to 5 dB in equal intervals of 5 dB and plotthe corresponding θ values as the proposed solution methodology makes progress towardsconvergence. Plots in the Figure 4.2 show that the outer algorithm may take up to 6iterations to achieve convergence. By running the proposed solution methodology multipletimes for a given snapshot of βlij values, we observe that the average number of iterationsrequired for convergence is about 4.5. Convergence at least to a local optimum is alwaysguaranteed because (i) the EE metric is bounded because the achievable rates and the powerexpenditure are bounded in our study, and (ii) the proposed solution methodology alwaysensures that a given EE level is either maintained or improved .Observations when (pp, pu) are optimized for EE, given M = 50, 100In Figure 4.3, we plot the EE values yielded by the proposed RA algorithm as a functionof the transmission power budget available, i.e., Pmax, when the number of BS antennasare fixed at M = 50 and M = 100 respectively. The corresponding pilot signal SNRs anddata signal SNRs are plotted in Figure 4.4. We compare the performance of the proposedalgorithm against two baseline scenarios (i) no RA is attempted and full power budget isalways utilized (indicated as “no RA” in Figures 4.3 and 4.4) and (ii) RA is performed butwith equal pilot and data signal powers (indicated as RA with pp = pu in the figure). When no774.7. Simulation Results1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 62468101214 x 105Iteration Progressθ value returned by outer algorithm  Pmax = −15 dBPmax = −10 dBPmax = −5 dBPmax = 0 dBPmax = 5 dBFigure 4.2: Proof of convergence of the proposed solution methodologyRA is performed, the EE curve attains a peak value and decreases gradually with increasingSNR budget. This is expected because the available power budget is always fully utilized(c.f. Figure 4.4). Consequently, power expenditure always increases with the increasingSNR budget. However, since the achievable rates saturate in the high SNR region (becauseMRC detection does not mitigate the increasing inter-user interference in the system), weobserve that the EE values attain peak values, followed by a gradual decrease when no RAis attempted.When RA is attempted with equal pilot and data powers, i.e., pp = pu, the availablepower budget is not always fully utilized (c.f. Figure 4.4). This is because full SNR budgetutilization may decrease the EE values when the available SNR budget is larger than acertain value. As a result, we observe that the EE curve for RA with pp = pu attains a peakvalue and this value is maintained thereafter.Observe from Fig. 4.3 that the proposed RA algorithm achieves significantly higher EE784.7. Simulation Results−30 −20 −10 0 10 20 3002468101214 x 105Transmit SNR Budget Pmax (dB)Energy Efficiency (bits/Joule)  M = 50, Proposed RAM = 50, RA with pp = puM = 50, No RAM = 100, Proposed RAM = 100, RA with pp = puM = 100, No RAW1W2TH1 TH2Figure 4.3: EE vs SNR budget Pmax for different RA schemes when M = 50, 100.−30 −20 −10 0 10 20 30−25−20−15−10−50510152025Transmit SNR Budget Pmax (dB)Pilot and Data SNR Allocated (dB)  Pilot SNR,M = 50, Proposed RAData SNR,M = 50, Proposed RAPilot SNR,M = 100, Proposed RAData SNR,M = 100, Proposed RAPilot and Data SNR,M = 50, RA with pp = puPilot and Data SNR,M = 100, RA with pp = puM = 50, No RAW1W2TH2TH1Figure 4.4: Pilot and data SNR vs SNR budget Pmax for different RA schemes when M =50, 100.794.7. Simulation Resultsvalues when compared to the other two baseline scenarios, particularly when the availableSNR budget is larger than 0 dB. This can be attributed to two important factors which areevident from Figure 4.4. Firstly, the proposed RA algorithm does not always assign pp = pu.Particularly when Pmax is larger than a certain threshold (labeled as TH1 and TH2 forM = 50 and 100 in Figures 4.3 and 4.4), pp is increased while adjusting pu such that theconstraint C1 is still maintained. This results in increased EE levels because the accuracyof MMSE estimation is increased (c.f. (4.3), (4.5)), thus enforcing a relative increase inthe achievable rates∑k R′lk w.r.t the power expenditure Ptot. The proposed RA algorithmcontinues to increase pp over a budget window (labeled as W1 and W2 for M = 50 and100 in Figures 4.3 and 4.4), until an improvement in the MMSE estimation accuracy canno longer improve the EE values. Secondly, beyond the highlighted budget windows, i.e.,when Pmax > (TH1 + W1) for M = 50 and Pmax > (TH2 + W2) for M = 100, the pp andpu values attain saturation and any additional transmit SNR budget is not utilized becausedoing so would reduce the system EE.Observations when (M, pp, pu) are optimized for EEIn Figures 4.5-4.7, we plot the performance of the proposed RA algorithm against twobaseline scenarios when the available SNR budget Pmax is increased from −25 dB to 25dB. Similar to our previous discussions, the baseline “no RA” refers to the scenario where noRA is performed and the available power budget is always fully utilized. The baseline “RAwith pp = pu” refers to the scenario where RA is performed but with equal pilot and datatransmit SNRs. However, unlike in the previous discussions, we assume that the baselinescenario “no RA” operates with the same number of BS antennas as used by the proposedRA algorithm. That is, for each SNR budget value, the proposed RA algorithm yields anoptimal M value and the “no RA” scheme operates with the same M value. This is doneso as to allow for a fair comparison against the proposed RA algorithm. When this is notdone, i.e., when the “no RA” scenario is not configured to use the same M as used by804.7. Simulation Results−30 −20 −10 0 10 20 3002468101214 x 105Transmit SNR Budget (dB)Energy Efficiency (bits/Joule)  Proposed RARA with pp = puNo RAFigure 4.5: EE vs SNR budget Pmax for different RA schemes when (M, pp, pu) are optimized.the proposed RA, the EE levels achieved by “no RA” will be drastically lower than theEE levels illustrated in Figure 4.5. This is because the “no RA” scenario always operateswith the maximum number of antennas, i.e., Mmax, thus incurring significantly higher powerexpenditure, particularly when optimal M is considerably lower than Mmax.Figure 4.5 provides a comparison of the EE levels achieved by the proposed RA algorithmagainst the two baseline scenarios discussed above. The corresponding pilot and data signalSNRs are plotted in Figure 4.6. In Figure 4.7, we plot the M values at which the proposedRA algorithm and the two baseline scenarios operate.Observe from Figure 4.5 that the proposed RA algorithm always performs at least aswell as the two baseline scenarios. When in the low SNR region, the proposed RA algorithmperforms equally well as the scenario with pp = pu. As we can observe from Figure 4.6, thisis because the proposed RA algorithm finds it optimal to operate with equal pilot and dataSNRs when the total available SNR budget is low. However, when the available SNR budgetis sufficiently large, say beyond 0 dB, we observe that the proposed RA algorithm achieves814.7. Simulation Results−25 −20 −15 −10 −5 0 5 10 15 20 25−30−20−100102030Transmit SNR Budget Pmax (dB)Power Allocation and Budget Utilized (dB)  Pilot SNR, Proposed RAData SNR, Proposed RASNR budget utilized, Proposed RAPilot SNR, Data SNR, andSNR budget utilized, RA with pp = puPilot SNR, Data SNR, andSNR budget utilized, No RAFigure 4.6: Pilot SNR, data SNR, and budget utilization vs Pmax for different RA schemeswhen (M, pp, pu) are optimized.significantly higher EE levels than the other two baseline scenarios. Also, for any given SNRbudget, note that the EE levels in Figure 4.5 are always higher than or equal to the EElevels observed in Figure 4.3 because unlike in the case of Figure 4.3, where M is assignedpredetermined values of 50 and 100, Figure 4.5 plots the scenario where M is also optimizedfor EE.As we can observe from Figure 4.6, the EE improvements achieved by the proposed RAalgorithm may be attributed to two major factors, namely, (i) the proposed RA algorithmoptimizes pp and pu separately and achieves high EE values by using higher pp than pu so asto improve the MMSE channel estimation accuracy, and (ii) the proposed RA algorithm doesnot fully utilize the available power budget after it attains a peak EE value because it realizesthat utilizing any additional SNR budget would result in reduced EE levels. Also observefrom Fig. 4.6 that the proposed RA algorithm does not exceed the total available power824.7. Simulation Results−30 −20 −10 0 10 20 30050100150200250300Transmit SNR Budget Pmax (dB)Number of BS Antennas M  Proposed RARA with equal pilot and data powersFigure 4.7: Optimal number of BS antennas M vs SNR budget Pmax when (M, pp, pu) areoptimized.budget even if it employs a significantly higher pp than pu when in the high SNR regime.This is because the UEs only use τ symbols for pilot transmissions and the remaining (T−τ)symbols are used for data transmissions. Since τ = K = 5 and T = 180, we observe that thetotal utilized SNR budget is much lower than the total available budget even if the proposedRA algorithm increases pp beyond pu by about 8 dB so as to achieve high EE levels.Observe from Figure 4.7 that the proposed RA algorithm and the baseline scenario “RA with pp = pu” yield the same optimal M values. Also, the proposed RA algorithmdoes not always fully utilize all the available BS antennas, i.e., M is not necessarily equal toMmax. Observe from (4.15) that this is mainly because the power expenditure in the systemincreases with M . As the power budget is increased, the proposed RA algorithm reducesM so as to ensure that there is no relative decrease in the achievable rates with respect topower expenditure in the system. This figure underlines the importance of modelling PC asa function in M . If PC was modelled as a constant quantity which is independent of M , wewould have always operated with M = Mmax antennas and thus at significantly lower EE834.7. Simulation Resultslevels.Effect of pilot contamination on EEIn Figure 4.8, we plot EE values yielded for the center cell by the proposed RA algorithmagainst the available SNR budget, i.e., Pmax, when different pilot reuse patterns are used inthe system. The “no pilot reuse”, “pilot reuse in 4 cells”, and “pilot reuse in 7 cells” scenarioshighlighted in the figure correspond to the scenarios where the same set of pilot sequencesare reused in 1, 4, and 7 cells in the system respectively. The EE values are obtained byoptimizing all the three design variables, i.e., (M, pp, pu), for EE. Comparisons are drawnagainst the same baseline scenarios as discussed in the previous subsection. As pilot reuse isincreased, we observe that the achievable EE levels become lower. This is expected becausean increase in pilot contamination adversely affects the achievable uplink rates, but has noadditional impact on the power expenditure in the system. The degradation in EE levels isnot considerably large, possibly because we do not consider a large number of UEs.Effect of increasing the number of UEsIn Figure 4.9, we consider a scenario where K = 10, with the same constraints on the antennabudget, i.e., α = 10 and Mmax = 300. When compared to our previous discussions, we haveincreased the number of UEs K from 5 to 10. When compared to Figure 4.8, where K = 5,we observe that the peak EE values in Figure 4.9 are lower even if the minimum numberof antennas M is now 100. This is because the increase in system throughput due to theincrease in M and K is counterweighted by (i) the increase in circuit power expenditure and(ii) the decrease in number of symbols available for data transmissions. When the numberof UEs is increased, we also observe that the relative improvement in EE due to the use ofdifferent pilot and data powers has diminished. This may be attributed to the increase inpilot sequence length τ because the proposed RA algorithm has to operate within the totalSNR budget available and therefore, cannot increase pp as much as it could in the case of844.7. Simulation Results−25 −20 −15 −10 −5 0 5 10 15 20 2502468101214 x 105Transmit SNR Budget (dB)Energy Efficiency (bits/Joule)  Proposed RA, no pilot reuseProposed RA, pilot reuse in 4 cellsProposed RA, pilot reuse in 7 cellsRA with pp = pu, no pilot reuseRA with pp = pu, pilot reuse in 4 cellsRA with pp = pu, pilot reuse in 7 cellsNo RA, no pilot reuseNo RA, pilot reuse in 4 cellsNo RA, pilot reuse in 7 cellsFigure 4.8: EE vs SNR budget Pmax under different pilot reuse scenarios for K = 5.−25 −20 −15 −10 −5 0 5 10 15 20 2502468101214 x 105Trasnmit SNR Budget Pmax (dB)Energy Efficiency (bits/Joule)  Proposed RA,no pilot reuseProposed RA,pilot reuse in 4 cellsProposed RA,pilot reuse in 7 cellsRA with pp = pu,no pilot reuseRA with pp = pu,pilot reuse in 4 cellsRA with pp = pu,pilot reuse in 7 cellsNo RA, no pilot reuseNo RA,pilot reuse in 4 cellsNo RA,pilot reuse in 7 cellsFigure 4.9: EE vs SNR budget Pmax under different pilot reuse scenarios for K = 10.854.8. SummaryK = 5. Lastly, similar to the case of K = 5, we observe that pilot contamination has anadverse effect on the achievable EE levels. However, we do no see a considerable difference inthe relative magnitude of EE degradation caused by pilot contamination when K is increasedfrom 5 to 10 because the pilot sequence length τ is also increased from 5 to 10 and the samepilot reuse patterns are compared.4.8 SummaryIn this chapter, we studied a challenging resource allocation problem for energy efficiency(EE) maximization of uplink data transmissions in a pilot-contaminated multicell massiveMIMO system with MRC detectors. To model the bit-per-joule EE, mathematical ex-pressions were derived for the achievable rates and the power consumption in the system.Thereby, an EE-maximization problem was formulated, wherein the objective function isnon-convex in our design variables, namely, the number of antennas per Base Station, thepilot signal power, and the data signal power. Since the optimization problem under inves-tigation is very difficult to solve in its original form, principles from fractional programmingwere used to transform it into a weighted-sum problem and an iterative resource allocationalgorithm was proposed, wherein an alternating optimization technique was used in eachiteration to decompose the problem into a sequence of solvable difference of convex (D.C.)programming subproblems.Simulation results reveal that higher EE levels can indeed be achieved by optimizing thepilot and data powers as separate variables, particularly when operating in the high SNRregime. Since we used a realistic power consumption model, where circuit power expenditureis an affine function in the number of BS antennas, we found that the optimal number of BSantennas decreases with increasing SNR budget. This observation shows that the numberof BS antennas should be dynamically activated or deactivated depending on the availablepower budget so as to achieve sustained operation at high EE levels. The effect of pilot con-864.8. Summarytamination was also investigated and it was observed that pilot reuse had an adverse impacton the achievable EE levels. Lastly, we also observed that the EE improvements obtainedfrom treating pilot and data signal powers as separate optimization variables diminishedwhen the number of UEs in the system were increased.87Chapter 5Conclusions and Future WorkAs the amount of traffic demand in the wireless industry increases over the next two decades,the joules-per-bit expenditure should be cut down to practically affordable values. Therefore,the bit-per-joule energy efficiency (EE) metric is emerging as a critical design criterion forthe next generation of wireless networks. One of the key technology enabler in this regard isthe recently proposed massive multiple-input multiple-output (MIMO) technology becauseit promises multiple orders of EE gains over current LTE networks. However, techniquesfor extracting large EE gains from massive MIMO (MM) networks have not been activelyinvestigated in the existing literature. Here, we have addressed this limitation by (i) review-ing MM technology from an EE perspective, (ii) critically analyzing the state-of-the-art andproposing new research directions for EE-maximization in “hybrid MM” networks, whereMM technology operates alongside other emerging 5G technologies, and (iii) proposing anovel resource allocation scheme for EE-maximization in MM networks.In Chapter 2, we reviewed various aspects of MM technology to develop an EE perspec-tive. Available literature on this topic was summarized and put together in an organizedmanner to help the reader in developing a critical perspective. As part of the review, weproposed a simple but realistic power consumption model for MM networks based on threemajor operations, namely, power amplifier, circuit, and site-specific operations. Simplicityof the proposed model facilitates ease of understanding and allows for reproducibility.In Chapter 3, we critically analyzed the state-of-the-art to identify several promisingresearch directions for EE-maximization in hybrid MM networks. Three prominent cate-gories of hybrid MM networks were analyzed, namely millimeter wave based MM networks,88Chapter 5. Conclusions and Future WorkMM-based heterogenous networks, and energy harvesting based MM networks. Since wehave analyzed both theoretical and practical limitations in the state-of-the-art, the proposedresearch directions, if pursued, will immensely help network operators in extracting large EEgains from hybrid MM deployments.In Chapter 4, we proposed a novel resource allocation (RA) scheme which optimizes thepilot power (pp), data power (pu), and number of base station (BS) antennas (M) for EE in anMM system. This proposal was driven by an intuitive idea that conventional RA practices,such as, equal pilot and data power allocation, full power budget utilization, and full antennabudget utilization at the BS, can lead to highly energy-inefficient communications in MMnetworks. This is firstly because the amount of hardware resources, such as antennas andRF chains, and the resulting power expenditure can be much higher in MM networks thanin current LTE networks. Secondly, using higher pilot power than data power can result inhigher EE because channel estimation accuracy is improved.To investigate the above mentioned idea, we formulated an EE-maximization problem,where (M, pp, pu) are optimized under power budget and antenna budget constraints. Sincethe resulting optimization problem is non-convex and is very difficult to solve in its origi-nal form, we proposed a novel solution approach where each iteration solves a sequence ofdifference of convex (DC) programming subproblems. Simulation studies were conducted as-suming uplink data transmissions, MRC detection, Rayleigh fading channels, and a realisticpower consumption model with circuit power as an affine function in M .The simulation results obtained in Chapter 4 are very interesting and can serve as aproof of concept for network operators when designing energy-efficient MM networks. Someexample guidelines which follow from our simulations are provided here. Firstly, using higherpilot power than data power can yield significant improvements in EE, particularly in the highSNR regime. Secondly, full power budget utilization is energy-efficient only in the low SNRregime. Thirdly, utilizing all the available BS antennas can lead to highly energy-inefficientoperations. In fact, BS antennas should be dynamically activated with the available power89Scope for Future Workbudget so as to ensure energy-efficient communications. Lastly, EE improvements from usinghigher pilot power than data power are more prominent under low-traffic conditions.There are two major limitations with the study conducted in Chapter 4. Firstly, weused an idealistic Rayleigh channel model and zero phase noise. This gave us maximumthroughput and EE performance. Using realistic channel models and non-zero phase noisewould certainly reduce the throughputs and EE levels. Secondly, we have not investigatedEE-maximization with respect to two important system variables, namely, the pilot sequencelength and the number of UEs in the system. When these design variables are optimized,the EE-maximization problem becomes much more complex (c.f. (4.12) (4.15) (4.16)) thanwhat we have encountered so far. This is because the pilot sequence length and the numberof UEs are much more strongly coupled within the EE metric (c.f. (4.16)). We plan toinvestigate this optimization problem in the near future.Scope for Future WorkFirstly, a resource allocation problem similar to the one discussed in Chapter 4 can beconducted to maximize energy efficiency in massive MIMO systems with ZF and MMSEdetectors. This is a non-trivial task because the achievable uplink rates for different UEsunder imperfect CSI and pilot contamination do not decouple as observed for MRC detectorsin (4.12). In addition, although ZF and MMSE detection methods offer better throughputrates than MRC in interference-limited systems, these methods also incur higher compu-tational complexities. As a result of these issues, we expect that the resource allocationresults for ZF and MMSE detectors will be different from those obtained for MRC detectors.Investigations in Chapter 4 may also be extended to downlink transmissions to study jointuplink-downlink resource allocation.Secondly, observe that the power consumption model in Chapter 4 assumes that thebackhaul operations consume a fixed amount of power per coherence interval. This may90Scope for Future Worknot be valid in practice because the power expenditure on backhaul operations depends onthe transmission rates. 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Optimal Filtering. pp. 93-95, Courier Corp., 2012.102Appendix AProof of results in Chapter 4A.1 Proof of Proposition 1We know from (4.3) that hˆlij is given byhˆlij =L∑i=qhlqj[Dˆli]j,j +1√τppwlj[Dˆli]j,jThe covariance matrix for hˆlij is given bycov (hˆlij) = E{(hˆlij − E{hˆlij})(hˆlij − E{hˆlij})T}= E{(hˆlij)(hˆlij)T}= (L∑q=1(√βlqj)2β2lijτ2p2p(1 +∑Lq=1 τppβlqj)2+ (1√τpp)2β2lijτ2p2p(1 +∑Lq=1 τppβlqj)2)IM= (β2lijτpp(∑Lq=1 βlqjτpp + 1)(1 +∑Lq=1 τppβlqj)2)IM= (τppβ2lij(1 +∑Lq=1 τppβlqj))IM= d′lijβlijIM . (from (4.3))(A.1)103A.2. Effect of Channel Estimation Error of Known Variance on Achievable RatesSimilarly, the covariance of h˜lij is given bycov (h˜lij) = cov (hlij − hˆlij)= cov (([I−D′li]j,j)hlij −L∑q=1,q 6=ihlqj[D′li]j,j −1√τppwlj[D′li]j,j)= ((√βlij)2(1 +∑Lq=1,q 6=i τppβlqj)2(1 +∑Lq=1 τppβlqj)2+L∑q=1,q 6=i(√βlqj)2β2lijτ2p2p(1 +∑Lq=1 τppβlqj)2+(1√τpp)2β2lijτ2p2p(1 +∑Lq=1 τppβlqj)2)IM=βlij(1 +∑Lq=1 τppβlqj)2((1 +L∑q=1,q 6=iτppβlqj)2 + τppβlij(1 +L∑q=1,q 6=iτppβlqj))IM=βlij(1 +∑Lq=1,q 6=i τppβlqj)(1 +∑Lq=1 τppβlqj)2(1 +L∑q=1,q 6=iτppβlqj + τppβlij)IM= (βlij(1 +∑Lq=1,q 6=i τppβlqj)(1 +∑Lq=1 τppβlqj))IM= (βlij −τppβ2lij(1 +∑Lq=1 τppβlqj))IM= βlij(1− d′lij)IM(A.2)A.2 Effect of Channel Estimation Error of KnownVariance on Achievable RatesIn the following, we provide an illustrative example on why treating channel estimationerror as part of additive noise yields a lower bound on the achievable rates in a wirelesscommunication system. This example is inspired from the paper entitled “The effect uponthe channel capacity in wireless communications of perfect and imperfect knowledge of thechannel” [45].104A.2. Effect of Channel Estimation Error of Known Variance on Achievable RatesConsider a scenario where a single user transmits a symbol X to the BS, where X isGaussian distributed with zero mean and variance σ2X . Assuming an AWGN channel withnoise variance σ2N , the received symbol Y at the BS is given by,Y = HX +N,where H is the channel strength and N is the noise. We assume that X, H, and N arestatistically independent. Given a channel estimate Hˆ, we can break H into two componentsHˆ and H˜, i.e., H = Hˆ + H˜, where H˜ is the zero-mean channel estimation error at the BS,with known variance σ2. Now, the mutual information I(X;Y ) between Y and X is givenbyI(Y ;X) = h(X)− h(X|Y ), (A.3)where h denotes differential entropy. Since we have chosen X to be Gaussian with varianceσ2X , we know the value of h(X). We now find an upper bound on h(X|Y ) so as to obtain alower bound on I(Y ;X). By definition of differential entropy,h(X|Y ) =∫h(X|Y = y)pY (y)dy.Since adding a constant does not change differential entropy,h(X|Y = y) = h(X − αy|Y = y). (A.4)Therefore, for any real α,h(X|Y ) = h(X − αY |Y ). (A.5)Since conditioning always decreases entropy, we have105A.2. Effect of Channel Estimation Error of Known Variance on Achievable Ratesh(X − αY |Y ) ≤ h(X − αY ) (A.6)Since the entropy of a random variable with a given variance is upper-bounded by theentropy of a Gaussian random variable with the same variance, we can re-write (A.5) ash(X|Y ) ≤ h(X − αY )≤ 12loge(2pie var (X − αY )),(A.7)where var(.) represents the variance of random variable under context. (A.7) is also validwhen we minimize the RHS over α. Let us pick α such that αY is the MMSE estimate ofX in terms of Y . Then [100],α =E[XY ]E[Y 2]=Hˆσ2XHˆσ2X + σ2H˜σ2X + σ2N(obtained upon simplification using the fact that X and Y are zero mean)(A.8)When α is chosen as above, the variance of X − αY becomesvar (X − αY ) = σ4Xσ2H˜+ σ2Nσ2XHˆ2σ2X + σ2H˜σ2X + σ2N. (A.9)Substituting (A.9) into (A.7) givesh(X|Y ) ≤ 12loge(2pieσ4Xσ2H˜+ σ2Nσ2XHˆ2σ2X + σ2H˜σ2X + σ2N) (A.10)Using this result in (A.3), we obtain a lower bound on the mutual information between Xand Y as follows106A.2. Effect of Channel Estimation Error of Known Variance on Achievable RatesI(X;Y ) ≥ 12loge(2pieσ2X)−12loge(2pieσ4Xσ2H˜+ σ2Nσ2XHˆ2σ2X + σ2H˜σ2X + σ2N)=12loge(1 +Hˆ2σ2Xσ2H˜σ2X + σ2N)(A.11)Interpretation from (A.11)From (A.11), we can interpret that the worst effect the channel estimation error can have isto behave as AWGN. The bound in (A.11) is equal to the capacity of the wireless channelwhen we send Gaussian signal with variance Hˆ2σ2X in an AWGN channel with effective noisewhose variance is σ2H˜σ2X + σ2N .The result in (A.11) is based on an assumption that the variance of channel estimationerror is known at the BS. Since we assume that the BS knows βlik values, the BS alsoknows the variance of channel estimation errors (c.f. (4.5)). Therefore, we use the aboveinterpretation and model channel estimation error as part of additive Gaussian noise in orderto obtain a lower bound on the rate expression, as given in (4.10).107A.3.ProofofProposition2A.3 Proof of Proposition 2From (4.11), we knowR′lk = B (1−τT) log2(1 + (E{pu∑Li=1∑Kj=1,(i,j) 6=(l,k) |hˆHllkhˆlij|2 + pu||hˆllk||2∑Li=1∑Kj=1(1− d′lij)βlij + ||hˆllk||2pu||hˆllk||4})−1)= B (1− τT) log2(1 + (E{pu∑Li=1∑Kj=1 |hˆHllkhˆlij|2 − pu||hˆllk||4 + pu||hˆllk||2∑Li=1∑Kj=1(1− d′lij)βlij + ||hˆllk||2pu||hˆllk||4})−1)= B (1− τT) log2(1 + (E{pu∑Li=1∑Kj=1,j 6=k |gˆlij|2pu||hˆllk||2+∑Li=1 pu|hˆHllkhˆlik|2pu||hˆllk||4− 1 + pu∑Li=1∑Kj=1(1− d′lij)βlijpu||hˆllk||2+1pu||hˆllk||2})−1),(A.12)where gˆlij , hˆHllkhˆlij||hˆllk|| , ∀i = 1 . . . L, j = 1 . . . K, j 6= k. Conditioned on hˆllk, gˆlij is a Gaussian random variable with zero meanand variance d′lijβlij ,τppβ2lij1+∑Li=1 τppβlij(c.f. Proposition 1), which does not depend on hˆllk. As a result, gˆlij is independent of hˆllk,108A.3.ProofofProposition2with its elements gˆlij ∼ CN (0, d′lijβlij). Using this observation, we can simplify (A.12) as followsR′lk = B (1−τT) log2(1 + (E{pu∑Li=1∑Kj=1,j 6=k |gˆlij|2pu||hˆllk||2+∑Li=1 pu|hˆHllkhˆlik|2pu||hˆllk||4− 1 + pu∑Li=1∑Kj=1(1− d′lij)βlijpu||hˆllk||2+1pu||hˆllk||2})−1)= B (1− τT) log2(1 + ((puL∑i=1K∑j=1,j 6=kE{|gˆlij|2}+ puL∑i=1K∑j=1(1− d′lij)βlij + 1)E{1pu||hˆllk||2}+L∑i=1β2lijβ2llk− 1)−1) (using 4.6)= B (1− τT)log2(1 + ((puL∑i=1K∑j=1,j 6=kτppβ2lij1 +∑Li=1 τppβlij+ puL∑i=1K∑j=1(βlij −τppβ2lij1 +∑Li=1 τppβlij) + 1)E{ 1pu||hˆllk||2}+L∑i=1(β2likβ2llk)− 1)−1)(A.13)Note that hˆllk ∼ CN (0, d′llkβllkIM). Therefore, hˆHllkhˆllk ∈ C1×1 has a complex Wishart distribution with M degrees of freedom.We now use the following result from random matrix theory to further simplify (A.13) [50]E{trace(A−1)} = mn−m, (A.14)where A is an m×m central complex Wishart matrix with n (n > m) degrees of freedom. Using this result, we obtainE{ 1pu||hˆllk||2} = 1pu(M − 1)d′llkβllk, for M ≥ 2=(1 +∑Li=1 τppβlik)pu(M − 1)τppβ2llk(A.15)Substituting (A.15) into (A.13),109A.3.ProofofProposition2R′lk = B (1−τT) log2(1 + ((puL∑i=1K∑j=1,j 6=kτppβ2lij1 +∑Li=1 τppβlij+ puL∑i=1K∑j=1(βlij −τppβ2lij1 +∑Li=1 τppβlij) + 1)(1 +∑Li=1 τppβlik)pu(M − 1)τppβ2llk+L∑i=1(β2likβ2llk)− 1)−1)= B (1− τT) log2(1 + ((1 + τppL∑i=1βlik)puL∑i=1K∑j=1βlij − puL∑i=1τppβ2lik + (1 +L∑i=1τppβlik) + (M − 1)τpppuL∑i=1,i 6=lβ2likτpppu(M − 1)β2llk)−1= B (1− τT) log2(1 +τpppu(M − 1)β2llkτpppu(L∑i=1βlikL∑i=1K∑j=1βlij −L∑i=1β2lik +L∑i=1,i 6=l(M − 1)β2lik) + puL∑i=1K∑j=1βlij + 1 + τppL∑i=1βlik)(A.16)To obtain the rate expression R′lk in (4.12), let us first define the following coefficient termsc1k , τβ2llk, c2k ,L∑i=1L∑j=1βlij, c3k , τL∑i=1βlikc4k , τL∑i=1,i 6=lβ2likc5k , c2kc3k − τL∑i=1β2lik (A.17)Substituting (A.17) into (A.16), we obtainR′lk(M, pp, pu) = B (1−τT) log2(1 +c1k(M − 1)pppuc2kpu + c3kpp + c4k(M − 1)pppu + c5kpppu + 1),which is the same as (4.12). This completes the proof.110A.4. Proof of Proposition 4A.4 Proof of Proposition 4The rate function R′lk(M ; pp0 , pu0) in (4.22) can be expressed asR′lk(M ; pp0 , pu0) = B (1−τT) log2((A1k + A2k)M + (A3k − A1k))−B (1− τT) log2(A2kM + A3k),(A.18)Substituting the expression forR′lk(M ; pp0 , pu0) from (A.18) and the expression for Ptot(M ; pp0 , pu0)from (4.23) into the expression for P3(θ) in (4.21), we obtainP3(θ) =maxM∈RK∑k=1B (1− τT) log2((A1k + A2k)M + (A3k − A1k))−B ((1− τT) log2(A2kM + A3k)− (θD1M +D2))subject to : C1,=minM∈RK∑k=1−B (1− τT) log2((A1k + A2k)M + ((A3k − A1k))+B (1− τT) log2(A2kM + A3k)− (θD1M +D2))subject to : C1,(A.19)where we have transformed the original maximization problem into an equivalent minimiza-tion problem. Let us now defineflk(M) = −B (1− τT) log2((A1k + A2k)M + (A3k − A1k)),glk(M, θ) = −B (1− τT) log2(A2kM + A3k) + θ(D1M +D2)(A.20)Substituting (A.20) into (A.19), we obtainP3(θ) =minM∈R+∑Kk=1 flk(M)− glk(M, θ)subject to : C1,(A.21)111A.4. Proof of Proposition 4which is the same as (4.24).Convexity of flk(M) and glk(M, θ)To prove that flk(M) and glk(M, θ) are convex, it is sufficient to prove that their second-orderderivates with respect to M are always positive.∇2Mflk(M) =(A1k + A2k)2B (1− τT)(A1k + A2k)M + (A3k − A1k)2> 0 (since both numerator and denominator are always positive)∇2Mglk(M, θ) =B (1− τT)A22k(A2kM + A3k)2> 0 ( since both numerator and denominator are always positive)Since flk(M) and glk(M, θ) are convex ∀(l, k), the objective function in (A.21) is the sum-mation of a set of functions, each of which is in turn a difference of convex (DC) function.Since the summation of DC functions is a DC function and the constraint C1 in (A.21) isconvex , the optimization problem in (A.21) is a DC programming problem. This completesthe proof.112

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