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Resource allocation in cooperative and heterogeneous wireless networks with energy harvesting Lohani, Sudha 2017

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Resource Allocation in Cooperative and HeterogeneousWireless Networks with Energy HarvestingbySudha LohaniB.E., Tribhuvan University, Nepal, 2010M.E., Asian Institute of Technology, Thailand, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)December 2017c© Sudha Lohani 2017AbstractThe number of wireless connected devices is increasing rapidly, owing to the increasing ap-plications of Internet of Things (IoT) devices. To address the coverage and capacity demandin the future, the fifth generation (5G) network will have heterogeneous architecture withdensely deployed small cells and relay nodes for cooperative communication. Since dense de-ployment of base stations and relay nodes incur high energy consumption, renewable energyharvesting is a promising technique of reducing non-renewable energy consumption. Mean-while, with increasing demand of IoT applications, self-sustaining battery life is direly neededin low power sensor-like devices. Since installation of bulky renewable energy harvesting in-frastructure is not feasible in such miniature sensor-like devices, wireless energy harvestingis another promising technique that enables self-sustaining battery life of such devices. Inthis thesis, we address the challenges of resource allocation in cooperative and heterogeneouswireless communication networks with renewable and wireless energy harvesting.First, we consider relay-based and user-based cooperation in uplink wireless-poweredcommunication (WPC) to mitigate the “doubly near-far” problem. We propose algorithmsto jointly optimize resource allocation for downlink energy harvesting and uplink informationtransmission in uplink WPC network with relay-based and user-based cooperation. Our al-gorithms improve throughput performance of user equipments that are far from access point.Next, we address new challenges of interference management in heterogeneous networks (Het-Nets) when downlink simultaneous information and power transfer (SWIPT) is enabled insmall cells. We jointly maximize energy harvesting rate and throughput of small cell userswhile keeping interference within tolerable level. In time-switching approach of SWIPT, weiiAbstractdemonstrate significant improvement in the energy harvesting rate by enabling flexible inter-ference tolerance in macrocell users. Finally, we address the conflict between maximizationof throughput and minimization of power cost in HetNets with renewable energy harvest-ing. We propose different online and offline algorithms to determine dynamic base stationactivation policy jointly with downlink resource allocation to optimize the trade-off betweenthroughput performance and the associated power cost. Our algorithms demonstrate sig-nificant increase in throughput and decrease in non-renewable power consumption whencompared to the baseline schemes. Performances of the proposed algorithms are analyzedthrough numerical simulations.iiiLay SummaryEnergy harvesting is envisioned as a key feature of future wireless networks. Wireless energyharvesting can elongate battery life of battery-constrained Internet of Things devices andrenewable energy harvesting can lower non-renewable energy consumption of network equip-ments. In this thesis, we propose different algorithms for uplink/downlink resource allocationin cooperative and heterogeneous wireless communication networks with energy harvestingconstraints. In wireless energy harvesting, we consider uplink wireless-powered communi-cation (WPC) as well as downlink simultaneous information and power transfer (SWIPT).For uplink WPC, our algorithms improve throughput performance of user equipments thatare far from access point by relay-based and user-based cooperation. For downlink SWIPT,our algorithms significantly improve the energy harvesting rate in small cells while satisfyingminimum throughput requirements of macrocell users in heterogeneous networks (HetNets).For renewable energy harvesting HetNets, our algorithms improve the throughput perfor-mance while decreasing the power cost of serving the hotspot users.ivPrefacePublications that resulted from the research presented in this thesis are as follows:• S. Lohani, R. A. Loodaricheh, E. Hossain and V. K. Bhargava, “On multiuser resourceallocation in relay-based wireless-powered uplink cellular networks,” IEEE Trans. Wire-less Commun., vol. 15, no. 3, pp. 1851-1865, Mar. 2016. (Linked to Chapter 2)• S. Lohani, R. A. Loodaricheh, E. Hossain and V. K. Bhargava, “Relay-based harvest-then-transmit protocol for uplink cellular networks,” in Proc. IEEE Globecom Work-shops (GC Wkshps), Dec. 2014, pp. 912-917. (Linked to Chapter 2)• S. Lohani, R. A. Loodaricheh, S. Mallick, E. Hossain and V. K. Bhargava, “Cooper-ative networks with wireless energy harvesting,” in Wireless-Powered CommunicationNetworks: Architectures, Protocols, and Applications, (D. Niyato, E. Hossain, D. Kim,V. Bhargava, and L. Shafai eds.), Cambridge University Press, 2016, pp. 135-169.(Linked to Chapter 2)• S. Lohani, S. Mallick, E. Hossain and V. K. Bhargava, “Resource allocation in OFDMA-based wireless-powered cooperative sensor networks,” in Proc. IEEE InternationalWIE Conference on Electrical and Computer Engineering (WIECON-ECE), Dec. 2015,pp. 65-69. (Linked to Chapter 3)• S. Lohani, E. Hossain and V. K. Bhargava, “On downlink resource allocation forSWIPT in small cells in a two-tier HetNet,” IEEE Trans. Wireless Commun., vol.15, no. 11, pp. 7709-7724, Nov. 2016. (Linked to Chapter 4)vPreface• S. Lohani, E. Hossain and V. K. Bhargava, “Resource allocation for wireless infor-mation and energy transfer in macrocell-small cell networks,” in Proc. IEEE 84thVehicular Technology Conference (VTC-Fall), Sep. 2016, pp. 1-5. (Linked to Chap-ter 4)• S. Lohani, E. Hossain and V. K. Bhargava, “Downlink power allocation for wirelessinformation and energy transfer in macrocell-small cell networks,” in Proc. IEEEWireless Communications and Networking Conference (WCNC), Apr. 2016, pp. 1-6.(Linked to Chapter 4)• S. Lohani, E. Hossain and V. K. Bhargava, “Joint resource allocation and dynamicactivation of energy harvesting small cells in OFDMA HetNets,” IEEE Trans. WirelessCommun., Accepted Dec. 2017. (Linked to Chapter 5)• S. Lohani, E. Hossain and V. K. Bhargava, “Joint resource allocation and dynamicbase station activation in energy harvesting HetNets,” in Proc. IEEE 30th CanadianConference on Electrical and Computer Engineering (CCECE), Apr. 2017, pp. 1-6.(Linked to Chapter 5)I am the primary researcher and author for all the research contributions made in this thesis.I conducted the literature review to identify the research problems. I formulated the researchproblems, performed mathematical analysis, and carried out the numerical simulations. Ialso wrote the manuscripts for each publication. The contributions of the co-authors of mypapers are as follows. Prof. Vijay K. Bhargava is my honorable supervisor. He has pro-vided valuable guidance, technical suggestions, and constructive feedback for identifying theresearch problem, making the research progress, and preparing the associated manuscripts.Prof. Ekram Hossain is the co-supervisor of my research during my PhD. I consulted himduring all my research works and he has provided valuable guidance, constructive tech-nical feedback, and also helped in editorial corrections while preparing the correspondingmanuscripts for publication. Dr. Shankhanaad Mallick was a post-doctoral fellow and Dr.viPrefaceRoya Arab Loodarichech was a PhD student in our research group. They provided contribu-tion in some of the above publications by offering technical feedback during the mathematicalanalysis and editorial feedback during preparation of the associated manuscripts.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview of Energy Harvesting in Wireless Networks . . . . . . . . . . . . . 31.1.1 Wireless Energy Harvesting . . . . . . . . . . . . . . . . . . . . . . . 31.1.2 Renewable Energy Harvesting . . . . . . . . . . . . . . . . . . . . . . 51.2 Overview of Heterogeneous and Cooperative Wireless Networks . . . . . . . 71.3 Open Issues in Cooperative and Heterogeneous Wireless Networks with En-ergy Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10viiiTable of Contents1.4 Related Work, Motivation, and Objective . . . . . . . . . . . . . . . . . . . 131.4.1 Doubly Near-Far Problem in Uplink WPC . . . . . . . . . . . . . . . 141.4.2 Rate-Energy Trade-off and Interference Issues in HetNets with SWIPT 161.4.3 Rate-Energy Trade-off in HetNets with Renewable Energy Harvesting 191.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 Resource Allocation in Uplink Wireless-Powered Communication Networkswith Relay-based Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . 252.2 System Model and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 272.3 Problem Formulations and Solution Approaches . . . . . . . . . . . . . . . . 332.3.1 Joint Power and Time Allocation: Scenario I . . . . . . . . . . . . . 332.3.2 Joint Power and Time Allocation: Scenario II . . . . . . . . . . . . . 382.4 Performance Evaluation Results . . . . . . . . . . . . . . . . . . . . . . . . 432.4.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 432.4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.4.3 Summary of Observations . . . . . . . . . . . . . . . . . . . . . . . . 533 Resource Allocation in Uplink Wireless-Powered Communication Networkswith User-based Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . 543.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . 543.2 System Model and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 553.3 Problem Formulation and Solution Approach . . . . . . . . . . . . . . . . . 573.4 Performance Evaluation Results . . . . . . . . . . . . . . . . . . . . . . . . 643.4.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 643.4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.4.3 Summary of Observations . . . . . . . . . . . . . . . . . . . . . . . . 67ixTable of Contents4 Resource Allocation for Downlink SWIPT in Small Cells in a Two-TierHetNet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . 684.2 System Model and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 704.3 Resource Allocation for Time-switching Approach: Problem Formulations andSolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.3.1 Scenario I: Negligible Co-tier Interference . . . . . . . . . . . . . . . 764.3.2 Scenario II: Non-negligible Co-tier Interference . . . . . . . . . . . . 814.4 Resource Allocation for Power-splitting Approach: Problem Formulation andSolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.5 Performance Evaluation Results . . . . . . . . . . . . . . . . . . . . . . . . 924.5.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 934.5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.5.3 Summary of Observations . . . . . . . . . . . . . . . . . . . . . . . . 1035 Joint Resource Allocation and Dynamic Activation of Energy HarvestingSmall Cells in HetNets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . 1045.2 System Model and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 1065.3 Offline Optimization: Problem Formulation and Solution Approach . . . . . 1115.3.1 Subchannel and Power Allocation for Given SBS Activation Policy . 1135.3.2 Discrete Binary PSO for Dynamic SBS Activation . . . . . . . . . . 1195.4 Online Optimization: Problem Formulations and Solution Approaches . . . 1205.4.1 Dynamic Programming-based Online Optimization . . . . . . . . . . 1225.4.2 Greedy Online Optimization . . . . . . . . . . . . . . . . . . . . . . 1255.5 Performance Evaluation Results . . . . . . . . . . . . . . . . . . . . . . . . 1295.5.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 129xTable of Contents5.5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1305.5.3 Summary of Observations . . . . . . . . . . . . . . . . . . . . . . . . 1396 Summary, Conclusions, and Future Work . . . . . . . . . . . . . . . . . . . 1416.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 1416.2 Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . 144Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156A Proof of Convexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157B Proof of Lemma 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158C Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160D Simplification of KKT Conditions . . . . . . . . . . . . . . . . . . . . . . . . 161xiList of Tables2.1 Received, harvested, and transmit power of UEs . . . . . . . . . . . . . . . . 485.1 Comparison among proposed algorithms (Scenario I) . . . . . . . . . . . . . 1315.2 Comparison among proposed algorithms (Scenario II) . . . . . . . . . . . . . 132xiiList of Figures1.1 Simultaneous wireless information and power transfer in downlink. The UEsharvest energy from the same information signal transmitted on downlink bythe access point (AP). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Wireless-powered communication in uplink. The AP makes downlink energytransmission first and then the UEs make uplink information transmissionwith the harvested energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Hybrid-powered base station. . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 Heterogeneous network deployment. Solid line indicates wireless link whiledashed line indicates backhaul link. . . . . . . . . . . . . . . . . . . . . . . . 82.1 Uplink WPC network with relay-based cooperation. . . . . . . . . . . . . . . 282.2 Relay-based harvest-then-transmit protocol. . . . . . . . . . . . . . . . . . . 282.3 Convergence of Algorithm 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.4 Time allocated versus energy harvesting efficiency. . . . . . . . . . . . . . . . 462.5 Energy allocated at relay node versus energy harvesting efficiency. . . . . . . 472.6 Throughput versus energy harvesting efficiency. . . . . . . . . . . . . . . . . 492.7 Throughput ratio versus energy harvesting efficiency. . . . . . . . . . . . . . 492.8 Average sum-throughput versus number of UEs. . . . . . . . . . . . . . . . . 502.9 Average sum-throughput versus attenuation factor. . . . . . . . . . . . . . . 512.10 Jain’s fairness index versus energy harvesting efficiency. . . . . . . . . . . . . 522.11 Jain’s fairness index versus number of UEs. . . . . . . . . . . . . . . . . . . . 52xiiiList of Figures3.1 Uplink WPC network with user-based cooperation. . . . . . . . . . . . . . . 563.2 Sum-throughput versus energy harvesting efficiency. . . . . . . . . . . . . . . 643.3 Sum-throughput versus energy harvesting efficiency. . . . . . . . . . . . . . . 653.4 System energy efficiency versus number of relays. . . . . . . . . . . . . . . . 664.1 Two-tier HetNet with SWIPT in small cells. . . . . . . . . . . . . . . . . . . 704.2 Sum-throughput of SUEs versus η. . . . . . . . . . . . . . . . . . . . . . . . 944.3 Sum-energy harvesting rate of SUEs versus η. . . . . . . . . . . . . . . . . . 954.4 Sum-throughput of SUEs versus R(tar). . . . . . . . . . . . . . . . . . . . . . 964.5 Sum-energy harvesting rate of SUEs versus R(tar). . . . . . . . . . . . . . . . 964.6 Average fraction of time/power allocated for ID process versus R(tar). . . . . 974.7 Sum-energy harvesting rate of SUEs versus Pm. . . . . . . . . . . . . . . . . 984.8 Sum-throughput of SUEs versus R(min). . . . . . . . . . . . . . . . . . . . . . 994.9 Sum-energy harvesting rate of SUEs versus R(min). . . . . . . . . . . . . . . . 994.10 Average received power for energy harvesting versus R(min). . . . . . . . . . . 1004.11 Sum-throughput of SUEs versus R(min,I). . . . . . . . . . . . . . . . . . . . . 1014.12 Sum-energy harvesting rate of SUEs versus R(min,I). . . . . . . . . . . . . . . 1014.13 Convergence and performance analysis of Algorithms 3 and 4. . . . . . . . . 1025.1 Two-tier HetNet with renewable energy harvesting in SBS. . . . . . . . . . . 1075.2 Convergence of DBPSO algorithm. . . . . . . . . . . . . . . . . . . . . . . . 1305.3 Variation in net reward with EH . . . . . . . . . . . . . . . . . . . . . . . . . 1335.4 Variation in average throughput with EH . . . . . . . . . . . . . . . . . . . . 1335.5 Variation in power consumption with EH . . . . . . . . . . . . . . . . . . . . 1355.6 Variation in average throughput with β. . . . . . . . . . . . . . . . . . . . . 1365.7 Variation in power consumption with β. . . . . . . . . . . . . . . . . . . . . 1375.8 Variation in average throughput with rth. . . . . . . . . . . . . . . . . . . . . 1385.9 Variation in power consumption with rth. . . . . . . . . . . . . . . . . . . . . 138xivList of Abbreviations3GPP : 3rd Generation Partnership Project4G : Fourth Generation5G : Fifth GenerationAP : Access PointAWGN : Additive White Gaussian NoiseDBPSO : Discrete Binary Particle Swarm OptimizationDEH : Downlink Energy HarvestingDEPA : Downlink Equal Power AllocationEH : Energy HarvestingHetNet : Heterogeneous NetworksHUE : Hotspot User EquipmentID : Information DecodingIoT : Internet of ThingsKKT : Karush Kuhn TuckerLTE-A : Long Term Evolution-AdvancedMBS : Macrocell Base StationMETIS : Mobile and wireless communications Enablers for theTwenty-twenty Information SocietyMINLP : Mixed Integer Non-Linear ProgrammingMTC : Machine Type CommunicationMUE : Macrocell User EquipmentxvList of AbbreviationsPSO : Particle Swarm OptimizationQoS : Quality of ServiceRF : Radio FrequencyRFID : Radio Frequency IdentificationRN : Relay NodeRRSA : Random Relay and Subcarrier AssignmentSBS : Small cell Base StationSNR : Signal-to-Noise RatioSUE : Small cell User EquipmentSWIPT : Simultaneous Wireless Information and Power TransferTN : Transmitting NodeUE : User EquipmentUIT : Uplink Information TransmissionWPC : Wireless-Powered CommunicationxviAcknowledgmentsI am very grateful to a number of people for their support and guidance in the journey of myPhD. Firstly, I would like to extend my deepest gratitude to my supervisor, Professor VijayK. Bhargava and my co-supervisor, Professor Ekram Hossain for their incredible support andguidance. I consider myself very lucky to have had the opportunity of working under thesupervision of such knowledgeable, supportive, and patient supervisors. This thesis wouldnot have been possible without their invaluable advice, critical comments, and constantencouragement.I would also like to thank Professor Vincent Wong, Professor Lutz Lampe, ProfessorVictor Leung, and Professor Alireza Nojeh for offering constructive suggestions and insightfulfeedback during my PhD qualifying exam and departmental exam.I would also like to extend my gratitude towards all the colleagues of my research lab fortheir friendly support and the fruitful discussions. I appreciate the help and encouragementthat I received from my senior colleagues, namely, Dr. Shankhanaad Mallick, Dr. Roya ArabLoodaricheh, Dr. Mai Hassan, Dr. Rindranirina Ramamonjison, and Dr. Hamidreza Boost-animehr. Special thanks go to Dr. Shankhanaad Mallick and Dr. Roya Arab Loodaricheh,with whom I had the chance to collaborate in some of my research works. Their technicalsuggestions and feedback have been very helpful in my research. This work was supportedby Natural Sciences and Engineering Research Council of Canada (NSERC).xviiDedicationI dedicate this thesis to my daughter, my husband, and my parents. My daughter, who wasborn just before I started writing my thesis, gave me a new dimension of encouragementand determination. I am eternally grateful to my mother for staying with me after the birthof my daughter, so that I could complete my thesis in time. I am thankful to both of myparents for laying a strong foundation for my education. Special thanks to my husband forall the support and sacrifices he made during the journey of my PhD.xviiiChapter 1IntroductionThe wireless communication industry has been expanding tremendously, both in terms oftechnology as well as subscribers. The journey of mobile communication has reached fourthgeneration (4G). Third Generation Partnership Project (3GPP) Release 10 known as LongTerm Evolution-Advanced (LTE-A) was ratified as 4G technology by International Telecom-munication Union in November 2010 [1]. It is now deployed in several parts of the world.Along the journey, subscriber demand has never failed to increase. For example, the numberof wireless connected devices is expected to increase from 15 billion in 2015 to 28 billion in2021 out of which 16 billion will be related to Internet of Things (IoT) [2]. With increasingapplication of IoT devices, there is increasing interest in incorporating IoT network undercellular communication technology [3, 4] and 1.5 billion IoT devices are expected to havecellular connectivity by 2021 [2]. Currently, researchers, users, and service providers are alllooking forward to the fifth generation (5G) technology as a solution to support the increasedcapacity and coverage demand of the legions of connected devices and users of 2020 and be-yond. For instance, Mobile and wireless communications Enablers for the Twenty-twentyInformation Society (METIS) project [5] has concretized the requirements of 5G wirelesscommunication networks and the research work towards standardization is on-going.One of the major challenges imposed upon 5G networks is tremendous increase in trafficvolume and legions of connected wireless devices. To address the coverage and capacitydemand of legions of devices in the future, 5G network is expected to have heterogeneousarchitecture with macro cells overlaid or underlaid by large number of smaller cells alongwith relay nodes deployed for cooperative communication [6]. This will impose additional1Chapter 1. Introductionresource management and interference management challenges. Moreover, increasing en-ergy efficiency whilst achieving better performance is another challenging requirement of the5G networks [5]. Increase of coverage and capacity leads towards higher consumption ofenergy [7]. Increasing energy consumption and consequent operational expenditure of thenetwork operators have motivated researchers towards the concept of “Green Communica-tion” which not only targets to reduce energy consumption in terms of environmental benefitbut also in terms of economic benefit. Meanwhile, with increasing number of low power IoTdevices, limited battery life of such miniature devices is another major performance bottle-neck.Lately, energy harvesting has received significant research attention in the field of wirelesscommunications. As the name suggests, energy harvesting is a technique by which energyof ambient sources (solar, wind, wireless, and others) is converted into electrical energy andused to power user/network equipments. Harvesting energy from renewable energy sources(solar, wind, and others), which is termed as renewable energy harvesting, has emerged asone of the enabling technologies for Green Communication [8]. This technology makes use ofperpetual renewable energy sources and reduces the consumption of high cost non-renewableenergy sources. Since installing renewable energy harvesting infrastructure is not feasible inlow-power miniature devices, wireless energy harvesting has also gained much attention inthe field of energy harvesting as a potential technique of elongating the battery life of suchbattery-constrained IoT devices [6]. Hence, energy harvesting is envisioned as a key featureof future wireless networks [6, 8].In this thesis, we address some challenges imposed by energy harvesting constraints onresource allocation in heterogeneous and cooperative networks. In the next section, weprovide brief overview of energy harvesting in wireless networks. We also provide a briefoverview of heterogeneous and cooperative networks in Section 1.2.21.1. Overview of Energy Harvesting in Wireless Networks1.1 Overview of Energy Harvesting in WirelessNetworksDepending upon the source of energy, energy harvesting can be broadly divided into twocategories: wireless energy harvesting and renewable energy harvesting. In this section, wewill discuss about these two energy harvesting technologies separately.1.1.1 Wireless Energy HarvestingThe concept of harvesting energy from the received wireless signal, known as wireless energyharvesting, has gained much research attention in the field of wireless communication net-works [9, 10] because of its ability to extend the battery life of small network nodes. Withthe increasing demand of IoT applications, self-sustaining battery life is direly needed insensor nodes [3, 11]. Providing grid power or renewable energy harvesting infrastructure toeach sensor node of a densely populated network may not be a viable option. Given thesmall size of the sensor nodes, they cannot have long battery life even if they are batteryoperated. Constantly changing or recharging the battery incurs high operational cost, re-quires constant human involvement, and may not be feasible in many network applications.Therefore, wireless energy harvesting is anticipated as one of the key features in the future ofIoT [12]. Self-sustaining battery life of sensor nodes will allow full exploitation of several IoTapplications such as embedded structure monitoring, industrial monitoring, environmentalmonitoring, and so on.There are two major concerns in wireless energy harvesting technology. Firstly, dueto the current hardware limitation, receiver circuits of UEs are not designed to harvestenergy while decoding the information. The authors of [13] have proposed a receiver circuitthat integrates the components of energy harvester and information decoder. However, theachievable throughput of such integrated receiver circuit is found to be much lower thanthat of the separated receiver. Therefore, receiver circuits of UEs need to have separate31.1. Overview of Energy Harvesting in Wireless NetworksAPUE1UE2Downlink Informaon TransmissionDownlink Energy TransmissionFigure 1.1: Simultaneous wireless information and power transfer in downlink. The UEs harvest energyfrom the same information signal transmitted on downlink by the access point (AP).information decoding and energy harvesting circuit. Energy harvesting circuits such asP2110 Powerharvester receiver [14] has already been commercially available. Secondly, thereceiver sensitivity of energy harvester is very poor (around −20 dBm) compared to thatof an information receiver (around −60 dBm) [15, 16]. If the received signal is significantlylower than −20 dBm, very little or no energy is harvested. This significantly reduces therange of wireless power transfer. For instance, in a certain experimental setting [15], wirelesspower transfer range is found to be around 11.38 meters for omnidirectional antenna and37.51 meters for directional antenna. In the experiment, the power harvested at a distance of10 m is found to be 12.94 µW with omnidirectional antenna and 140.73 µW with directionalantenna. Since the received signal power is in the range of µW, wireless energy harvestingis applicable in very small nodes of wireless communication network with minimum powerrequirements, such as sensor nodes1 or RFID tags [15,18,19].Wireless energy harvesting technology has been investigated in two different paradigmsof wireless communication discussed separately in the following.Simultaneous wireless information and power transferSimultaneous wireless information and power transfer (SWIPT) is used in downlink com-munication phase to transmit wireless energy to the UEs whilst transmitting downlink in-1Transmit power requirement of some sensor devices such as TelosB can be low as −24 dBm [17].41.1. Overview of Energy Harvesting in Wireless Networksformation to them as shown in Fig. 1.1. For SWIPT, since current receiver circuits haveseparate information decoding and energy harvesting circuits, the received signal is shared,either by splitting the power of the received signal, called power-splitting approach, or bysharing the time of signal reception, called time-switching approach, among the informationdecoder and the energy harvester [13, 20]. In power-splitting approach, UEs use a radiofrequency (RF) splitter [21] to split a fraction of the received signal to information decodingcircuit and the rest to energy harvesting circuit (e.g., P2110 Powerharvester receiver [14]).In time-switching approach, UEs use a switch [22] to connect the RF input to energy har-vesting circuit for a fraction of transmission time and to information decoding circuit for theremaining of transmission time. Refer to [23] and references therein for time-switching andpower-splitting receiver circuit architectures for SWIPT.Wireless-powered communicationWhen the UEs are making uplink transmission, it is not possible to transmit energy to themvia SWIPT technique. Hence, another important paradigm of wireless energy harvestingis wireless-powered communication (WPC) in the uplink [24–26]. In this technique, uplinkinformation transmission phase is preceded by downlink energy harvesting phase, where thewireless charging signal is transmitted by the access point to the UEs. The energy, harvestedduring downlink energy harvesting time, is utilized by the UEs to make uplink informationtransmission to the access point as shown in Fig. 1.2. It is termed as harvest-then-transmitprotocol in [24].In this thesis, we address the challenges of resource allocation in uplink WPC as well asdownlink SWIPT.1.1.2 Renewable Energy HarvestingWhile wireless energy harvesting is suitable in small nodes of the network, renewable energyharvesting is a promising technique of reducing the power cost of bigger network nodes such51.1. Overview of Energy Harvesting in Wireless NetworksAPUE1UE2Uplink Informaon TransmissionDownlink Energy TransmissionFigure 1.2: Wireless-powered communication in uplink. The AP makes downlink energy transmission firstand then the UEs make uplink information transmission with the harvested energy.as base stations. In the era of rapidly increasing network density, and hence the energydemand, renewable energy harvesting has emerged as an enabling technology to lower thecarbon footprint of wireless networks. There have been several studies in the literatureconsidering solar or wind energy harvesting for the base stations [27, 28]. Some renewableenergy sources can be more efficient in specific time and location only. For example, if solarenergy harvesting is implemented, the system may not operate if it is cloudy for a longduration. Similar limitations apply to all natural sources of energy. Designing a devicecapable of harvesting energy from more than one sources can be a promising solution to thatproblem. One such hybrid energy harvesting model using solar energy and wind energy ispresented in [27]. To ensure the continuous operation of the network equipments, it is betterto add a constant energy source (power grid or battery) to the system. Fig. 1.3 depicts abase station powered by solar energy, wind energy, and constant energy source (power grid).However, the design should be such that energy consumption from the constant energy sourceis kept to minimum [29].Due to the uncertainty of energy arrival in renewable energy harvesting systems, energyarrival becomes a random process to be considered in resource allocation schemes. The energythat will be harvested in future will not be of any use in the current packet transmission.Hence causality constraint is added in the resource allocation problem of renewable energyharvesting systems [30,31]. In this thesis, we address the challenges of resource allocation in61.2. Overview of Heterogeneous and Cooperative Wireless NetworksBa eryWind turbineSolar panelBase sta onPower gridFigure 1.3: Hybrid-powered base station.such renewable energy harvesting networks with causality constraints.1.2 Overview of Heterogeneous and CooperativeWireless NetworksHeterogeneous networks (HetNets) comprise of different tiers of network overlaying or un-derlaying each other along with relay nodes as shown in Fig. 1.4. Typically larger cells,termed as macro cell are overlaid/underlaid by smaller cells. Although macro cells are usu-ally designed to provide coverage to a larger area, there can be coverage holes due to differentgeographical obstructions and poor channel conditions. Also, there might be high demandin certain areas, called hotspots. Hence, smaller cells are designed to support the capacitydemand of hotspots or serve the users in the coverage holes. Cooperative communicationwith relay nodes can also be used for providing coverage in the coverage holes, instead ofdeploying a small cell. In that case, the relay node receives the signal from the base stationand forwards them to the users in the coverage holes. We will discuss more about relay-based and user-based cooperation in wireless communications subsequently. If macro celland small cell base stations are powered by the same source of energy, deployment of smallercells increases energy efficiency of the network as transmit power requirement of the base71.2. Overview of Heterogeneous and Cooperative Wireless NetworksMBSFemto cellMicro cellPico cellBase sta onRelay nodeUser equipmentMacro cellFigure 1.4: Heterogeneous network deployment. Solid line indicates wireless link while dashed lineindicates backhaul link.stations decreases significantly, owing to the reduced transmission distances [7].While multi-tier architecture provides a low cost solution for increasing capacity andcoverage, there are significant technical challenges in the design and deployment of such net-works [32]. Different tiers of network can be overlaid with dedicated spectrum for each tier orunderlaid to reuse the same spectrum, which is also called co-channel deployment. Deploy-ment of different network tiers in dedicated channels results in an inefficient usage of spec-trum whereas co-channel deployment gives rise to co-tier and cross-tier interferences [33–36].However, co-channel deployment is essential to address the capacity demand of increasingnumber of UEs [6]. In this thesis, different challenges that arise in interference managementand resource allocation in co-channel deployment of multi-tier network with wireless andrenewable energy harvesting will be considered.As mentioned previously, cooperative communication can also be used to serve the usersin coverage holes. When direct link between the macro base station and a group of usersin a certain geographical area is poor, a relay node can be installed such that channel gainof the link between the base station and the relay node as well as that between the relaynode and the users are significantly better. The simplest from of cooperative communicationcan be demonstrated in a simple three terminal network with one source node, one relaynode, and one destination node. With the promising concept of full-duplex communication,81.2. Overview of Heterogeneous and Cooperative Wireless Networkssource node to relay node communication can happen simultaneously while the receivedsignal is forwarded in the relay node to destination node link [37]. However, due to highinterference challenges, half-duplex relaying may be desirable where the source node to relaynode communication and relay node to destination node communication is separated in timedomain or frequency domain. In this thesis, we consider half-duplex relaying.There are different forwarding policies defined for the relays [38]. The most commonly an-alyzed forwarding policies in the literature are amplify-and-forward and decode-and-forward.Amplify-and-forward is simple forwarding policy in which the relay amplifies the received sig-nal and transmits it to the destination. This improves the signal-to-noise ratio of the signalreceived at the destination. The main disadvantage of this forwarding policy is that the relayamplifies the received noise signal along with the information signal, before forwarding them,which curtails the resulting signal-to-noise gain at the destination. In decode-and-forwardpolicy, the relay first decodes the received message, and then makes the transmission ofthe re-encoded message. In this case, channel gain of the link between the source and therelay must be strong enough to ensure successful decoding at the relay. In this thesis, onlyamplify-and-forward policy is considered.For cooperative communication, instead of deploying dedicated relay nodes, different UEsof the network can also be designed to cooperate by acting as a relay node for other UEs.Since installing dedicated relay nodes can incur higher installation as well as operationalcosts, cooperative communication among UEs of the network is gaining significant researchattention. With cooperation among UEs of the network, without added infrastructure, theoverall system capacity can be remarkably improved utilizing the spatial diversity due togeographical separation of the cooperating UEs [39]. In this thesis, we consider relay-basedand user-based cooperation in wireless-powered networks.91.3. Open Issues in Cooperative and Heterogeneous Wireless Networks with Energy Harvesting1.3 Open Issues in Cooperative and HeterogeneousWireless Networks with Energy HarvestingHere, some open issues in the context of cooperative and heterogeneous wireless networkswith energy harvesting are reviewed.• Doubly Near-Far Problem in Uplink WPCThe UEs far from the access point receive weak radio signal due to distance dependentattenuation and channel fading effects. In wireless energy harvesting systems, recep-tion of weak signals not only hampers the achievable throughput, but also lowers theamount of harvested energy and the effect is more severe due to poor receiver sensi-tivity of energy harvester. If the uplink data transmission is powered by the harvestedenergy, deterioration of harvested energy implies lower uplink transmit power, whichin turn further deteriorates the information rate. Therefore, severe “doubly near-far”problem has been noticed in uplink WPC networks since the UEs far from the accesspoint suffer from distance dependent attenuation during downlink energy harvestingas well as uplink information transmission [24]. As in the case of traditional wirelessnetworks, relay-based and user-based cooperation can enhance the performance of theUEs far from the access point. However, in such WPC networks, uplink informationtransmission is highly dependent on downlink energy harvesting phase and hence jointuplink and downlink resource allocation is of high importance. Joint considerationof uplink and downlink phase in such WPC network with relay-based and user-basedcooperation increases complexity of the resource allocation problem.• Interference Issues in HetNets with Downlink SWIPTWith the foreseeable upsurge in IoT application and devices, joint investigation ofSWIPT along with co-channel deployment of multi-tier HetNets will be significant inthe design of future wireless networks. As discussed in Section 1.2, multi-tier network101.3. Open Issues in Cooperative and Heterogeneous Wireless Networks with Energy Harvestingarchitecture with co-channel deployment is essential to provide sustainable service tothe legions of wireless connected devices expected in the near future [6]. Also, as dis-cussed in Section 1.1, wireless energy harvesting is a promising technology to elongatebattery life of the low power IoT devices. Hence, it is important to consider SWIPT inHetNets. If SWIPT is enabled in HetNets, challenges associated with wireless powertransfer along with multi-tier network design converge into a common platform andincrease complexity of the resource allocation problem.As discussed in Section 1.1, considering poorer receiver sensitivity of an energy har-vester (around −20 dBm) in comparison to that of an information receiver (around−60 dBm) [15,16], applicability of wireless power transfer is limited in small transmis-sion distances to serve low power miniature devices, like sensor nodes. In this context,application of SWIPT in small cells to serve low-power sensor-like devices is promising.However, due to poor receiver sensitivity of energy harvester, even with the small dis-tance, in order to ensure significant wireless power transfer, the small cell base stationsneed to transmit at a level much higher than that in traditional multi-tier communi-cation networks. High transmit power of small cell base stations increases undesiredco/cross-tier interference in co-channel deployment of multi-tier HetNets. Hence, weface contradicting challenges, where interference mitigation demands transmit power ofsmall cell base stations to remain in lower range while wireless power transfer demandsthe opposite. Therefore, interference management in multi-tier network needs to beconsidered with a new approach to incorporate SWIPT in small cells.• Rate-Energy Trade-off in Downlink SWIPTAs discussed in Section 1.1, due to current receiver circuit limitations, UEs need tohave separate information decoding and energy harvesting circuits for SWIPT and thereceived signal has to be either switched in time domain or split in power domain [13,20]. Therefore, resource allocation techniques significantly differ in downlink SWIPT111.3. Open Issues in Cooperative and Heterogeneous Wireless Networks with Energy Harvestingand uplink WPC. In uplink WPC, throughput directly depends on energy transmissionin the downlink and hence maximizing the uplink throughput implies optimal sharingof time for downlink energy transmission and uplink information transmission [24].However, in downlink SWIPT, allocating more time/power to energy harvesting processresults in a lower throughput, whereas doing that to information decoding processresults in lower harvested energy and hence, obtaining the optimal trade-off is critical.It is termed as rate-energy trade-off [13, 20]. Moreover, when SWIPT is enabled insmall cells in a multi-tier network, co/cross-tier interference received by the small cellusers acts as an additional source of energy and increases their harvested energy onone hand, while degrading their throughput performance on the other [40]. Therefore,it is important to design interference-aware resource allocation framework that jointlyoptimizes achievable throughput and energy harvesting rate.• Rate-Energy Trade-off in HetNets with Renewable Energy HarvestingIncreasing throughput and reducing overall power cost of the network are among thekey objectives set for future wireless networks [6,8]. Intuitively, increasing throughputleads to increase in power cost and hence obtaining optimal rate-energy trade-off isone of the main design objectives in wireless networks. As discussed in Section 1.2,multi-tier HetNet architecture is envisioned as a key feature of future cellular networksto maximize total throughput of the system [6]. However, resource allocation in suchnetworks needs to be carefully designed to mitigate cross and co-tier interferences [33–36]. If macrocell and small cell base stations rely on same source of energy, offloadingusers to small cell in a multi-tier network can also reduce overall power consumptionof the network [7]. However, with the availability of diverse energy sources, the costof different energy sources vary and hence, the network should be carefully designedto obtain optimal trade-off between throughput performance and power cost of thenetwork. If the cost of energy source in small base stations is very high, multi-tierarchitecture may result in increased power cost of the network, which is not desirable.121.4. Related Work, Motivation, and ObjectiveThere are several approaches, explored in the literature, for minimizing power cost ofthe network. As discussed in Section 1.1, renewable energy harvesting in base stations isone way of minimizing overall power cost of the network. Nevertheless, if base stationsare designed to harvest energy from the nature, there are additional constraints inresource allocation, such as power allocation is constrained by the causality of energyarrival [30,31]. For robustness, energy harvesting base stations are also provided with abackup non-renewable power supply such as on-site generator or grid power supply [29].In that case, increasing throughput may lead to higher consumption of non-renewableenergy if the harvested energy is not sufficient. Therefore, obtaining optimal trade-offbetween throughput performance and power cost is a major research concern in suchenergy harvesting networks as well [41].One way of optimizing throughput performance and power cost in energy harvestingHetNet is dynamically switching base stations on and off with varying availability ofharvested energy and traffic condition of the network. It may be desirable to turnthe energy harvesting base station off if its harvested energy is very low and/or theparticular base station is under severe interference constraint, and/or number of activeusers in the corresponding cell is very low [42]. However, dynamic base station acti-vation imposes challenges in ensuring quality of service (QoS) demand of the users inthe switched off cells, which increases the complexity of resource allocation problem inHetNets with energy harvesting constraints.1.4 Related Work, Motivation, and ObjectiveHere, the prior works regarding the open issues in the context of cooperative and hetero-geneous wireless networks with energy harvesting are reviewed. The shortcomings in theexisting literature are highlighted to provide the motivations and objectives of our research.131.4. Related Work, Motivation, and Objective1.4.1 Doubly Near-Far Problem in Uplink WPCAs discussed in Section 1.3, “doubly near-far” problem arises in uplink WPC networks due todistance dependent attenuation in both downlink energy harvesting and uplink informationtransmission phases. There are several ways explored in the literature to overcome distancedependent attenuation in WPC networks. The authors in [43, 44] propose to overlay uplinkcommunication networks with microwave power stations (called beacons) for wireless trans-mission of energy to the UEs. With even distribution of such power beacons, all UEs in anetwork can harvest comparable amount of energy. However, it requires the UEs to havededicated antennas for microwave power receiver, which may not be desirable. Similarly, theauthors in [45] propose regular periodic use of dedicated vehicular RF source that moves inoptimal route to provide wireless energy to all UEs in the network. However, this solutionapproach increases the operational cost due to regular periodic vehicular movement.It is well-known that relay-based and user-based cooperation improves end-to-end chan-nel quality and capacity for UEs far from the access points, thus improving the coverageof communication networks [46–48]. Recently, relay-based and user-based cooperation hasgained much research attention in both downlink SWIPT and uplink WPC [49–59]. Thereare various ways of cooperation for relay nodes in wireless communication networks withdownlink SWIPT. The relay nodes can be designed to perform simultaneous informationand energy relaying to enhance both the information capacity and harvested energy of thedestination nodes by exploiting spatial diversity. In that case, the relay node needs to firstharvest energy from the information it is going to relay, and then forward that informationwith the harvested energy. Such cooperation is needed in the network where both the des-tination nodes and the relay nodes are energy constrained. If the relay nodes have theirown unconstrained power supply, they can be designed to perform simultaneous informa-tion relaying and power transfer to boost the information capacity and harvested energyof the destination nodes [49]. In this case, the relay nodes do not harvest energy from theinformation they are relaying. On the other hand, in the network where the destination141.4. Related Work, Motivation, and Objectivenodes are not energy constrained, the relay nodes can be designed to perform simultaneousinformation relaying and energy harvesting, which adds harvested energy as an incentive forrelaying information signal [50]. This in turn increases the number of wireless nodes willingto serve as a relay. New relaying protocols, for relay nodes capable of harvesting energy fromthe received wireless signal, are proposed in [50–52] while power allocation strategies in suchenergy harvesting relay nodes are discussed in [53,54].In WPC networks, the relay nodes can serve in both downlink energy harvesting anduplink information transmission phase. If the relay nodes do not want to utilize their ownenergy, they can be designed to forward energy signal from the access point to the destinationnodes in downlink energy harvesting phase. In that case, the relay node needs to first harvestenergy from the downlink signal and then forward it with the harvested energy, treating it likean information signal [55]. In this way, the destination nodes receive energy from multiplepaths, which is known as multi-path energy routing [56], and thus the harvested energy indownlink energy harvesting phase is much higher.However, if the relay nodes are willing to contribute their own energy, they can bedesigned as supplementary sources of energy signal during the downlink energy harvestingphase. Since the relay nodes do not spend any time in harvesting energy from transmissionof the access point, the destination nodes receive much higher energy to harvest. In theuplink, the relay nodes simply act as traditional relay. However, using dedicated relay nodesto transmit wireless charging signal in the downlink has not been well investigated in theliterature. The authors in [57–59] propose uplink cooperation among wireless-powered UEsto enhance their end-to-end channel capacity. This concept can also be applied to enhancethroughput of UEs far from the access point. In such wireless-powered uplink cooperativenetworks, uplink information transmission is highly dependent on downlink energy harvestingphase and hence joint uplink and downlink resource allocation is of high importance. Thisincreases the complexity of the resource allocation problems. However, the existing workssimplify the problem by either assuming a simple three-node network or ignoring power151.4. Related Work, Motivation, and Objectiveallocation in joint uplink and downlink resource allocation.The shortcomings in the existing literature motivate us to pursue the following objectivesin the context of uplink WPC:• Design WPC network with dedicated relay nodes to broadcast wireless charging signal,for distant users, in the downlink and then relay their information signal to the accesspoint in the uplink.• Joint optimization of downlink and uplink resource allocation for multiuser uplinkWPC networks with relay-based cooperation.• Joint optimization of downlink and uplink resource allocation for multiuser uplinkWPC network with user-based cooperation, for the scenarios where installing dedicatedrelay nodes is not feasible.The contributions in Chapter 2 address the first two objectives. The third objective istackled in Chapter 3. The contributions made regarding these objectives are explained atthe beginning of the corresponding chapters.1.4.2 Rate-Energy Trade-off and Interference Issues in HetNetswith SWIPTAs we discussed in Section 1.3, considering limitation in service distance and energy harvest-ing rate of wireless power transfer, application of SWIPT in small cells to serve low-powersensor-like devices is promising. Wireless power transfer within small transmission distanceshas been widely investigated in the literature [13,18,20]. However, multi-tier network archi-tecture is not considered in the aforementioned works. The authors of [15] propose integratingwireless power transfer capability in small cells of a HetNet to elongate the battery life oflow power miniature devices and discuss different opportunities and challenges. However,161.4. Related Work, Motivation, and Objectiveout-of-band energy transmission is considered and the issues of rate-energy trade-off andinterference management are not investigated.As discussed in Section 1.3, it is important to optimize the rate-energy trade-off inSWIPT. Most of the existing works in SWIPT have proposed different resource alloca-tion algorithms to maximize the throughput performance while ensuring minimum energyharvesting rate [40, 60]. The authors in [61] propose beamforming and resource allocationalgorithm to maximize energy harvesting rate while ensuring minimum throughput, but con-sider spatially separated energy harvesting and information decoding UEs. To the best ofour knowledge, joint optimization of energy harvesting rate and throughput together hasnot been considered in the literature. To attain the optimal rate-energy trade-off, it is im-portant to optimize the power-splitting/time-switching factors in SWIPT. Comparison oftime-switching and power-splitting approaches of SWIPT has been done in [13,20] by char-acterizing the rate-energy trade-off for these approaches. However, performance comparisonof these two approaches has not been done in a multi-tier network setting under interferenceconstraints.As discussed in Section 1.3, when SWIPT is considered in small cells of HetNets, itis essential to address the cross and co-tier interference issues. While interference signalsdeteriorate the throughput in traditional networks, they improve energy harvesting ratein SWIPT networks. The concept of harvesting energy from intended signal as well asunintended noise/interference signal is considered in [40,62]. However, in the aforementionedworks, interference signal is treated as a random variable. The authors in [63,64] demonstratehow transmit power allocation changes in a network with multiple transmitter-receiver pairswhen the receivers harvest energy from both information and interference signal. However,the aforementioned works do not consider HetNet architecture.Numerous research works have been done on interference-aware resource allocation inmulti-tier HetNets with co-channel deployment [33–36]. The resource allocation scheme tomitigate co-tier interference in dense deployment of small cells is proposed in [33] where171.4. Related Work, Motivation, and Objectivecross-tier interference is treated as white noise. Joint resource allocation and admission con-trol scheme to optimize the performance of both macro-tier and small-tier users, assumingnegligible co-tier interference, is proposed in [34]. The authors in [35] propose resource al-location algorithm based on game-theoretic approach where small cell users and macrocellusers compete with each other to maximize their own performance. A low-complexity inter-ference management scheme is proposed in [36] where the base stations in each tier evaluatethe interference received from only one user, called ‘reference user’, to incorporate effect ofoverall cross-tier interference. However, the aforementioned works do not consider SWIPTin HetNets. As discussed in Section 1.3, when SWIPT is enabled in small cells of HetNets,we face contradicting challenges, where interference mitigation demands transmit power ofsmall cell base stations to remain in lower range while wireless power transfer demands theopposite. Hence, interference management in multi-tier networks needs a new look to in-corporate SWIPT in small cells. To the best of our knowledge, interference-aware resourceallocation for SWIPT in small cells in a multi-tier HetNet has not been well investigated inthe literature.The shortcomings in the existing literature motivate us to pursue the following objectivesin the context of downlink SWIPT in HetNet:• Overcome the contradicting challenges of SWIPT in HetNets, where interference miti-gation demands the transmit power of small cell base stations to remain in lower rangewhile wireless power transfer demands the opposite.• Joint optimization of energy harvesting rate and achievable throughput in SWIPT toobtain optimal rate-energy trade-off under interference constraints of the HetNets.• Performance comparison of time-switching and power-splitting techniques of SWIPTin HetNets, under the interference constraints.The aforementioned objectives are addressed in Chapter 4. The contributions maderegarding these objectives are clarified at the beginning of the chapter.181.4. Related Work, Motivation, and Objective1.4.3 Rate-Energy Trade-off in HetNets with Renewable EnergyHarvestingAs discussed in Section 1.3, one way of optimizing throughput performance and power costin energy harvesting HetNet is dynamically switching base stations on and off with varyingavailability of harvested energy and traffic condition of the network. Dynamic activation ofbase stations to minimize the power cost of traditional wireless networks is well-investigatedin the literature. In [65], sleep duration of base station is optimized with varying trafficcondition to minimize the power cost of a network. However, multi-tier architecture andenergy harvesting capabilities are not considered in the work. The challenges of dynamicbase station activation in wireless networks with multi-tier architecture and energy harvestingcapability are discussed in [66].Dynamic base station activation and resource allocation in multi-tier networks is wellinvestigated in the literature [67–70]. To obtain optimal trade-off between throughput per-formance and power cost, in [69], maximization of energy efficiency is chosen as objective andbase station activation is optimized. With a similar objective, the authors of [70] optimizebase station activation jointly with user association. However, the aforementioned works donot consider energy harvesting capability in the base stations.The concept of optimizing base station activation policy to overcome the temporal mis-match between traffic demand and energy arrival is proposed in [71] for energy harvestingnetworks. To minimize the cost of non-renewable energy consumption, the authors of [72]optimize energy purchase policy, while the authors of [73] optimize base station activationpolicy jointly with energy purchase policy, considering traffic load at the base station andarrival of renewable energy. However, aforementioned works do not optimize resource allo-cation along with base station activation policy. The authors of [74] propose optimal basestation activation policy along with resource allocation to minimize grid power consumptionof hybrid powered base stations while ensuring QoS provision to the users. However, the191.4. Related Work, Motivation, and Objectiveaforementioned works do not consider multi-tier networks (or HetNets).Joint resource allocation and dynamic base station activation in energy harvesting Het-Nets has not been well-investigated in the literature. In most areas, macro base stations arealready deployed with grid power supply. However, there would be a need of deploying newsmall base stations to meet the growing demand of the hotspots. To reduce the consumptionof non-renewable energy sources with increasing base station density, small base stationsshould be equipped with renewable energy sources. Therefore, consideration of energy har-vesting capability in small base stations of a multi-tier network would be very important.In such a network, to minimize the non-renewable power consumption while maximizing thethroughput performance, it is essential to jointly consider base station activation policy alongwith resource allocation considering both interference and energy harvesting constraints. Tothe best of our knowledge, joint optimization of interference-aware and energy-aware resourceallocation with dynamic base station activation in energy harvesting HetNets has not beenwell-investigated in the literature. The authors of [75] optimize the “On” time of the energyharvesting base stations in a K-tier network. However, interference-aware resource alloca-tion and energy-aware power allocation is not considered. Base station on/off strategies, userassociation, and power control is studied in a two-tier network with energy harvesting basestations in [76]. However, a greedy technique is adopted by considering only one time period,and interference-aware frequency reuse among different tiers is not considered. Characteriza-tion of different performance metrics in a multi-tier network consisting of energy harvestingbase stations is presented in [77], where the energy harvesting base stations are active onlywhen they have enough harvested energy. However, optimization of base station activationstrategy is not considered.The shortcomings in the existing literature motivate us to pursue the following objectivesin the context of rate-energy trade-off in HetNets with energy harvesting:• Optimize the trade-off between throughput performance and power cost in energyharvesting HetNets while ensuring QoS provision to all users.201.5. Thesis Outline• Design interference-aware and energy-aware resource allocation jointly with dynamicactivation of energy harvesting base stations in HetNets.The contributions made in Chapter 5 revolve around the aforementioned objectives. Thecontributions made regarding these objectives are clarified at the beginning of the chapter.1.5 Thesis OutlineThe rest of this thesis is organized as follows:• In Chapter 2, we consider uplink WPC networks with relay-based cooperation wherethe relay node transmits energy charging signal in the downlink and relays the infor-mation signal in the uplink. Considering the limitation on available energy at the relaynode and the total transmission time, we propose different resource allocation frame-works for two different relay-based harvest-then-transmit scenarios. First, we proposean iterative algorithm to optimize time and relay node power allocation (for downlinkwireless charging and uplink data transmission/relaying) for both scenarios. Then,we jointly optimize time and power allocation for one scenario. Optimization prob-lems are solved using convex optimization techniques. From the simulation results, weevaluate the throughput performance of the UEs, evaluate the fairness of the systemusing Jain’s fairness index, and examine the resource allocated for downlink energyharvesting and uplink information transmission phases. It is observed that most of theavailable resources (transmission time and relay node energy) are allocated for wire-less energy harvesting which is similar to that observed for downlink SWIPT in theexisting literature. Simulation results on comparison of different relay-based scenar-ios reveal interesting insights and demonstrate remarkable improvement of throughputand fairness performance of uplink WPC networks in the presence of relay node.• In Chapter 3, we study joint resource allocation for downlink energy transmission as211.5. Thesis Outlinewell as uplink information transmissions in a wireless-powered uplink cooperative net-work. To overcome the performance loss of the UEs that are far from the access point,cooperation among the UEs is considered in the uplink. As downlink power allocationaffects the energy harvesting rate of the UEs and hence their uplink throughput, down-link and uplink resource allocation are jointly performed. The joint optimization prob-lem of power allocation, subcarrier allocation, and relay selection is a mixed-integernonlinear programming (MINLP) problem. Nevertheless, we obtain the optimal so-lution based on dual decomposition technique and relaxation of the binary integerconstraints. From the simulation results, we evaluate the sum throughput and energyefficiency of the network. Simulation results show the effectiveness of our proposedscheme and performance improvements over the benchmark schemes.• In Chapter 4, we perform downlink resource allocation for SWIPT in small cells un-derlaying a macrocell in a two-tier HetNet. We consider both time-switching andpower-splitting approaches of SWIPT. We optimize downlink transmit power of smallcell base stations along with time-switching/power-splitting variables for SWIPT tojointly maximize energy harvesting rate and achievable throughput of small cell userswhile ensuring minimum throughput of the macrocell user. To jointly optimize achiev-able throughput and energy harvesting rate of small cell users, we use scalarizationtechnique of multi-objective programming. We formulate a resource allocation prob-lem with the objective of maximizing weighted sum of normalized throughput andenergy harvesting rate. In the time-switching approach, the resource allocation prob-lem is a MINLP problem. To solve the MINLP problem, we relax the binary integerconstraint and then identify the condition at which the obtained solution satisfies thatconstraint. In both the time-switching and power-splitting approaches, when co-tierinterference is non-negligible, the formulated problem is solved sub-optimally by iter-atively maximizing the minorant of the non-convex objective function. A special casewith negligible co-tier interference is considered in time-switching approach and the221.5. Thesis Outlineoptimal solution is obtained by using convex optimization techniques. From the sim-ulation results, we evaluate sum-throughput and sum-energy harvesting rate of smallcell users. Simulation results demonstrate that when macrocell users have flexible in-terference tolerance levels in time-switching approach, energy harvesting rate of smallcell users is significantly enhanced. The results also highlight the improvement in en-ergy harvesting rate in the presence of co-tier interference signal and reveal interestingtrade-off in achievable throughput and energy harvesting rate.• In Chapter 5, we jointly optimize resource allocation with dynamic activation of en-ergy harvesting base stations in a two-tier HetNet. We consider both energy harvestingconstraints and interference constraints along with time-variation in channel condition,user activity, and energy arrival. We optimize the trade-off between throughput perfor-mance of the small cell (or hotspot) users and the associated power cost by maximizingthe net reward, where positive reward is associated with achievable throughput of thehotspot users and negative reward with the corresponding non-renewable power con-sumption. QoS requirements of hotspot users as well as macrocell users are consideredin the optimization problem. Assuming the availability of non-causal information, wepropose offline resource allocation algorithm using discrete binary particle swarm op-timization and dual decomposition technique. Assuming the availability of statisticalinformation of future values, we propose dynamic programming-based online algorithm.Finally, we propose simple and greedy online algorithm assuming lack of any kind offuture information. From the simulation results, we evaluate the net reward generatedby different algorithms, throughput performance of hotspot users, and the correspond-ing non-renewable power consumed. Simulation results demonstrate the performancesof the proposed offline, dynamic programming-based online, and greedy online algo-rithms and highlight the scenarios where performance of the proposed algorithms aresignificantly better than the baseline schemes.231.5. Thesis Outline• In Chapter 6, summary and concluding remarks are provided and possible future re-search directions are discussed.24Chapter 2Resource Allocation in UplinkWireless-Powered CommunicationNetworks with Relay-basedCooperationIn this chapter, we consider uplink WPC network and address the challenge of joint al-location of resources for downlink energy harvesting and uplink information transmissionwhen dedicated relay nodes are deployed to mitigate the “doubly near-far” problem. Theaccomplished works and research contributions of this chapter are briefly described in thefollowing.2.1 Accomplished Works and Research ContributionsIn this chapter, we consider a network where the uplink communication of UEs is pow-ered by wireless energy harvesting, based on the concept of harvest-then-transmit [24]. Toenhance the performance of UEs far from the access point (far-UEs) and improve fairness(and thereby mitigate the doubly near-far problem), we utilize relay-based cooperation insuch WPC network. Relay nodes are designed to independently broadcast wireless chargingsignal for far-UEs in the downlink and then relay their information signal to access pointin the uplink. For such relay-based WPC, we propose resource allocation methods (i.e.,252.1. Accomplished Works and Research Contributionsmethods for allocation of downlink energy harvesting/uplink information transmission timesand downlink/uplink transmit power of relay node) with the objective of maximizing totalnetwork throughput. Note that, without relays, fairness among the UEs (e.g., in terms ofuplink capacity) can be maximized by using max-min or proportional fair objective function.However, it is well-known that, with such an objective, the overall sum-throughput would re-duce [24,78,79]. Therefore, we utilize relay-based cooperation to improve performance of thefar-UEs, which leads to better fairness without losing the overall throughput performance ofthe network. In the rest of the chapter, allocation of downlink energy harvesting and uplinkinformation transmission times of the UEs is referred to as time allocation. Allocation ofuplink and downlink relay node transmit power is referred to as power allocation.We investigate resource allocation in two relay-based harvest-then-transmit scenarios de-pending on whether the far-UEs harvest energy from the RF transmission of both relaynode and access point (Scenario I) or from the relay node only (Scenario II). In all cases, weformulate sum-throughput maximization problems for resource allocation. For Scenario I,due to computational intractability of joint power and time allocation problem, we proposean iterative power and time allocation algorithm. For Scenario II, we jointly optimize timealong with transmit power of the relay node. Since the formulated problem for joint timeand power allocation is non-convex, we convert it into a convex joint time and energy allo-cation problem by implementing change of variables. The problem is solved in closed-formby solving Karush-Kuhn-Tucker (KKT) conditions on the Lagrangian of the correspondingconvex optimization problem. We also propose an iterative power and time allocation algo-rithm for this scenario. We analyze and compare the proposed resource allocation methodsfor WPC networks with relay-based cooperation under both Scenario I and Scenario II.Also, we compare the performance, of WPC networks with relay-based cooperation to thatwithout the relay nodes, in terms of resource allocation, throughput, and fairness. To thisend, we identify the suitable resource allocation method for WPC networks with relay-basedcooperation.262.2. System Model and AssumptionsThe rest of the chapter is organized as follows. The system model and assumptions areexplained in Section 2.2. Section 2.3 presents the problem formulation and solution approach.Performance evaluation results are presented and analyzed in Section 2.4.2.2 System Model and AssumptionsWireless-powered communication networks with relay-based cooperationWe consider an uplink communication network (Fig. 2.1) in which uplink transmission ofUEs is powered by the energy harvested from wireless charging signal transmitted by the APand/or the relay node. We particularly consider harvest-then-transmit protocol [24] to poweruplink transmission of UEs. In this protocol, a fraction of each time frame is dedicated totransmit wireless charging signal from the AP/relay nodes and is termed as downlink energyharvesting (DEH) time. Uplink data transfer is then performed by UEs using the harvestedenergy in the remaining time termed as uplink information transmission (UIT) time. In theDEH phase, the energy harvesting circuit (e.g., P2110 Powercaster receiver [14]) harvestsenergy from the received wireless charging signal. The energy harvesting and conversion lossis indicated by energy harvesting efficiency η1. η2 fraction of the harvested energy is used foruplink transmission and remaining fraction is lost in receiver circuit power consumption2.For simplicity, we assume that all the energy harvested during DEH time is used for uplinktransmission in UIT time.An amplify-and-forward relay node is installed at a fixed distance from the AP to servethe far-UEs. The UEs served by the AP are termed as near-UEs from now on. We assumeprior knowledge on the number of UEs with some data to transmit in the uplink. We considerthat there are N near-UEs and K far-UEs. The total of DEH and UIT time is denoted byT . The DEH time, in which the AP and the relay node send wireless charging signal and theUEs harvest energy from it, is denoted by t(d). The remaining uplink transmission duration2Note that we use fixed η2 which causes the receiver circuit power consumption to become proportionalto the harvested energy.272.2. System Model and AssumptionsFigure 2.1: Uplink WPC network with relay-based cooperation.t(d)Tt1(n) ... tN(n) t1(f) ... tK(f)DEH time (All UEs)UIT time(Near-UEs)UIT time(Far-UEs)R BSUERFigure 2.2: Relay-based harvest-then-transmit protocol.is shared by both near and far-UEs to transmit their data to the AP. The time dedicated forUIT of each near-UE is denoted by ti(n), i = 1, 2, ..., N and that of each far-UE is denotedby tj(f), j = 1, 2, ..., K, as shown in Fig. 2.2. Therefore,t(d) +N∑i=1ti(n) +K∑j=1tj(f) ≤ T. (2.1)The transmit power of the AP is PA. Energy available at the relay node per transmissionblock is Emax. Note that such a relay node may be operated by battery or by energy harvestedfrom the nature. Therefore, transmit power of the relay node needs to be optimally allocatedto maximally utilize its available energy. In this work, we assume to have prior knowledgeof channel conditions. Channel power gains of the link between AP and ith near-UE, relaynode and ith near-UE, AP and relay node, AP and jth far-UE, and relay node and jth far-UEare denoted by gA,i, gR,i, gA,R, hA,j, and hR,j, respectively.282.2. System Model and AssumptionsRelay-based harvest-then-transmit scenariosWe consider two different scenarios:• Scenario I : The relay node transmits a power beacon in the downlink and acts asa traditional relay node in the uplink. In the downlink, both the AP and the relaynode independently broadcast their own wireless charging signal in DEH time. Sincethe far-UEs receive signal from the AP transmission as well, they harvest energy fromAP as well as relay node transmission. The near-UEs harvest energy from the APtransmission only since the relay node antenna directs the wireless charging signaltowards far-UEs. In the uplink, the relay node simply amplifies and forwards theuplink information of each far-UE to the AP in their UIT time while near-UEs makedirect uplink transmission to the AP in their UIT time.• Scenario II : Similar to Scenario I, the relay node transmits a power beacon in thedownlink and acts as a traditional relay node in the uplink. However, because of highpath-loss in the link between the AP and far-UEs, the energy harvested by far-UEsfrom the AP transmission is assumed to be negligible. In other words, far-UEs areassumed to harvest energy only from the relay node transmission.Since the relay node and the AP transmit wireless charging signal simultaneously, itis necessary to study the resource allocation and the network performance when far-UEsharvest energy from both the transmissions. Nevertheless, we will see later that the optimalsolution of resource allocation problem in Scenario I is analytically intractable. Therefore,Scenario II is considered with a simplifying assumption to make the resource allocationproblem computationally tractable. Next, we will discuss how to model the two scenarios.Modeling scenario IIn Scenario I, the relay node transmits its own wireless charging signal along with the AP inthe DEH time. Far-UEs harvest energy from both the relay node and the AP transmission292.2. System Model and Assumptionswhereas near-UEs harvest energy from the transmission from AP only. We will now discussDEH and UIT processes separately in the following.Downlink wireless charging/energy harvesting: In DEH time t(d), the AP broadcastswireless charging signal with power PA. At the same time, the relay node also broadcastsits wireless charging signal with power P(rd). Energy harvested by each near and far-UE aregiven byEi(n) = η1PAgA,it(d), ∀i (2.2)Ej(f) = η1(PAhA,j + P(rd)hR,j)t(d), ∀j. (2.3)Uplink information transmission: Both near and far-UEs harvest certain amount ofenergy, given in (2.2) and (2.3), which they use for uplink transmission. In the following, wewill discuss UIT of near and far-UEs separately.UIT of Near-UE : The transmit power of a near-UE i is given by: Pi(n) = η2Ei(n)/ti(n), ∀i.The throughput of that UE in bits/second/Hertz (bps/Hz) is thus given byR(sc-I)i(n) =ti(n)Tlog2(1 +gA,iPi(n)Nw), ∀i (2.4)where Nw is additive white Gaussian noise (AWGN) power at the AP. From (2.2) and (2.4),we can writeR(sc-I)i(n) =ti(n)Tlog2(1 +νit(d)ti(n)), ∀i (2.5)where νi =ηPAg2A,iNwand η = η1η2.UIT of Far-UE : The transmit power of each far-UE is given by: Pj(f) =η2Ej(f)tj(f)/2, ∀j,where the factor of 2 is introduced due to half-duplex relaying. In the second phase, signalreceived from each far-UE is amplified and forwarded to the AP by the relay node withpower Pj(ru). Signal-to-noise ratio (SNR) of the signal received at the AP, corresponding to302.2. System Model and Assumptionseach far-UE is given bySNRj(f) =(Pj(ru)Pj(f)gA,RhR,j)/(Pj(f)hR,j +Nw)Nw(1 +Pj(ru)gA,RPj(f)hR,j+Nw) , ∀j. (2.6)Assuming that the noise power is negligible in comparison to signal power, we ignore thehigher order term (N2w) in the denominator. From (2.3) and (2.6),SNRj(f) =fα(j)(P(rd))fβ(Pj(ru))t(d)Nw(fα(j)(P(rd))t(d) + fβ(Pj(ru))tj(f)) , ∀j (2.7)where fα(j)(P(rd)) = 2ηhR,j(PAhA,j + P(rd)hR,j)is a function of power allocation variableP(rd) and fβ(Pj(ru)) = Pj(ru)gA,R is a function of power allocation variable Pj(ru). Using (2.7),the throughput of each far-UE in bps/Hz can thus be given byR(sc-I)j(f) =tj(f)2Tlog2(1 + SNRj(f)). (2.8)Since the available energy at the relay node is limited to Emax in each transmission block,we haveP(rd)t(d) +K∑j=1Pj(ru)tj(f)2≤ Emax. (2.9)Modeling scenario IIIn Scenario II, we assume that the energy harvested by far-UE from the AP transmissionis negligible in comparison to that harvested from the relay node transmission. The energyharvested by each near and far-UE in the DEH time are given byEi(n) = η1PAgA,it(d), ∀i (2.10)Ej(f) = η1P(rd)hR,jt(d), ∀j. (2.11)312.2. System Model and AssumptionsThe UEs make uplink transmission using the energy harvested during the DEH time. Fol-lowing similar analysis as in the case of Scenario I, the uplink throughput of each near-UEis given byR(sc-II)i(n) =ti(n)Tlog2(1 +νit(d)ti(n)), ∀i. (2.12)Similarly, SNR of the signal received at the AP (corresponding to each far-UE) is given bySNRj(f) =2ηh2R,jgA,RPj(ru)P(rd)t(d)Nw(gA,RPj(ru)tj(f) + 2ηh2R,jP(rd)t(d)), ∀j. (2.13)Using (2.13), the throughput of each far-UE in bps/Hz can thus be given byR(sc-II)j(f) =tj(f)2Tlog2(1 + SNRj(f))=tj(f)2Tlog2(1 +δαjβP(rd)Pj(ru)t(d)αjP(rd)t(d) + βPj(ru)tj(f)), ∀j(2.14)where αj = 2ηh2R,j, β = gA,R, and δ =1Nw. Since the energy available at the relay node islimited to Emax in each transmission block, (2.9) defines the total energy constraint at therelay node.In this chapter, we will determine the optimal allocation of DEH and UIT time alongwith downlink/uplink relay node transmit power by formulating an optimization problemwith the objective of maximizing the sum-throughput of the network. For Scenario I, due tothe complexity of the problem, we will use iterative algorithm for resource allocation, wheretime allocation is optimized for given power allocation and power allocation is optimized forgiven time allocation. For Scenario II, we will perform joint allocation of DEH and UIT timealong with downlink/uplink transmit power. However, for fair comparison among the twoscenarios, we use the iterative algorithm for resource allocation in Scenario II as well. Inthe rest of the chapter, power allocation refers to allocation of uplink and downlink transmitpower at the relay node while time allocation refers to allocation of DEH time and UIT timeof all UEs.322.3. Problem Formulations and Solution Approaches2.3 Problem Formulations and Solution Approaches2.3.1 Joint Power and Time Allocation: Scenario IIn order to optimize DEH and UIT time along with relay node transmit power, we formulatethe sum-throughput maximization problem as follows:maximizet(d),t(n),t(f),P(rd),P(ru)∑Ni=1R(sc-I)i(n) +∑Kj=1R(sc-I)j(f)subject toC1 : t(d) +∑Ni=1 ti(n) +∑Kj=1 tj(f) ≤ TC2 : P(rd)t(d) +∑Kj=1 Pj(ru)tj(f)2≤ EmaxC3 : t(d) ≥ 0; ti(n) ≥ 0, ∀i; tj(f) ≥ 0, ∀jC4 : P(rd) ≥ 0; Pj(ru) ≥ 0, ∀j(2.15)where t(n) = [t1(n), t2(n), ..., tN(n)], t(f) = [t1(f), t2(f), ..., tK(f)], and P(ru) = [P1(ru), P2(ru), ...,PK(ru)]. C1 is the constraint on total time (given by (2.1)) and C2 is energy constraint atthe relay node (given by (2.9)). C3 and C4 are non-negativity constraints on time and powervariables, respectively. The objective function of the problem in (2.15) is highly complicatedin terms of the optimization variables and its optimal solution is analytically intractable.We simplify the problem by setting P(rd) = Pj(ru) = PR. The throughput of far-UE given in(2.8) can be re-written as:R(sc-I)j(f) =tj(f)2Tlog2(1 +2ηhR,j (PAhA,j + PRhR,j)PRgA,Rt(d)Nw(2ηhR,j (PAhA,j + PRhR,j) t(d) + PRgA,Rtj(f))) , ∀j. (2.16)We can see that, the throughput expressions of far-UEs are still non-convex and in-tractable for joint power and time allocation. Thus, we propose to solve this problem intwo phases iteratively. In one phase, for a given power allocation, optimal time allocationis performed while in another phase, for a given time allocation, optimal power allocation isperformed.332.3. Problem Formulations and Solution ApproachesPower allocationFor a given time allocation, the throughput expression of a far-UE given in (2.16) can bere-written as:R(sc-I)j(f) =tj(f)2Tlog2(1 +αj(1)PR + αj(2)P2Rαj(3) + αj(4)PR), ∀j (2.17)whereαj(1) = 2ηhR,jhA,jgA,RPAt(d) αj(2) = 2ηh2R,jgA,Rt(d)αj(3) = Nw2ηhR,jPAhA,jt(d) αj(4) = Nw(2ηh2R,jt(d) + gA,Rtj(f)).We know that the throughput of near-UE does not depend on relay node transmit power.Therefore, the sum-throughput maximization problem in (2.15) becomesmaximizePR∑Kj=1 R(sc-I)j(f)subject toC˜2 : PR(t(d) +∑Kj=1tj(f)2)≤ EmaxC˜4 : PR ≥ 0(2.18)where C˜2 is energy constraint at the relay node and C˜4 is non-negativity constraint on thepower allocation variable. The objective function is still non-convex in terms of the opti-mization variable. However, a careful inspection of the objective function and the constraintleads us to the optimal solution for power allocation.Lemma 1 : At optimality, the energy constraint C˜2 of the optimization problem in (2.18)is tightly satisfied, i.e.,PR =Emax(t(d) +∑Kj=1tj(f)2) . (2.19)Proof : The objective function is monotonically increasing in PR which can be verified byshowing∂R(sc-I)j(f)∂PR> 0. The constraint C˜2 is also monotonically increasing in PR. Therefore,the constraint C˜2 must hold with equality at optimality. This completes the proof. Thus, (2.19) is used to determine the optimal constant relay node transmit power. Next,342.3. Problem Formulations and Solution Approacheswe will see how to determine optimal time allocation for given constant power allocation.Time allocationFor given power allocation PR, the throughputs of far-UEs given in (2.16) can be re-writtenas:R(sc-I)j(f) =tj(f)2Tlog2(1 +δαjβt(d)αjt(d) + βtj(f)), ∀j, where (2.20)αj = 2ηhR,j (PAhA,j + PRhR,j) , β = PRgA,R, δ =1Nw. (2.21)Then the sum-throughput maximization problem in (2.15) becomesmaximizet(d),t(n),t(f)∑Ni=1R(sc-I)i(n) +∑Kj=1R(sc-I)j(f)subject to C1, C3.(2.22)The throughput of near-UE given by (2.5) and far-UE given by (2.20) can be proven tobe convex functions of optimization variables using the concavity of log function and theperspective operation [80]. Hence, the optimization problem in (2.22) is convex in terms oftime variables and can be solved optimally by using convex optimization techniques [80].The partial Lagrangian of the problem in (2.22) is given byL(t(d), t(n), t(f), λ) =N∑i=1R(sc-I)i(n) +K∑j=1R(sc-I)j(f) − λ(t(d) +N∑i=1ti(n) +K∑j=1tj(f) − T)(2.23)where λ is non-negative Lagrange multiplier corresponding to the constraint C1. The con-straint C3 is not included in the Lagrangian and will be satisfied later (in Lemma 2). UsingKKT stationarity conditions and differentiating (2.23) with respect to t(d), ti(n), and tj(f),352.3. Problem Formulations and Solution Approacheswe obtain the following equations, respectively:N∑i=1νi1 + xi+K∑j=1δαj2(1 +δβyj1+yj)(1 + yj)2= λ∗T ln(2) (2.24)ln(1 + xi)− xi/(1 + xi) = λ∗T ln(2), ∀i (2.25)ln(1 +δβyj1 + yj)− δβyj(1 +δβyj1+yj)(1 + yj)2= 2λ∗T ln(2), ∀j (2.26)where xi =νit∗(d)t∗i(n), ∀i and yj = αjt∗(d)βt∗j(f), ∀j. Also, t∗(d), t∗(n), t∗(f), and λ∗ are primal and dualoptimal solutions of the problem in (2.22).Lemma 2 : xi and yj are both constants for all values of i and j if t∗(d), t∗i(n), t∗j(f) > 0, i.e.,x = xi =νit∗(d)t∗i(n),∀i; y = yj =αjt∗(d)βt∗j(f),∀j. (2.27)Proof : Let us define: f1(xi) = ln(1 + xi) − xi1+xi . Differentiating f1(xi) with respect toxi, we obtain: f′1(xi) =xi(1+xi)2 . If t∗(d), t∗i(n) > 0, then xi > 0 and f′1(xi) > 0 which meansf1(xi) is an increasing function. To satisfy f1(xi) = λ∗T ln(2) = constant, given in (2.25), xishould be a constant. Similarly, we can prove that yj should be a constant. This completesthe proof. Using Lemma 2, (2.24) to (2.26) can be re-written as∑Ni=1 νi1 + x+δ∑Kj=1 αj2(1 + δβy1+y)(1 + y)2= λ∗T ln(2) (2.28)ln(1 + x)− x/(1 + x) = λ∗T ln(2) (2.29)ln(1 +δβy1 + y)− δβy(1 + δβy1+y)(1 + y)2= 2λ∗T ln(2). (2.30)Thus from the set of N + K + 1 equations represented by (2.24) to (2.26), we obtain a setof three non-linear equations (2.28) to (2.30) for three unknown variables x, y, and λ∗ whichcan be uniquely solved. It should be noted that the number of equations to be solved is362.3. Problem Formulations and Solution Approachesconstant regardless of the number of UEs in the system.Lemma 3 : The primal feasibility condition (constraint C1) is satisfied with strict equality,i.e.,t∗(d) +N∑i=1t∗i(n) +K∑j=1t∗j(f) − T = 0. (2.31)Proof : We know that x, y > 0 (see Lemma 2). Since νi, αj, δ, β > 0, ∀i, j, from (2.28),we can say that λ∗ > 0. Then, to satisfy the KKT complementary slackness condition[λ∗(t∗(d) +∑Ni=1 t∗i(n) +∑Kj=1 t∗j(f) − T ) = 0], the primal feasibility condition must be satisfiedwith strict equality. This completes the proof. Proposition 1 : The optimal DEH and UIT time allocation, denoted by t∗(d), t∗i(n), and t∗j(f)are given byt∗(d) =T1 +∑Ni=1 νix∗ +∑Kj=1 αj/βy∗, t∗i(n) =νit∗(d)x∗, ∀i, and t∗j(f) =αjt∗(d)βy∗, ∀j (2.32)where x∗ and y∗ are the unique solutions of (2.28) to (2.30).Proof : When the solution of (2.28) to (2.30) are obtained, (2.27) can be used in (2.31)to obtain t∗(d). Then, t∗i(n) and t∗j(f) are obtained from the definitions of x and y in (2.27).This completes the proof. Hence, t∗(d) gives the optimal DEH time, t∗i(n) gives the optimal UIT times of near-UEs,and t∗j(f) gives the optimal UIT times of far-UEs to maximize the sum-throughput of thenetwork. We see that the UIT times of all UEs depend on channel power gain of their linksto the AP and the relay node.Iterative power and time allocationAlgorithm 1 summarizes the iterative power and time allocation procedure. Given theinitial time allocation, relay node transmit power is optimally determined. Then the optimaltime allocation is determined using the obtained relay node transmit power. This process is372.3. Problem Formulations and Solution Approachesrepeated till convergence is reached.Algorithm 1 Iterative Power and Time Allocation AlgorithmRequire: Initialize l = 0, t(l)(d),t(l)i(n), and t(l)j(f).1: repeat2: Determine relay node transmit power, P(l)R with (2.19)3: Define νi, αj, β, and δ using (2.21)4: Solve (2.28) to (2.30) to find x∗ and y∗5: Find t∗(d), t∗i(n), and t∗j(f) using (2.32)6: Update l← l + 1; t(l)(d) = t∗(d), t(l)i(n) = t∗i(n), and t(l)j(f) = t∗j(f)7: until Convergence of∑Ni=1R(sc-I)i(n) +∑Kj=1R(sc-I)j(f)2.3.2 Joint Power and Time Allocation: Scenario IIIn this section, we jointly allocate transmit power of the relay node along with DEH andUIT times of all UEs with the objective of maximizing sum-throughput in Scenario II of theproposed relay-based WPC network. The sum-throughput maximization problem is writtenasmaximizet(d),t(n),t(f),P(rd),P(ru)∑Ni=1R(sc-II)i(n) +∑Kj=1R(sc-II)j(f)subject to C1, C2, C3, C4.(2.33)The objective function and constraint C2 are not convex. We will see subsequently that it ispossible to jointly allocate time and power optimally in Scenario II. However, for the sake offair comparison between Scenarios I and II, we allocate time and power using same iterativealgorithm proposed for Scenario I described here briefly.Iterative power and time allocationFor a given initial time allocation, power allocation can be performed using the approachsimilar to that in Scenario I. Setting P(rd) = Pj(ru) = PR, the optimal power allocation forScenario II is determined by using (2.19).382.3. Problem Formulations and Solution ApproachesWith the given relay node transmit power PR, the throughput of far-UEs given in (2.14)can be re-written asR(sc-II)j(f) =tj(f)2Tlog2(1 +δα˜jβ˜t(d)α˜jt(d) + β˜tj(f)), ∀j (2.34)where α˜j = 2ηh2R,jPR and β˜ = gA,RPR. It should be noted that the throughput expressionis similar to that of Scenario I given in (2.20). The throughput expression of near-UEs inScenario II given in (2.12) is same as that of Scenario I given in (2.5). Hence the optimaltime allocation can be obtained by using the similar approach as in Scenario I. Therefore,joint power and time allocation can be performed iteratively as defined in Algorithm 1.Optimal power and time allocationTo solve the problem in (2.33) optimally, we implement the following changes of variables:E(rd) = P(rd)t(d), Ej(ru) = Pj(ru)tj(f)/2, ∀j. (2.35)Here, E(rd) and Ej(ru) are the energy allocated at relay node for transmitting wireless chargingsignal and relaying uplink information signal of each far-UE, respectively. Using (2.35), wecan re-write (2.14) asR˜(sc-II)j(f) =tj(f)2Tlog2(1 +δαjβE(rd)Ej(ru)tj(f)2(αjE(rd) + 2βEj(ru))) . (2.36)392.3. Problem Formulations and Solution ApproachesThe sum-throughput maximization problem in (2.33) now becomesmaximizet(d),t(n),t(f),E(rd),E(ru)∑Ni=1 R(sc-II)i(n) +∑Kj=1 R˜(sc-II)j(f)subject to C1, C3C ′2 : E(rd) +∑Kj=1 Ej(ru) ≤ EmaxC ′4 : E(rd) ≥ 0; Ej(ru) ≥ 0, ∀j(2.37)where E(ru) = [E1(ru), E2(ru), ..., EK(ru)]. The joint power and time allocation problem nowbecomes a joint energy and time allocation problem. C ′2 is the energy constraint of therelay node equivalent to C2 of problem in (2.33). C′4 is the non-negativity constraint onenergy allocation variables. The objective function of the problem in (2.37) is concave.The proof of convexity is provided in Appendix A. The modified constraint C ′2 as well asother constraints are affine in terms of the optimization variables. Therefore, it is a convexoptimization problem and can be solved by using convex optimization techniques. Thepartial Lagrangian of the problem in (2.37) is given byL(t(d), t(n), t(f), E(rd),E(ru), µ1, µ2) =N∑i=1R(sc-II)i(n) +K∑j=1R˜(sc-II)j(f)− µ1(t(d) +N∑i=1ti(n) +K∑j=1tj(f) − T)− µ2(E(rd) +K∑j=1Ej(ru) − Emax) (2.38)where µ1 and µ2 are non-negative Lagrange multipliers corresponding to constraints C1and C ′2, respectively. The non-negativity constraints C3 and C′4 are not included in theLagrangian and will be satisfied later (in Lemma 4). Since the problem is convex, we canfind its optimal solution by using KKT conditions [80]. Let us denote the primal anddual optimality values of the problem in (2.37) as t∗(d), t∗(n), t∗(f), E∗(rd),E∗(ru), µ∗1, and µ∗2. Bydifferentiating (2.38) w.r.t. t(d), ti(n), tj(f), E(rd), and Ej(ru), respectively and using KKT402.3. Problem Formulations and Solution Approachesstationarity conditions, we obtainN∑i=1νi1 + xi= µ∗1T ln(2) (2.39)ln(1 + xi)− xi1 + xi= µ∗1T ln(2), ∀i (2.40)ln(1 + yj)− yj1 + yj= 2µ∗1T ln(2), ∀j (2.41)K∑j=1δαj(1− zj)21 + yj= 2µ∗2T ln(2) (2.42)2δβz2j1 + yj= 2µ∗2T ln(2), ∀j (2.43)where xi =νit∗(d)t∗i(n), aj =1αjE∗(rd)yj =δ(aj + bj)t∗j(f), bj =12βE∗j(ru)zj =bjaj + bj.(2.44)Lemma 4 : xi, yj, and zj are constant and independent of i or j if t∗(d), t∗i(n), t∗j(f), E∗(rd),E∗j(ru) > 0, i.e.,x = xi =νit∗(d)t∗i(n), ∀i, y = yj = δ(aj + bj)t∗j(f), ∀j, z = zj = bjaj + bj, ∀j. (2.45)The proof is similar to the proof of Lemma 2 and is omitted. Using Lemma 4, (2.39) to(2.43) can be re-written, respectively, as∑Ni=1 νi1 + x= µ∗1T ln(2) (2.46)ln(1 + x)− x1 + x= µ∗1T ln(2) (2.47)ln(1 + y)− y1 + y= 2µ∗1T ln(2) (2.48)∑Kj=1 δαj(1− z)21 + y= 2µ∗2T ln(2) (2.49)412.3. Problem Formulations and Solution Approaches2δβz21 + y= 2µ∗2T ln(2). (2.50)In this way, from N + 2K + 2 equations represented in (2.39) to (2.43), we achieve fiveequations shown in (2.46) to (2.50) with five variables which can be solved in closed form.It should be noted that the number of equations to be solved remains constant regardlessof the number of UEs. Next, we present the closed-form solution of the above mentionedequations.Lemma 5 : The solution of (2.46) to (2.50) is given byx∗ =∑Ni=1 νi − 1W(e−1(∑Ni=1 νi − 1)) − 1, µ∗1 = ∑Ni=1 νi(1 + x∗)T ln(2) (2.51)y∗ = −1− 1W(−e−(2µ∗1T ln(2)+1)) , z∗ = 2∑Kj=1 αj −√8∑Kj=1 αjβ2∑Kj=1 αj − 4β(2.52)where W(.) is Lambert W-function [81]. See Appendix B for the proof.Lemma 6 : The primal feasibility KKT conditions (constraints C1 and C′2) are satisfiedwith strict equality, i.e.,t∗(d) +N∑i=1t∗i(n) +K∑j=1t∗j(f) − T = 0, E∗(rd) +K∑j=1E∗j(ru) − Emax = 0. (2.53)The proof is similar to that of Lemma 3 and is omitted. Using the results of Lemma 4,5, and 6, we obtain the optimal time and energy allocation in closed-form in the following.Proposition 2 : The optimal time and relay node energy allocation denoted by t∗(d), t∗(n),t∗(f), E∗(rd), and E∗(ru) are given byE∗(rd) =2βz∗Emax2βz∗ + (1− z∗)∑Kj=1 αj , E∗j(ru) = (1− z∗)αjEmax2βz∗ + (1− z∗)∑Kj=1 αj , ∀j (2.54)422.4. Performance Evaluation Resultst∗j(f) =z∗ (1− z∗) 2δβαjEmaxy∗(2βz∗ + (1− z∗)∑Kj=1 αj) , ∀j, t∗(d) =T −∑Kj=1 t∗j(f)1 +∑Ni=1 νix∗, t∗i(n) =νit∗(d)x∗, ∀i.(2.55)See Appendix C for the proof. The solution shows that the time allocated for UIT ofeach far-UE and energy allocated at the relay node for information relaying are proportionalto channel gain of the link between that UE and the relay node along with energy availableat the relay node. Similarly, the time allocated for UIT of each near-UE is proportional tochannel gain of the link between that UE and the AP along with the AP transmit power.Finally, we can obtain the optimal relay node power allocation from the optimal time andenergy allocation as follows:P ∗(rd) = E∗(rd)/t∗(d), P∗j(ru) = 2E∗j(ru)/t∗j(f), ∀j.Thus, we jointly obtain the optimal time and relay node power allocation solution in closed-form for Scenario II.2.4 Performance Evaluation ResultsWe evaluate the performance of the resource allocation algorithms proposed for differentscenarios of WPC networks with relay-based cooperation. We also compare the performanceof the WPC networks with relay-based cooperation to that without the relay nodes [24].2.4.1 Simulation ParametersThe channel gain for the link between source and destination is computed as hs,d = 10−3d−α,where α is path-loss attenuation factor, d is the distance, and reference path-loss at a distanceof 1 m is 30 dB for operating frequency of 900 MHz [82]. Unless stated otherwise, α = 2.7is used for simulations considering urban environment [82]. AWGN power is assumed to be432.4. Performance Evaluation ResultsIteration1 2 3 4 5 6 7 8 9Averagesumthroughput(bps/Hz)6.016.026.036.046.056.066.07Sc-ISc-IIFigure 2.3: Convergence of Algorithm 1−90 dBm. The transmit power of the AP is 41 dBm and the energy available at the relaynode is 20 J. The total transmission time is T = 2 s. Energy harvesting efficiency is η1 = 50%and η2 = 75% due to receiver circuit power consumption. Relay node is fixed at a distanceof 6 m from the AP. When two UEs are considered to be present in the system (i.e., N = 1and K = 1), near-UE and far-UE are assumed to be at a distance of 6 m and 12 m fromthe AP, respectively. We also simulate the system model in the presence of multiple nearand far-UEs. In this case, we randomly generate locations of near-UEs (maximum distancebeing 6 m) and far-UEs (maximum distance being 12 m) in each simulation and average theresults over 1000 different random realizations. In each realization, the numbers of near andfar-UEs are assumed to be equal.442.4. Performance Evaluation Results2.4.2 Simulation ResultsConvergence of iterative algorithmFig. 2.3 presents the average sum-throughput of UEs determined by using Algorithm 1 inScenarios I and II, plotted against iteration indices. N = 5 near-UEs and K = 5 far-UEsare considered in the system for the simulation. For both scenarios, the algorithm convergesin 4− 5 iterations. Also, the performance loss of Scenario II compared to Scenario I is foundto be fairly small.Resource allocationThe amount of allocated time for DEH and UIT is presented in Fig. 2.4 for varying energyharvesting efficiency η1. In relay-based systems, energy allocated at relay node for trans-mitting wireless charging signal and relaying uplink information is presented in Figs. 2.5(a)and 2.5(b), respectively. For these results, N = 1 near-UE and K = 1 far-UE are consid-ered in the network. Most of the available energy is allocated for wireless charging which isanalogous to the result in downlink SWIPT [13,20] where most of the power is allocated toenergy harvester. Energy allocated for wireless charging is the highest in Scenario II withoptimal resource allocation which again shows that for optimality, maximum available en-ergy is dedicated for wireless charging. Interestingly, introduction of relay node relaxes thetime allocated for wireless charging which allows more time for transmission of far-UE. Thisis because relay node acts as an additional source of wireless charging signal. When its avail-able energy is optimally utilized in Scenario II, DEH time decreases the most (Fig. 2.4(a))and UIT time of far-UE increases the most (Fig. 2.4(c)). Increase in UIT time of far-UEis accompanied with slight decrease in UIT time of near-UE (Fig. 2.4(b)). With increas-ing energy harvesting efficiency, DEH time decreases and UIT time of near-UE increasesas more energy can be harvested in less time when energy harvesting efficiency is higher.However, UIT time of far-UE decreases and relay nodes spend more energy in DEH phase452.4. Performance Evaluation ResultsEnergy harvesting efficiency (η1)0.4 0.5 0.6 0.7 0.8 0.9 1Chargingtime[t(d)](s)0.340.360.380.40.420.440.46Sc-I(Iterative)Sc-II(Optimal)Sc-II(Iterative)No-relay(a)Energy harvesting efficiency (η1)0.4 0.5 0.6 0.7 0.8 0.9 1Transmissiontime[t1(n)](s)1.21.251.31.351.41.451.51.551.6Sc-I(Iterative)Sc-II(Optimal)Sc-II(Iterative)No-relay(b)Energy harvesting efficiency (η1)0.4 0.5 0.6 0.7 0.8 0.9 1Transmissiontime[t1(f)](s)00.050.10.150.20.250.30.350.4Sc-I(Iterative)Sc-II(Optimal)Sc-II(Iterative)No-relay(c)Figure 2.4: Time allocated versus energy harvesting efficiency.462.4. Performance Evaluation ResultsEnergy harvesting efficiency (η1)0.4 0.5 0.6 0.7 0.8 0.9 1Chargingenergy[E(rd)](J)1515.51616.51717.51818.51919.520Sc-I(Iterative)Sc-II(Optimal)Sc-II(Iterative)(a)Energy harvesting efficiency (η1)0.4 0.5 0.6 0.7 0.8 0.9 1Relayingenergy[E1(ru)](J)00.511.522.533.544.55Sc-I(Iterative)Sc-II(Optimal)Sc-II(Iterative)(b)Figure 2.5: Energy allocated at relay node versus energy harvesting efficiency.472.4. Performance Evaluation ResultsTable 2.1: Received, harvested, and transmit power of UEsScenarios Received Power (Downlink) Harvested Energy Transmit Power (Uplink )Prx(n) Prx(f) E(n) E(f) P(n) P(f)dBm dBm µJ µJ dBm dBmScenario II -10.01 -3.67 18.39 79.11 -19.71 -4.57OptimalScenario II -10.01 -5.24 20.59 61.76 -19.43 -4.02IterativeScenario I -10.01 -5.05 20.53 64.38 -19.42 -3.99IterativeNo Relay -10.01 -18.14 22.07 3.4 -19.63 -11.51to compensate the loss in uplink throughput of far-UEs due to decrease in its UIT time.In Table 2.1, we present the received power, harvested energy, and uplink transmit powerof both near-UE and far-UE when N = 1, K = 1, η1 = 50%, and η2 = 75%. From thetable, we see that the receiver sensitivity of energy harvesting circuit (around −20 dBm)is satisfied in both near-UE and far-UE in all the scenarios. It should be noted that thereceived power of far-UE is much lower in the scenario without the relay node. However, forfair comparison, we have assumed that the energy is harvested with efficiency of η1 = 50%in all cases, irrespective of the received power level. We see that, the uplink transmit powersof both near-UE and far-UE are within the transmit power range (0 dBm to −24 dBm) ofsensor nodes such as TelosB [17] and MICAz [83].Throughput performanceIn Fig. 2.6, we plot throughput of both near-UE and far-UE againt varying energy harvestingefficiency η1, when N = 1 and K = 1. We can see that far-UE throughput increases inboth scenarios with relay-based cooperation. In Fig. 2.7, we plot the ratio of throughputof far-UE to that of near-UE. Significant increase in throughput ratio implies remarkableimprovement in throughput of far-UE relative to the near-UE. The uplink throughput ofnear-UE increases while that of far-UE decreases with increasing energy harvesting efficiencywhich is in accordance with the variation in time allocation with energy harvesting efficiency.482.4. Performance Evaluation ResultsEnergy harvesting efficiency (η1)0.4 0.5 0.6 0.7 0.8 0.9 1Throughput(bps/Hz)0123456Near-UE( Sc-I:Iterative)Near-UE(Sc-II:Optimal)Near-UE( Sc-II:Iterative)Near-UE(No-relay)Far-UE( Sc-I:Iterative)Far-UE(Sc-II:Optimal)Far-UE( Sc-II:Iterative)Far-UE(No-relay)Figure 2.6: Throughput versus energy harvesting efficiency.Energy harvesting efficiency (η1)0.4 0.5 0.6 0.7 0.8 0.9 1Throughputratio00.050.10.150.20.250.3Sc-I(Iterative)Sc-II(Optimal)Sc-II(Iterative)No-relayFigure 2.7: Throughput ratio versus energy harvesting efficiency.492.4. Performance Evaluation ResultsNumber of UEs2 3 4 5 6 7 8 9 10Averagesumthroughput(bps/Hz)4.555.566.57Sc-I (Iterative)Sc-II (Optimal)Sc-II (Iterative)No relayFigure 2.8: Average sum-throughput versus number of UEs.In Fig. 2.8, the average sum-throughput is plotted against varying number of UEs. Itis observed that the average sum-throughput increases with increasing number of UEs. InFig. 2.9, the average sum-throughput is plotted against attenuation factor when N = 5 near-UEs and K = 5 far-UEs are present in the network. The sum-throughput decreases withincreasing path-loss attenuation and the performance gain due to relay-based cooperationis more prominent when path-loss attenuation is high. From the simulation results, it isobserved that the throughput performances of both Scenarios I and II with iterative resourceallocation are very close to each other which validates our assumption (made in Scenario II)that energy harvested by far-UEs from the AP transmission is negligible. Scenario II hasmaximum performance gain when resources are optimally allocated.502.4. Performance Evaluation ResultsAttenuation factor (α)2.5 3 3.5 4 4.5 5 5.5Averagesumthroughput(bps/Hz)01234567Sc-I (Iterative)Sc-II (Optimal)Sc-II (Iterative)No relayFigure 2.9: Average sum-throughput versus attenuation factor.Fairness performanceWe then evaluate fairness using Jain’s fairness index3 [84]. In Fig. 2.10, we plot Jain’sfairness index against varying energy harvesting efficiency when N = 1 and K = 1. InFig. 2.11, we plot Jain’s fairness index against varying number of UEs. The figures showthat fairness performance of both scenarios with relay-based cooperation is superior to thatwithout relay node [24]. However, Jain’s fairness index decreases with increasing energyharvesting efficiency which due to increase in throughput of near-UE and decrease in thatof far-UE. This shows that the effectiveness of relay-based cooperation in terms of fairnessperformance is more prominent when energy harvesting efficiency is low. The figures areconsistent with the observations that Scenarios I and II have fairly similar performance withiterative resource allocation and that optimal resource allocation improves performance ofScenario II.3If xi, i = 1, 2, ..., N is the throughput of each of N users, then Jain’s fairness index is given by: f(x) =(∑Ni=1 xi)2N∑Ni=1 x2i. The fairness index has the range of 0 < f(x) ≤ 1, where a higher number indicates a betterfairness.512.4. Performance Evaluation ResultsEnergy harvesting efficiency (η1)0.4 0.5 0.6 0.7 0.8 0.9 1Jain’sfairnessindex0.50.550.60.650.70.750.8Sc-I(Iterative)Sc-II(Optimal)Sc-II(Iterative)No-relayFigure 2.10: Jain’s fairness index versus energy harvesting efficiency.Number of UEs2 3 4 5 6 7 8 9 10Jain’sfairnessindex0.40.450.50.550.60.650.70.75Sc-I (Iterative)Sc-II(Optimal)Sc-II (Iterative)No relayFigure 2.11: Jain’s fairness index versus number of UEs.522.4. Performance Evaluation Results2.4.3 Summary of ObservationsThe simulation results demonstrate how the presence of relay nodes allows more uplink trans-mission time by reducing the downlink energy harvesting time. This causes improvementof throughput of far-UEs, sum-throughput, and fairness. Therefore, relay-based coopera-tion improves fairness without any loss in overall throughput performance. However, theeffectiveness of relay-based cooperation in WPC networks is more prominent when path-loss attenuation is high and energy harvesting efficiency is low. With iterative power andtime allocation, Scenario I provides a slightly better performance than that of Scenario II.However, the performance difference is negligible which validates our assumption (madein Scenario II) that energy harvested by far-UEs from the AP transmission is negligible.Simulation results demonstrate that the performance significantly improves due to optimalallocation of resources in Scenario II. Therefore, Scenario II is preferable in WPC networkswith relay-based cooperation to maximize the throughput performance with lower compu-tational complexity.53Chapter 3Resource Allocation in UplinkWireless-Powered CommunicationNetworks with User-basedCooperationIn Chapter 2, we considered deployment of dedicated relay nodes for mitigating the “doublynear-far” problem in uplink WPC networks. However, deployment of dedicated relay nodesmay not always be feasible or may incur high installation costs. Hence, in this chapter, weconsider user-based cooperation in such uplink WPC network and perform joint resourceallocation for downlink energy harvesting phase and uplink information transmission phase.The accomplished works and research contributions of this chapter are briefly described inthe following.3.1 Accomplished Works and Research ContributionsIn this chapter, we consider an uplink WPC network where the uplink communication of UEsis powered by wireless energy harvesting. Based on the concept of harvest-then-transmit [24],UEs first harvest energy from the AP in DEH phase. Then, in UIT phase, the UEs, thatdo not have their own data to transmit, relay uplink information signal for the transmittingUEs. The transmission of different UEs are orthogonal in frequency. To optimize uplink543.2. System Model and Assumptionsthroughput performance of the transmitting UEs, we optimally allocate downlink transmitpower of the AP for DEH phase jointly with relay selection, subchannel allocation, and powerallocation for UIT phase. Although the formulated MINLP problem is solved by relaxingthe integer constraints, the resulting solution is shown to always satisfy the constraints ofthe original problems, hence satisfying the condition of optimality.The rest of the chapter is organized as follows. The system model and assumptions arepresented in Section 3.2. In Section 3.3, the optimization problem is formulated and thesolution approach is proposed. Numerical results are presented in Section 3.4.3.2 System Model and AssumptionsConsider an uplink communication network as shown in Fig. 3.1. As in sensor network, let usassume there is an idle period before each uplink transmission. The idle period is dedicatedfor DEH where the AP transmits downlink wireless charging signal and all UEs harvestenergy from the received signal. The AP is connected to the grid power. However, UEsare assumed to have no battery power and hence rely on harvested energy for their uplinktransmissions. In the UIT period, the UEs, that are located closer to the AP and do not haveany data to transmit are available to act as relay nodes (RNs) for other data-transmittingUEs which have poor channel quality to the AP. In the following, data-transmitting UEswill be referred as transmitting nodes (TNs). For simplicity we assume that we know whichUEs have data to transmit and which are available as relay nodes and we also have theirlocation information.Let us assume that there are K TNs with poor uplink channel quality and R RNswith strong uplink channels. We consider that the available bandwidth is divided into Nsubchannels, each with bandwidth of B. Channel gain of the links between AP to RN r insubchannel n are denoted by hnA,r, where r ∈ {1, 2, ..., R} and n ∈ {1, 2, ..., N}. Channel gainof the links between RN r to TN k in subchannel n are given by hnr,k, where k ∈ {1, 2, ..., K}.553.2. System Model and AssumptionsAccess pointRelay nodeTransmitting nodeEnergyInformationFigure 3.1: Uplink WPC network with user-based cooperation.Channel gain of the links between AP and TN k in subchannel n are given by gnA,k. TheDEH period is denoted by τe and the UIT period is denoted by τt.During the DEH period, the AP transmits wireless charging signal in all subchannelswith power P nA. The energy harvested by the RNs and the TNs are given by:Er =N∑n=1P nAhnA,rητe, ∀r, Ek =N∑n=1P nAgnA,kητe, ∀kwhere η is the energy harvesting efficiency.In the UIT phase, each TN’s transmission is amplified and forwarded by their selectedRNs in their selected subchannels. The subchannel and relay assignment variable is denotedby snk,r. If an RN r is selected as a relay for a TN k in subchannel n, then snk,r = 1 andotherwise snk,r = 0. The achievable throughput in bits per second per Hertz (bps/Hz) of TNk, assisted by relay r in subchannel n is given as:Rnk,r =12log21 + P n(1)k,r P n(2)r,A hnr,khnA,rNw(Pn(1)k,r hnr,k + Pn(2)r,A hnA,r +Nw) ,∀n, r, k (3.1)where Nw is the AWGN power. Pn(1)k,r is the uplink transmission power of the TN k inthe subchannel n paired with the relay r. Pn(2)r,A is the transmission power of the RN r563.3. Problem Formulation and Solution Approachin the subchannel n in the second phase. The factor of 12is due to half-duplex relaying4.Assuming AWGN power to be much lower than the signal power, higher order term (Nw)2is ignored in the rest of this chapter. The total achievable throughput of TN k is given byRk =∑Nn=1∑Rr=1 snk,rRnk,r, ∀k.In this chapter, to maximize uplink sum-throughput of all transmitting UEs, we willjointly optimize the following variables of the network: (i) downlink transmit power of theAP, (ii) uplink transmit power of the TNs and RNs, (iii) relay selection and subchannelassignment. It should be noted that uplink transmit power of the TNs and the RNs dependon their harvested energy which depends on downlink transmit power of the AP. Therefore,it is necessary to jointly allocate downlink transmit power of the AP along with uplinktransmit power of the TNs and RNs. In addition, subchannel allocation and relay selectionshould be optimally performed in the uplink. Therefore, to jointly perform downlink/uplinkpower allocation, uplink relay selection and subchannel allocation, we will formulate anoptimization problem with the objective of maximizing the sum-throughput of the network.3.3 Problem Formulation and Solution ApproachIn the following, we formulate an optimization problem to jointly perform downlink/uplinkpower allocation, uplink relay selection and subchannel allocation, as follows:maximizePK,PR,PA,S∑Kk=1Rksubject toC1 : snk,r ∈ {0, 1}, ∀r, k, nC2 :R∑r=1K∑k=1snk,r ≤ 1, ∀n(3.2)4Note that, unlike our assumption, if DEH phase actually consumes some portion of the transmissiontime, the factor changes from 12 toτt/2τt+τe.573.3. Problem Formulation and Solution ApproachC3 :R∑r=1N∑n=1snk,rPn(1)k,r ≤N∑m=1PmA gmA,kητeτt2, ∀kC4 :K∑k=1N∑n=1snk,rPn(2)r,A ≤N∑m=1PmA hmA,rητeτt2, ∀rC5 : Pn(1)k,r , Pn(2)r,A ≥ 0, ∀n, r, kC6 : PmA ≥ 0, ∀m ∈ {1, 2, .., N}C7 :N∑m=1PmA ≤ PAmaxwhere PK, PR, PA, and S denote uplink transmit power of the TNs, uplink transmit powerof the RNs, downlink transmit power of the AP and subchannel and relay assignment vari-ables, respectively. Constraint C1 shows that snk,r are binary integer variables as discussedpreviously. C2 ensures that a subchannel is not used by more than one TN-RN pair, toeliminate the interference. C3 and C4 indicate that the total energy spent by TNs and RNsduring the UIT period cannot be higher than that harvested during the DEH period. Thefactor of 1/2 is present in the constraints due to half-duplex relaying. Note that energyconsumption at the transceiver circuit of UEs are assumed to be negligible and thereforenot considered in the problem. C5 and C6 impose non-negativity constraint on the powervariables. C7 indicates total power budget of the AP during the DEH period.The optimization problem (3.2) is an MINLP problem. The solution to such a problemis computationally very difficult to obtain in this form. Therefore, to solve the problem, werelax the binary integer subchannel allocation and relay selection variables to be continuousin the interval, i.e. snk,r ∈ [0, 1]. Next, we define following auxiliary variables:P˜n(1)k,r = snk,rPn(1)k,r ,∀n, r, k (3.3)P˜n(2)rk,A= snk,rPn(2)r,A ,∀n, r, k. (3.4)583.3. Problem Formulation and Solution ApproachUsing (3.3) and (3.4), the throughput expression given in (3.1) can be re-written asR˜nk,r =12log21 + P˜ n(1)k,r P˜ n(2)rk,Ahnr,khnA,rsnk,r(P˜n(1)k,r hnr,k + P˜n(2)rk,AhnA,r)Nw ,∀n, r, k. (3.5)With the relaxation and change of variables, the problem (3.2) can be written asmaximizeP˜K,P˜R,PA,S∑Kk=1 R˜ksubject to C2, C6, C7C˜1 : snk,r ∈ [0, 1], ∀r, k, nC˜3 :R∑r=1N∑n=1P˜n(1)k,r ≤N∑m=12gmA,kPmA ητe/τt, ∀kC˜4 :K∑k=1N∑n=1P˜n(2)rk,A≤N∑m=12hmA,rPmA ητe/τt, ∀rC˜5 : P˜n(1)k,r , P˜n(2)rk,A≥ 0, ∀n, r, k(3.6)where R˜k =∑Rr=1∑Nn=1 snk,rR˜nk,r. The objective function of the re-formulated problem (3.6)is concave, constraints C˜3 and C˜4 are affine, C˜1 is a boundary constraint, and hence theproblem becomes convex optimization problem. The concavity of function f(P˜n(1)k,r , P˜n(2)rk,A) =1+P˜n(1)k,r P˜n(2)rk,Ahnr,khnA,r(P˜n(1)k,r hnr,k+P˜n(2)rk,AhnA,r)Nwin terms of power variables can be proven by computing its Hessianwhose eigenvalues are non-positive. The throughput expression can be proven to be concavewith respect to power as well as subchannel and relay assignment variables due to increasingconcave nature of log function and by perspective operation [80], similar to Appendix A.Therefore, the problem can be solved optimally using dual decomposition technique [85], asexplained in the following.593.3. Problem Formulation and Solution ApproachFirst, we define the following partial Lagrangian [80] for the problem:L(P˜K, P˜R,PA,S,λ,µ) =K∑k=1R˜k −K∑k=1λk{R∑r=1N∑n=1P˜n(1)k,r −N∑m=12PmA gmA,kητe/τt}−R∑r=1µr{K∑k=1N∑n=1P˜n(2)rk,A−N∑m=12PmA hmA,rητe/τt} (3.7)where λ = {λ1, λ2, ..., λk} and µ = {µ1, µ2, ..., µr} are non-negative Lagrange multipliers forconstraints C˜3 and C˜4, respectively. Then, Lagrangian dual function [80] of the problem isformulated as follows:g (λ,µ) = maximizeP˜K,P˜R,PA,SL(P˜K, P˜R,PA,S,λ,µ)subject to C˜1, C2, C˜5, C6, C7.(3.8)Maximization of the Lagrangian to obtain the dual function in (3.8) is our subproblem.After obtaining the dual function, the dual problem is formulated as follows:minimizeλ0,µ0g(λ,µ). (3.9)Since the primal problem is convex, strong duality holds and solution of the dual problemin (3.9) gives us the solution of the primal problem [80]. Next, we will discuss the solutionapproach of the subproblem as well as the dual problem.Solving the subproblemFrom careful inspection of the Lagrangian in (3.7), we know that maximization problemin (3.8) is a separable problem [85]. Therefore, the Lagrangian dual function can be decom-603.3. Problem Formulation and Solution Approachposed into two functions as follows:g1 (λ,µ) = maximizeP˜K,P˜R,SL1(λ,µ, P˜K, P˜R,S)subject to C˜1, C2, C˜5(3.10)g2 (λ,µ) = maximizePAL2(λ,µ,PA)subject to C6, C7(3.11)whereg(λ,µ) = g1(λ,µ) + g2(λ,µ) (3.12)L1(λ,µ, P˜K, P˜R,S) =K∑k=1R˜k −K∑k=1R∑r=1N∑n=1λkP˜n(1)k,r −R∑r=1K∑k=1N∑n=1µrP˜n(2)rk,A(3.13)L2(λ,µ,PA) =N∑m=12PmA{K∑k=1λkgmA,k +R∑r=1µrhmA,r}ητe/τt. (3.14)The maximization problem in (3.11) is a linear programming problem and can be solvedby interior-point method [80]. Note that the constraints C˜1 − C2, and C˜5 are incorporatedin (3.10) and C6 − C7 are incorporated in (3.11). The maximization problem in (3.10) canbe re-formulated as two step maximization problem as follows:g1 (λ,µ) = maximizeSmaxP˜K,P˜RL1(λ,µ, P˜K, P˜R,S)subject to C˜1, C2, C˜5.(3.15)To maximize L1(λ,µ, P˜K, P˜R,S) in terms of power variables, let us apply KKT stationaritycondition [80] as follows:∂L1(λ,µ, P˜K, P˜R,S)∂P˜n(1)k,r= 0, ∀r, k, n (3.16)613.3. Problem Formulation and Solution Approach∂L1(λ,µ, P˜K, P˜R,S)∂P˜n(2)rk,A= 0, ∀r, k, n. (3.17)Solving (3.16) and (3.17) for the power variables, we get following relation between thesubchannel and relay selection variables and power variables:P˜n(1)k,r = snk,r[12λkY nk,rlog2− NwYnk,rhnr,k]+(3.18)P˜n(2)rk,A=snk,rβnk,r[12λkY nk,rlog2− NwYnk,rhnr,k]+(3.19)where βnk,r =√(hnA,rµrhnr,kλk), Y nk,r =βnk,rhnr,k+hnA,rhnA,rand [x]+ = max(0, x). Using (3.18) and (3.19),the dual function in (3.15) can be re-written as:g1 (λ,µ) = maximizeSK∑k=1R∑r=1N∑n=1snk,rXnk,rsubject to C1, C2(3.20)whereXnk,r ={Rn∗k,r −(λk +µrβnk,r)Znk,r}(3.21)Znk,r =[12λkYnk,rlog2− NwYnk,rhnr,k]+(3.22)Rn∗k,r =12log2(1 +Znk,rhnr,kNwY nk,r). (3.23)The constraint C˜5 is not included in (3.20) because it is already satisfied in (3.18) and (3.19).The maximization problem in (3.20) is a linear programming problem. However, it shouldbe noted that, maximizing the objective function of the problem in (3.20) requires selectionof the highest element of R×K matrix [Xnk,r] for each subchannel n. Therefore, subchannel623.3. Problem Formulation and Solution Approachand relay assignment variables are determined as follows:snk,r =1, if (r∗, k∗) = argmaxr,kXnk,r0, otherwise.(3.24)It should be noted that, despite the relaxation of subchannel and relay assignment variables,the optimal solution of the problem in (3.20) is always integer and hence, the obtainedsolution satisfies all constraints of our original problem in (3.2) [86].Solving the dual problemThe dual problem is solved by subgradient method [87] as follows:λ(it+1)k =[λ(it)k + ∆λk(R∑r=1N∑n=1P˜n(1)k,r −N∑m=12PmA gmA,kητe/τt)]+, ∀k (3.25)µ(it+1)r =[µ(it)r + ∆µr(K∑k=1N∑n=1P˜n(2)rk,A−N∑m=12PmA hmA,rητe/τt)]+, ∀r (3.26)where ∆λk and ∆µr are positive constant step size for the subgradient method. For convexoptimization problems, the subgradient method is guaranteed to converge for small step sizeand the proof of convergence can be found in [87]. The solution approach is summarized inAlgorithm 2.Algorithm 2 Proposed Joint Resource Allocation SchemeRequire: Initialize λ(it)k , µ(it)r for it = 1.1: repeat2: Compute Xnk,r, ∀n, r, k using (3.21).3: Determine snk,r, ∀n, r, k using (3.24).4: Compute P˜n(1)k,r and P˜n(2)rk,Ausing (3.18) and (3.19), respectively.5: Determine P nA by solving the problem in (3.11) using interior-point method.6: Compute λ(it+1)k and µ(it+1)r using (3.25) and (3.26).7: Assign it← it+ 1.8: until Convergence of g(λ,µ).633.4. Performance Evaluation ResultsEnergy harvesting efficiency η0.25 0.5 0.75 1Sum-throughput(bps/Hz)1416182022242628303234 N=8,P=47dBmN=8,P=46dBmN=4,P=47dBmN=4,P=46dBmFigure 3.2: Sum-throughput versus energy harvesting efficiency.3.4 Performance Evaluation Results3.4.1 Simulation ParametersChannel gain for the link between source and destination is computed as hs,d = Rf210−3d−α,where d is the distance, path-loss attenuation factor is α = 2.7 [82], and Rf is Rayleighdistributed fading coefficient implying exponential distribution of Rf2 with unit mean [88]5.Reference path-loss at a distance of 1 m is 30 dB [82]. AWGN power is 10−11 W. The DEHtime and the UIT time are defined as τe = 0.5 and τt = 1 second. Unless otherwise stated,energy harvesting efficiency is 50% and transmit power budget of the AP is 46 dBm. Themaximum service distance of the network is 10 meters. Simulations are repeated over 1000different random fading channels and the results are averaged.643.4. Performance Evaluation ResultsEnergy harvesting efficiency η0.25 0.5 0.75 1Sum-throughput(bps/Hz)681012141618ProposedDEPARRSAFigure 3.3: Sum-throughput versus energy harvesting efficiency.3.4.2 Simulation ResultsIn Fig. 3.2, we analyze the sum-throughput performance of the proposed resource allocationscheme for different energy harvesting efficiency η, number of subchannels, and transmitpower budget of the AP assuming R = K = 4. The sum-throughput performance of thesystem improves with increasing energy harvesting efficiency of the UEs. It is because,with higher energy harvesting efficiency, the nodes can harvest more energy and hence makeuplink transmission/relaying with higher transmit power. Increase in transmit power budgetof AP for downlink DEH phase leads to higher sum-throughput of the system. Similarly, thesum-throughput performance increases with increasing number of subchannels.In Fig. 3.3, we plot the sum-throughput of the network against energy harvesting effi-ciency for N = K = R = 4. We also compare the performance of our proposed algorithmwith two benchmark schemes. In downlink equal power allocation6 (DEPA) scheme, transmit5Note that, in comparison to the previous chapter, we have added Rayleigh distributed fading coefficientin computation of the channel gain in this chapter.6Equal power allocation has been compared with optimal power allocation for UIT phase in the litera-ture [89]. In this chapter, we compare the optimal power allocation with equal power allocation in downlinkDEH phase.653.4. Performance Evaluation ResultsNumber of relays2 4 6 8Systemenergyefficiency(bits/Joule/Hz)00.10.20.30.40.50.60.70.8RRSADEPAProposedFigure 3.4: System energy efficiency versus number of relays.power of the AP is equally allocated among all subchannels and the uplink resource alloca-tion is done optimally. In random relay and subchannel assignment (RRSA) scheme [89],the relay selection and subchannel assignment is performed randomly. We notice that, op-timal relay selection and subchannel assignment remarkably improve the sum-throughputperformance. In addition, joint downlink power allocation along with uplink resource alloca-tion further improves the performance of the network. This shows the effectiveness of jointdownlink and uplink resource allocation in wireless-powered networks.In Fig. 3.4, the bar chart shows the average system energy efficiency for different numberof relays in the network assuming K = 4 and N = 8. The performance of the proposedscheme is compared with the aforementioned benchmark schemes. System energy efficiencyis mathematically defined as Rsum/Psum, where Rsum and Psum are the sum-throughput andsum-power consumption of the network, respectively. The total transmit power of the APremains the same despite the increase in number of relays. However, with more relays presentin the system, the achievable throughput of the network increases significantly. Therefore,the system energy efficiency improves with the increase in number of relay nodes.663.4. Performance Evaluation Results3.4.3 Summary of ObservationsComparison of the proposed resource allocation algorithm with the benchmark schemesdemonstrates the importance of joint consideration of DEH and UIT phase in resource allo-cation in the uplink WPC networks. Also the performance variation of the proposed algo-rithm with varying number of relays demonstrates the advantage of user-based cooperationin uplink WPC networks.67Chapter 4Resource Allocation for DownlinkSWIPT in Small Cells in a Two-TierHetNetAs discussed in Chapter 1, wireless energy harvesting is studied in two different paradigmsof wireless communication: (i) uplink WPC, and (ii) downlink SWIPT. In Chapters 2 and 3,we studied resource allocation in uplink WPC networks with relay-based and user-basedcooperation. In this chapter, we consider downlink SWIPT and solve the resource allocationproblem to obtain optimal rate-energy trade-off while addressing the interference manage-ment issues that arise when SWIPT is enabled in small cells of HetNets. The accomplishedworks and research contributions of this chapter are briefly described in the following.4.1 Accomplished Works and Research ContributionsIn this chapter, we investigate the problem of downlink resource allocation for SWIPT insmall cells underlaying a macrocell (i.e. a co-channel deployment scenario) in a two-tier Het-Net. Considering that current receiver circuits have separate information decoder and energyharvester, we consider both signal sharing approaches of SWIPT: time-switching and power-splitting. To obtain optimal rate-energy trade-off in SWIPT, we jointly allocate downlinktransmit power of small cell base stations (SBSs) along with time-switching/power-splittingvariables to optimize the throughput and energy harvesting rates of small cell UEs. To684.1. Accomplished Works and Research Contributionsjointly optimize achievable throughput and energy harvesting rate of small cell UEs, we usescalarization technique of multi-objective programming. We formulate a resource allocationproblem with the objective of maximizing the weighted sum of normalized throughput andenergy harvesting rate.In the time-switching approach, to address the challenge of interference management, weconsider flexible interference tolerance levels in macrocell UEs to provide a degree of freedomfor SBSs to adjust their transmit powers for information and power transfer. We jointly allo-cate downlink transmit power along with time-switching variables in two different scenarios:with negligible co-tier interference and with non-negligible co-tier interference. In both sce-narios, the formulated problems are MINLP problems and we solve them by relaxing thebinary integer constraint and then identifying the condition at which the obtained solutionsatisfies that constraint of the original problem. For the scenario with non-negligible co-tier interference, we propose a sub-optimal resource allocation framework based on iterativemaximization of the minorant of the non-convex objective function. For the scenario withnegligible co-tier interference, we determine the optimal resource allocation using convexoptimization techniques. In the power-splitting approach, we propose a resource allocationframework, based on iterative maximization of the minorant of the non-convex objectivefunction, to determine downlink transmit power and power-splitting variables, when co-tierinterference is non-negligible.The rest of the chapter is organized as follows. System model and assumptions areexplained in Section 4.2. Sections 4.3 and 4.4 present problem formulations and solutionapproaches of resource allocation for the time-switching and power-splitting approaches ofSWIPT. Performance evaluation results are presented in Section 4.5.694.2. System Model and AssumptionsInforma on TransferPower TransferMUESBSSBSMBSSUEFigure 4.1: Two-tier HetNet with SWIPT in small cells.4.2 System Model and AssumptionsTwo-tier HetNet modelWe consider a two-tier HetNet with S small cells underlaying a macrocell as shown in Fig. 4.1.We assume that small cells are deployed to serve sensor-like IoT devices with low powerrequirements while the macrocell UE may have high power requirement. The macrocell UE(MUE) is denoted by um and served by the macrocell base station (MBS). The small cellUEs (SUEs) are denoted by us, s ∈ {1, 2, ..., S} and served by an SBS in each small cell.We divide one transmission block of duration T into N time slots. The MUE and the SUEsare assumed to be active and associated to their serving base stations for the time period ofconsideration. Fading condition is assumed to be constant over each time slot. htj,j and htj,k,t ∈ {1, 2, ..., N}, denote the channel gain of the link from base station j to its UE uj and toUE uk, served by base station k, respectively. MBS downlink transmit power is assumed tobe P tm = Pm, ∀t. To simplify the exposition, without loss of generality, we assume that onlyone channel of bandwidth B is available and hence shared by the macrocell and small cellsto serve one UE in each cell during one transmission block.704.2. System Model and AssumptionsSWIPT in small cellsAs shown in Fig. 4.1, SWIPT is enabled in small cells. Assuming that the SUEs are sensor-like IoT devices with low power requirements, to elongate their battery life, they are consid-ered to be capable of harvesting energy from the received signal. The energy harvested inone downlink transmission block can be stored in the battery for future or can be used inthe next uplink transmission. Due to large transmission distance in macrocell and diversepower requirements of macrocell users, wireless energy harvesting is not considered in theMUE. With incorporation of SWIPT in small cells, we will investigate two signal sharingapproaches: time-switching and power-splitting. As shown in Fig. 4.1, the MUE receivescross-tier interference from the SBS transmission (both information and power transmis-sion). Therefore, to maximize wireless power transfer while guaranteeing QoS provisioningto the MUE, in time-switching approach, we assume flexible interference tolerance in MUE.To maximize the benefit of such flexible interference tolerance of MUE, we assume thatenergy harvesting (EH) and information decoding (ID) phase of all the SUEs are synchro-nized. If interference tolerance of MUE is high in EH phase and all SUEs are harvestingenergy, then the transmit power of SBSs can be increased to allow significant wireless powertransfer. The interference tolerance level of MUE can then be lowered in ID phase to ensureQoS provisioning to the MUE despite the corresponding loss of throughput in EH phase.However, optimal mode selection and resource allocation is crucial to ensure that minimumthroughput requirement of MUE is satisfied while optimal trade-off is achieved for SUEs.Next we will formulate the expressions of achievable throughput and energy harvestingrate of SUEs with time-switching and power-splitting approaches of SWIPT.Time-switching approachLet us assume that, in each time slot, the SUEs either decode information or harvest energyfrom the received signal. αtI and αtE are time-switching variables where αtI = 1 in ID mode,and αtE = 1 in EH mode such that αtI + αtE ≤ 1, ∀t. P ts,I denotes downlink transmit power714.2. System Model and Assumptionsof SBS s in time slot t in ID mode and P ts,E denotes that in EH mode. Let R(tar) and E(tar)denote the target throughput and energy harvesting rate of the SUEs in bits per secondper Hertz (bps/Hz) and Joules per second (Jps), respectively. Let R(min) be the minimumthroughput requirement of the MUE. In order to give an extra degree of freedom for SBSsto adjust the transmit powers in EH and ID mode, let us define following two parameters:R(min,E) is the minimum throughput ensured in the MUE during EH mode and R(min,I) isthat during ID mode. The achievable throughput of the MUE over one transmission periodis then given by Rm =∑Nt=11N(αtIR(min,I) + αtER(min,E)). Note that for a given transmitpower of the MBS, to achieve the above rate, the interference caused by the SBSs will needto be controlled accordingly. The achievable throughput and energy harvesting rate of SUEs,over one transmission period, are given byRs =N∑t=1αtINlog2(1 +P ts,Ihts,s∑Sj=1,j 6=s Ptj,Ihtj,s + χtm,s +Nsp),∀s (4.1)Es =N∑t=1αtEηN(S∑j=1P tj,Ehtj,s + χtm,s),∀s (4.2)where χtm,s = Pmhtm,s + Nw, and η is energy harvesting efficiency. Nw and Nsp are antennanoise power and signal processing noise power7, respectively. Note that SUEs harvest energyfrom signal transmitted by their serving SBSs, co-tier interference signal transmitted by otherSBSs, cross-tier interference signal transmitted by the MBS (Fig. 4.1) as well as antennanoise.Power-splitting approachIn power-splitting approach, each SUE splits power of the received signal into two fractionsand shares it among information decoder and energy harvester. Let us assume that in eachtime slot, each SUE uses ρtI(s) fraction of signal power for ID process and ρtE(s) for EH process7Antenna noise and signal processing noise are both assumed to be AWGN. However, antenna noise isintroduced in the RF band while signal processing noise is introduced during RF band to baseband conversionfor information decoding [20].724.2. System Model and Assumptionssuch that ρtI(s) + ρtE(s) ≤ 1, ∀t, s. P ts denotes downlink transmit power of SBS s in time slott. To maintain consistency with time-switching approach, we assume that ρtI(s) = ρtI andρtE(s) = ρtE, ∀s. In this case, the achievable throughput and energy harvesting rate of SUEsare given by8Rs =N∑t=11Nlog21 + ρtIP tshts,sρtI(∑Sj=1,j 6=s Ptjhtj,s + χtm,s)+Nsp ,∀s (4.3)Es =N∑t=1ρtEηN(S∑j=1P tjhtj,s + χtm,s), ∀s. (4.4)Note that, unlike time-switching approach, EH and ID processes are not separated in timedomain in power-splitting approach, and hence R(min) is the minimum throughput thatshould be ensured for the MUE in each time slot. In other words, power-splitting approachlacks that additional degree of freedom which we have exploited in time-switching approach.The comparison of time-switching and power-splitting approaches is even more important inmulti-tier network due to this inherent difference between the two approaches.In this chapter, we optimize downlink transmit powers and time-switching/power-splittingvariables to maximize the achievable throughput as well as energy harvesting rate of eachSUE over one transmission block. This requires a multi-objective programming approach.In this work, we use scalarization method of solving multi-objective programming problemto formulate a single objective function [90]. The target throughput and energy harvestingrate of SUEs are R(tar) and E(tar), respectively. Following scalarization method, the com-bined single objective is to maximize the weighted sum of normalized throughput and energyharvesting rate where R(tar) and E(tar) are used for normalization. The weighted sum of nor-malized throughput and energy harvesting rate of each SUE is given by ws,IRsR(tar)+ws,EEsE(tar),where ws,I and ws,E are weights that indicate the priority of each SUE for throughput per-formance and energy harvesting rate performance, respectively. The weights ws,I and ws,E8Note that the power splitter is assumed to be an ideal passive device that does not introduce any splittingloss or noise [13,62].734.3. Resource Allocation for Time-switching Approach: Problem Formulations and Solutionsare assumed to remain constant over one transmission block and can be determined at thebeginning of each transmission block, depending on various factors such as energy remainingin the battery, energy leakage in the battery, scheduled future uplink transmissions of theSUE, and so on.Remark 1: Note that the proposed system model can be extended to multi-user and mul-tichannel scenario in each cell. In that case, optimization of subcarrier allocation is alsorequired along with downlink transmit power and time-switching/power-splitting variables.However, to simplify the exposition, we assume a single channel system without explicitlyconsidering user scheduling.Now that we have formulated the expressions of throughput and energy harvesting ratewe will discuss resource allocation problems and the corresponding solution approaches forboth time-switching and power-splitting approaches of SWIPT in the next sections.4.3 Resource Allocation for Time-switchingApproach: Problem Formulations and SolutionsIn this section, we will formulate resource allocation problems to jointly optimize time-switching variables along with downlink transmit power of SBSs to maximize the weightedsum of normalized throughput and energy harvesting rate of SUEs over one transmissionblock. The optimization problem is formulated as follows:maximizePI,PE,αI ,αE∑Ss=1(ws,IRsR(tar)+ ws,EEsE(tar))subject toC1 : αtI , αtE ∈ {0, 1}, ∀tC2 : αtI + αtE ≤ 1, ∀t(4.5)744.3. Resource Allocation for Time-switching Approach: Problem Formulations and SolutionsC3 : αtI(S∑s=1P ts,Ihts,m − I tmax,I)≤ 0, ∀tC4 : αtE(S∑s=1P ts,Ehts,m − I tmax,E)≤ 0, ∀tC5 :N∑t=11N(αtIR(min,I) + αtER(min,E)) ≥ R(min)C6 : Pts,I , Pts,E ≤ Ps(max), ∀s, tC7 : Pts,I , Pts,E ≥ 0, ∀s, twhere PI = {P ts,I ,∀s, t}, PE = {P ts,E,∀s, t}, αI = {αtI ,∀t}, αE = {αtE,∀t}, I tmax,I =Pmhtm,m2R(min,I)−1 −Nw −Nsp, and Itmax,E =Pmhtm,m2R(min,E)−1 −Nw −Nsp. C1 is binary integer constrainton time-switching variables. C2 ensures that SUEs are either in EH or ID mode, but notboth. C3 ensures that if SUEs are in ID mode, the sum interference received by the MUEis not higher than I tmax,I in each time slot. C4 imposes similar constraint in EH mode. C5ensures that throughput of the MUE over one transmission block is greater than or equalto R(min). C6 and C7 are boundary constraints on power variables. The problem in (4.5)is not convex due to the presence of interference terms in Rs and is an MINLP problemdue to constraint C1. Such a problem is difficult to solve in its original form. To make theproblem tractable, we relax the time-switching variables as 0 ≤ αtI , αtE ≤ 1. Note that thisrelaxation will allow the system to operate in both EH and ID mode in any time slot bysharing the time available in that slot, according to the factor αtE and αtI , which is possibleto implement. We also define auxiliary power variables asP˜ ts,I = αtIPts,I , P˜ts,E = αtEPts,E, ∀s, t. (4.6)It should be noted that, despite the relaxation, the problem is still non-convex due to inter-ference terms in the denominator. Now, we will solve the problem in two scenarios. Notethat co-tier interference can be negligible due to heavy wall losses in indoor deployment of754.3. Resource Allocation for Time-switching Approach: Problem Formulations and Solutionssmall cells. First, we will solve the problem for the scenario where co-tier interference amongsmall cells is negligible. However, co-tier interference may not be negligible in outdoor de-ployment of small cells. Therefore, we will also provide a sub-optimal solution approach forthe case with non-negligible co-tier interference.4.3.1 Scenario I: Negligible Co-tier InterferenceUsing (4.6) and discarding the co-tier interference terms, the throughput and energy har-vesting rate of SUEs given in (4.1) and (4.2) can be respectively re-written asR˜s =N∑t=1αtINlog2(1 +P˜ ts,Ihts,sαtI(χtm,s +Nsp)), ∀sE˜s =N∑t=1ηN(P˜ ts,Ehts,s + αtEχtm,s), ∀s.(4.7)Using (4.6) and (4.7), the optimization problem in (4.5) can be re-written asmaximizeP˜I,P˜E,αI ,αE∑Ss=1(ws,IR˜sR(tar)+ ws,EE˜sE(tar))subject toC2, C5C˜1 : 0 ≤ αtI , αtE ≤ 1, ∀tC˜3 :S∑s=1P˜ ts,Ihts,m − αtII tmax,I ≤ 0, ∀tC˜4 :S∑s=1P˜ ts,Ehts,m − αtEI tmax,E ≤ 0, ∀tC˜6 : P˜ts,I − αtIPs(max) ≤ 0, ∀s, tC˜7 : P˜ts,E − αtEPs(max) ≤ 0, ∀s, tC˜8 : P˜ts,I , P˜ts,E ≥ 0, ∀s, t(4.8)where P˜I = {P˜ ts,I ,∀s, t} and P˜E = {P˜ ts,E, ∀s, t}. The constraints have been modified ac-cording to the definition of auxiliary variables in (4.6). Note that constraints C˜6 and C˜7764.3. Resource Allocation for Time-switching Approach: Problem Formulations and Solutionsensure that auxiliary power variables P˜ ts,I and P˜ts,E are zero if time-switching variablesαtI and αtE are zero, respectively. Since log2(1 +P˜ ts,Ihts,sχtm,s+Nsp)is a concave function of P˜ ts,I ,αtINlog2(1 +P˜ ts,Ihts,sαtI(χtm,s+Nsp))can be proven to be a concave function of P˜ ts,I and αtI by usingperspective operation [80] and therefore R˜s becomes a sum of concave functions. Since R˜sis a concave function and E˜s is a linear function of the optimization variables, the objectivefunction of the problem in (4.8) is concave, and the constraints are affine. Therefore, itis a convex optimization problem which can be solved optimally using convex optimizationtechniques [80]. The partial Lagrangian of the problem is given byL(P˜I, P˜E,αI ,αE,λ, γ)=S∑s=1(ws,IR˜sR(tar)+ ws,EE˜sE(tar))−N∑t=1λt(αtI + αtE − 1)− N∑t=1γt(S∑s=1P˜ ts,Ihts,m − αtII tmax,I) (4.9)where λ, γ are non-negative Lagrange multipliers associated with constraints C2 and C˜3,respectively. Other constraints are not included in the Lagrangian and will be satisfied later.Since the problem in (4.8) is a convex optimization problem, the solution can be obtainedby solving the following dual problem [80]:minimizeλ,γmaxP˜I,P˜E,αI ,αEL(P˜I, P˜E,αI ,αE,λ, γ)subject to C˜1, C˜4, C5, C˜6 − C˜8,λ, γ  0.(4.10)The solution of the dual problem in (4.10) can be iteratively obtained by dual decomposi-tion technique [85]. In each iteration, for given dual variables (Lagrange multipliers), thesubproblems are solved to obtain the primal variables (power and time-switching variables).Then the master problem updates the dual variables using the solution of the subproblems.The iterative procedure is continued till convergence is attained.774.3. Resource Allocation for Time-switching Approach: Problem Formulations and SolutionsSolving the subproblemWhen the dual variables are known, to solve for the primal variables, we will exploit the factthat for a convex optimization problem, at optimality, KKT conditions must be satisfied [80].Based on the KKT conditions, we can verify that, at optimality, time-switching variablesαtI , αtE, and auxiliary power variables P˜ts,I are related to each other as follows:αtE = 1− αtI , ∀t (4.11)P˜ ts,I = αtI[ws,Iγthts,mN log(2)R(tar)− χtm,s +Nsphts,s]Ps(max)0,∀s, t (4.12)where [x]ab indicates x = a if x > a and x = b if x < b. (4.11) and (4.12) are obtained bysimplifying the KKT conditions and the details of derivation are shown in Appendix D. Notethat boundary constraints C˜6 and C˜8 are included in (4.12).Using the relation of optimization variables given in (4.11) and (4.12), we can re-writethe subproblem of the dual problem given in (4.10) asmaximizeαI ,P˜E∑Nt=1(αtIR˜tsum +∑Ss=1 P˜ts,EHts,s)subject toCˆ1 : 0 ≤ αtI ≤ 1, ∀tCˆ4 :S∑s=1P˜ ts,Ehts,m ≤ (1− αtI)I tmax,E, ∀tCˆ5 :N∑t=1αtI ≥ Υ(min)Cˆ7 : P˜ts,E ≤ (1− αtI)Ps(max), ∀s, tCˆ8 : P˜ts,E ≥ 0, ∀s, t, where(4.13)R˜tsum =S∑s=1[ws,INR(tar)log2(1 +Pˆ ts,Ihts,sχtm,s +Nsp)− ws,Eχtm,sηNE(tar)− γthts,mPˆ ts,I]+ γtI tmax,I ,∀t,784.3. Resource Allocation for Time-switching Approach: Problem Formulations and SolutionsH ts,s =ηws,Ehts,sNE(tar),∀s, t,Pˆ ts,I =[ws,Iγthts,mN log(2)R(tar)− χtm,s +Nsphts,s]Ps(max)0,∀s, t,Υ(min) =N(R(min) −R(min,E))(R(min,I) −R(min,E)) ,and the constant terms are removed from the objective function. It should be noted that theconstraints Cˆ1, Cˆ4, Cˆ5, Cˆ7, and Cˆ8 are derived from the constraints of the problem in (4.10)using (4.11). Note that the constraint Cˆ5 now dictates the minimum amount of time thatshould be allocated for ID process in order to ensure that minimum throughput requirementof the MUE is satisfied. The problem in (4.13) is a linear programming problem and can besolved optimally by using interior-point method.Lemma 7 : If Υ(min) is an integer, then the resulting solution satisfies constraint C1 of theoriginal optimization problem in (4.5), and therefore, is the optimal solution of the originalproblem [91].Proof : First, let us assume that the optimal solution has only one non-integer time-switching variable 0 < αt1I < 1, for t = t1 and all the constraints are satisfied. In that case,if Υ(min) is an integer and Cˆ5 has been satisfied,∑Nt=1,t 6=t1 αtI = Υ(min). To prove that theoptimal solution always has integer time-switching variables, we will prove that the non-integer solution is not the optimal solution, by contradiction. Let us explore three differentcases now.Case I : Let us say R˜t1sum > αt1I R˜t1sum +∑Ss=1 P˜t1s,EHt1s,s =⇒ R˜t1sum >∑Ss=1P˜t1s,E1−αt1IH t1s,s, thenincreasing αt1I to α∗t1I = 1 will force P˜t1s,E to be P˜∗t1s,E = 0, ∀s (due to constraint Cˆ7) and willfurther maximize the objective function. It can be verified that the new solution will alsosatisfy all the constraints of the problem.Case II : On the other hand, if R˜t1sum < αt1I R˜t1sum+∑Ss=1 P˜t1s,EHt1s,s =⇒ R˜t1sum <∑Ss=1P˜t1s,E1−αt1IH t1s,s,then decreasing αt1I to α∗t1I = 0 zero will increase P˜t1s,E to P˜∗t1s,E =P˜t1s,E1−αt1I,∀s (on account ofconstraint Cˆ7) and will further maximize the objective function. It can be verified that the794.3. Resource Allocation for Time-switching Approach: Problem Formulations and Solutionsnew solution will also satisfy all constraints of the problem.Case III : If R˜t1sum = αt1I R˜t1sum+∑Ss=1 P˜t1s,EHt1s,s, then setting either αt1∗I = 0 or αt1∗I = 1 willimply corresponding change in P˜ t1s,E, but the objective function will remain the same and allconstraints of the problem will remain satisfied.By these three cases, we prove by contradiction that the solution with one non-integertime-switching variable is not the optimal solution. Similar argument can be used to provethat the solution with two non-integer time-switching variables is also not the optimal so-lution, and so on. Therefore, we prove by contradiction, that the solution of the problemin (4.13) will satisfy binary integer constraint C1 of the original optimization problem andhence is the optimal solution of the original problem, if Υ(min) is an integer. This completesthe proof. Solving the master problemThe optimal value of dual variables can be obtained by using well-known subgradient method [87]to update the dual variables as follows:γt(it+1) =[γt(it) + ∆γt(S∑s=1P˜ ts,Ihts,m − αtII tmax,I)]+,∀t (4.14)where ∆γt is the step size and [x]+ enforces the non-negativity constraint on dual variables.Updated dual variables are then used to obtain new solution for the subproblems. Thisprocess is iterated until convergence. Convergence of subgradient method to the globallyoptimal solution is guaranteed for convex optimization problem for small step size [87].After obtaining optimal solution, the optimal power allocation can be recovered by using therelation in (4.6).804.3. Resource Allocation for Time-switching Approach: Problem Formulations and Solutions4.3.2 Scenario II: Non-negligible Co-tier InterferenceIn this scenario, we assume that the co-tier interference is non-negligible. In this case, beforerelaxing the time-switching variables and using the auxiliary power variables given in (4.6),let us re-write the problem in (4.5) asmaximizePI,PE,αI ,αE∑Nt=1(f(PIt,PEt, αtI , αtE)− g(PIt, αtI))subject toC1 − C7(4.15)where PIt = {P ts,I , ∀s}, PEt = {P ts,E, ∀s}, ∀t, andf(PIt,PEt, αtI , αtE) =S∑s=1[ws,IαtINR(tar)log2(S∑j=1P tj,Ihtj,s + χtm,s +Nsp)+ws,EαtEηNE(tar)(S∑j=1P tj,Ehtj,s + χtm,s)],∀t(4.16)g(PIt, αtI) =S∑s=1ws,IαtINR(tar)log2(S∑j=1,j 6=sP tj,Ihtj,s + χtm,s +Nsp),∀t. (4.17)Now, let us relax the time-switching variables and use the definition of auxiliary powervariables given in (4.6). With the auxiliary power variables, (4.16) and (4.17) can be re-written asf˜(P˜tI, P˜tE, αtI , αtE) =S∑s=1[ws,IαtINR(tar)log2(S∑j=1P˜ tj,IαtIhtj,s + χtm,s +Nsp)+ws,EηNE(tar)(S∑j=1P˜ tj,Ehtj,s + αtEχtm,s)],∀t(4.18)g˜(P˜tI, αtI) =S∑s=1ws,IαtINR(tar)log2(S∑j=1,j 6=sP˜ tj,IαtIhtj,s + χtm,s +Nsp),∀t (4.19)where P˜tI = {P˜ ts,I , ∀s} and P˜tE = {P˜ ts,E, ∀s}, ∀t. It should be noted that f˜(P˜tI, P˜tE, αtI , αtE)and g˜(P˜tI, αtI) can both be proven to be concave functions of P˜ts,I , P˜ts,E, αtI , and αtE due814.3. Resource Allocation for Time-switching Approach: Problem Formulations and Solutionsto concavity of perspective operation and concavity of log function. Therefore, problemin (4.15) can be re-written, with difference of concave functions in the objective, as follows:maximizeP˜I,P˜E,αI ,αE∑Nt=1(f˜(P˜tI, P˜tE, αtI , αtE)− g˜(P˜tI, αtI))subject to C˜1, C2, C˜3, C˜4, C5, C˜6 − C˜8.(4.20)The constraints of the problem in (4.20) are same as that of the modified problem in (4.8)of Scenario I and derived in a similar manner. We know that the constraints are affine butthe objective function is neither concave nor convex. Finding the optimal solution to sucha problem is difficult it its original form. However, we can find suboptimal solution to theproblem in (4.20) by using successive convex approximation method where we iterativelymaximize the concave minorant [92–94] of the objective function. First of all, we will definethe concave minorant in the following definition.Definition 1 : Since g˜(Xt) is a concave function, it is upper bounded by its first-orderTaylor approximation g˜(Xt(k)) +∇g˜(Xt(k))> (Xt −Xt(k)), and therefore, f˜(Xt,Yt)− g˜(Xt)is bounded below by its concave minorant f˜(Xt,Yt)− g˜(Xt(k))−∇g˜(Xt(k))> (Xt −Xt(k)) inthe neighborhood of Xt(k) [92, 94] asf˜(Xt,Yt)− g˜(Xt) ≥ f˜(Xt,Yt)− g˜(Xt(k))−∇g˜(Xt(k))> (Xt −Xt(k)) (4.21)where Xt = {αtI , P˜ ts,I ,∀s}, Yt = {αtE, P˜ ts,E, ∀s} are used for simplicity and conciseness of theexpression.We know that∇g˜(Xt(k))> (Xt −Xt(k)) = S∑s=1Us(P˜t(k)I , αt(k)I )(P˜ ts,I − P˜ t(k)s,I)+ V (P˜t(k)I , αt(k)I )(αtI − αt(k)I)824.3. Resource Allocation for Time-switching Approach: Problem Formulations and SolutionswhereUs(P˜tI, αtI) =∂g˜(P˜tI, αtI)∂P˜ ts,I=S∑l=1,l 6=swl,Ihts,lNR(tar)log(2)(∑Sj=1,j 6=lP˜ tj,Ihtj,lαtI+ χtm,l +Nsp) ,∀sV (P˜tI, αtI) =∂g˜(P˜tI, αtI)∂αtI=S∑s=1ws,INR(tar)−∑Sj=1,j 6=sP˜ tj,Ihtj,sαtIlog(2)(∑Sj=1,j 6=sP˜ tj,Ihtj,sαtI+ χtm,s +Nsp)+ log2(S∑j=1,j 6=sP˜ tj,Ihtj,sαtI+ χtm,s +Nsp)].Therefore, we can write the concave minorant of the objective function asΦ(k)TS(P˜I, P˜E,αI ,αE) =N∑t=1(f˜(P˜tI, P˜tE, αtI , αtE)− g˜(P˜t(k)I , αt(k)I )−S∑s=1Us(P˜t(k)I , αt(k)I )(P˜ ts,I − P˜ t(k)s,I)− V (P˜t(k)I , αt(k)I )(αtI − αt(k))).(4.22)Now we will define the following convex subproblem to maximize the concave minorant ofthe objective function in the neighborhood of (P˜(k)I , α(k)I ):maximizeP˜∗I ,P˜∗E,αI∗,αE∗Φ(k)TS(P˜I, P˜E,αI ,αE)subject to C˜1, C2, C˜3, C˜4, C5, C˜6 − C˜8.(4.23)Maximizing the concave minorantWe know that subproblem defined in (4.23) is a convex optimization problem with affineconstraints. Therefore, it can be solved optimally using convex optimization techniques [80].834.3. Resource Allocation for Time-switching Approach: Problem Formulations and SolutionsLet us define the partial Lagrangian of the problem asL(k)(P˜I , P˜E,αI ,αE,λ,γ) = Φ(k)TS(P˜I, P˜E,αI ,αE)−N∑t=1λt(αtI + αtE − 1)− N∑t=1γt(S∑s=1P˜ ts,Ihts,m − αtII tmax,I)(4.24)where λ, γ are non-negative Lagrange multipliers associated with constraints C2 and C˜3 asin Scenario I. Other constraints are not included in the Lagrangian and will be satisfied later.Since the problem in (4.23) is convex, the solution can be obtained by solving the followingdual problem [80]:minimizeλ,γmaxP˜I,P˜E,αI ,αEL(k)(P˜I, P˜E,αI ,αE,λ, γ)subject to C˜1, C˜4, C5, C˜6 − C˜8,λ, γ  0.(4.25)The solution of dual problem in (4.25) can be iteratively obtained by dual decompositiontechnique [85]. For given dual variables, the subproblems are solved to obtain the optimalpower and time-switching variables. Then the master problem updates the dual variablesusing the solution of the subproblems. The iterative procedure is continued until convergence.Solving the subproblemAs in Scenario I, to solve for the primal variables, we will exploit the fact that for convexoptimization problem, at optimality, KKT conditions [80] must be satisfied. Based on theKKT conditions, we can verify that, at optimality, the time-switching variables and auxiliarypower variables are related to each other as follows:αtE = 1− αtI , ∀t (4.26)P˜ ts,I = αtI[xts]Ps(max)0,∀s, t (4.27)844.3. Resource Allocation for Time-switching Approach: Problem Formulations and Solutionswhere xts is the solution of S ×N equations given asS∑l=1wl,Ihts,lNR(tar)log(2)(∑Sj=1 xtjhtj,l + χtm,l +Nsp) − Us(P˜t(k)I , αt(k)I )− γthts,m = 0, ∀s, t. (4.28)(4.26) and (4.27) are obtained by simplifying the KKT conditions and the details of derivationare similar to that given in Appendix D for Scenario I. Note that boundary constraints C˜6and C˜8 are included in (4.27).Using the relations in (4.26) and (4.27), we can re-write the subproblem of the dualproblem in (4.25) asmaximizeαI∗,P˜E∗∑Nt=1(αtIGt +∑Ss=1∑Sj=1 P˜tj,EHtj,s)subject to Cˆ1, Cˆ4, Cˆ5, Cˆ7, Cˆ8(4.29)whereGt =∑Ss=1[ws,Ilog2(∑Sj=1 Pˆtj,Ihtj,s+χtm,s+Nsp)NR(tar)− Us(P˜t(k)I , αt(k)I )Pˆ ts,I − ws,Eηχtm,sNE(tar)− γthts,mPˆ ts,I]+γtI tmax,I − V (P˜t(k)I , αt(k)I ), ∀t, H tj,s =ws,Eηhtj,sNE(tar),∀j, t, s, Pˆ ts,I = [xts]Ps(max)0 ,∀s, t, and constantterms have been removed from the objective function. It should be noted that the con-straints Cˆ1, Cˆ4, Cˆ5, Cˆ7, and Cˆ8 are derived using (4.26) and are same as that of problem in(4.13) of Scenario I. Again, the problem in (4.29) is a linear programming problem and canbe solved optimally using interior-point method. Lemma 7 holds true for the solution of theproblem in (4.29) as well and it can be verified in a similar manner.Solving the master problemAs in Scenario I, optimal values of dual variables can be obtained by using subgradientmethod [87] to update the dual variables as given in (4.14).Updated dual variables are then used to obtain new solution for primal variables. Thisprocess is iterated till convergence. Convergence of subgradient method to globally optimal854.3. Resource Allocation for Time-switching Approach: Problem Formulations and Solutionssolution is guaranteed for a convex optimization problem. A new concave minorant is thendefined in neighborhood of the optimal solution of the subproblem, using (4.22), and theprocess is iterated until convergence. Algorithm 3 summarizes the resource allocation frame-work described for Scenario II. Iterative maximization of concave minorant of the differenceof concave functions is guaranteed to converge and the proof of convergence is similar tothat in [95]. Note that, in both scenarios of time-switching approach, with the help of dualdecomposition technique, a linear programming problem with reduced number of variablesis rendered from the relaxed convex optimization problem to identify the condition at whichsolution of the relaxed convex optimization problem satisfies binary integer constraint of theoriginal MINLP problem.Algorithm 3 Resource Allocation Algorithm for Scenario II of Time-switching ApproachRequire: Initialize k = 0 and P˜t(k)s,I , αt(k)I ,∀s, t1: repeat2: Define concave minorant of objective function using (4.22)3: Formulate convex subproblem as defined in (4.23)4: Initialize dual variables γt, ∀t5: repeat6: Solve (4.28) for xts, ∀s, t7: Solve the problem in (4.29) for αt∗I and P˜t∗s,E, ∀s, t, using interior-point method8: Compute αt∗E , P˜t∗s,I , ∀s, t, using (4.26) and (4.27)9: Update dual variables γt using subgradient method as given in (4.14)10: until Convergence11: Update k ← k + 1; P˜ t(k)s,I = P˜ t∗s,I , αt(k)I = αt∗I ,∀s, t12: until Convergence13: Calculate P ts,I and Pts,E using the relation in (4.6)864.4. Resource Allocation for Power-splitting Approach: Problem Formulation and Solution4.4 Resource Allocation for Power-splittingApproach: Problem Formulation and SolutionProblem formulationIn power-splitting approach, SUEs split the received power into two fractions and share itamong EH and ID circuits in each time slot. The resource allocation problem, to maximizeweighted sum of normalized throughput and energy harvesting rate of the SUEs over onetransmission block, is given bymaximizeP,ρI ,ρE∑Ss=1(ws,IRsR(tar)+ ws,EEsE(tar))subject toCa : ρtI + ρtE ≤ 1,∀t, Cd :P ts ≤ Ps(max),∀s, tCb : 0 ≤ ρtI , ρtE ≤ 1,∀t, Ce :P ts ≥ 0,∀s, tCc :S∑s=1P tshts,m − I tmax ≤ 0,∀t(4.30)where P ∈ {P ts , ∀s, t}, ρI ∈ {ρtI , ∀t}, and ρE ∈ {ρtE, ∀t}. Constraints Ca and Cb ensurethat total power received by EH and ID circuits together cannot be greater than that receivedby power-splitter. Since EH and ID processes are not separated in time domain, R(min) isthe minimum throughput that should be ensured for MUE in each time slot to ensure thatthroughput of the MUE over one transmission block is greater than or equal to R(min).This requires maximum sum-interference received by the MUE to be less than or equal toI tmax =Pmhtm,m2R(min)−1 −Nw −Nsp in each time slot, as indicated by Cc9. Cd and Ce are boundaryconstraints on power variables. All constraints along with the objective of the problem in(4.30) can be separated in time domain. Therefore, from (4.30), N maximization problems9Note that constraint Cc of the problem formulated for power-splitting approach in (4.30) is equivalentto constraint C5 of the problem formulated for time-switching approach in (4.5) since both of them ensurethat throughput of the MUE is greater than or equal to R(min) over one transmission block, hence ensuringa fair comparison between these two approaches.874.4. Resource Allocation for Power-splitting Approach: Problem Formulation and Solutioncan be formulated and independently solved. Therefore, from now on, we will show thesolution approach for one time-slot. We will simply eliminate superscript t from the definedvariables and parameters.Solution approachObjective function of the problem in (4.30) is very complicated in terms of optimizationvariables. For tractability, we introduce auxiliary power variables: Ps,I = ρIPs and Ps,E =ρEPs, ∀s. The achievable throughput and energy harvesting rate, given in (4.3) and (4.4),respectively, can be re-written asR˜s =1Nlog2(1 +Ps,Ihs,s∑Sj=1,j 6=s Pj,Ihj,s + ρIχm,s +Nsp)E˜s =ηN(S∑j=1Pj,Ehj,s + ρEχm,s), ∀s.(4.31)With introduction of auxiliary power variables, problem in (4.30) can be re-written asmaximizePI,PE,ρI ,ρE∑Ss=1(ws,I R˜sR(tar)+ws,EE˜sE(tar))subject to Ca, CbC˜c1 :S∑s=1Ps,Ihs,m − ρIImax ≤ 0C˜c2 :S∑s=1Ps,Ehs,m − ρEImax ≤ 0C˜d1 : Ps,I − ρIPs(max) ≤ 0,∀sC˜d2 : Ps,E − ρEPs(max) ≤ 0,∀sC˜e : Ps,I , Ps,E ≥ 0,∀s(4.32)where constraints C˜c1, C˜c2, C˜d1, C˜d2, and C˜e are re-written using the definition of newauxiliary power variables, PI = {Ps,I ,∀s}, and PE = {Ps,E,∀s}. The problem in (4.32) is884.4. Resource Allocation for Power-splitting Approach: Problem Formulation and Solutionnot convex but can be represented as a difference of concave functions as follows:S∑s=1(ws,IR˜sR(tar)+ws,EE˜sE(tar))= fPS(PI,PE, ρI , ρE)− gPS(PI, ρI)wherefPS(PI,PE, ρI , ρE) =S∑s=1[ws,INR(tar)log2(S∑j=1Pj,Ihj,s + ρIχm,s +Nsp)+ws,EηNE(tar)(S∑j=1Pj,Ehj,s + ρEχm,s)]gPS(PI, ρI) =S∑s=1ws,INR(tar)log2(S∑j=1,j 6=sPj,Ihj,s + ρIχm,s +Nsp).Following Definition 1, the concave minorant, Φ(k)PS(PI,PE, ρI , ρE), of the objective functionsuch that Φ(k)PS(PI,PE, ρI , ρE) ≤ fPS(PI,PE, ρI , ρE) − gPS(PI, ρI), can be defined in theneighborhood of (PI(k), ρ(k)I ) asΦ(k)PS(PI,PE, ρI , ρE) =fPS(PI,PE, ρI , ρE)− gPS(PI(k), ρ(k)I )−S∑s=1Us(PS)(PI(k), ρ(k)I )(Ps,I − P (k)s,I)− V(PS)(PI(k), ρ(k)I )(ρI − ρ(k)I)(4.33)whereUs(PS)(PI, ρI) =∂gPS(PI, ρI)∂Ps,I=S∑l=1,l 6=swl,Ihs,lNR(tar)log(2)(∑Sj=1,j 6=l Pj,Ihj,l + ρIχm,l +Nsp) ,∀sV(PS)(PI, ρI) =∂gPS(PI, ρI)∂ρI=S∑s=1ws,Iχm,sNR(tar)log(2)(∑Sj=1,j 6=s Pj,Ihj,s + ρIχm,s +Nsp) .894.4. Resource Allocation for Power-splitting Approach: Problem Formulation and SolutionTherefore, the problem of maximizing concave minorant of the objective function in neigh-borhood of (PI(k), ρ(k)I ) can be written asmaximizePI∗,PE∗,ρ∗I ,ρ∗EΦ(k)PS(PI,PE, ρI , ρE)subject toCa, Cb, C˜c1, C˜c2, C˜d1, C˜d2, C˜e.(4.34)The problem in (4.34) has concave objective function and affine constraints and hence isa convex optimization problem which can be solved using convex optimization techniquesdiscussed in the following.Let us define the partial Lagrangian of the problem in (4.34) as follows:L(k)(PI,PE, ρI , ρE, λ, γ1, γ2,β1,β2) = Φ(k)PS(PI,PE, ρI , ρE)− λ (ρI + ρE − 1)−γ1(S∑s=1Ps,Ihs,m − ρIImax)− γ2(S∑s=1Ps,Ehs,m − ρEImax)−S∑s=1β1s(Ps,I − ρIPs(max))− S∑s=1β2s(Ps,E − ρEPs(max))(4.35)where λ, γ1, γ2, β1, and β2 are non-negative Lagrange multipliers associated with con-straints Ca, C˜c1, C˜c2, C˜d1, and C˜d2, respectively. Constraints Cb and C˜e are not included inthe Lagrangian and will be satisfied later.Lemma 8 : At optimality, the auxiliary power allocation variables and power-splittingvariables are related to each other as follows:ρ∗E = 1− ρ∗I (4.36)P ∗s,E =(1− ρ∗I)ρ∗IP ∗s,I ,∀s. (4.37)Proof : Differentiating (4.35) with respect to ρE and applying the KKT stationarityconditions, we obtain∑Ss=1ws,Eηχm,sNE(tar)− λ+ γ2Imax +∑Ss=1 β2sPs(max) = 0. Since all the otherterms in the left hand side of the equation are positive, in order to satisfy the stationarity904.4. Resource Allocation for Power-splitting Approach: Problem Formulation and Solutioncondition, λ > 0 is strictly satisfied. Then to satisfy the KKT slackness condition, theconstraint associated with the Lagrange multiplier λ must be tightly satisfied as given in(4.36). Then, (4.37) follows from (4.36) and the definition of auxiliary variables. Thiscompletes the proof. Lemma 9 : P ∗s,I and ρ∗I are obtained by solving the following set of equations and inequal-ities:S∑l=1wl,Ihs,lNR(tar)log(2)(∑Sj=1 Pj,Ihj,l + ρIχm,l +Nsp) + 1− ρIρIS∑l=1wl,Eηhs,lNE(tar)−Us(PS)(PI(k), ρ(k)I )− γ1hs,m = 0, ∀s(4.38)S∑l=1 wl,Iχm,lNR(tar)log(2)(∑Sj=1 Pj,Ihj,l + ρIχm,l +Nsp) − wl,EηNE(tar)(S∑j=1Pj,Ihj,lρ2I+ χm,l)−V(PS)(PI(k), ρ(k)I ) + γ1Imax = 0(4.39)Ps,I ≥ 0, 0 ≤ ρI ≤ 1. (4.40)Proof : In the power-splitting approach, if maximum transmit power Ps(max) is sufficientlyhigh and maximum tolerable interference on MUE Imax is sufficiently low, we can assumethat the transmit power Ps,I is always constrained by the interference constraint Cc1 andhence the boundary constraint Cd1 is never tightly satisfied10. In that case β1s should be0 to satisfy the slackness condition. Also, using relations given in (4.36) and (4.37) inLemma 8, the partial Lagrangian given in (4.35) can be re-written in terms of Ps,I , ∀s andρI . Then, differentiating the new Lagrangian with respect to Ps,I and ρI , and then usingKKT stationarity conditions as shown in Appendix D for Scenario I, we obtain (4.38) and(4.39), respectively. It should be noted that the constraints Cb and C˜e are satisfied in the10Note that the assumption cannot be made in the time-switching approach because, by lowering theminimum rate requirement of MUE in the EH mode, the maximum tolerable interference of MUE is increasedand hence transmit power of SBSs can be constrained either by the interference constraint or by the boundaryconstraint.914.5. Performance Evaluation Resultssolution by including the KKT primal feasibility conditions in (4.40). This completes theproof. As in previous scenarios, the optimal value of dual variable γ1 can be obtained by usingsubgradient method to update the dual variable [87]. Updated dual variable is then usedto obtain new solution for primal variables. This process is iterated until convergence.The solution obtained is then used to obtain new concave minorant, defined in (4.33) andthe process is repeated until convergence. Algorithm 4 summarizes the resource allocationframework described in this section. Note that with the help of dual decomposition technique,we identify the relationship between power-splitting and transmit power variables, and reducethe number of unknown variables to solve in each inner iteration of Algorithm 4.Algorithm 4 Resource Allocation Algorithm for Power-splitting ApproachRequire: Initialize k = 0 and P(k)s,I , ρ(k)I ,∀s1: repeat2: Define concave minorant of objective function using (4.33)3: Formulate convex subproblem defined in (4.34) and initialize dual variable γ14: repeat5: Solve (4.38)-(4.40) to obtain P ∗s,I , ∀s and ρ∗I6: Compute ρ∗E and P∗s,E, ∀s using (4.36)-(4.37)7: Update dual variable γ1 using subgradient method as given in (4.14) for Scenario I8: until Convergence9: Update k ← k + 1; P (k)s,I = P ∗s,I , ∀s, ρ(k)I = ρ∗I10: until Convergence11: Calculate Ps = Ps,I/ρI ,∀s4.5 Performance Evaluation ResultsIn this section, we present and analyze simulation results for the proposed resource allocationmodels of different SWIPT scenarios in a two-tier HetNet and also compare them with theperformance of the traditional two-tier communication network11. In particular, we evaluate11Note that throughput expression and power allocation problem for traditional two-tier network modelcan be derived from that of SWIPT-based network with power-splitting approach by setting ρtI = 1, ρtE = 0and the solution approach can be extracted accordingly.924.5. Performance Evaluation Resultssum-throughput (Rsum =∑Ss=1Rs) and sum-energy harvesting rate (Esum =∑Ss=1Es) ofSUEs under different scenarios.4.5.1 Simulation ParametersWe consider a single macrocell with the MBS at the origin. There are S = 2 small cellsat a distance of 100 m from the MBS. Both small cells have an SUE at a distance of 3 to10 m from the SBS. An MUE is located close to the small cells. The transmit power Pmof MBS and maximum transmit power Ps(max) of SBSs are both assumed to be 46 dBm.Channel models from [96] are used to compute the channel gains. The path-loss, in dB, inthe link from SBS to its SUE is 38.46 + 20logD, SBS to other UEs is 38.46 + 20logD + Lw,MBS to an SUE is 15.3 + 37.6logD+Lw, and MBS to MUE is 15.3 + 37.6logD, respectively,where D is the distance between the transmitter and the receiver in meters. Lw accountsfor the losses due to walls and is assumed to be 1 dB in our simulations. The antenna noisepower is assumed to be 10−13 W, signal processing noise power to be 3 dB stronger thanthe antenna noise power, each downlink time is divided into N = 4 time slots, and ws,I andws,E are set to 1. Unless stated otherwise, energy harvesting efficiency η is 50%12, minimumthroughput requirement of MUE is 1 bps/Hz, and target throughput and energy harvestingrate of SUEs are 1 bps/Hz and 1 µJps, respectively. Unless stated otherwise, in the scenarioswith time-switching approach, the minimum throughput of MUE ensured in EH time is 0.05bps/Hz and that in ID time is 2 bps/Hz. All the simulations are repeated for 1000 differentRayleigh fading channel realizations and the results are averaged.12Wireless energy harvesting efficiency is found to be as high as 65.2% when the received RF power is −22dBm in [23,97]. However, for fair comparison, unless stated otherwise, we use η = 50% in all scenarios.934.5. Performance Evaluation Resultsη0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Rsum(bps/Hz)2.533.544.555.566.57Power-splittingTime-switching:Sc-I(R(min,E) = 0.05 bps/Hz)Time-switching:Sc-II(R(min,E) = 0.05 bps/Hz)Time-switching:Sc-I(R(min,E) = 0.5 bps/Hz)Time-switching:Sc-II(R(min,E) = 0.5 bps/Hz)Figure 4.2: Sum-throughput of SUEs versus η.4.5.2 Simulation ResultsVariation of Rsum and Esum with energy harvesting efficiency ηWhen η is very small, SUEs can harvest very little energy from the received signal whichdecreases the normalized energy harvesting rate. Therefore, more time is allocated to IDprocess to maximize the objective. For this reason, we notice higher Rsum and lower Esum forlower η (Figs. 4.2 and 4.3). With increasing η, time allocated to EH process increases becauseof which Esum increases and Rsum decreases. However, beyond a certain value of η (e.g. 20%when R(min,E) = 0.05 bps/Hz), the time allocated to ID process cannot be decreased furtherin order to satisfy the minimum throughput requirement of MUE (as indicated by constraintCˆ5 in problem (4.13) and (4.29)). After that point, Rsum saturates. However, Esum keepsimproving with increasing η. In the case with power-splitting approach, Rsum remains almostthe same while Esum increases with increasing η.We observe that, when R(min,E) = 0.05 bps/Hz, Esum is much higher in the time-switchingapproach compared to the power-splitting approach. This is because of the additional degree944.5. Performance Evaluation Resultsη0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Esum(Jps)10-710-610-5Power-splittingTime-switching:Sc-I(R(min,E) = 0.05 bps/Hz)Time-switching:Sc-II(R(min,E) = 0.05 bps/Hz)Time-switching:Sc-I(R(min,E) = 0.5 bps/Hz)Time-switching:Sc-II(R(min,E) = 0.5 bps/Hz)Figure 4.3: Sum-energy harvesting rate of SUEs versus η.of freedom provided by isolating EH process from ID process in time domain and increasingthe interference tolerance level of MUE during the EH phase. However, when R(min,E)increases to 0.5 bps/Hz, interference tolerance of MUE in EH phase decreases and thereforeEsum decreases significantly. In fact, η must be very high (50 − 60%) for time-switchingapproach to have significant improvement over power-splitting approach in Esum. The gainin Esum, however, comes at the cost of lower Rsum in comparison to the power-splittingapproach. Comparing the two scenarios of time-switching approach, Esum is higher in thescenario with non-negligible co-tier interference at the cost of lower Rsum.Variation in Rsum and Esum with target throughput of SUEsIn the time-switching approach, with increasing R(tar), the normalized throughput (ws,IRsR(tar))decreases, and therefore, more time is allocated to EH process than ID process to maximizethe objective (Fig. 4.6). Therefore, Rsum decreases while Esum increases with increasingR(tar)(Fig. 4.4 and 4.5). However, after a certain value, the sum-throughput of SUEs Rsum954.5. Performance Evaluation ResultsR(tar) (bps/Hz)0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Rsum(bps/Hz)2.533.544.555.566.57Power-splitting (E(tar) = 1µJps)Time-switching:Sc-I (E(tar) = 1µJps)Time-switching:Sc-II (E(tar) = 1µJps)Power-splitting (E(tar) = 10µJps)Time-switching:Sc-I (E(tar) = 10µJps)Time-switching:Sc-II (E(tar) = 10µJps)Figure 4.4: Sum-throughput of SUEs versus R(tar).R(tar) (bps/Hz)0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Esum(Jps)×10-500.20.40.60.811.21.41.61.82Power-splitting (E(tar) = 1µJps)Time-switching:Sc-I (E(tar) = 1µJps)Time-switching:Sc-II (E(tar) = 1µJps)Power-splitting (E(tar) = 10µJps)Time-switching-I (E(tar) = 10µJps)Time-switching:Sc-II (E(tar) = 10µJps)Figure 4.5: Sum-energy harvesting rate of SUEs versus R(tar).964.5. Performance Evaluation ResultsR(tar) (bps/Hz)0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Averagefractionoftime/powerallocatedforinformationdecoding00.10.20.30.40.50.60.70.80.91Power-splitting (E(tar) = 1µJps)Time-switching:Sc-I (E(tar) = 1µJps)Time-switching:Sc-II (E(tar) = 1µJps)Power-splitting (E(tar) = 10µJps)Time-switching:Sc-I (E(tar) = 10µJps)Time-switching:Sc-II (E(tar) = 10µJps)Figure 4.6: Average fraction of time/power allocated for ID process versus R(tar).stabilizes which is because time allocated for ID process cannot be lower than a certain valueto ensure minimum throughput requirement of MUE (constraint Cˆ5 of problem (4.13) and(4.29)). Similarly, when E(tar) is higher, Esum decreases and Rsum increases because higherE(tar) decreases the normalized energy harvesting rate (ws,EEsE(tar)) and therefore, more timeis allocated to ID process (Fig. 4.6). In the power-splitting approach, we observe that lesspower is allocated to ID process with increasing R(tar) and decreasing E(tar) (Fig. 4.6) for thesimilar reason explained in the case of time-switching approach. However, since interferencesignal and antenna noise are split by the same ratio as the information signal, the sum-throughput of SUEs remains unaffected by this variation in R(tar) as well as E(tar).Variation of Rsum and Esum with transmit power of MBSWhen Pm increases from 46 dBm to 48 dBm, sum-energy harvesting rate Esum increasesby about 1.5 times in all the scenarios (Fig. 4.7). With increase in Pm, SBSs can transmithigher power but SUEs will also suffer from higher cross/co-tier interference. Hence, sum-974.5. Performance Evaluation ResultsPm (dBm)46 46.2 46.4 46.6 46.8 47 47.2 47.4 47.6 47.8 48Esum(Jps)×10-500.511.522.533.5Power-splittingTime-switching:Sc-ITime-switching:Sc-IIFigure 4.7: Sum-energy harvesting rate of SUEs versus Pm.throughput of the SUEs Rsum has been observed to remain unchanged with increase in Pm.The plot is omitted due to lack of interesting insights.Variation of Rsum and Esum with minimum throughput requirements of MUEIn the time-switching approach, with increasing R(min), minimum time, that should be allo-cated to ID process to ensure that minimum throughput requirement of the MUE is satisfied,increases (constraint Cˆ5 of problem (4.13) and (4.29)). Therefore, Rsum increases (Fig. 4.8)and Esum decreases (Fig. 4.9). On the other hand, in the power-splitting approach, withincreasing R(min), the interference tolerance of the MUE further decreases which restrictsthe transmit power of the SUEs. This causes both Esum as well as Rsum to decrease withincreasing R(min). Esum increases with increasing η while Rsum decreases with increasingη and then saturates which agrees with the result shown in Figs. 4.2 and 4.3. Interest-ingly, sum-throughput performance of traditional two-tier communication network is sameas that of SWIPT network with power-splitting approach. It is mainly because, as long984.5. Performance Evaluation ResultsR(min) (bps/Hz)1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2Rsum(bps/Hz)234567η=100%η=50%η=10%No-SWIPTTime-switching: Sc-IITime-switching:Sc-IPower-splittingFigure 4.8: Sum-throughput of SUEs versus R(min).R(min) (bps/Hz)1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2Esum(Jps)10-710-610-510-4Time-switching: Sc-IITime-switching: Sc-IPower-splittingSolid Line: η = 100%Dashed Line:η = 50%Dash-dotted Line:η = 10%Figure 4.9: Sum-energy harvesting rate of SUEs versus R(min).994.5. Performance Evaluation ResultsR(min) (bps/Hz)0.8 1 1.2 1.4 1.6 1.8 2 2.2Averagereceivedpowerforenergyharvesting(dBm)-35-30-25-20-15-10-50Power-splittingTime-switching: Sc-ITime-switching: Sc-IIFigure 4.10: Average received power for energy harvesting versus R(min).as the power-splitting factor ρtI is not arbitrarily small and the signal processing noise isnegligible in comparison to the interference signal, throughput expression of the SUE withpower-splitting approach is not affected by the power-splitting factor. This also indicatesthat, due to severe interference constraint imposed in the presence of macrocell UEs, energyharvesting rate is so small in power-splitting approach that downlink power is allocated tomaximize the normalized throughput as in the case of a traditional two-tier network.Due to the additional degree of freedom provided in the time-switching approach wherethe EH and ID processes are separated in time domain and the interference tolerance limitof MUE is increased in EH phase, the average received power of SUEs during EH processis much higher (equal to or more than −15dBm) in time-switching approach, compared topower-splitting approach (below −25 dBm13) as shown in Fig. 4.10. Given that the energyharvesting receiver sensitivity is one of the crucial issues in wireless energy harvesting sys-tems, using time-switching approach opens up the possibility of successful wireless powertransfer in small cells underlaying the macrocells. With increasing R(min,I), Rsum decreases13Note that, in our simulations, we use 50% energy harvesting efficiency, irrespective of the received power.1004.5. Performance Evaluation ResultsR(min,I) (bps/Hz)1 1.5 2 2.5Rsum(bps/Hz)012345678910Time-switching:Sc-I (R(min,E) = 0.05 bps/Hz)Time-switching:Sc-I (R(min,E) = 1 bps/Hz)Time-switching:Sc-II (R(min,E) = 0.05 bps/Hz)Time-switching:Sc-II (R(min,E) = 1 bps/Hz)Power-splittingFigure 4.11: Sum-throughput of SUEs versus R(min,I).R(min,I) (bps/Hz)1 1.5 2 2.5Esum(Jps)×10-500.20.40.60.811.21.41.61.82Time-switching:Sc-I (R(min,E) = 0.05 bps/Hz)Time-switching:Sc-I (R(min,E) = 1 bps/Hz)Time-switching:Sc-II (R(min,E) = 0.05 bps/Hz)Time-switching:Sc-II (R(min,E) = 1 bps/Hz)Power-splittingFigure 4.12: Sum-energy harvesting rate of SUEs versus R(min,I).1014.5. Performance Evaluation ResultsIteration1 2 3 4 5 6 7ObjectiveFunction-4-202468Power-splitting (Algorithm 4)Time-switching:Sc-II (Algorithm 3)Power-splitting (OPTI)Time-switching:Sc-II (OPTI)Figure 4.13: Convergence and performance analysis of Algorithms 3 and 4.and Esum increases (Figs. 4.11 and 4.12) because the minimum throughput requirement ofMUE can be satisfied by allocating lesser time to ID process (constraint Cˆ5 of problem(4.13) and (4.29)). However, when R(min,E) increases from 0.05 to 1 bps/Hz, it implies theinterference tolerance level of MUE is not much high in the EH process which remarkablyreduces Esum. In fact, the time-switching approach results in even worse Esum performancethan power-splitting approach, when R(min,I) = R(min,E) = 1. This demonstrates the impor-tance of flexible interference tolerance levels in the MUE to maximize energy harvesting rateperformance of SUEs in the time-switching approach.Performance and convergence analysisThe value of the objective function in each iteration of maximizing the concave minorantin Algorithms 3 and 4 are plotted in Fig. 4.13 for S = 2 (for R(min,I) = 2 bps/Hz andRmin,E = 0.1 bps/Hz). Both algorithms converge (upto 5 decimal digits) in around fouriterations. The obtained value of the objective function upon convergence is compared withthe result obtained by solving the non-concave problem directly with OPTI solver [98] which1024.5. Performance Evaluation Resultsis a MATLAB toolbox to solve optimization problems. It is noted that the performance loss,due to approximation of the non-concave function by its concave minorant, is very small.Also, weighted sum of normalized throughput and energy harvesting rate of SUEs is higherin time-switching approach when compared to power-splitting approach.4.5.3 Summary of ObservationsFrom the simulation results, we observe that the achievable energy harvesting rate of SUEs isprofoundly curbed by the minimum throughput requirement of MUE. In the time-switchingapproach, isolating the EH process from the ID process and increasing interference tolerancelevel of the MUE during EH process allow the SBSs to transmit higher power during theEH process. This increases the energy harvesting rate of SUEs. Since EH and ID processcannot be isolated in power-splitting approach, unlike the observation in [20], an inferiorenergy harvesting rate performance is observed, but a better throughput performance isattained. However, performance of the time-switching approach is worse if the MUE doesnot have flexible interference tolerance levels during EH and ID periods. Increasing R(min,I)and decreasing R(min,E) result in better sum-energy harvesting rate but increasing R(min,I)lowers sum-throughput of SUEs. Hence these parameters should be carefully chosen toattain optimal rate-energy trade-off in SUEs. In the time-switching approach, while co-tierinterference causes degradation in throughput performance of SUEs, it provides remarkableimprovement in the energy harvesting rate.103Chapter 5Joint Resource Allocation andDynamic Activation of EnergyHarvesting Small Cells in HetNetsIn Chapters 2-4, we studied resource allocation in cooperative and heterogeneous networkswith wireless energy harvesting. However, wireless energy harvesting is only applicable inlow power miniature devices of the networks, such as sensor nodes, since the energy harvestedis in the range of micro Watts. While wireless energy harvesting is a promising techniqueto elongate the battery life of small nodes in the network, renewable energy harvesting is apromising technique to reduce the power cost of bigger network nodes such as base stations.In this chapter, we consider renewable energy harvesting in small cells of HetNets and performenergy-aware and interference-aware resource allocation jointly with dynamic activation ofenergy harvesting base stations to optimize the trade-off between throughput performanceand power cost of such network. The accomplished works and research contributions of thischapter are briefly described in the following.5.1 Accomplished Works and Research ContributionsIn this chapter, we consider a two-tier HetNet with co-channel deployment and renewableenergy harvesting capability in the small base stations. To optimize the trade-off betweenthroughput performance and power cost of serving the small cell (or hotspot) users, we1045.1. Accomplished Works and Research Contributionsconsider the problem of resource allocation and dynamic base station activation in such anetwork. Information about traffic demand or user activity of the network is needed to op-timize dynamic base station activation and resource allocation in multi-tier networks [99].When the base stations are energy harvesting in nature, information about arrival of har-vested energy is also required along with that about user activity and traffic demand [71].Therefore, in this chapter, considering variation in channel condition, user activity, andarrival of harvested energy, we investigate interference-aware and energy-aware resource al-location jointly with dynamic activation of SBSs in a two-tier network, where MBS is alwaysactivated for reliable operation.To optimize the trade-off between throughput performance and power cost of serving thehotspot users, we associate positive reward for their attained throughput, negative reward(penalty) for corresponding non-renewable power consumption, and formulate an optimiza-tion problem to maximize the net reward over a number of time slots. Resource allocation isjointly performed to ensure interference-aware frequency reuse among macrocell and hotspotusers when the SBS is activated, and the hotspot users are offloaded to the SBS, while en-suring orthogonal frequency allocation among them when the SBS is deactivated, and thehotspot users are served by the MBS. QoS provisioning is guaranteed by satisfying min-imum throughput requirement of all macrocell and hotspot users in all time slots underconsideration.The formulated problem is solved as an offline problem assuming availability of non-causal information about channel condition, user activity, and energy harvested for theconsidered time period. Since non-causal information is unavailable in practice, we alsosolve the problem as an online problem using causal information only. The online problemis solved in two ways: using dynamic programming where statistical information of futurevalues are available; and using greedy technique where no information of future values areavailable. Algorithms are proposed to solve the online and offline optimization problemsin two stages: (i) determining base station activation variables; (ii) determining resource1055.2. System Model and Assumptionsallocation variables. We use discrete binary particle swarm optimization [100] to determinebase station activation variables in offline algorithm. Numerical results are presented toanalyze and compare the performances of the proposed algorithms with the baseline schemes.Three baseline schemes are used for comparison with the proposed algorithms: (i) Always OnScheme, where the SBSs are always activated, (ii) Always Off Scheme, where the SBSs arealways deactivated, and (iii) Heuristic Scheme, where the SBS activation policy is determinedheuristically.The rest of the chapter is organized as follows. The system model and assumptionsare explained in Section 5.2. Sections 5.3 and 5.4 present the offline and online problemformulations with solution approaches. Finally, performance evaluation results are presentedand analyzed in Section 5.5.5.2 System Model and AssumptionsNetwork model and user behaviorWe consider downlink communication in a cellular network with one MBS and NT UEs. Weconsider a scenario where H UEs are concentrated in a small area or hotspot and remainingM UEs are distributed elsewhere, where NT = M + H. An SBS is set up to serve HUEsin the hotspot, thus creating a two-tier network with co-channel deployment as shown inFig. 5.1. The UEs in hotspot are referred to as hotspot UEs (HUEs) and denoted by Uh,h ∈ {1, 2, ..., H}. The UEs distributed elsewhere are called macrocell UEs (MUEs) anddenoted by Um, m ∈ {1, 2, ...,M}. Note that the UEs considered in our system model canbe viewed as test points as in [67]. If a new user becomes active at the test point denotedby HUE Uh inside the hotspot at time t, the activity indicator H th will be 1 and it will be0 when the user leaves the hotspot. Similarly, M tm is used as activity indicator of the testpoint denoted by MUE Um. However, to retain the focus of our work on the problem ofresource allocation in an energy harvesting HetNet, details of user mobility and hand-off are1065.2. System Model and AssumptionsSBSMBSMUEHUESolar PanelSBSBSFigure 5.1: Two-tier HetNet with renewable energy harvesting in SBS.not incorporated in the system model.Hybrid energy model and dynamic SBS activationThe SBS is equipped with energy harvesting capability along with a non-renewable energysource. The source of renewable energy, for instance, can be solar panels as shown in Fig. 5.1The energy harvesting rate in time slot t is denoted by Et in joules per second (Jps). Fromhere onward, the terms power and energy will be used interchangeably. If harvested energyis not enough, the SBS draws power from non-renewable energy source. If harvested energyis surplus to the requirement, the SBS stores it in a battery. Note that activation of the SBSincreases throughput of HUEs, but also increases non-renewable power consumption if theharvested energy is not enough. Therefore, we assume that the SBS can be switched on oroff, for optimal performance. At is the SBS activation variable which is set to 1 if the SBS isactivated in time slot t and 0 otherwise. Hence, the network will be a two-tier network withco-channel deployment when the SBS is activated and a single tier network when the SBSis deactivated. Note that HUEs are offloaded to the SBS if it is activated and are served by1075.2. System Model and Assumptionsthe MBS otherwise14.Channel modelThe available bandwidth is divided into N subchannels. hn,tM,m and hn,tS,m denote power gain ofnth subchannel from MBS and SBS, respectively, to MUE Um, in time slot t. Similarly, gn,tM,hand gn,tS,h denote power gain of nth subchannel from MBS and SBS, respectively, to HUE Uhin time slot t. Channel power gain includes distance-dependent gain and multi-path fadinggain.Statistical modeling of channel, energy, and user activityChannel gains, energy arrival, and user activities are modeled as independent random pro-cesses and their probability distribution are known via long term measurements. Channelgains and harvested energy have been widely assumed to follow Markov model [30,101–103].Similarly, user activity can also be modeled as a two-state Markov model [104,105].Resource allocation variablesP n,tS = Pn,tNe+ P n,tRe denotes transmit power of the SBS in subchannel n in time slot t whereP n,tNe is power drawn from the non-renewable energy source and Pn,tReis that from the batterystoring harvested energy. σn,tM,m, ρn,tM,h, and ρn,tS,h are subchannel allocation variables. σn,tM,m is1 if subchannel n is allocated by MBS to MUE Um in time t and ρn,tS,h is 1 if it is allocatedby SBS to HUE Uh. Note that in case the SBS is deactivated, the network operates as asingle tier network and HUEs associate with the MBS. ρn,tM,h is 1 if subchannel n is allocatedby MBS to UE Uh in time t. The MBS transmits with power PM in each subchannel.14Considering the amount of energy harvested, hotspot users can be partially offloaded to the active SBSto minimize non-renewable power consumption, which requires optimization of user association variables foroptimal performance. However, optimization of user association is beyond the scope of this chapter.1085.2. System Model and AssumptionsThroughput reward and power consumption penaltyThe throughput of an active MUE Um is given by Rtm =∑Nn=1 σn,tM,mlog2 (1+PMhn,tM,mAt∑Hh=1Hthρn,tS,h(Pn,tRe +Pn,tNe )hn,tS,m+Nw), ∀m, t, where Nw is the AWGN power. Note that the in-terference terms will be present only when the SBS is activated and the network operatesin two-tier mode. Similarly, throughput of an active HUE Uh, when the SBS is switched onand off are, respectively, given byRth(on) =N∑n=1ρn,tS,hlog2(1 +(P n,tNe + Pn,tRe)gn,tS,hPMgn,tM,h +Nw),∀h, t (5.1)Rth(off) =N∑n=1ρn,tM,hlog2(1 +PMgn,tM,hNw), ∀h, t. (5.2)Rth(on) gives throughput of HUE Uh if the SBS is activated and Rth(off) gives its throughput ifthe SBS is deactivated and the HUE is associated to the MBS instead. Hence, at any timet, throughput of an HUE is given by Rth = AtRth(on) + (1−At)Rth(off). Note that, we considerpower expenditure associated with downlink transmissions at the base stations, and hence,we consider downlink throughput of UEs. The throughput reward15 generated by HUEs isgiven byRtrew = rth(AtH∑h=1H thRth(on) + (1− At)H∑h=1H thRth(off)),∀t (5.3)where rth indicates reward per unit of achievable throughput of HUEs. Due to energycausality, the energy arrival process constrains power drawn from the battery that storesharvested energy ast∑τ=1Aτ(H∑h=1N∑n=1Hτhρn,τS,hPn,τReαS)≤t∑τ=1Eτ−1, ∀t (5.4)where E0 is energy harvested before first time slot of consideration. The actual power con-sumption in the SBS is αS times the transmitted power due to additional power consumption15Note that the reward function is defined as a linear function of throughput [106], ignoring the effect ofdiminished marginal utility.1095.2. System Model and Assumptionsin RF chain when the SBS is switched on [107]. Note that we do not consider static powerconsumption of the SBS because it is constant in both on and off states, thus becomingindependent of resource allocation and SBS activation decisions. It is assumed to rely onnon-renewable energy source for stable operation. From now onward, the power consumptionwill simply refer to dynamic power consumption of the active base station.The non-renewable power expenditure at the SBS and the MBS for serving HUEs is givenbyP tSBS = AtH∑h=1N∑n=1H thρn,tS,hPn,tNeαS, PtMBS =(1− At) H∑h=1N∑n=1H thρn,tM,hPMαM , ∀t. (5.5)Note that dynamic power consumption in the SBS becomes zero when it is deactivated dueto inclusion of the variable At in (5.4) and (5.5). Power expenditure at the MBS for servingHUEs is αM times the transmit power accounting for RF transmission efficiency of the MBS.As the MBS is always activated, we do not consider its static power consumption which isindependent of resource allocation and SBS activation decisions. The power consumptionpenalty incurred by serving HUEs is given byP tpen = rg[AtH∑h=1N∑n=1H thρn,tS,hPn,tNeαSβ +(1− At) H∑h=1N∑n=1H thρn,tM,hPMαM], ∀t (5.6)where rg is penalty per unit of non-renewable power consumed to serve HUEs. β is penaltyincrease factor assuming that cost of non-renewable energy source of the SBS is β times morethan that of the MBS. We know that activating the SBS will increase the sum throughputof HUEs which increases the throughput reward. However, if the harvested energy is notenough, non-renewable power consumption may increase which increases associated powerconsumption penalty. Note that, non-renewable power is also consumed at the MBS to serveHUEs if the SBS is deactivated. Hence, it is important to determine whether it is optimalto activate or deactivate the SBS.In this chapter, we will develop optimization problem to maximize the net reward of1105.3. Offline Optimization: Problem Formulation and Solution Approachserving HUEs16 over T time slots while ensuring QoS to all HUEs and MUEs. For this,we will consider three different scenarios. First, we will perform offline optimization for adeterministic scenario where the information of user activity, channel condition, and energyarrival of all time slots of consideration are available. Next, we will consider online optimiza-tion for a more practical scenario where the future information about user activity, channelcondition, and energy arrival are not available but their statistics are known. Finally, wewill consider a greedy online resource allocation framework where we maximize the rewardfunction for one time slot at a time.Remark 1: Note that the system model can be extended to a scenario with multiplehotspots. In that case, we have to consider co-tier interference among hotspots along withcross-tier interference. However, to simplify the exposition, we consider a single hotspotonly.5.3 Offline Optimization: Problem Formulation andSolution ApproachIn this section, we assume the availability of future information about channel gains, renew-able energy arrival, and user activity. Our objective is to determine SBS activation, downlinkpower, and subchannel allocation to maximize the net reward of serving HUEs(Rtrew − P tpen)over T time slots. The problem can be written asmaximizeA,ρS ,ρM ,σM ,PRe ,PNe∑Tt=1(Rtrew − P tpen)subject to C1 :(Rtm −Rmin)M tm ≥ 0,∀m, tC2I : At(Rth(on) −Rmin)H th ≥ 0,∀h, tC2II : (1− At)(Rth(off) −Rmin)H th ≥ 0, ∀h, t(5.7)16Focusing on maximizing the reward of serving the hotspot users could be important when hotspots withhigher user density are generated in some events and maximizing their throughput is given higher priorityin comparison to the macrocell users.1115.3. Offline Optimization: Problem Formulation and Solution ApproachC3 :M∑m=1σn,tM,mMtm + (1− At)H∑h=1ρn,tM,hHth ≤ 1,∀n, tC4 : AtH∑h=1ρn,tS,hHth ≤ 1,∀n, tC5 :t∑τ=1Aτ(H∑h=1N∑n=1Hτhρn,τS,hPn,τReαS)≤t∑τ=1Eτ−1, ∀tC6 : AtH∑h=1[H thρn,tS,h(P n,tRe + Pn,tNe)hn,tS,mMtm] ≤ Imax, ∀m,n, tC7 : At, ρn,tS,h, ρn,tM,h, σn,tM,m ∈ {0, 1},∀m,n, h, tC8 : Pn,tRe, P n,tNe ≥ 0,∀n, twhere PRe = {P n,tRe ,∀n, t}, PNe = {P n,tNe ,∀n, t} , ρM = {ρn,tM,h, ∀n, t, h}, ρS = {ρn,tS,h, ∀n, t, h},and σM = {σn,tM,m,∀n, t,m}. Constraint C1, C2I , and C2II ensure QoS provisioning forall active UEs. C3 and C4 ensure orthogonal frequency allocation among active UEs byMBS as well as SBS to avoid intra-cell interference. Note that C3 ensures that, if the SBSis deactivated, the MBS allocates one subchannel to only one UE out of all HUEs andMUEs, in one time slot. C5 is energy causality constraint as given in (5.4). C6 ensuresthat interference imposed on active MUEs by the SBS is not more than Imax. Imposing amaximum interference constraint on transmit power of SBSs to protect MUEs is well adoptedin the literature [108]. C7 imposes binary integer constraint on subchannel allocation andSBS activation variables. C8 imposes non-negativity constraint on power variables.The problem is an MINLP problem due to the presence of binary integer SBS activationand subchannel allocation variables. Therefore, the optimal solution of such a problem iscomputationally intractable. To obtain the suboptimal solution, we can solve the problem intwo stages iteratively. In the first stage, we can perform subchannel and power allocation forgiven SBS activation variables. In the next stage, we can optimize SBS activation variablesfor given subchannel and power allocation variables. To optimize SBS activation variables,we will use discrete binary particle swarm optimization (PSO) [100] due to its faster conver-1125.3. Offline Optimization: Problem Formulation and Solution Approachgence [109,110]. In the following, we will solve the subchannel and power allocation problemfor known SBS activation variables.5.3.1 Subchannel and Power Allocation for Given SBSActivation PolicyFor a given SBS activation policy, the SBS activation variables of the problem in (5.7)become known parameters. However, the problem still remains an MINLP problem due tothe presence of binary integer subchannel allocation variables and is difficult to solve in itscurrent form. To directly solve the problem, we can use OPTI [98], which is a free MATLABtoolbox capable of solving non-linear and discrete optimization problems. However, weare not able to obtain insightful analytical results. Therefore, we relax the subchannelallocation variables to take any value between 0 to 1 and define auxiliary power variables asP˜ n,th,Re = ρn,tS,hPn,tReand P˜ n,th,Ne = ρn,tS,hPn,tNe, ∀h, n, t. Note that such a relaxation of subchannelallocation variables allows multiple UEs to share a subchannel in time domain within atransmission frame [34,41,111]. Although the relaxation gives an upper bound of the optimalsolution, it is claimed in [41] that for a large number of subchannels, the solution of therelaxed problem is asymptotically optimal with respect to the original problem formulation.Then, the throughput of an HUE Uh when the SBS is activated, given in (5.1), can bere-written asR˜th(on) =N∑n=1ρn,tS,hlog21 +(P˜ n,th,Re + P˜n,th,Ne)gn,tS,hρn,tS,h(PMgn,tM,h +Nw) , ∀h, t. (5.8)The throughput reward generated by HUEs is then given by R˜trew = rth(At∑Hh=1 HthR˜th(on)+(1− At)∑Hh=1H thRth(off)). The power consumption penalty incurred by serving HUEs, given1135.3. Offline Optimization: Problem Formulation and Solution Approachin (5.6), can be re-written asP˜ tpen = rg[AtH∑h=1N∑n=1H thP˜n,th,NeαSβ +(1− At) H∑h=1N∑n=1H thρn,tM,hPMαM], ∀t. (5.9)Note that, due to the presence of subchannel and power allocation variables in the de-nominator, Rtm cannot be rendered convex even with relaxation of subchannel allocationvariables and introduction of auxiliary power variables. Hence, for analytical tractability,in our problem, we take a pessimistic approach and define the worst-case approximation ofMUE throughput as R˜tm =∑Nn=1 σn,tM,mlog2(1 +PMhn,tM,mAtImax+Nw), ∀m, t to ensure that minimumthroughput requirement of active MUEs is satisfied even when the received interference ismaximum. Note that such a worst-case approximation is commonly adopted in the literaturefor tractability of analysis [34,36,112]. Using the worst-case approximation of MUE through-put, relaxed subchannel allocation variables, auxiliary power variables, and (5.8)-(5.9), theoptimization problem in (5.7) can be re-written asmaximizeρS ,ρM ,σM ,P˜Re ,P˜Ne∑Tt=1(R˜trew − P˜ tpen)subject to C3, C4, C2IIC˜1 :(R˜tm −Rmin)M tm ≥ 0,∀m, tC˜2I : At(R˜th(on) −Rmin)H th ≥ 0,∀h, tC˜5 :t∑τ=1Aτ(H∑h=1N∑n=1Hτh P˜n,τh,ReαS)≤t∑τ=1Eτ−1, ∀tC˜6 : AtH∑h=1[H th(P˜ n,th,Re + P˜n,th,Ne)hn,tS,mMtm]≤ Imax,∀m,n, tC˜7 : 0 ≤ ρn,tS,h, ρn,tM,h, σn,tM,m ≤ 1, ∀m,n, h, tC˜8 : P˜n,th,Re, P˜ n,th,Ne ≥ 0,∀n, h, t(5.10)where constraints C˜1, C˜2I , C˜5−C˜8 are re-written form of the corresponding constraints of theproblem in (5.7) using worst case approximation of MUE throughput, relaxed subchannel1145.3. Offline Optimization: Problem Formulation and Solution Approachallocation variables, auxiliary power variables, and (5.8). Since R˜th(on) can be proven to bea concave function of optimization variables by using perspective operation [80] and Rth(off)and P˜ tpen are affine functions of optimization variables, the objective function of the problemin (5.10) is a concave function of the optimization variables and the constraints are eitheraffine or convex. Therefore, solution of the problem can be obtained by solving its dualproblem [80] discussed in the following.The partial Lagrangian of the problem in (5.10) is given by [80]L(ρS,ρM ,σM , P˜Re , P˜Ne ,λ, δ,η)=T∑t=1(R˜trew − P˜ tpen)−H∑h=1T∑t=1λh,tAt(Rmin − R˜th(on))H th−T∑t=1δt[t∑τ=1AτH∑h=1N∑n=1Hτh P˜n,τh,ReαS −t∑τ=1Eτ−1]−M∑m=1N∑n=1T∑t=1ηm,n,t[AtH∑h=1H th(P˜ n,th,Re + P˜n,th,Ne)hn,tS,mMtm − Imax](5.11)where λ, δ, and η are non-negative Lagrange multipliers associated with constraints C˜2I ,C˜5, and C˜6, respectively. Other constraints are not included in the Lagrangian and will besatisfied later. Using the Lagrangian given in (5.11), we can formulate the dual problem ofthe problem in (5.10) as follows:minimizeλ,δ,ηmaxρS ,ρM ,σM ,P˜Re ,P˜NeL(ρS,ρM ,σM , P˜Re , P˜Ne ,λ, δ, η)subject to λ, δ,η  0, C˜1, C2II , C3, C4, C˜7, C˜8.(5.12)We can use dual decomposition method [85] to solve (5.12). In the dual decompositionmethod, in each iteration, we will first solve the subproblem to obtain the primal variables(subchannel and power allocation variables) using the given value of dual variables (Lagrangemultipliers). Then the master problem is solved to determine the dual variables using theobtained values of primal variables. The iteration is continued till convergence is attained.1155.3. Offline Optimization: Problem Formulation and Solution ApproachSolving the subproblemsTo solve for the primal variables, we exploit the fact that, for a convex optimization problem,the optimal solution must satisfy KKT conditions. Differentiating (5.11) with respect to P˜ n,th,Reand P˜ n,th,Ne , respectively, and using the KKT stationarity condition, we obtainP˜n,t(it)h,Re+P˜n,t(it)h,Ne=ρn,t(it)S,h[rth + λ(it)h,t(log2){∑Tτ=tδ(it)τ αS+∑Mm=1 η(it)m,n,thn,tS,mM tm} −PMgn,tM,h +Nwgn,tS,h]+, ∀h, n, t(5.13)P˜n,t(it)h,Ne+P˜n,t(it)h,Re= ρn,t(it)S,h[rth + λ(it)h,t(log2) {rgαSβ +∑Mm=1 η(it)m,n,thn,tS,mMtm}− PMgn,tM,h +Nwgn,tS,h]+, ∀h, n, t(5.14)where [x]+ ensures non-negativity of transmit power of the SBS and it is iteration index ofdual decomposition method. We see that sum of P˜n,t(it)h,Reand P˜n,t(it)h,Necan be defined eitherby (5.13) or (5.14) and that power allocation variables are interdependent on each other.To overcome the interdependency of power variables and to ensure maximum utilization ofrenewable power, we simplify (5.13) as [29,41]P˜n,t(it)h,Re= ρn,t(it)S,h Pˆn,t(it)h,Re, ∀h, n, t (5.15)wherePˆn,t(it)h,Re=[rth + λ(it)h,t(log2) {∑Tτ=t δ(it)τ αS +∑Mm=1 η(it)m,n,thn,tS,mM tm} −PMgn,tM,h +Nwgn,tS,h]+,∀h, n, t. (5.16)However, the sum of P˜n,t(it)h,Reand P˜n,t(it)h,Neshould strictly satisfy either (5.13) or (5.14). There-fore, using (5.14) and (5.15), we obtainP˜n,t(it)h,Ne= ρn,t(it)S,h Pˆn,t(it)h,Ne, ∀h, n, t (5.17)1165.3. Offline Optimization: Problem Formulation and Solution ApproachwherePˆn,t(it)h,Ne=[rth + λ(it)h,t(log2) {rgαSβ +∑Mm=1 η(it)m,n,thn,tS,mMtm}− PMgn,tM,h +Nwgn,tS,h− Pˆ n,t(it)h,Re]+,∀h, n, t.(5.18)Note that the non-negativity constraint C˜8 is satisfied in (5.16) and (5.18). The powerallocations in (5.15) and (5.17) are in the form of multi-level water filling whererth+λ(it)h,t(log2){rgαSβ+∑Mm=1 η(it)m,n,thn,tS,mMtm}andrth+λ(it)h,t(log2){∑Tτ=t δ(it)τ αS+∑Mm=1 η(it)m,n,thn,tS,mMtm}are the water levelsfor P˜ n,th,Ne and P˜n,th,Re, respectively.Using (5.15) and (5.17) in (5.8) and (5.9), R˜th(on) and P˜tpen become a linear function ofsubchannel allocation variables asR˜t(it)h(on) =N∑n=1ρn,t(it)S,h log2(1 +(Pˆn,t(it)h,Ne+ Pˆn,t(it)h,Re)gn,tS,hPMgn,tM,h +Nw), ∀h, t (5.19)P˜ t(it)pen = rg[AtH∑h=1N∑n=1H thρn,t(it)S,h Pˆn,t(it)h,NeαSβ +(1− At) H∑h=1N∑n=1H thρn,tM,hPMαM]∀t. (5.20)The throughput reward generated by HUEs is then given by R˜t(it)rew = rth(At∑Hh=1HthR˜t(it)h(on)+(1− At)∑Hh=1 H thRth(off)). Using (5.15)-(5.20), the net reward we want to maximize becomesa linear function of ρ(it)S , ρM , and σM in each iteration and the subproblem in (5.12) canbe re-written asmaximizeρS(it),ρM ,σM∑Tt=1(R˜t(it)rew − P˜ t(it)pen)+ χsubject to C˜1, C2II , C3, C4, C˜7(5.21)where χ =∑Hh=1∑Tt=1 λh,tAtR˜t(it)h(on)Hth −∑Tt=1 δt∑tτ=1Aτ∑Hh=1∑Nn=1Hτhρn,τ(it)S,h Pˆn,τ(it)h,ReαS −∑Mm=1∑Nn=1∑Tt=1 ηm,n,tAt∑Hh=1Hthρn,t(it)S,h(Pˆn,t(it)h,Re+ Pˆn,t(it)h,Ne)hn,tS,mMtm. The objective func-tion as well as the constraints of problem in (5.21) are now linear. Hence, the problemin (5.21) is a linear program and can be solved optimally using interior-point method. Oncethe subchannel allocation variables are known, the auxiliary power variables can be deter-mined by using (5.15) and (5.17). Note that the constraints that were not considered in the1175.3. Offline Optimization: Problem Formulation and Solution Approachpartial Lagrangian are included in (5.21).Solving the master problemThe master problem can be solved by using the subgradient method [87] to update dualvariables in each iteration as follows:λ(it+1)h,t =[λ(it)h,t + ∆λAt(Rmin − R˜t(it)h(on))H th]+, ∀h, t (5.22)δ(it+1)t =[δ(it)t + ∆δ(t∑τ=1AτH∑h=1N∑n=1Hτh P˜n,τ(it)h,ReαS −t∑τ=1Eτ−1)]+, ∀t (5.23)η(it+1)m,n,t =[η(it)m,n,t + ∆η(AtH∑h=1(P˜n,t(it)h,Re+ P˜n,t(it)h,Ne)H thhn,tS,mMtm − Imax)]+, ∀m,n, t (5.24)where ∆λ, ∆δ, and ∆η are step sizes and [x]+ enforces non-negativity constraint on dualvariables.The master problem and the subproblems are iteratively solved until convergence. Con-vergence of subgradient method to the globally optimal solution is guaranteed for convexoptimization problem for small step size [87]. Algorithm 5 summarizes the subchannel andpower allocation framework, for given SBS activation policy. Note that the linear programgiven in (5.21) can also be separated into T linear programming problems and solved simul-taneously. However, all of T optimization problems must be solved before updating the dualvariables.Remark 2: Note that, in the scenario with multiple hotspots, due to the presence of co-tierinterference terms in throughput expression of the HUEs, subchannel and power allocationproblem becomes highly complicated. However, if we use the worst-case approximation ofthroughput of HUEs by defining an upper bound on the received interference, as done forMUEs, the solution approach becomes similar to the one used in the scenario with singlehotspot.1185.3. Offline Optimization: Problem Formulation and Solution ApproachAlgorithm 5 Subchannel and Power Allocation Algorithm for Given SBS Activation PolicyRequire: Offline information on channel gains, user activities, and energy arrivals1: Initialize it = 1 and λ(it),δ(it), η(it)2: repeat3: Compute Pˆn,t(it)h,Reand Pˆn,t(it)h,Ne, ∀n, t, h using (5.16) and (5.18), respectively4: Formulate the linear programming problem as given in (5.21) and solve it usinginterior-point method to determine ρS(it), ρM , and σM5: Determine P˜n,t(it)h,Reand P˜n,t(it)h,Ne,∀n, t, h using (5.15) and (5.17)6: Update dual variables λ(it+1), δ(it+1), η(it+1) using subgradient method as given in(5.22)-(5.24)7: it← it+ 18: until Convergence5.3.2 Discrete Binary PSO for Dynamic SBS ActivationIn discrete binary PSO (DBPSO) [100], we first initialize an array of particles, correspondingto SBS activation variables, where position code of each particle i is given asA(i,itp) =[A1(i,itp), A2(i,itp), .., AT(i,itp)],∀i ∈ {1, 2, ..., P} (5.25)where At(i,itp) is SBS activation decision for time t given by particle i in the iteration itp of theDBPSO algorithm and itp = 1 upon initialization. T defines the dimension of the problemand P is the swarm size. We also initialize arrays of velocities of particles asV(i,itp) = [v1(i,itp), v2(i,itp), .., vT(i,itp)],∀i. (5.26)The subchannel and power allocation framework given in the previous section is used tomaximize the net reward function corresponding to each particle in each iteration. Thepersonal best position code of each particle Apbest(i) saves the position code of particle i inthe iteration itp if it resulted in maximum net reward in comparison to all past iterations.The overall best position code of all particles Agbest saves the position code of particle i initeration itp if it resulted in maximum net reward in comparison to all particles in all past1195.4. Online Optimization: Problem Formulations and Solution Approachesiterations. Then, velocities of the particles are updated in each iteration as follows [100]:vt(i,itp+1) =[vt(i,itp) + φt1(Atpbest(i)− At(i,itp))+ φt2(Atgbest − At(i,itp))]Vmax−Vmax, ∀i, t (5.27)where φt1 and φt2 are the randomly generated positive number between 0 and 1. Vmax and−Vmax provide upper and lower bound on the velocity of the particles. Then the particlesare updated in each iteration as follows [100]:if rand() < S(vt(i,itp+1)) then At(i,itp+1) = 1else At(i,itp+1) = 0(5.28)where S() is a sigmoid function and rand() is quasirandom number selected from the range[0, 1] [100]. Note that S(vt(i,itp+1)) gives the probability that At(i,itp+1)will take on the valueof 1 in the next iteration. The above described procedure is iterated until convergence isattained. Algorithm 6 summarizes framework for optimizing the SBS activation variablesalong with subchannel and power allocation variables.Remark 3: Note that, in the scenario with multiple (K) hotspots, the dimension of theDBPSO problem will increase from T to T×K. Hence, for higher values of K, the dimensionof the DBPSO problem will be large. However, we can use multiple variations of the PSOalgorithm proposed in the literature for high dimensional problems [113, 114].5.4 Online Optimization: Problem Formulations andSolution ApproachesIn this section, we optimize SBS activation, subchannel allocation, and power allocation vari-ables using only the causal information of energy arrival, channel gains, and user activities.Since future values of these parameters are not known, we can follow two approaches: (i)if statistical information of future values are available through long term measurements, we1205.4. Online Optimization: Problem Formulations and Solution ApproachesAlgorithm 6 Offline Resource Allocation AlgorithmRequire: Offline information on channel gains, user activities, and energy arrival1: Initialize P particles of A(i,itp), V(i,itp), ∀i = 1, 2, ...P and iteration index itp = 12: Initialize personal best value of each particle, fbest(i) and overall best value of all particles,fbest to a small value3: repeat4: for i = 1 : P do5: Determine subchannel and power allocation for A = A(i,itp), using Algorithm 5 andletfmax(i,itp) = max∑Tt=1(R˜trew − P˜ tpen)|At=At(i,itp)6: Update personal best position of each particleif fmax(i,itp) > fbest(i), then Apbest(i) = A(i,itp), fbest(i) = fmax(i,itp)7: Update the overall best position of all particlesif fmax(i,itp) > fbest, then Agbest = A(i,itp), fbest = fmax(i,itp)8: end for9: Update the velocity using (5.27)10: Update the position of the particles using (5.28)11: itp ← itp + 112: until Convergence13: Select Agbest for SBS activation and the corresponding subchannel and power allocationfor resource allocation.1215.4. Online Optimization: Problem Formulations and Solution Approachescan maximize the expected value of the net reward function for the considered time slots; (ii)in the absence of any kind of future information, we can maximize net reward of the currenttime slot using the causal information available. In the following, we will first provide adynamic programming-based online solution to maximize expected value of net reward overa number of time slots [115]. Then we will provide a greedy online solution approach tomaximize net reward of the current time slot.5.4.1 Dynamic Programming-based Online OptimizationWith the availability of causal information and statistics of future information, the SBS acti-vation, subchannel allocation, and power allocation variables can be optimized to maximizethe expected value of net reward function asmaximizeA,ρS ,ρM ,σM ,PRe ,PNe∑Tt=1 EU,E,F{Rtrew − P tpen}subject to C1 − C8(5.29)where U , E, and F denote random user activity, energy arrival, and channel fading, re-spectively. EU,E,F{.} denotes the statistical expectation with respect to user activity, energyarrival, and channel fading. Note that, in (5.29), the sum of the expected values of netreward function is maximized instead of the instantaneous values. The constraints are sameas those of the offline problem in (5.7). However, if we define a new parameter Bt indicatingthe amount of energy available in the battery that stores the harvested energy in time slott, constraint C5 of the problem in (5.29) can also be written asC5a : AtH∑h=1N∑n=1H thρn,tS,hPn,tReαS ≤ Bt, ∀t (5.30)1225.4. Online Optimization: Problem Formulations and Solution Approacheswhere Bt = Et−1, if t = 1 and the battery state has the following dynamics:Bt =t−1∑τ=0Eτ −t−1∑τ=1Aτ(H∑h=1N∑n=1Hτhρn,τS,hPn,τReαS)or, Bt = Bt−1 + Et−1 − At−1H∑h=1N∑n=1H t−1h ρn,t−1S,h Pn,t−1ReαS, if, t = 2, ..., T.(5.31)Note that the system model can be characterized as a dynamic system where• Random parameters are Et−1, U t, and F t, where Et−1 denotes energy arrived at theend of previous time slot, U t = {M tm, ∀m,H th, ∀h} denotes user activity in the currenttime slot, and F t = {fn,t, ∀n} denotes channel fading condition in the current timeslot.• State of the system is given by St = (Bt, Et−1, U t, F t), where Bt denotes battery statein the current time slot which is updated according to (5.31)• Decision variables to be selected in each time slot t are At,ρtS, ρtM , σtM ,P tRe, P tNe .• The net reward function in each time t is (Rtrew − P tpen) where Rtrew and P tpen are givenin (5.3) and (5.6), respectively.Our objective is to maximize expected value of the net reward over T time slots. Theoptimal solution can be obtained by using Bellman’s equation and backward induction [115].For the last time slot, that is t = T , the maximum reward can be computed asFor t = T, J t(St) = maximizeAt,ρtS ,ρtM ,σtM ,PtRe,P tNe(Rtrew − P tpen)subject to C1 − C4, C5a, C6 − C8(5.32)where constraint C5a denotes the battery constraint as given in (5.30) and the remainingconstraints are similar to those in (5.7) for time slot t. Then, by backward induction, the1235.4. Online Optimization: Problem Formulations and Solution Approachesmaximum reward of remaining time slots t = T − 1, T − 2, ..., 2, 1 can be computed asJ t(St) = maximizeAt,ρtS ,ρtM ,σtM ,PtRe,P tNe(Rtrew − P tpen)+ J¯ t+1(St, At,P tRe, ρtS)subject to C1 − C4, C5a, C6 − C8(5.33)whereJ¯ t+1(St, At,P tRe, ρtS) = EU,E,F{J t+1(St+1|St, At,P tRe, ρtS)}, ∀t. (5.34)(5.34) can be calculated if the probability density functions of U , E and F are available.Note that, in addition to the current state, future state also depends on SBS activationvariable At, power allocation variables P tRe , and subchannel allocation variables ρtS, due tothe battery dynamics. The problems in (5.32) and (5.33) are still non-convex due to thecoupling of binary integer SBS activation and subchannel allocation variables. However, ineach time slot t, we can solve the problem for At = 0 and At = 1 and choose the one thatmaximizes the reward for that time slot. Then, we can relax the binary integer constraintof subchannel allocation variables, 0 ≤ ρn,tS,h, ρn,tM,h, σn,tM,m ≤ 1, introduce auxiliary power vari-ables, P˜ n,th,Re = ρn,tS,hPn,tRe, ∀h, n and P˜ n,th,Ne = ρn,tS,hP n,tNe , ∀h, n, and use worst-case approximationof throughput of MUEs, as done in Section 5.3. With fixed At, new auxiliary power vari-ables, relaxed subchannel allocation variables, and worst-case approximation of throughputof MUEs, the problems in (5.32) and (5.33) are both convex optimization problems and canbe optimally solved.Using the dynamic programming method mentioned above, resource allocation is done intwo phases: planning and implementation. In the planning phase, the problem in (5.32) issolved for all possible BT , UT , and F T and the corresponding resource allocation decisionsare stored in a look-up table. Then the problem in (5.33) is solved recursively for eachtime slot t = T − 1, T − 2, ..., 2, 1. In each time slot, the problem is solved for differentpossible Bt, U t, and F t and probability distribution of U , E, and F are used to compute theexpected future reward. The corresponding resource allocation decisions are stored in the1245.4. Online Optimization: Problem Formulations and Solution Approacheslook-up table. In the implementation phase, at the beginning of each time slot, the resourceallocation decision corresponding to the state St at that time slot is extracted from the look-up table. The aforementioned resource allocation framework is summarized in Algorithm 7.Algorithm 7 Dynamic Programming-based Online Resource Allocation Algorithm1: Planning2: for x = 0 : 1 do3: Compute JT (ST )|AT=x by solving the problem in (5.32), for t = T , ∀BT , UT , F T4: Denote optimal values as(ρ∗TS ,ρ∗TM ,σ∗TM ,P∗TRe,P ∗TNe) |AT=x5: end for6: Store A∗T = argmaxxJT (ST )|AT=x, and(ρ∗TS ,ρ∗TM ,σ∗TM ,P∗TRe,P ∗TNe) |AT=A∗T on look-uptable ∀BT , UT , F T7: for t = T − 1 : 1 do8: for x = 0 : 1 do9: Compute J t(St)|At=x by solving the problem in (5.33), ∀Bt, U t, F t, using probabilitydistribution of U , E, and F10: Denote optimal values as(ρ∗tS ,ρ∗tM ,σ∗tM ,P∗tRe,P ∗tNe) |At=x11: end for12: Store A∗t = argmaxxJt(St)|At=x, and(ρ∗tS ,ρ∗tM ,σ∗tM ,P∗tRe,P ∗tNe ,) |At=A∗t on look-uptable ∀Bt, U t, F t13: end for14: Implementation15: for t = 1 : T do16: Collect information on Et−1, U t, and F t17: Update Bt using (5.31).18: Return(A∗t,ρ∗tS ,ρ∗tM ,σ∗tM ,P∗tRe,P ∗tNe)for Bt, U t, F t from look-up table19: end for5.4.2 Greedy Online OptimizationDue to the curse of dimensionality, computational complexity in dynamic programmingmethod discussed above increases exponentially with the number of users, subchannels, andtime slots. Also, statistical information of the future values may not always be accuratelyavailable. Therefore, in this section, we present a greedy online optimization algorithm whichhas a much lower computational complexity and does not need any information on future1255.4. Online Optimization: Problem Formulations and Solution Approachesvalues of user activity, channel fading, and energy arrival. In greedy online optimizationtechnique, we simply maximize the net reward function of each time slot based on availablecausal information on battery level, user activity, energy arrival, and channel fading. Theproblem can be formulated asmaximizeAt,ρtS ,ρtM ,σtM ,PtRe,P tNe(Rtrew − P tpen)subject to C1 − C4, C5a, C6 − C8(5.35)where the constraints are same as those in (5.32) and (5.33). Rtrew and Ptpen are given in(5.3) and (5.6), respectively. The problem in (5.35) is non-convex due to the coupling ofbinary integer SBS activation and subchannel allocation variables. Therefore, as discussed indynamic programming-based online algorithm, we will solve the problem for At = 1 as wellas At = 0 and choose the value that maximizes the reward function. For fixed SBS activationvariable, the problem in (5.35) becomes subchannel and power allocation problem.Remark 4: Note that, in the scenario with multiple hotspots, there will be multiple SBSactivation variables in each time slot and hence the online solution approach should also usethe DBPSO algorithm to optimize the SBS activation variables.Subchannel and power allocation for given SBS activation decisionFor fixed SBS activation variable, the problem in (5.35) is still non-convex due to binaryinteger constraint on subchannel allocation variables, and non-convexity of Rth(on), Rtm, andP tpen. Therefore, we relax the subchannel allocation variables, 0 ≤ ρn,tS,h, ρn,tM,h, σn,tM,m ≤ 1, intro-duce auxiliary power variables, P˜ n,th,Re = ρn,tS,hPn,tRe, ∀h, n and P˜ n,th,Ne = ρn,tS,hP n,tNe , ∀h, n, and useworst-case approximation of throughput of MUEs, as done in Section 5.3. With fixed SBSactivation variable, relaxed subchannel allocation variables, auxiliary power variables, R˜th(on)and power consumption penalty P˜ tpen become convex functions of optimization variables asgiven in (5.8) and (5.9), respectively, and hence the net reward function R˜trew − P˜ tpen is also1265.4. Online Optimization: Problem Formulations and Solution Approachesconvex. Therefore, the problem in (5.35) can be transformed into a convex optimizationproblem similar to (5.10) and solved optimally [80]. As in Section 5.3, we solve this prob-lem iteratively by dual decomposition technique. In each iteration of dual decompositiontechnique, we optimize the subchannel and power allocation variables using given values ofLagrange multipliers and then update the Lagrange multipliers using subgradient method.Solving the subproblem: To optimize the subchannel and power allocation variables,using KKT conditions of optimality, we haveP˜ n,th,Re = ρn,tS,hPˆn,th,Re, P˜ n,th,Ne = ρn,tS,hPˆn,th,Ne, ∀h, n (5.36)wherePˆ n,th,Re = rth + γh(log2)(θαS +∑Mm=1 µm,nhn,tS,mMtm) − PMgn,tM,h +Nwgn,tS,h+ , ∀h, n (5.37)Pˆ n,th,Ne = rth + γh(log2)(rgαSβ +∑Mm=1 µm,nhn,tS,mMtm) − PMgn,tM,h +Nwgn,tS,h− Pˆ n,th,Re+ , ∀h, n. (5.38)γh, ∀h, θ, and µm,n, ∀m,n are Lagrange multipliers associated with the convexified con-straints similar to C˜2I , C˜5, and C˜6 of the problem in (5.10). The details of derivation aresimilar to those for the offline optimization problem presented in Section 5.3. Power allo-cations given in (5.36) are also in multi-level water-filling form where the water levels forP˜ n,th,Re and P˜n,th,Neare given by rth+γh(log2)(θαS+∑Mm=1 µm,nhn,tS,mMtm)and rth+γh(log2)(rgαSβ+∑Mm=1 µm,nhn,tS,mMtm),respectively. Note that the offline power allocation scheme considered Lagrange multipliersof causality constraint of all future time slots of consideration while the greedy scheme con-siders that of current slot only. Hence, offline power allocation scheme uses the harvestedpower more conservatively.Using (5.36), R˜th(on) and P˜tpen given in (5.8) and (5.9) can be re-written as linear functionsof subchannel allocation variables as given in (5.19) and (5.20), respectively. The reward1275.4. Online Optimization: Problem Formulations and Solution Approachesfor achievable throughput given in (5.3) becomes a linear function of subchannel allocationvariables. Then, for each iteration, the problem in (5.35) can be transformed into a linearprogramming problem similar to (5.21) and solved optimally using interior-point method.Using the obtained subchannel allocation variables, power allocation variables are determinedusing (5.36).Solving the master problem: Finally, the Lagrange multipliers can be updated using thewell-known subgradient method similar to (5.22)-(5.24). Subgradient method is guaranteedto converge to the globally optimal solution for convex optimization problems [87].After subchannel and power allocation variables are obtained, the battery level is updatedfor the next time slot, using (5.31). The greedy online resource allocation framework issummarized in Algorithm 8.Algorithm 8 Greedy Online Resource Allocation Algorithm1: for t = 1 : T do2: Collect information on Et−1, U t, F t and update Bt using (5.31).3: for x = 0 : 1 do4: Initialize dual variables γ,θ, and µ.5: repeat6: Compute Pˆ n,th,Re and Pˆn,th,Neusing (5.37) and (5.38), respectively.7: Formulate the linear programming problem similar to (5.21) and solve it usinginterior-point method to determine fmax|At=x = maxρtS ,ρtM ,σtM(R˜trew − P˜ tpen)|At=xand let (ρ∗tS , ρ∗tM , σ∗tM )|At=x denote the subchannel allocation variables.8: Determine (P˜ ∗n,th,Re , P˜∗n,th,Ne)|At=x,∀n, h using (5.36).9: Update dual variables γ, θ, µ using subgradient method.10: until Convergence11: end for12: Select A∗t = argmaxx fmax|At=x, and(P ∗tRe ,P∗tNe,ρ∗tS ,ρ∗tM ,σ∗tM) |At=A∗t13: end for1285.5. Performance Evaluation Results5.5 Performance Evaluation ResultsWe evaluate performances of the proposed offline/online algorithms and compare them withthose of the baseline schemes. We choose three baseline schemes for comparison: (i) AlwaysOn Scheme, where At = 1, ∀t, (ii) Always Off Scheme, where At = 0, ∀t, and (iii) HeuristicScheme, where At = 0 if Et−1 = 0, At = 1 if Et−1 > Eth, and At = 0 or 1 with equalprobability if 0 < Et−1 ≤ Eth, where Eth is defined threshold. The resource allocation forthese baseline schemes can be optimized using Algorithm 5 for given SBS activation policy.We compare the net reward generated by different algorithms, throughput performance ofHUEs, and non-renewable power consumed at SBS and MBS to serve HUEs (simply referredto as power consumption from here onward).5.5.1 Simulation ParametersWe consider a single macrocell with the MBS at the origin. There is one hotspot at a distanceof 100 m from the MBS with H = 2 HUEs. An SBS is installed at the center of the hotspotsuch that HUEs are located at distance of 3 to 10 m from the SBS. There are M = 2 MUEslocated close to the hotspot. T = 4 consecutive time slots and N = 4 subchannels, each ofbandwidth 20 KHz are considered in the simulations. In each time slot t, energy harvestingrate Et takes a value from the set {0, EH , 2EH} with equal probability. For the HeuristicScheme, we set the energy threshold Eth to be EH . The activity indicators of MUEs andHUEs take a value from the set {0, 1} with equal probability. The fading condition of anysubchannel n in a time t, fn,t, follows exponential distribution with unit mean. Note thatchannel gain, energy harvesting rate, and activity indicators of the MUEs and HUEs areassumed to follow zeroth order Markov model in our simulations. The path-loss, in dB, inthe link from SBS to the UEs is 38.46 + 20logD and MBS to the UEs is 15.3 + 37.6logD,based on the channel models from [96], where D is the distance between transmitter andreceiver in meters. The minimum throughput requirement of MUEs and HUEs are set as1295.5. Performance Evaluation ResultsFigure 5.2: Convergence of DBPSO algorithm.Rmin = 50 Kbps. Transmit power of the MBS is set to PM = 46 dBm. We assume rth tobe 0.01/Kbps while rg to be 0.1/Watt. Assuming cost of non-renewable energy source (e.g.on site energy generator) of the SBS is higher than that of the MBS (e.g. grid power), weset β = 10. The maximum interference tolerable to MUEs Imax is 10−8 W and AWGN noisepower Nw is 10−13 W. Based on the results of [107], we set αS = 25, indicating that thetransmit power is only 4% of the total dynamic power consumption in an SBS. However,unlike SBS, the signal processing and other power consumption overhead of the MBS canbe assumed to be constant since they vary negligibly with the traffic load [107]. Therefore,considering 50% power amplifier efficiency, we set αM = 2.5.5.2 Simulation ResultsConvergenceFig. 5.2 shows convergence behavior of the DBPSO algorithm used in Algorithm 6, for oneparticular realization of arrival of harvested energy, channel fading, and user activity, forEH = 4 Jps. We observe that, the DBPSO algorithm converges to the same value when thenumber of particles P = 4 or P = 6 although convergence is faster when P = 6 as compared1305.5. Performance Evaluation ResultsTable 5.1: Comparison among proposed algorithms (Scenario I)Algorithm Net SBS Average Average power Average powerreward activation throughput consumption in consumption in(Kbps) SBS (Watts) MBS (Watts)Offline 2.7661 0, 1, 1, 1 77.204 0 4.6654Dynamic 1.8634 0, 1, 1, 1 62.96 0.0043 4.7428Greedy 1.7365 1, 1, 0, 1 59.879 0.2308 2.3347to P = 4. The obtained value of the objective function upon convergence is compared withthe result obtained by solving the original problem directly with the OPTI solver [98] whichis a free MATLAB toolbox capable of solving non-linear and discrete optimization problems.It is noted that the performance loss in the proposed offline algorithm is small despite theapproximations used in subchannel and power allocation algorithm.Comparison among the proposed algorithmsWe compare performances of the proposed algorithms by tabulating results obtained for eachof the proposed algorithms for two different scenarios. We tabulate SBS activation decisionmade by the proposed algorithms, resulting average throughput of HUEs, average powerconsumption at the SBS and that at the MBS to serve HUEs, and the net reward, whenEH = 4 Jps. In Scenario I, we consider one random realization of energy arrival and useractivity where energy harvesting rate in the 4 considered time slots are EH , 2EH , 0, and2EH , number of active MUEs are 2, 1, 1, and 2, while number of active HUEs are 2, 2, 1, and1, respectively. To understand the effect of user activity variation, we consider that fadingcondition of all the subchannels remain same during the considered time slots. The resultsare presented in Table 5.1. The proposed offline algorithm and dynamic programming-basedonline algorithm turn the SBS off in the first time slot. It is because, with two MUEs active,the interference constraint is more severe which curbs throughput performance of HUEshence resulting in lower net reward. However, the greedy online algorithm turns the SBSon whenever energy arrived is non-zero resulting in lower average throughput performance1315.5. Performance Evaluation ResultsTable 5.2: Comparison among proposed algorithms (Scenario II)Algorithm Net SBS Average Average power Average powerreward activation throughput consumption in consumption in(Kbps) SBS (Watts) MBS (Watts)Offline 2.7766 0, 1, 1, 1 59.5 0 4.9586Dynamic 1.7684 0, 1, 1, 1 59.409 0.2308 5.1524Greedy 1.5205 1, 1, 1, 1 54.561 0.7111 0and higher power consumption at the SBS, and hence lower net reward17. Although thedynamic programming-based online algorithm results in SBS activation decision similar tothat of the offline algorithm, the offline algorithm yields a better throughput performance,a lower power consumption, and hence higher net reward.In Scenario II, we consider another random realization of energy arrival where energyharvesting rate in the 4 considered time slots are EH , EH , 2EH , and EH , respectively. Tounderstand the effect of time-variation of channel fading, all sub-channels of considerationare assumed to have same fading condition in one time slot and the channel fading is as-sumed to take values 0.8220, 1.4635, 2.8, and 1.2683, respectively in the 4 time slots underconsideration. To understand the effect of channel fading variation, all of the UEs are as-sumed to be active during all time slots under consideration. The results are presented inTable 5.2. The offline algorithm and the dynamic programming-based online algorithm turnthe SBS off in the first time slot when the channel fading is in the worst condition. Otherobservations are similar to those of Scenario I.Variation with EHFigs. 5.3-5.5 show variation in net reward, average throughput, and average power consump-tion with variation in EH , respectively. Net rewards generated by the proposed algorithmsare much higher than those by the baseline schemes (Fig. 5.3) since average throughputsare higher (Fig. 5.4) and power consumptions are lower (Fig. 5.5). Specifically, note that17Total power consumption is numerically lower in greedy algorithm than that in other proposed algo-rithms. However, since the penalty per unit power consumption at the SBS is higher by the factor β, theincurred penalty becomes comparable or higher.1325.5. Performance Evaluation ResultsEH (Jps)2.5 3 3.5 4 4.5Netreward-5-4-3-2-10123OfflineDynamicGreedyBaseline(heuristic)Baseline(always on)Baseline(always off)Solid line: Imax = 10× 10−9Dotted line: Imax = 5× 10−9Figure 5.3: Variation in net reward with EH .EH (Jps)2.5 3 3.5 4 4.5Averagethroughput(Kbps)45505560657075OfflineDynamicGreedyBaseline(heuristic)Baseline(always on)Baseline(always off)Solid line: Imax = 10× 10−9Dotted line: Imax = 5× 10−9Figure 5.4: Variation in average throughput with EH .1335.5. Performance Evaluation Resultspower consumption at the MBS is much lower than that in Always Off Scheme and powerconsumption at the SBS is much lower than that in Always On Scheme. Although the totalpower consumption is numerically smallest for Always On Scheme, the incurred penalty ishigher since penalty per unit power consumption at the SBS is higher by factor β. For lowervalues of EH , performance of the Heuristic Scheme is better than those of the Always OnScheme and the Always Off Scheme since the SBS activation decision is taken consideringthe amount of energy arrived. As expected, performance of the offline algorithm is the best,which is followed by the dynamic programming-based online algorithm and then the greedyonline algorithm. The reason behind such result can be understood from the results of somespecific scenarios presented in Tables 5.1 and 5.2. Although power consumption at the MBSfor offline and dynamic programming-based online algorithms are higher, greedy online al-gorithm incurs a higher penalty for power consumption. This is because power consumptionat the SBS is higher and penalty per unit power consumption is higher at the SBS by thefactor β. The differences among performances of the proposed algorithms in terms of powerconsumption and hence the net reward are observed to be small when EH is very low or veryhigh. This is because, when harvested energy is very small, the SBS is mostly deactivated,hence resulting in maximum power consumption in the MBS. When the harvested energyis very high, the SBS is mostly activated with minimum power consumption in the MBS aswell as the SBS. Since the SBS is never activated in Always Off Scheme, its performancedoes not vary with EH .Variation with ImaxIn Figs. 5.3-5.5, we compare performance of the proposed offline algorithm for differentvalues of Imax. When interference tolerance of MUEs (Imax) is lowered, throughput of HUEsdecrease (Fig. 5.4) since transmit power of the SBS is lowered due to interference constraintC6. However, non-renewable power consumption at the MBS decreases and that at the SBSincreases (Fig. 5.5). It is because SBS is activated more often when Imax is lowered. This1345.5. Performance Evaluation ResultsFigure 5.5: Variation in power consumption with EH .highlights the impact of interference-aware resource allocation on SBS activation decision.The net reward of serving HUEs also decreases slightly with lower Imax (Fig. 5.3), mainlydue to lowered throughput performance.Variation with βFigs. 5.6-5.7 show performance variation of the proposed algorithms in comparison to thebaseline schemes, with varying β, for EH = 3 Jps. When β is very low, penalty of powerconsumption in the SBS is comparable to that in the MBS. Since power consumption in theSBS is always smaller than that in the MBS, the proposed algorithms maximize throughputof HUEs by always turning the SBS on, resulting in performance similar to that of AlwaysOn Scheme. Hence, power consumption at the SBS to serve HUEs is maximum and thatat the MBS is zero (Fig. 5.7). As β increases, power consumption at the SBS decreasesand that at the MBS increases. Average throughput of HUEs decrease to a minimum pointwhen β = 2.5 because at this point power consumption is reduced at the SBS but the MBSis not serving HUEs. After this point, throughput performance of the proposed algorithmsgradually increase and become prominently higher than that of Always On Scheme (Fig. 5.6).1355.5. Performance Evaluation Resultsβ0 2 4 6 8 10 12 14 16 18 20Averagethroughput(Kbps)4550556065707580OfflineDynamicGreedyBaseline(heuristic)Baseline(always on)Baseline(always off) Solid line: Hotspot radius=10 mDotted line: Hotspot radius=15 mFigure 5.6: Variation in average throughput with β.When β is higher than 10, power consumption at the SBS reduces to zero and that at theMBS stabilizes to a maximum value indicating that, for these values of β, the SBS is activatedto consume harvested energy only. However, in the Heuristic Scheme, power consumption atthe SBS does not become zero since SBS is activated whenever the arrived energy is higherthan EH , regardless of β. The Always Off Scheme results in the lowest average throughputof HUEs and maximum power consumption at the MBS.Variation with hotspot sizeIn Figs. 5.6-5.7, we compare the performance of the proposed offline algorithm for differenthotspot size. When radius of the hotspot is increased, power allocated to SBS should increaseto overcome the propagation loss. Therefore, for lower values of β, power consumption at theSBS is higher (Fig. 5.7). However, due to interference constraint C6, the increase in transmitpower cannot fully overcome the propagation loss and hence throughput of HUEs decreases(Fig. 5.6). Therefore, for larger values of β, the SBS is deactivated more often and HUEs are1365.5. Performance Evaluation ResultsFigure 5.7: Variation in power consumption with β.served by the MBS which causes increase in MBS power consumption and decrease in SBSpower consumption (Fig. 5.7). This also highlights the impact of interference-aware resourceallocation decision on SBS activation decision.Variation with rthFigs. 5.8-5.9 show performance variation of the proposed algorithms in comparison to thebaseline schemes, with varying rth, for EH = 3 Jps. Since increasing rth implies an in-crease in throughput reward, with increasing rth, the average throughput of HUEs increase(Fig. 5.8) at the cost of higher power consumption at the MBS (Fig. 5.9). This increase israpid when rth increases from 0.015/Kbps up to 0.025/Kbps, after which the values come tosaturation. The Always Off Scheme exhibits a lower throughput performance and a higherpower consumption at the MBS in comparison to other algorithms until rth is less than0.015/Kbps after which the throughput performance and power consumption at the MBS1375.5. Performance Evaluation ResultsFigure 5.8: Variation in average throughput with rth.Figure 5.9: Variation in power consumption with rth.1385.5. Performance Evaluation Resultsincreases rapidly and becomes comparable to that of the proposed algorithms. At the satu-ration point, in the proposed algorithms, power consumption at the SBS becomes zero andthat at the MBS becomes comparable to that of the Always Off Scheme, indicating that,from this point onward, SBSs are mostly deactivated. However, in the Heuristic Scheme,since the SBS is activated whenever harvested energy is higher than EH , power consumptionat SBS also increases with increasing rth, as in the Always On Scheme. Given that rg isset to 0.1/Watt, it should be noted that gain of the proposed algorithms is prominent whenrth is much smaller than rg. For the Always On Scheme, with increasing rth, the rate ofincrease of throughput performance is much lower since SBS transmit power cannot increasesignificantly due to the interference constraint C6.5.5.3 Summary of ObservationsThe effects of arrival of harvested energy, channel conditions as well as number of activeMUEs on performance of the proposed algorithms highlight the importance of joint consid-eration of energy-aware and interference-aware resource allocation in a multi-tier networkwith energy harvesting base stations. The performance variation with Imax and hotspot sizealso highlight the impact of interference-aware resource allocation decision on SBS activationdecision. Since it uses causal as well as non-causal information, the offline algorithm resultsin a higher achievable throughput of HUEs with minimum power consumption penalty hencegenerating the highest net reward. Because it only utilizes statistical information insteadof non-causal information, the dynamic programming-based online algorithm exhibits aninferior throughput performance and a higher power consumption in comparison to the of-fline algorithm. However, differences in performances among the three proposed algorithmsdiminish when the amount of energy harvested is very small or very high. The proposedalgorithms are most effective when penalty of power consumption at the SBS is higher thanthat at the MBS. For lower values of β, the proposed algorithms try to maximize achievablethroughput of HUEs by always associating them to the SBS and the performance becomes1395.5. Performance Evaluation Resultssimilar to that of the Always On Scheme. Similarly, the proposed algorithms are most ef-fective when reward per unit achievable throughput rth is much lower than penalty per unitpower consumption rg. For higher values, the proposed algorithms try to maximize achiev-able throughput of HUEs at the cost of very high power consumption at the MBS and theperformance becomes similar to that of the Always Off Scheme. Although the HeuristicScheme is inferior to the proposed algorithms, it is superior to the Always On Scheme andthe Always Off Scheme since the SBS activation decision takes the energy arrival informationinto account.140Chapter 6Summary, Conclusions, and FutureWork6.1 Summary and ConclusionsIn this thesis, we addressed different challenges of uplink and downlink resource allocation inheterogeneous and cooperative communication networks with energy harvesting constraints.As wireless energy harvesting is envisioned as promising technique for elongating battery lifeof small network devices such as sensor nodes, in Chapters 2-4, we studied resource alloca-tion for uplink and downlink communication with wireless energy harvesting. To addressthe challenges introduced in uplink as well as downlink resource allocation of wireless energyharvesting networks, we considered uplink WPC in Chapters 2-3 and downlink SWIPT inChapter 4. In uplink WPC, uplink information transmission is highly dependent on down-link energy harvesting phase and hence we developed algorithms to perform joint uplinkand downlink resource allocation considering relay-based and user-based cooperation to mit-igate the “doubly near-far” problem. On the other hand, in downlink SWIPT, informationtransmission rate and energy harvesting rate are two contradicting requirements. Hence,in Chapter 4, we developed resource allocation algorithms to optimize rate-energy trade-offwhile addressing the interference management challenge in HetNets with SWIPT. Whilewireless energy harvesting is suitable in small nodes of the network, renewable energy har-vesting is a promising technique for reducing the power cost of bigger network nodes suchas base stations. Since maximizing the throughput performance at the cost of minimum1416.1. Summary and Conclusionsnon-renewable energy consumption is a challenging requirement of such energy harvestingnetworks, in Chapter 5, we designed base station activation and resource allocation algorithmto optimize the trade-off between throughput performance and power cost while consideringthe energy harvesting and interference constraints in HetNets with renewable energy harvest-ing base stations. In the following, we present the concluding remarks on the contributionsmade in this thesis.In Chapter 2, we proposed two scenarios for uplink WPC networks with relay-based co-operation. In Scenario I, far-UEs harvest energy from RF transmission of the access pointas well as the relay node; and in Scenario II, far-UEs harvest from relay node transmissiononly and near-UEs harvest from the transmission of the access point only. We proposed dif-ferent resource allocation methods to maximize uplink sum-throughput, considering limitedtransmission time and energy available at the relay node. From simulation results, we ob-served that, most of the available resources (time/energy) have to be dedicated for wirelesscharging process. Addition of relay node resulted in a higher throughput of far-UEs andsum-throughput as well as fairness. Simulation results also revealed that the performanceof Scenario II is significantly better with optimal resource allocation when compared to theiterative resource allocation and that Scenarios I and II have similar performances with it-erative resource allocation. Therefore, the resource allocation methods for Scenario II canbe recommended for uplink WPC networks with relay-based cooperation.In Chapter 3, we investigated resource allocation problem in uplink WPC networks withuser-based cooperation. We assumed that all UEs harvest energy from downlink transmissionof the access point in energy harvesting phase. In uplink information transmission phase,the UEs were designed to cooperate among each other to enhance their throughput perfor-mance. Since uplink sum-throughput performance relies on the harvested energy, channelallocation, and relay selection, we proposed a novel resource allocation scheme to jointly op-timize downlink and uplink power allocation along with uplink subcarrier and relay selection.From simulation results, we demonstrated the efficacy of our proposed resource allocation1426.1. Summary and Conclusionsscheme in comparison to two benchmark schemes in terms of throughput and system energyefficiency.In Chapter 4, we investigated resource allocation problem for SWIPT in small cells under-laying a macrocell in a two-tier HetNet. By using scalarization technique of multi-objectiveprogramming, we jointly optimized achievable throughput as well as energy harvesting ratesof small cell users. We proposed different resource allocation frameworks for time-switchingas well as power-splitting approaches of SWIPT. In the time-switching approach, macro-cell users were designed to have flexible interference tolerance levels, to provide a degreeof freedom for small cell base stations to adjust their transmit powers in energy harvest-ing and information decoding process. Scenarios with and without co-tier interference wereinvestigated in the time-switching approach to explore the effect of interference. Numeri-cal results demonstrated the trade-off between achievable throughput and energy harvestingrate of small cell users, and highlighted the improvement in achieved energy harvesting ratesdue to the flexibility in interference tolerance levels of macrocell users in the time-switchingapproach, when compared with the power-splitting approach. Also, the results showed sig-nificant improvement in energy harvesting rate of small cell users in the presence of co-tierinterference at the cost of degraded throughput performance.In Chapter 5, we investigated energy-aware and interference-aware resource allocationjointly with dynamic activation of energy harvesting base stations in a two-tier HetNet takinginto account the varying channel condition, user activity, and arrival of harvested energy.While ensuring QoS provisioning to hotspot users as well as macrocell users, we optimizedthe trade-off between throughput performance of the hotspot users and the associated powercost, by maximizing the net reward over a number of time slots. For that, positive rewardwas associated with achievable throughput of the hotspot users and negative reward withthe corresponding power consumption at the small cell or macrocell base station. We solvedthe problem in offline and online mode assuming the presence and absence of non-causalinformation, respectively. For the online solution, we proposed a dynamic programming-1436.2. Future Research Directionsbased online algorithm, assuming presence of statistical information of the future values,and a greedy online algorithm, assuming lack of any future information. Numerical resultsdemonstrated the advantage of the proposed offline algorithm over the online algorithms andthat of the dynamic programming-based online algorithm over the greedy online algorithm.From the results, we also identified the scenarios where the proposed algorithms performbetter than the baseline schemes.6.2 Future Research DirectionsIn this section, we propose some possible research directions that can be followed from thisthesis.• Since both renewable energy harvesting and wireless energy harvesting are emergingand promising concepts for the future wireless networks, considering the co-existence ofthese two paradigms will be important. Co-existence of renewable and wireless energyharvesting would open following research directions from our accomplished works:– In the context of uplink WPC networks with relay-based and user-based coopera-tion, relay node and access points can be designed to harvest energy from the na-ture and the UEs to harvest energy from the wireless signal. In that case, resourceallocation problem would have additional causality constraint on availability ofenergy at the access points and relay nodes, which would further complicate theanalysis of the resource allocation problem.– In Chapter 4, we have considered SWIPT in HetNets, while we have consideredrenewable energy harvesting in HetNets in Chapter 5. In the future work, con-sidering renewable energy harvesting in the base stations and SWIPT to the UEsof small cells would be interesting. In that case, the interference managementchallenges that arise in SWIPT in HetNets and energy management challenges1446.2. Future Research Directionsthat arise in renewable energy harvesting base stations would merge into a singleresource allocation problem, hence increasing the complexity of the problem.• In our research works, we assume to have perfect knowledge of the channel state infor-mation. However, the channel state information may not be perfect due to estimationerrors and uncertainties. Therefore, robust resource allocation [116] can be a possiblefuture extension of the works accomplished in this thesis.• In Chapters 4 and 5, we assume to have information about some network parameters(such as channel state, user activity, and arrival of harvested energy) ahead of timein some scenarios. To acquire such network information ahead of time, applicationof machine learning algorithms in communication networks is gaining much researchattention recently [117]. One possible future extension of our work could be jointconsideration of machine learning algorithm and resource allocation algorithm in suchscenarios.• In the context of uplink WPC network with relay-based cooperation, we consider op-timal time allocation but do not consider relay and subcarrier selection. In the futurework, joint optimization of downlink energy harvesting time, uplink information trans-mission time, relay and subcarrier selection, along with downlink and uplink powerallocation can be considered. With increased number of optimization variables, the re-source allocation will be difficult to solve and hence finding a computationally efficientsolution approach will be important.• In the context of SWIPT in HetNets, we have proposed the resource allocation algo-rithms for different scenarios assuming each cell has one channel available to serve oneuser at a time. One possible future research direction could be considering a multi-userand multi-channel scenario in a cell. In that case, optimization of subcarrier alloca-tion will be essential along with downlink power and power-splitting/time-switchingvariables.1456.2. Future Research Directions• In the context of both downlink SWIPT and uplink WPC, we have considered a con-stant energy harvesting efficiency of the energy harvester, irrespective of the receivedpower. However, energy harvesting efficiency of energy harvesting circuits highly de-pends on received power [14]. Hence, dependency of energy harvesting efficiency onreceived power can be considered in the future extension of the work.• In the context of uplink WPC as well as downlink SWIPT, our works do not considerdirective transmission of narrower energy beam. Directive beamforming can signifi-cantly increase energy harvesting efficiency [118] and should be considered for futureextensions of the works accomplished in the thesis. However, beamforming vectors areadditional optimization variables, thus increasing complexity of the resource allocationproblem.• In the context of base station activation and resource allocation in energy harvestingHetNets, we divide the users as hotspot users and macrocell users based on geograph-ical location and simplify the user association scheme. For future extension, we caninvestigate joint optimization of user association [119] along with resource allocationand base station activation. 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Rabaey, “Far-field RF wireless powertransfer with blind adaptive beamforming for Internet of things devices,” IEEE Access,vol. 5, pp. 1743–1752, 2017.[119] S. Maghsudi and E. Hossain, “Distributed user association in energy harvesting densesmall cell networks: A mean-field multi-armed bandit approach,” IEEE Access, vol. 5,pp. 3513–3523, 2017.155Appendices156Appendix AProof of ConvexityIt can be proven that R(sc-II)i(n) (given in (2.12)) is a concave function of t(d) and ti(n) by usingperspective operation [80]. To prove the convexity of R˜(sc-II)j(f) (given in (2.36)) in tj(f), E(rd),and Ej(ru), let us define a function f(E(rd), Ej(ru)) asf(E(rd), Ej(ru)) =(1 +δαjβE(rd)Ej(ru)αjE(rd) + 2βEj(ru)).The Hessian of f(E(rd), Ej(ru)) is given by∇2f(E(rd), Ej(ru)) =4δα2jβ2(E(rd)αj + 2βEj(ru))3 −E2j(ru) Ej(ru)E(rd)Ej(ru)E(rd) −E2(rd) .The eigenvalues of the Hessian ∇2f(E(rd), Ej(ru)) are given asλ1 = 0, λ2 = −4δα2jβ2(E(rd)αj + 2βEj(ru))3 (E2(rd) + E2j(ru)) .Since λ1, λ2 ≤ 0, the Hessian matrix ∇2f(E(rd), Ej(ru)) is a negative semidefinite matrix andtherefore, f(E(rd), Ej(ru)) is a concave function. Since log(.) is an increasing concave function,log2(1 +δαjβE(rd)Ej(ru)αjE(rd)+2βEj(ru))is also a concave function. Then, R˜(sc-II)j(f) is also a concave functionof tj(f), E(rd), and Ej(ru) by perspective operation. Hence,∑Ni=1R(sc-II)i(n) +∑Kj=1 R˜(sc-II)j(f) is sumof concave functions and hence is a concave function. This completes the proof.157Appendix BProof of Lemma 5From (2.46) and (2.47), we haveln(1 + x)− x1 + x=∑Ni=1 νi1 + x. (B.1)By letting x˜ = 1 + x and A =∑Ni=1 νi and simplifying (B.1), we obtainA− 1x˜e(A−1x˜ ) = (A− 1) e−1 =⇒ wew = e−1 (A− 1) , where w = A− 1x˜. (B.2)Using (B.2) and the definition of Lambert-W function [81], we getw =W (e−1 (A− 1)) (B.3)where W(.) is the Lambert-W function [81]. Therefore, using w = A−1x˜, x˜ = 1 + x, andA =∑Ni=1 νi in (B.3), we obtain x∗ =∑Ni=1 νi−1W(e−1(∑Ni=1 νi−1))− 1. The expression for y∗ can beobtained in similar way by letting y˜ = 1 + y and B = 2µ∗1T ln(2) and simplifying (2.48) afterwhich we obtain(−1y˜)e(−1y˜ ) = −e−(B+1) =⇒ wew = −e−(B+1), where w = −1y˜.Now, to prove the expression for z∗ in (2.52), let us use (2.49) and (2.50) to obtain2δβz2 =K∑j=1αjδ(1− z)2 =⇒ z2(K∑j=1αj − 2β)− 2K∑j=1αjz +K∑j=1αj = 0. (B.4)158Appendix B. Proof of Lemma 5Equation (B.4) is a quadratic equation and therefore the solution is given byz =2∑Kj=1 αj ±√8∑Kj=1 αjβ2(∑Kj=1 αj − 2β) .Considering that z = zj =bjaj+bj, ∀j, we know that the solution should satisfy z < 1. Thesolution that satisfies the condition is: z∗ =2∑Kj=1 αj−√8∑Kj=1 αjβ2∑Kj=1 αj−4β, which can be easily verifiedconsidering different cases such as 2β >∑Kj=1 αj, 2β <∑Kj=1 αj, and 2β =∑Kj=1 αj. Thiscompletes the proof.159Appendix CProof of Proposition 2Using definition of aj, bj in (2.44), and z in (2.45), we getE∗j(ru) =(1− zz)αjE∗(rd)2β. (C.1)Now, using (C.1), to simplify the relation of energy variables in (2.53), we obtainE∗(rd) =2βz∗Emax2βz∗ + (1− z∗)∑Kj=1 αj . (C.2)We obtain (2.54) from (C.1) and (C.2). Again, using definitions of aj, bj in (2.44), and yin (2.45), we obtaint∗j(f) =δy(1αjE∗(rd)+ 12βE∗j(ru)) . (C.3)Then, we obtain the expression for t∗j(f) in (2.55) from (2.54) and (C.3). Using definition of xin (2.45) to simplify relation of DEH and UIT times in (2.53), we obtain: t∗(d) =T−∑Kj=1 t∗j(f)1+∑Ni=1νixand ti(n) is obtained by using definition of x in (2.45). This completes the proof.160Appendix DSimplification of KKT ConditionsSince the problem in (4.8) is a convex optimization problem, KKT conditions should besatisfied. Differentiating (4.9) with respect to αtE and using the KKT stationarity condition,we obtain∂L(P˜I, P˜E,αI ,αE,λ, γ)∂αtE= 0⇒ λt=S∑s=1ηws,Eχtm,sNE(tar),∀t. (D.1)Since the right hand side of (D.1) is strictly positive, the dual variable λt > 0 must be satisfiedfor all t. Then, to satisfy the KKT slackness condition, the constraint (C2) corresponding tothe dual variables λ must be satisfied with strict equality, i.e. αtI + αtE = 1, ∀t which leadsto (4.11). By differentiating (4.9) with respect to P˜ ts,I and then using the KKT stationaritycondition, we obtainws,Ihts,sNR(tar)log(2)(χtm,s+Nsp)(1+P˜ ts,Ihts,sαtI(χtm,s+Nsp))−γthts,m = 0 which can be simplifiedto obtain (4.12).161

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