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RF energy harvesting in a decode-and-forward wireless relay network Elmorshedy, Lina 2016

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RF Energy Harvesting in aDecode-and-Forward Wireless RelayNetworkbyLina ElmorshedyB.Sc., Faculty of Engineering, Alexandria University, 2008A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)April 2016c© Lina Elmorshedy 2016AbstractWireless communication has experienced tremendous growth over the past threedecades. This led to the development of many novel technologies aimed at en-hancing the system performance due to the limited availability of radio resources.Cooperative relaying is a promising technology which enhances transmission relia-bility using simple hardware. However, the extra power consumed for the process ofinformation relaying may be an issue. Recent advances in wireless energy transferhave made it possible for self-sustainable relays that power themselves by capturingambient energy wirelessly. In this thesis we focus on two technologies, namely, co-operative relaying which enhances the energy efficiency and reliability by allowingmulti-hop communication with low power nodes, and Radio Frequency (RF) en-ergy harvesting which obviates the need for a battery by capturing the ambient RFenergy and using it as a source power.In the first part of the thesis, we study RF energy harvesting in a Decode-and-Forward (DF) Wireless Relay Network (WRN) in the presence of an interferernode. We consider the Time Switching Relaying (TSR) protocol, the Power SplittingRelaying (PSR) protocol and we propose a new hybrid TSR-PSR protocol. Wederive expressions for the outage probability and throughput in the delay-sensitivetransmission mode for the three relaying protocols, and compare their performances.For simplicity, we neglect the energy harvested from the interferer signal.In the second part, we study the general case in which we include the effectiiAbstractof harvesting energy from the interferer signal. Expressions for the outage proba-bility and throughput in the delay-sensitive transmission mode are derived for thethree relaying protocols. Numerical results are presented to illustrate the effect ofincluding RF energy harvesting from the interferer.In the third part, we study shared and non-shared power allocation schemes fora two-hop DF WRN with multiple source-destination pairs. The pairs communicatevia a single relay which harvests RF energy from the source transmissions in thepresence of an interfering signal. The studied schemes are compared in terms of out-age probability, throughput in the delay-sensitive transmission mode and fairness.iiiPrefaceChapter 2 is based on a manuscript titled “RF Energy Harvesting in DF RelayNetworks in the Presence of an Interfering Signal” that has been accepted for pub-lication in the 2016 IEEE International Conference on Communications (ICC). Themanuscript is co-authored by myself as the first author, my supervisor, Dr. CyrilLeung and S. A. Mousavifar, a former PhD student in our group. I was the primaryresearcher in this work. I came up with the idea of the research independently. Mycontributions included conducting the literature review, identifying and formulatingthe research problem, and carrying out the mathematical analysis and simulationsunder the supervision of Dr. Cyril Leung. S. A. Mousavifar also provided valuablecomments and helped me by providing technical and editorial feedback while writingthe associated manuscript for publication.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Cooperative Relaying in Wireless Networks . . . . . . . . . . . . . . 21.2 Energy Harvesting in Wireless Networks . . . . . . . . . . . . . . . 21.3 Resource Allocation in Wireless Networks . . . . . . . . . . . . . . . 51.4 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 6vTable of Contents2 RF Energy Harvesting in a Decode-and-Forward Wireless RelayNetwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 TSR-based Energy Harvesting . . . . . . . . . . . . . . . . . . . . . 142.4.1 Outage Probability . . . . . . . . . . . . . . . . . . . . . . . 152.4.2 Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5 PSR-based Energy Harvesting . . . . . . . . . . . . . . . . . . . . . 182.5.1 Outage Probability . . . . . . . . . . . . . . . . . . . . . . . 182.5.2 Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.6 Hybrid TSR-PSR-based Energy Harvesting . . . . . . . . . . . . . . 202.6.1 Outage Probability . . . . . . . . . . . . . . . . . . . . . . . 212.6.2 Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.7 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 RF Energy Harvesting from Interference Signals in a DF WirelessRelay Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1 Motivation and Contributions . . . . . . . . . . . . . . . . . . . . . 313.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.3 TSR-based Energy Harvesting . . . . . . . . . . . . . . . . . . . . . 333.3.1 Outage Probability and Throughput Analysis . . . . . . . . 333.4 PSR-based Energy Harvesting . . . . . . . . . . . . . . . . . . . . . 373.4.1 Outage Probability and Throughput Analysis . . . . . . . . 373.5 Hybrid TSR-PSR-based Energy Harvesting . . . . . . . . . . . . . . 383.5.1 Outage Probability and Throughput Analysis . . . . . . . . 39viTable of Contents3.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454 Power Allocation in a DF Wireless Relay Network with RF EnergyHarvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.4 Non-Shared Power Allocation Scheme (NSPA) . . . . . . . . . . . . 524.5 Shared Power Allocation . . . . . . . . . . . . . . . . . . . . . . . . 544.5.1 Equal Power Allocation (EPA) . . . . . . . . . . . . . . . . . 554.5.2 R−D Channel Dependent Power Allocation (RDCD) . . . 574.5.3 Max-Min R−D Rate Power allocation (MMRD) . . . . . . 584.5.4 Weighted-Sum-Rate Maximization of all R−D links PowerAllocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . 745.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78viiList of Tables4.1 Simulation parameter values . . . . . . . . . . . . . . . . . . . . . . . 644.2 Comparison between different shared allocation schemes - NSPA worstof all . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73viiiList of Figures1.1 (a) Time Switching (TS) receiver architecture (b) Power Splitting(PS) receiver architecture . . . . . . . . . . . . . . . . . . . . . . . . 42.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 TSR protocol at the relay . . . . . . . . . . . . . . . . . . . . . . . . 142.3 PSR protocol at the relay . . . . . . . . . . . . . . . . . . . . . . . . 182.4 Hybrid TSR-PSR protocol at the relay . . . . . . . . . . . . . . . . 202.5 Outage probability versus α for the TSR protocol . . . . . . . . . . . 232.6 Outage probability versus ρ for the PSR protocol . . . . . . . . . . . 242.7 Outage probability versus α for the hybrid protocol with various ρvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.8 Throughput versus α for the hybrid and the TSR protocols . . . . . 252.9 Throughput versus ρ for the hybrid and the PSR protocols . . . . . 262.10 Throughput versus Ps for TSR, PSR and the hybrid protocol . . . . 272.11 Throughput versus PI for TSR, PSR and the hybrid protocol . . . . 282.12 Throughput versus d3 for TSR, PSR and the hybrid protocol . . . . 292.13 Throughput versus d4 for TSR, PSR and the hybrid protocol . . . . 303.1 Hybrid TSR-PSR protocol at the relay . . . . . . . . . . . . . . . . . 38ixList of Figures3.2 Outage Probability versus α for the TSR protocol . . . . . . . . . . 413.3 Throughput versus α for the TSR and the hybrid protocols and versusρ for the PSR protocol . . . . . . . . . . . . . . . . . . . . . . . . . 423.4 Throughput versus PI for the TSR, PSR and the hybrid protocols . 423.5 Throughput versus Ps for the TSR, PSR and the hybrid protocols . 433.6 Throughput versus d3 for the TSR, PSR and the hybrid protocols . 443.7 Throughput versus d4 for the TSR, PSR and the hybrid protocols . 444.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.2 Time Slot Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.3 Outage Probability versus ρ for the NSPA and the EPA schemes . . 654.4 Outage Probability versus ρ for the EPA and the RDCD schemes . . 664.5 Outage Probability versus ρ for the MMRD and the RDCD schemes 674.6 Outage Probability versus ρ for the RDCD and the WSRM schemes 684.7 Outage Probability versus ρ for the WSRM with dynamic and con-stant µi’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.8 Worst user throughput versus Ps . . . . . . . . . . . . . . . . . . . . 704.9 Total network throughput versus Ps . . . . . . . . . . . . . . . . . . 714.10 Fairness Index versus ρ . . . . . . . . . . . . . . . . . . . . . . . . . . 72xList of AcronymsAF Amplify-and-ForwardCCI Co-channel InterferenceCDF Cumulative Distribution FunctionCSI Channel State InformationDF Decode-and-ForwardDS Dual-SourceEPA Equal Power AllocationKKT Karush-Kuhn-TuckerMABC Multiple Access BroadcastMMRD Max-Min Relay-Destination rateNSPA Non-Shared Power Allocationpdf probability density functionPS Power SplittingPSR Power Splitting RelayingRDCD Relay-Destination Channel DependentxiList of AcronymsRF Radio Frequencyrv Random VariableSBS Single-Best-SourceSFS Single-Fixed-SourceSIR Signal to Interference RatioSNR Signal to Noise RatioSWIPT Simultaneous Wireless Information and Power TransferTDBC Time Division BroadcastTS Time SwitchingTSR Time Switching RelayingTWRN Two-Way Relay NetworkWRN Wireless Relay NetworkWSN Wireless Sensor NetworkWSRM Weighted-Sum-Rate MaximizationxiiList of Symbolsα The time switching ratioγth The SIR threshold valueΓD The SIR at the destination nodeΓR The SIR at the relay nodeη The energy harvesting efficiencyθi Fraction of total power at relay assigned to link R−Diµi Weight assigned to link R−Diρ The power splitting ratioτds Throughput in the delay-sensitive moded1 Distance from interferer node to relay noded2,i Distance from interferer node to i-th destination noded3,i Distance from i-th source node to relay noded4,i Distance from relay node to i-th destination nodeEhr Energy harvested at the relayEi(.) Exponential integral functionFI Fairness indexm Path loss exponentN Number of source-destination pairsPI Interferer transmit powerPout Outage probabilityxiiiList of SymbolsPr Relay transmit powerPs Source transmit powerRi,d Data rate at i-th destinationRi,r Data rate from i-th source to relayxivAcknowledgementsI would like to express my sincerest gratitude to my supervisor, Professor Cyril Le-ung, first for accepting me as a Masters student in his group, and most importantlyfor his continuous support and invaluable guidance throughout my Masters program.I am very much grateful for his time, patience, critical suggestions and helpful com-ments. Without his immense knowledge and constant encouragement this thesiswould have never been possible. I am also thankful to, Seyed Ali Mousavifar, a for-mer PhD student in the data communications group, for his constructive suggestionsand helpful advice during my research.I would like to express my heartfelt gratitude to my biggest supporter, amazingfriend and loving husband, Ossama Elmorshedy, who is also my colleague in theElectrical and Computer Engineering department in UBC. His rock solid beliefsin my capabilities have always been my greatest source of motivation throughoutour life. Without his unconditional support and love, I would not have been ableto complete this thesis. Special thanks to my parents, sister and brother for theirsupport, continuous advice and motivation during the past years.Last but not least, I would like to express my gratitude to my lab mates for theirinvaluable support, and friendship during my Masters program. I am also thankfulto all my colleagues in the Electrical and Computer Engineering department in UBCfor the fun we had in the last two years making my graduate studies such a greatexperience.xvAcknowledgementsThis work was supported in part by the Natural Sciences and Engineering Re-search Council (NSERC) of Canada under Grant RGPIN 1731-2013.xviDedicationI dedicate this thesis to my family. My deepest feeling of gratitude goes to myloving mother, Hala Elmorshedy, to whom I owe where I am today. I am grate-ful for her unconditional sacrifice, relentless support and her continuous words ofwisdom and encouragement which have always been my constant guide throughoutmy life. Many thanks to my sister and best friend, Omniah and my dear brother,Zeyad for their unconditional love and support. My sincerest expression of love andappreciation goes to my husband, Ossama, for his exceptional sacrifice and encour-agement throughout my Masters program. I would also like to dedicate this thesisto my daughter and my greatest blessing, Joury, whose presence have been and willalways be the biggest inspiration in my whole life.xviiChapter 1IntroductionWireless communication systems have been experiencing very rapid growth due tothe demand for wireless services over the past three decades. An important researchobjective is to find solutions to meet such increasing demands given the limitedavailability of radio resources. Cooperative communications allow users within anetwork to collaborate with each other in the process of information transmission,given the broadcast nature of wireless networks. This can lead to enhanced en-ergy efficiency, improved network connectivity and increased reliability. As a re-sult cooperative communications have been found to improve the performance ofresource-constrained wireless networks [1]-[3].Moreover, the performance of wireless communication systems is constrained bythe limited battery life of wireless devices. Hence, energy harvesting has receivedsignificant attention recently. Energy harvested from the surrounding environment(i.e. wind, heat, solar, etc.) can be used to prolong the network lifetime, andto eliminate the need for replacing or recharging the batteries of wireless nodes.In many cases, replacing the node batteries may be costly, toxic, undesirable orimpractical. More recently energy harvesting from Radio Frequency (RF) signals hasbeen studied as a promising solution to prolong the lifetimes of energy-constrainedwireless networks ([4] and references therein).In this chapter, we briefly present the fundamentals of cooperative relaying,energy harvesting and a basic overview of resource optimization in wireless commu-11.1. Cooperative Relaying in Wireless Networksnication systems. An outline of the thesis is also provided.1.1 Cooperative Relaying in Wireless NetworksCooperative relaying is a novel technology which improves the energy efficiency andthe reliability of wireless networks by employing intermediate relay nodes betweenvarious source and destination nodes. This allows short distance multi-hop com-munication with low powered nodes, instead of long distance direct communicationwith high powered nodes. It provides a larger coverage area and longer networklifetime, thus improving the performance of wireless communication systems.There are different relaying protocols for cooperative networks such as Amplify-and-Forward (AF) and Decode-and-Forward (DF) [5]. In DF relaying, the relaynode receives the signal sent by the source node, decodes it and then forwards it tothe destination node. In AF relaying, the relay node receives the signal sent by thesource node, amplifies it and then forwards it to the destination node.1.2 Energy Harvesting in Wireless NetworksLimited device battery life has always been a key concern in the design of wire-less communication systems. Energy harvesting has been proposed as a promisingsolution to that problem, such that energy is captured and stored from externalsurrounding sources. This technology has received significant attention recently spe-cially with the emergence of miniature electronics devices and low power WirelessSensor Network (WSN) systems, in which the finite lifetime of the node batterieslimits the lifetime of their applications [6]. The benefits of energy harvesting arisein applications where the charging of the batteries is one of the major problemsto be addressed, specially when the wireless nodes are located in difficult to access21.2. Energy Harvesting in Wireless Networksenvironments or even inaccessible places, or the number of wireless nodes is quitelarge and are distributed in a wide area.Various sources of renewable energy such as solar, mechanical, wind and thermalenergy can be used to power wireless communication networks [6]-[8]. However, themain problem of energy harvesting from renewable sources is its random nature.This makes it unreliable since it depends on the energy availability that may varywith location, time and weather conditions. Therefore, it is not easy to predict theamount of energy that can be harvested from the environment which makes resourceallocation in such systems a challenging problem.Recently, wireless energy transfer has been introduced for RF energy harvestingin wireless communication systems through a paradigm referred to as SimultaneousWireless Information and Power Transfer (SWIPT) [9],[10]. In SWIPT, the RFenergy transfer and information transmission are performed in the downlink at thesame time, which is possible since RF signals carry both energy and informationsimultaneously. Therefore the energy-constrained nodes can decode information aswell as harvest energy from the received RF signal.An ideal receiver design which can simultaneously extract power and decodeinformation from the same received signal was considered in [11] and [12]. However,the assumption of simultaneous information decoding and energy harvesting fromthe same received signal used in [11] and [12] was found to be unrealistic as notedin [13]. It was found in [13] that practical circuits used for harvesting energy fromthe RF signals are not able to directly decode the information carried by the signal.This is due to the different functionality of the antennas used by the informationtransceiver and energy harvester in addition to the considerably different powersensitivities of receivers, i.e. -20 to -10 dBm for energy harvesting and -60 dBm forinformation decoding. This led to the design of two practical receiver architectures,31.2. Energy Harvesting in Wireless NetworksFigure 1.1: (a) TS receiver architecture (b) PS receiver architecturenamely the Time Switching (TS) and the Power Splitting (PS) receiver architecturesas shown in Fig. 1.1.The TS receiver alternately switches between harvesting energy and decodinginformation. The received RF signal yR(t) is first sent to the energy harvestingreceiver for an amount of time αT , and then to the information receiver for anamount of time (1 − α)T , where T is the time duration in which the informationsignal is transmitted from the source node to the destination node. In the PSreceiver the power of the incoming signal is split into two streams by what is calledthe PS ratio, i.e. ρ. A portion,√ρyR(t), of the received signal is sent to theenergy harvesting receiver and the remaining portion,√(1− ρ)yR(t), of the signaldrives the information receiver. Such receivers have been widely adopted in the41.3. Resource Allocation in Wireless Networksliterature [14],[15],[19]. Based on those designs, Time Switching Relaying (TSR)and Power Splitting Relaying (PSR) protocols have been proposed in [19] for RFenergy harvesting in cooperative relay networks.One of the main challenges facing the wireless energy transfer technology is thehigh propagation loss. It is shown in [16] that the RF energy transfer distance rangesfrom 3 to 15 meters for mobile devices depending on the strength of the radiatedpower, which varies from 1 to 100 Watts. Therefore, RF energy harvesting is onlysufficient for powering wireless sensor nodes with low power requirements. Poweringdevices with larger power requirements has to be performed using additional specialstations, called power beacons, which are mainly dedicated for RF energy transferto mobile devices [17]. Another important challenge is the safety issue, since it hasbeen reported that the exposure limit to microwave radiation, in the 2.4 and 5.8GHz frequency bands, averaged over 30 minutes is equal to 10 W/m2 according tothe international safety standards [18]. However, this can be mitigated by usingphase arrays with smart beamforming techniques, which can ensure the safety inwireless energy transfer using dedicated RF sources [16].1.3 Resource Allocation in Wireless NetworksEnergy sharing has emerged as a promising research area in energy harvesting wire-less systems, where the wireless network nodes share their energy resources to en-hance the energy efficiency of the network. However, finding the most efficientstrategy to utilize the harvested energy to satisfy user requirements, has becomea challenging problem for researchers. Various objectives for wireless communica-tion systems have been studied in the literature resulting in different energy al-location strategies. Those objectives include, lifetime maximization, throughputmaximization, outage probability minimization, energy efficiency maximization, to-51.4. Organization of the Thesistal transmit power minimization, transmission time minimization and total energyconsumption minimization [30]-[36]. The target objective depends on the studiedapplication and the performance measure under consideration.For the work on power allocation in wireless cooperative energy harvesting sys-tems done in this thesis, it is assumed that only statistical Channel State Informa-tion (CSI) is available at a central managing node. This assumption may be morerealistic for energy-constrained networks than assuming full channel CSI availabilitywhich requires significant amount of CSI feedback. For a system with a large num-ber of users, it is more practical to consider distributed resource allocation schemes[31]. Those schemes achieve a reasonable tradeoff between the performance measureunder consideration and the system complexity, which is a challenging task and isout of the scope of this thesis.1.4 Organization of the ThesisThe structure of the thesis is as follows• In Chapter 2, we consider a DF Wireless Relay Network (WRN) consistingof a source node, destination node and an energy-constrained relay node inthe presence of an interfering signal. The relay node is capable of RF energyharvesting. For simplicity, we neglect the effect of the RF energy harvestedfrom the interfering signal and study the case where the relay harvests RFenergy from the source node. The RF signal sent by the source node carriesinformation which is forwarded via the relay to a destination. We study theperformance of three relaying protocols, the TSR protocol, the PSR protocoland a proposed hybrid TSR-PSR protocol. Analytical expressions for the out-age probability and throughput in the delay-sensitive transmission mode arederived for the three protocols. A comparison of the throughput performances61.4. Organization of the Thesisof these protocols for different system parameter values is then presented.• In Chapter 3, we extend our study in Chapter 2 to include the case where theenergy-constrained relay node harvests energy from the RF signal sent by thesource node in addition to the RF signal of the interferer node. We deriveclosed-form expressions for the outage probability as well as upper and lowerbounds for the considered energy-constrained relay network. We also deriveclosed-form expressions for the achievable throughputs in the delay-sensitivetransmission mode, for the TSR, PSR and the hybrid TSR-PSR protocols.Finally, we present results to illustrate the effect of harvesting energy fromthe interference signal on the system performance.• In Chapter 4, various power allocation schemes to distribute the relay’s powerare studied for a DF WRN consisting of multiple source-destination pairsand one DF relay. The source-destination pairs communicate via the energy-constrained relay which harvests wireless energy from the RF signals trans-mitted by the source nodes. First a non-shared power allocation scheme isstudied in which the RF energy harvested from the i-th source is used to for-ward information from the relay to the i-th destination. Several shared powerallocation schemes are also studied: (1) an equal power allocation scheme,(2) a relay-destination channel dependent scheme, (3) a scheme which maxi-mizes the minimum rate of all relay-destination links, and (4) a scheme whichmaximizes a weighted-sum-rate of all relay-destination links. Expressions forthe outage probability and the throughput in the delay-sensitive transmis-sion mode are derived for each power allocation scheme. The performances ofthe different allocation schemes are compared in terms of outage probability,throughput and fairness.71.4. Organization of the Thesis• Chapter 5 provides the main findings of the thesis and discusses some possiblefuture research directions.8Chapter 2RF Energy Harvesting in aDecode-and-Forward WirelessRelay NetworkIn this chapter we study wireless energy harvesting in a DF WRN in the presence ofan interfering signal. The relay node is energy-constrained and harvests energy fromthe RF signal of the source node. We state the motivation of our work followed byour main contributions. The system model is then presented and analytical expres-sions for the outage probability and throughput in the delay-sensitive transmissionmode are derived for three different relaying protocols. Numerical results are finallypresented to compare between the performance of the studied relaying protocols.2.1 MotivationCooperative relaying where intermediate relays assist a source node with the trans-mission of information to its intended destination is commonly used to improve theenergy efficiency of wireless communication systems. However, the relays may beenergy-constrained, i.e. no fixed power supply at the relay. Hence, wireless en-ergy harvesting has been studied as a promising solution to prolong the lifetimesof energy-constrained cooperative relay networks [19]-[26]. Based on the commonly92.1. Motivationused energy harvesting receiver architectures discussed previously, TSR and PSRprotocols have been proposed in [19] for RF energy harvesting in cooperative relaynetworks.In [20], the throughput of an AF Two-Way Relay Network (TWRN) with anenergy-constrained relay node is derived. Multiple Access Broadcast (MABC) pro-tocol and Time Division Broadcast (TDBC) protocol are considered as two-wayrelaying protocols. Also three wireless power transfer policies are proposed, namelyDual-Source (DS) power transfer, Single-Fixed-Source (SFS) power transfer andSingle-Best-Source (SBS) power transfer, based on the TS receiver architecture.However, interference is not considered when deriving the throughput in [20]. Theergodic capacity of a DF relay network is studied in [21], in which the energy-constrained relay harvests energy from both the received information signal as wellas the Co-channel Interference (CCI) signals using the TSR protocol. The achievablethroughput is determined based on the derived expression for the ergodic capacity as-suming delay-tolerant transmission. A scenario in which multiple source-destinationpairs communicate with the help of energy-constrained relays is studied in [22]. Thisstudy is focused on the optimal design of SWIPT in relay interference channels. Aprofile of PS ratios for all relays is derived using game theory, where each link ismodeled as a strategic player whose aim is to maximize its individual achievablerate by choosing the relay’s PS ratio. The sum-rate of all links is considered as thenetwork-wide performance metric in [22].In [23], optimal dynamic power splitting policies for the PSR protocol at theenergy-constrained relay are studied, to minimize the outage probability of an AFrelay network when full CSI and partial CSI are available. The policy with full CSIis found to achieve the best performance but extra system overhead is incurred forchannel estimation which is considered to be perfect in this study. In [24], a source102.2. Contributionsforwards information to a destination via multiple energy-constrained relays in aDF relay network. Two relay selection schemes are discussed depending on the CSIavailability, and their outage performances are studied. It is found that there isa tradeoff between the number of relays in the system and the energy harvestingefficiency of the relays. However, no TS or PS is performed in [24] as it is assumedthat only one function can be performed in a given time slot. Wireless energyharvesting in a cognitive relay network is studied in [25], where the secondary relayand the secondary source harvest RF energy from the primary signal using the TSRprotocol. The interference constraints on the primary and secondary networks areconsidered in [25] and the outage probability is derived. However, the effect ofvarying the TS ratio on the outage performance was not studied.2.2 ContributionsIn this chapter, we study wireless energy harvesting and information processing ina DF WRN. The relay is energy-constrained and harvests energy from the sourcetransmissions. The network is subject to interference which affects the system per-formance. We consider TSR and PSR protocols in [6] for RF energy harvesting atthe relay node and we also propose a hybrid TSR-PSR protocol. The outage proba-bilities and the throughputs of the three protocols are analyzed in the delay-sensitivetransmission mode.The main contributions of this chapter are summarized as follows:• We propose a hybrid TSR-PSR protocol which enables wireless energy harvest-ing and information processing at the energy-constrained relay node, based ona combination of the TS and PS receiver architectures.• We derive closed-form expressions for the outage probability as well as upper112.3. System Modeland lower bounds. We also derive closed-form expressions for the achievablethroughputs in the delay-sensitive transmission mode of the energy-constrainedrelay network, for the TSR, PSR and the hybrid TSR-PSR protocols.• We compare the throughput performances of the three protocols for differentsystem parameters. We show that the throughput of the hybrid protocol isgenerally higher than those of TSR and PSR.The remainder of the chapter is organized as follows. In section 2.3, we presentour system model. In Sections 2.4, 2.5 and 2.6, we derive the outage probabilityand the achievable throughput for the TSR, PSR and hybrid protocols, respectively.Numerical results and discussion are presented in section 2.7, followed by a summaryin section 2.8.2.3 System ModelAs shown in Fig. 2.1, we consider a DF cooperative relay network, in which theinformation is transmitted by a source node S to a destination node D through anenergy-constrained relay node R. There is no direct link between the source nodeand the destination node so that the relay assists the transmission of the sourceinformation to the destination. The relay harvests energy from the source whichtransmits at a fixed power Ps. The relay then uses the harvested energy to transmitthe information to the destination. We adopt the harvest-use approach in which theharvested energy cannot be stored beyond the current time slot, due to hardwarelimitation [26]. Moreover, the power required at the relay for information processingis assumed to be negligible compared to the power required for signal transmissionfrom the relay to the destination [13].The channel gain coefficients from the source to the relay and from the relay122.3. System ModelFigure 2.1: System Modelto the destination node are denoted by h1 and h2, respectively. We consider aninterfering transmitter I located at distances d1 and d2 from the relay and thedestination nodes, respectively, while the corresponding channel gains are denotedby f1 and f2. We assume that the interference power is not large enough for RFenergy harvesting at the relay. The inter-node distances S → R and R → D aredenoted by d3 and d4, respectively. We neglect the effect of noise in our systemmodel as the interference power is assumed to be much higher than the noise power.The interference powers received at the relay and the destination are given as [25]PI,R =PI |f1|2dm1, (2.1)PI,D =PI |f2|2dm2, (2.2)respectively, where PI is the interferer transmit power, and m is the path lossexponent.All links are assumed to be Rayleigh block fading, i.e. the channel is constantover a time slot T , and independent and identically distributed from one slot to132.4. TSR-based Energy Harvestinganother. Hence |h1|2, |h2|2, |f1|2 and |f2|2 are exponentially distributed randomvariables (rvs) with parameters λ1, λ2, ν1 and ν2 respectively. We consider the TSand PS receiver architectures with PSR and TSR protocols as well as a proposedhybrid TSR-PSR protocol, for the task of energy harvesting and information decod-ing at the relay node. In the following sections, we derive expressions for the outageprobability of each of the relaying protocols as well as the achievable throughputsfor the delay-sensitive transmission mode.2.4 TSR-based Energy HarvestingThe transmission slot structure for the TSR protocol for information decoding andenergy harvesting at the relay node is illustrated in Fig. 2.2.Figure 2.2: TSR protocol at the relayThe slot duration is denoted by T , and α is the fraction of that duration used bythe relay for RF energy harvesting from the received source signal. The remainingtime (1−α)T is used as follows: (1−α)T/2 is used for source to relay communication,and (1−α)T/2 is used for relay to destination communication. The energy harvestedby the relay and its transmit power are given byEhr =ηPs|h1|2dm3αT, (2.3)142.4. TSR-based Energy HarvestingPr =Ehr(1− α)T/2 =2ηPs|h1|2αdm3 (1− α), (2.4)respectively, where 0 < η < 1 is the energy conversion efficiency and Ps is the sourcepower. For notational simplicity, we will replace |h1|2, |h2|2, |f1|2 and |f2|2 with X1,X2, Z1 and Z2, respectively. Then the SIRs at the relay and the destination aregiven respectively asΓR =Ps|h1|2dm1dm3 PI |f1|2=PsX1β1,3PIZ1=ρRX1Z1, (2.5)ΓD =Pr|h2|2dm2dm4 PI |f2|2=2ηPsαX1X2β2,4dm3 (1− α)PIZ2=ρDX1X2Z2, (2.6)wheredm1dm3anddm2dm4are replaced by β1,3 and β2,4 respectively, andPsβ1,3PI and2ηPsαβ2,4dm3 (1−α)PIare replaced by ρR and ρD respectively.2.4.1 Outage ProbabilityThe outage probability is defined as the probability that the Signal to InterferenceRatio (SIR) is below a predefined threshold (γth). The DF relay network is consid-ered to be in outage if either the S→ R link or the R→ D link suffers an outage.In other words, the SIR at the relay or at the destination is smaller than γth. Notethat ΓR and ΓD in (2.5) and (2.6) respectively, are statistically dependent since theyare both functions of X1. The outage probability is given asPout = 1− Pr {ΓR ≥ γth,ΓD ≥ γth} . (2.7)Conditioning the outage probability expression on X1, we can express Pout asPout = 1−∫ ∞0Pr {ΓR ≥ γth|X1 = x1}×Pr {ΓD ≥ γth|X1 = x1} fX1(x1)dx1. (2.8)152.4. TSR-based Energy HarvestingLetting,J1 = Pr {ΓR ≥ γth|X1 = x1} = Pr{ρRx1Z1≥ γth}= Pr{Z1 ≤ ρRx1γth}= 1− e−ρRx1γthν1 , (2.9)and,J2 = Pr {ΓD ≥ γth|X1 = x1}= Pr{ρDx1X2Z2≥ γth}= Pr{X2 ≥ Z2γthρDx1}. (2.10)Conditioning J2 in (2.10) on Z2 and taking the expected value of the results overthe distribution of Z2, we haveJ2 = 1ν2∞∫0e− z2γthρDx1λ2 e− z2ν2 dz2 =ρDx1λ2γthν2 + ρDx1λ2(2.11)therefore we can write Pout asPout = 1− 1λ1∞∫0(J1 × J2) e−x1λ1 dx1= 1− 1λ1∞∫0ρDx1λ2γthν2 + ρDx1λ2(1− e−ρRx1γthν1)e− x1λ1 dx1= 1− 1λ1∞∫0x1x1 + c(1− e−dx1)e− x1λ1 dx1 (2.12)where c = γthν2ρDλ2 and d =ρRγthν1. The integral in (2.12) can be solved as follows [27]∞∫0xx+ ce−axdx = cecaEi (−ca) + 1a162.4. TSR-based Energy Harvestingwhere Ei (x) = − ∫∞−x e−tt dt is the exponential integral function. Thus,Pout = 1− 1λ1(cecλ1Ei(−cλ1)+ λ1 − cecEEi (−cE)− 1E)= − cλ1ecλ1Ei(−cλ1)+cλ1ecEEi (−cE) + 1λ1E, (2.13)where E = d+ 1/λ1. Given that E1 (x) = −Ei (−x), then Pout can be rewritten asPout =cλ1ecλ1E1(cλ1)− cλ1ecEE1 (cE) +1λ1E(2.14)The exponential integral function, E1(x), can be upper and lower bounded by[28]:12e−x ln(1 +2x) < E1(x) < e−x ln(1 +1x), (2.15)thus we have the following upper and lower bounds on Pout:Pout−upper =cλ1ln(1 +λ1c)− cλ1ln(1 +1cE)+1λ1E, (2.16)Pout−lower =c2λ1ln(1 +2λ1c)− c2λ1ln(1 +2cE)+1λ1E. (2.17)2.4.2 ThroughputThe achievable throughput for the delay-sensitive transmission mode is defined asthe throughput achieved such that the destination node has to decode the receivedsignal in its time slot. In this mode, the throughput in units of bit/s/Hz, is defined asthe maximum constant rate Rds, where Rds = log2(1 +γth), that can be maintainedover fading blocks with a specified outage probability, i.e. the throughput is givenby [19]τds =(1−α)T2TRds(1− Pout) = 1− α2Rds(1− Pout). (2.18)172.5. PSR-based Energy Harvesting2.5 PSR-based Energy HarvestingWhen the PS receiver is implemented at the relay, a fraction ρ, i.e. power-split ratio,of the source power Ps is used for energy harvesting while the remaining power, i.e.(1− ρ)Ps, is used for information decoding, as shown in Fig. 2.3.Figure 2.3: PSR protocol at the relayThus, the energy harvested at the relay and its transmit power are given byEhr =ηρPs|h1|2dm3× T2, (2.19)Pr =EhrT/2=ηρPsX1dm3. (2.20)The portion of the received signal used for information decoding can be expressedasyR =√(1− ρ)Psdm3h1xs, (2.21)where xs is the signal transmitted from the source node.2.5.1 Outage ProbabilityThe SIRs at the relay and the destination can be expressed respectively asΓR =Ps(1− ρ)|h1|2dm1dm3 PI |f1|2=Ps(1− ρ)X1β1,3PIZ1= ρR2X1Z1, (2.22)182.5. PSR-based Energy HarvestingΓD =Pr|h2|2dm2dm4 PI |f2|2=ηρPsX1X2β2,4dm3 PIZ2= ρD2X1X2Z2. (2.23)The outage probability is defined as in (2.7) and following a similar derivation as inSubsection 2.4.1, the outage probability can be expressed asPout =c2λ1ec2λ1E1(c2λ1)− c2λ1ec2E2E1 (c2E2) +1λ1E2. (2.24)Using the upper and lower bounds for the exponential integral in (2.15), we obtainexpressions similar to Pout−upper in (2.16) and Pout−lower in (2.17) as followsPout−upper =c2λ1ln(1 +λ1c2)− c2λ1ln(1 +1c2E2)+1λ1E2, (2.25)Pout−lower =c22λ1ln(1 +2λ1c2)− c22λ1ln(1 +2c2E2)+1λ1E2, (2.26)where c is replaced by c2 =γthν2ρD2λ2, and E is replaced by E2 =ρR2γthν1+ 1λ1 .2.5.2 ThroughputSimilar to our previous derivation in Subsection 2.4.2, we evaluate the throughputfor the delay-sensitive transmission mode. For the PS receiver, we haveτds =T/2TRds(1− Pout) = 12Rds(1− Pout). (2.27)By comparing the throughput expressions in (2.18) and (2.27) for TSR and PSRrespectively, we can observe that the throughput in PSR is generally higher than thatin TSR given that the outage probabilities for PSR and TSR are quite similar. Thiscan be further explained by the fact that the PSR protocol uses T/2 for source torelay communication and the remaining T/2 for relay to destination communication.Two functions are performed within the first T/2 block which are harvesting RF192.6. Hybrid TSR-PSR-based Energy Harvestingenergy from the source signal as well as source to relay information transmission. Inthe second T/2 block, the relay to destination information transmission takes place.On the other hand the TSR uses a dedicated fraction of time αT just for RF energyharvesting from the source transmissions. Then the remaining portion of time isdivided into two halves, the first half is for source to relay information transmission,and the other half is for relay to destination information transmission. Therefore theoverall amount of time for information transmission in the TSR protocol is usuallylesser than that in the PSR, which may generally lead to a lower throughput.2.6 Hybrid TSR-PSR-based Energy HarvestingIn this section, we consider a hybrid TS and PS receiver architecture which resultsin a generalized version of PSR and TSR as shown in Fig. 2.4. The PSR protocolFigure 2.4: Hybrid TSR-PSR protocol at the relayis a special case of this hybrid protocol when β = 0 and α = 0.5, while the TSRprotocol is a special case when ρ = 0 and α = 1−β2 . The portion of time βT is usedfor energy harvesting from the source power Ps. The source signal is divided intotwo streams during the portion of time αT . During this time a fraction of the powerρPs is used for energy harvesting from the source signal by the relay node, and afraction (1−ρ)Ps is used for decoding the information signal at the relay node. The202.6. Hybrid TSR-PSR-based Energy Harvestingremaining T − αT − βT is the portion of time used for information transmissionbetween the relay and the destination node.2.6.1 Outage ProbabilityThe energy harvested by the relay and the relay transmit power are given byEhr =ηPsX1dm3βT +ηρPsX1dm3αT, (2.28)Pr =Ehr(1− α− β)T =ηPsX1βdm3 (1− α− β)+ηρPsX1αdm3 (1− α− β). (2.29)The SIRs at the relay and destination nodes are given byΓR =Ps(1− ρ)X1β1,3PIZ1= ρR3X1Z1, (2.30)ΓD =PrX2β2,4PIZ2= ρD3X1X2Z2, (2.31)where ρD3 =ηPsβ2,4PIdm3 (1−α−β) (β + ρα). Using (2.7), we can derive the outage probabil-ity for the hybrid protocol asPout =c3λ1ec3λ1E1(c3λ1)− c3λ1ec3E3E1 (c3E3) +1λ1E3, (2.32)where c3 =ν2γthρD3λ2and E3 =ρR3γthν1+ 1λ1 .2.6.2 ThroughputFollowing the analysis in Subsection 2.4.2, the throughput for the proposed hybridTSR-PSR in the delay-sensitive transmission mode can be obtained asτds = (1− α− β)Rds(1− Pout). (2.33)212.7. Numerical ResultsIt was found in the cases we studied that β = 0 provided the best throughput.This follows our previous explanation of the superiority of the PSR over the TSRprotocol, which is due to using a dedicated portion of time only for energy harvestingin the TSR, thus leading to a decrease in the overall information transmission time.In this case (2.33) reduces toτds = (1− α)Rds(1− Pout). (2.34)Note that when β = 0, the hybrid protocol in Fig. 2.4 becomes a generalizedversion of the PSR protocol in Fig. 2.3 with a factor α (instead of 12 used in theconventional PSR protocol), which denotes the fraction of time used for source torelay communication. The remaining fraction, i.e. (1− α), is then used for relay todestination communication. The proposed hybrid protocol can perform better thanthe PSR protocol if the parameters α and ρ are well chosen. This can be explainedsince the S−R and the R−D link gains are generally different, and thus it maybe better to assign more time to the channel with the poorer channel condition.2.7 Numerical ResultsIn this section we present numerical results to validate the outage probability andthroughput expressions derived for the proposed relay-assisted network with RF en-ergy harvesting. We examine the outage probability and the throughput expressionsas a function of α and ρ, moreover we show the throughput as a function of Ps, PI ,d3 and d4. We assume that the source, relay, and destination nodes are located at(0, 0), (1, 0), and (2, 0) on the X-Y plane respectively, while the interferer nodeis located at (1.5, 2). The energy harvesting efficiency η is set to 1, the path lossexponent m = 4, the SIR threshold value γth = 0 dB, and the means of all the222.7. Numerical Resultschannel gain coefficients λ1, λ2, ν1 and ν2 are equal to 5. The simulation resultswere obtained over 106 Rayleigh channel realizations.0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.040.060.080.10.120.140.160.180.20.220.24α Outage Probability,  Pout  SimulationTheo. Exact (2.14)Lower bound (2.16)Upper bound (2.17)Figure 2.5: Outage probability versus α for the TSR protocolFig. 2.5 shows the outage probability in (2.14) for the TSR protocol, the upperand lower bounds in (2.16) and (2.17) respectively, as well as the simulation results.Fig. 2.6 shows the outage probability in (2.24) for the PSR protocol, as well as theupper and lower bounds. It can be seen from Figs. 2.5 and 2.6 that there is goodagreement between the simulation and the analytical results. In addition to that,both figures show that the lower bound for the outage probability gives a betterapproximation than the upper bound. Moreover Fig. 2.6 shows that there is anoptimal PS value, i.e. ρ, which results in the minimum outage probability.232.7. Numerical Results0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.10.150.20.250.30.350.40.450.50.550.6ρ Outage Probability,  Pout  SimulationTheo. Exact (2.24)Lower bound (2.25)Upper bound (2.26)Figure 2.6: Outage probability versus ρ for the PSR protocolThe outage probability results for the hybrid protocol are shown in Fig. 2.7,where we plot Pout as a function of α for different values of ρ. It can be observedfrom Fig. 2.7 that the outage probability decreases as α increases. On the otherhand, 0.3 ≤ ρ ≤ 0.7 generally gives the best outage probability performance asshown in the figure. Note that the TS ratio, i.e. α, should not be increased to itsmaximum possible value since there is a tradeoff between the outage probability andthe throughput of the hybrid and the TSR protocols, which mainly depends on thechoice of the parameter α, as illustrated in Fig. 2.8.242.7. Numerical Results0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.10.20.30.40.50.60.70.80.91α Outage Probability,  Pout  Sim., ρ=0.9Theo. (2.32)Sim., ρ=0.7Theo. (2.32)Sim., ρ=0.5Theo. (2.32)Sim., ρ=0.3Theo. (2.32)Sim., ρ=0.1Theo. (2.32)Figure 2.7: Outage probability versus α for the hybrid protocol with various ρvalues0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.10.20.30.40.50.60.7α Throughput,  τ ds  Sim.TSRSim.Hybrid− ρ=0.1Sim.Hybrid− ρ=0.3Sim.Hybrid− ρ=0.5Sim.Hybrid− ρ=0.7Sim.Hybrid− ρ=0.9Figure 2.8: Throughput versus α for the hybrid and the TSR protocols252.7. Numerical ResultsFig. 2.8 shows the throughput as a function of α, i.e. the TS ratio, for theTSR protocol as well as the hybrid protocol for various fixed ρ values, i.e. the PSratio. It can be observed that the hybrid protocol outperforms the TSR protocolwith well-chosen TS and PS parameters. It can be seen from the figure that thebest throughput performance of the hybrid protocol can be achieved with PS ratiosin the range, 0.3 ≤ ρ ≤ 0.7, and the TS ratios in the range, 0.1 ≤ α ≤ 0.3. This wassimilarly observed in Fig. 2.7 which showed that the best outage probability of thehybrid protocol was obtained for the same range of the PS ratios as in Fig. 2.8.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.10.20.30.40.50.60.7ρ Throughput,  τ ds  Sim.PSRSim.Hybrid− α=0.1Sim.Hybrid− α=0.2Sim.Hybrid− α=0.3Sim.Hybrid− α=0.5Sim.Hybrid− α=0.7Figure 2.9: Throughput versus ρ for the hybrid and the PSR protocolsFig. 2.9 shows the throughput as a function of ρ, i.e. the PS ratio, for thePSR protocol as well as the hybrid protocol for various fixed α values, i.e. the TS262.7. Numerical Resultsratio. As expected when α = 12 the throughput of the hybrid protocol coincideswith that of the PSR protocol since they become the same. Moreover it is observedfrom the figure that the hybrid protocol outperforms the PSR protocol when theparameters α and ρ are properly chosen. The best throughput performance of thehybrid protocol can be achieved with a TS ratio in the range, 0.1 ≤ α ≤ 0.3, for awide range of the chosen PS ratio.1 2 3 4 5 6 7 8 9 100.30.40.50.60.70.80.91Ps Throughput,  τ ds  PSR, ρ=0.4Sim.TSR, α=0.1Sim.Hybrid, α=0.4, ρ=0.6Sim.Hybrid, α=0.6, ρ=0.4Sim.Hybrid, α=0.4, ρ=0.9Sim.Hybrid, α=0.2, ρ=0.6Sim.Figure 2.10: Throughput versus Ps for TSR, PSR and the hybrid protocolFig. 2.10 shows the throughput as a function of Ps for the three protocols. Itcan be seen that as Ps increases, the throughput increases for all protocols. This isexpected since an increase in the source power will lead to an increase in the energyharvested by the relay. The PSR outperforms the TSR, as explained previously and272.7. Numerical Resultsby observing their expressions in (2.27) and (2.18) respectively. We also observe thatthe hybrid protocol outperforms both the TSR and the PSR protocols dependingon the choice of the TS and PS ratios. In Fig. 2.10 the hybrid protocol gives thebest throughput performance for α = 0.2 and ρ = 0.6.1 2 3 4 5 6 7 8 9 100.10.20.30.40.50.60.70.8PI Throughput,  τ ds  Sim.Hybrid, α=0.6, ρ=0.7Sim.Hybrid, α=0.2, ρ=0.5Sim.Hybrid, α=0.4, ρ=0.7Sim.TSR, α=0.2Sim.PSR, ρ=0.6Figure 2.11: Throughput versus PI for TSR, PSR and the hybrid protocolFig. 2.11 shows the throughput as a function of PI for the three protocols. Asto be expected, the throughput decreases as PI increases since the SIR decreasesleading to an increase in the outage probability. We note that for high values of PI ,i.e. low SIR values, the throughput of the TSR protocol becomes slightly better thanthat of the PSR, which was previously observed in [19] for low signal-to-noise-ratios(SNRs). Furthermore we note that the hybrid protocol gives the best throughput282.7. Numerical Resultsperformance for well-chosen values of α and ρ (e.g. α = 0.2, ρ = 0.5).0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.10.20.30.40.50.60.7d3 Throughput,  τ ds  PSR, ρ=0.4Sim.TSR, α=0.1Sim.Hybrid, α=0.3, ρ=0.4Sim.Hybrid, α=0.3, ρ=0.9Sim.Hybrid, α=0.6, ρ=0.9Sim.Figure 2.12: Throughput versus d3 for TSR, PSR and the hybrid protocolFig. 2.12 shows the throughput as a function of d3 which is the distance betweenthe source and relay nodes. As expected, the throughput decreases as d3 increases.The hybrid protocol gives the best throughput performance for α = 0.3, ρ = 0.4.On the other hand Fig. 2.13 shows the throughput as a function of d4 whichis the distance between the relay and destination nodes. It can be observed thatthe throughput decreases as d4 increases which is expected and similarly observedin the previous figure. The hybrid protocol gives the best throughput performancefor α = 0.3 and 0.5 ≤ ρ ≤ 0.7, while the PSR outperforms the TSR protocol asobserved in all the figures presented so far.292.8. Summary0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.10.20.30.40.50.60.70.80.9d4 Throughput,  τ ds  Sim.TSR, α=0.2Sim.PSR, ρ=0.4Sim.Hybrid, α=0.1, ρ=0.2Sim.Hybrid, α=0.3, ρ=0.7Sim.Hybrid, α=0.3, ρ=0.5Figure 2.13: Throughput versus d4 for TSR, PSR and the hybrid protocol2.8 SummaryThree wireless energy harvesting protocols for DF relay networks in presence ofinterference were studied. Analytical expressions for the outage probability andthe throughput in the delay-sensitive transmission mode were derived and validatedusing computer simulations. Numerical results were used to show the effect ofvarious system parameters on the throughput of the studied protocols. The resultsdemonstrate that the proposed hybrid protocol generally yields a better throughputperformance than the TSR and PSR protocols given that the TS and PS ratios arechosen properly.30Chapter 3RF Energy Harvesting fromInterference Signals in a DFWireless Relay NetworkIn Chapter 2, we studied the outage probability and the throughput of a WRN withan energy-constrained relay harvesting RF energy from the source transmissions inthe presence of interference. In this chapter we study the case when the relay har-vests RF energy from both the source transmissions as well as the interference. Wederive the outage probability and the throughput and compare the results with thoseobtained in Chapter 2 to examine the effect of harvesting energy from interferenceon the system performance.3.1 Motivation and ContributionsIn the previous chapter, we studied the case when the RF energy that the relay canharvest from the interference signal is assumed to be negligible. In this chapter westudy the more general case when this assumption is dropped. The outage probabil-ity and throughput derivations in this general case are somewhat more complex thanthose obtained in Chapter 2. We then study the effect of harvesting energy fromthe interference on the system performance, given the same system configuration313.2. System Modelassumed in Chapter 2. The contributions of this chapter are as follows:• We derive closed-form expressions for the outage probability, as well as upperand lower bounds, for the considered energy-constrained relay network. Wealso derive closed-form expressions for the achievable throughputs in the delay-sensitive transmission mode, for the TSR, PSR and the hybrid TSR-PSRprotocols. The derived expressions are generalized versions of the expressionsobtained in Chapter 2.• We compare the throughput performance of each of the TSR, PSR and thehybrid protocols, with and without RF energy harvesting from the interfer-ence assuming the same system parameters as in Chapter 2. We examine theimprovement achieved to test the validity of neglecting the energy harvestedfrom the interference signal.The remainder of this chapter is organized as follows. Section 3.2 describes oursystem model. The system outage probability and the throughput in the delay-sensitive transmission mode are derived in Sections 3.3, 3.4 and 3.5, for the TSR,PSR and hybrid protocols, respectively. Numerical results are presented in Section3.6, followed by a summary in Section 3.7.3.2 System ModelOur system model is similar to that studied in Chapter 2, Fig. 2.1. The onlydifference is that we include the effect of RF energy harvesting from the interferencesignal in addition to the source signal, instead of the source signal alone as assumedin Chapter 2. Our goal here is to compare the performance in terms of the outageprobability and throughput for each of the TSR, PSR and the hybrid protocols withthe corresponding achieved performance presented in Chapter 2.323.3. TSR-based Energy Harvesting3.3 TSR-based Energy HarvestingThe transmission slot structure is the same as in Fig. 2.2, where the slot durationis denoted by T , and αT is the time used by the relay for RF energy harvestingfrom the received source signal and the interference signal. The remaining time isdivided equally such that (1−α)T/2 is used for source to relay communication, and(1 − α)T/2 is used for relay to destination communication. The energy harvestedby the relay and its transmit power are given respectively byEhr =(ηPsX1dm3+ηPIZ1dm1)αT, (3.1)Pr =Ehr(1− α)T/2 =2ηPsX1αdm3 (1− α)+2ηPIZ1αdm1 (1− α), (3.2)where 0 < η < 1 is the energy conversion efficiency, Ps is the source power and PIis the interferer transmit power. The SIRs at the relay and at the destination areΓR =PsX1dm1dm3 PIZ1= ρRX1Z1, (3.3)ΓD =PrX2dm2dm4 PIZ2= (a1X1 + b1Z1)X2Z2=WX2Z2, (3.4)where we replacedm1dm3anddm2dm4by β1,3 and β2,4 respectively, thus a1 =2ηPsβ2,4αdm3 (1−α)PI ,b1 =2ηβ2,4αdm1 (1−α) and W = a1X1 + b1Z1.3.3.1 Outage Probability and Throughput AnalysisThe DF relay network is considered to be in outage, if either the SIR at the relaynode or that at the destination node is below some predefined threshold γth, whichis given byPout = 1− Pr {ΓR ≥ γth,ΓD ≥ γth} . (3.5)333.3. TSR-based Energy HarvestingFrom the SIR expressions in (3.3) and (3.4) we observe that they are independent.The outage probability can thus be expressed asPout = 1− (Pr {ΓR ≥ γth} × Pr {ΓD ≥ γth}) = 1− (IR × ID) . (3.6)Now we evaluate IR and ID as followsIR = Pr{ρRX1Z1≥ γth}= Pr{X1 ≥ γthZ1ρR}=1ν1∫ ∞0e− γthz1ρRλ1 × e−z1ν1 dz1=1ν1× e−(γthρRλ1+ 1ν1)−(γthρRλ1+ 1ν1)∞0=ρRλ1ν1γth + ρRλ1, (3.7)ID =∫ ∞0Pr {ΓD ≥ γth|W = w} × fW (w)dw. (3.8)Now ID|W can be evaluated asID|W = Pr {ΓD ≥ γth|W = w}= Pr{wX2Z2≥ γth}= Pr{X2 ≥ γthZ2w}=1ν2∫ ∞0e− γthz2wλ2 × e−z2ν2 dz2=1ν2× e−(γthwλ2+ 1ν2)−(γthwλ2+ 1ν2)∞0=wλ2γthν2 + wλ2=ww + c, (3.9)where c = γthν2λ2 .To find an expression for ID in (3.8) we need the probability density function343.3. TSR-based Energy Harvesting(pdf) of the rv W = U + V , where U = a1X1 and V = b1Z1. Since a1 andb1 are constants, X1 and Z1 are exponentially distributed independent RandomVariable (rv)s, then U and V are exponentially distributed independent rvs as wellwith means a1λ1 and b1ν1 respectively, and pdfsfU (u) =1a1λ1e− ua1λ1 , (3.10)fV (v) =1b1ν1e− vb1ν1 . (3.11)Therefore the sum W = U + V is a rv with a density function fW (w), given by theconvolution of fU and fV [29]fW (w) =∫ ∞−∞fU (w − x)× fV (x)dx =∫ w0fU (w − x)× fV (x)dx,W ≥ 0=1a1λ1× 1b1ν1∫ w0e−(w−xa1λ1)× e−(xb1ν1)dx=e−wa1λ1a1λ1b1ν1∫ w0e−x(1b1ν1− 1a1λ1)dx=e−wa1λ1a1λ1b1ν1×−e−x(1b1ν1− 1a1λ1)1b1ν1− 1a1λ1w0=1a1λ1 − b1ν1 ×(e−wa1λ1 − e−wb1ν1). (3.12)Substituting (3.12) into (3.8) yieldsID = 1a1λ1 − b1ν1 ×∫ ∞0ww + c×(e−wa1λ1 − e−wb1ν1)dw. (3.13)The expression in (3.13) can be written in terms of the exponential integral function353.3. TSR-based Energy HarvestingE1(.) [27] asID = 1a1λ1 − b1ν1 ×[−ce ca1λ1E1(ca1λ1)+ a1λ1 + cecb1ν1E1(cb1ν1)− b1ν1].(3.14)Upper and lower bounds can be obtained as in (2.15) asID−lower = 1a1λ1 − b1ν1 ×[−c2ln(1 +2a1λ1c)+ a1λ1 +c2ln(1 +2b1ν1c)− b1ν1],(3.15)ID−upper = 1a1λ1 − b1ν1 ×[−c ln(1 +a1λ1c)+ a1λ1 + c ln(1 +b1ν1c)− b1ν1].(3.16)Substituting the derived expressions, (3.7) for IR, and (3.14)-(3.16) for ID, ID−lowerand ID−upper respectively, in (3.6), the outage probability as well as the upper andlower bounds can be obtained as followsPout,TSR = 1− (IR × ID) , (3.17)Pout−upper,TSR = 1− (IR × ID−upper) , (3.18)Pout−lower,TSR = 1− (IR × ID−lower) . (3.19)Following the analysis in Chapter 2, Subsection 2.4.2, the throughput for the TSRprotocol in the delay-sensitive transmission mode can be obtained asτds,TSR =(1− α2)×Rds (1− Pout,TSR) . (3.20)363.4. PSR-based Energy Harvesting3.4 PSR-based Energy HarvestingThe PSR protocol transmission slot structure is shown in Fig. 2.3. The totalslot duration T is divided equally such that half of it is used for source to relaycommunication while the other half is used for relay to destination communication.The relay harvests a fraction ρ of the source’s signal power, while it decodes theinformation signal using the remaining source power, i.e. (1 − ρ)Ps in the first T2 .The energy harvested by the relay and its transmit power are given as followsEhr =(ηρPsX1dm3+ηρPIZ1dm1)× T2, (3.21)Pr =EhrT/2=ηρPsX1dm3+ηρPIZ1dm1. (3.22)3.4.1 Outage Probability and Throughput AnalysisThe SIRs at the relay node and the destination node are given byΓR =Ps(1− ρ)X1dm1dm3 PIZ1= ρR2X1Z1, (3.23)ΓD =PrX2dm2dm4 PIZ2= (a2X1 + b2Z1)X2Z2=WX2Z2, (3.24)where a2 =ηρPsβ2,4dm3 PI, b2 =ηρβ2,4dm1, ρR2 =Ps(1−ρ)dm1dm3 PIand W = a2X1 + b2Z1. From(3.23) and (3.24), it can be seen that ΓR and ΓD are independent. The outageprobability is thus given by (3.6).Expressions for IR and ID can be obtained in a way similar to that in Subsection3.3.1IR = Pr{ρR2X1Z1≥ γth}=ρR2λ1ν1γth + ρR2λ1, (3.25)ID = 1a2λ1 − b2ν1 ×[−ce ca2λ1E1(ca2λ1)+ a2λ1 + cecb2ν1E1(cb2ν1)− b2ν1],(3.26)373.5. Hybrid TSR-PSR-based Energy Harvestingwhere c = γthν2λ2 . Upper and lower bounds for ID are similar to (3.15) and (3.16)respectively, where a1 and b1 are replaced by a2 and b2. Substituting (3.25) and(3.26) in (3.6), we obtain the outage probability, i.e. Pout,PSR, for the PSR protocol.The throughput for the PSR protocol in the delay-sensitive transmission mode isobtained using the Pout,PSR expression as followsτds,PSR =12×Rds (1− Pout,PSR) . (3.27)3.5 Hybrid TSR-PSR-based Energy HarvestingIn this section we consider the transmission slot structure in Fig. 3.1 which is thesame as the one in Fig. 2.4 with β = 0. The hybrid slot structure is a generalizedversion of the PSR protocol in which the total slot duration T is not divided equally,but rather by a fraction α. The fraction α, denotes the time used for source to relaycommunication, which constitutes energy harvesting and information transmission.The remaining fraction, i.e. (1−α), is used for relay to destination communication.Figure 3.1: Hybrid TSR-PSR protocol at the relay383.5. Hybrid TSR-PSR-based Energy HarvestingThe energy harvested by the relay and its transmit power are given byEhr =(ηρPsX1dm3+ηρPIZ1dm1)× αT, (3.28)Pr =Ehr(1− α)T =ηραPsX1dm3 (1− α)+ηρPIZ1dm1 (1− α), (3.29)where α and ρ should be chosen carefully in order to adjust the throughput perfor-mance of the hybrid protocol as shown in Chapter 2.3.5.1 Outage Probability and Throughput AnalysisThe SIRs at the relay node and the destination node for the hybrid protocol areΓR =Ps(1− ρ)X1dm1dm3 PIZ1= ρR2X1Z1, (3.30)ΓD =PrX2dm2dm4 PIZ2= (a3X1 + b3Z1)X2Z2=WX2Z2, (3.31)where a3 =ηραPsβ2,4dm3 (1−α)PI , b3 =ηραβ2,4dm1 (1−α) and W = a3X1 + b3Z1. Note that ΓR in (3.30)and ΓD in (3.31) are independent. The outage probability, i.e. Pout,hybrid, for thehybrid protocol can thus be obtained by finding expressions for IR and ID, andsubstituting them in (3.6), as done in Subsection 3.3.1. From (3.30), it can be seenthat ΓR for the hybrid protocol is equal to that for PSR protocol in (3.23), thus theexpression for IR is equal to that in (3.25). The expression for ID can be obtainedasID = 1a3λ1 − b3ν1 ×[−ce ca3λ1E1(ca3λ1)+ a3λ1 + cecb3ν1E1(cb3ν1)− b3ν1].(3.32)Upper and lower bounds for ID are similar to (3.15) and (3.16) respectively, byreplacing a1 and b1 by a3 and b3 respectively. Finally the throughput of the hybrid393.6. Numerical Resultsprotocol in the delay-sensitive transmission mode can be obtained asτds,hybrid = (1− α)×Rds (1− Pout,hybrid) . (3.33)3.6 Numerical ResultsIn this section we present numerical results to validate the outage probability,throughput expressions and the upper and lower bounds derived for the WRNdiscussed, considering RF energy harvesting from the information as well as theinterference signals. We compare the performance achieved when harvesting energyfrom the interference and information signals versus harvesting energy from theinformation signal alone, a case which was studied in Chapter 2. The system con-figuration is the same as in Chapter 2: the source, relay, destination and interferernodes are located at (0, 0), (1, 0), (2, 0) and (1.5, 2) on the X-Y plane respectively.The energy harvesting efficiency η = 1, the path loss exponent m = 4, the SIRthreshold value γth = 0 dB, and the means of all the channel gain coefficients λ1,λ2, ν1 and ν2 are equal to 5.Fig. 3.2 shows the outage probability for the TSR protocol in (3.17) versus α, i.e.the TS ratio, as well as the upper and lower bounds in (3.18) and (3.19) respectively,and the simulation results. It can be seen that the lower bound given in (3.18) iscloser to the exact outage probability curve than the upper bound in (3.19), whichwas similarly observed in Chapter 2.In Fig. 3.3 we plot the throughput of the TSR and the hybrid protocols versusα while the throughput of the PSR protocol is shown versus ρ. We compare thethroughput of each when harvesting RF energy from the interference and informa-tion signals versus the case when harvesting RF energy from the information signalonly. It can be seen that there is a slight increase in the throughput performance403.6. Numerical Results0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.040.060.080.10.120.140.160.180.20.220.24α Outage Probability,  Pout  SimulationTheo. Exact (3.17)Upper bound (3.19)Lower bound (3.18)Figure 3.2: Outage Probability versus α for the TSR protocolwhen considering RF energy harvesting from the interference. This small improve-ment can be explained by the fact that both the relay and the destination nodes aresubject to interference from the interferer node. Therefore the gain achieved fromharvesting the RF energy from the interference signal by the relay node is offset bythe decrease in the SIR at the destination node caused by the interference signal.Fig. 3.4 shows the throughput for the studied relaying protocols versus theinterference power PI , with and without harvesting energy from the interferencesignal. It can be observed that the throughput decreases as PI increases. There is aslight performance improvement when considering RF energy harvesting from boththe interference and information signals. This improvement is more noticeable forthe TSR and the hybrid protocols than that for the PSR protocol.413.6. Numerical Results0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.10.20.30.40.50.6α, ρ Throughput, τds  Sim.− TSRPI and PsSim.− TSRPs onlySim.− PSRPI and PsSim.− PSRPs onlySim., ρ=0.7 − HybridPI and PsSim., ρ=0.7− HybridPs onlyFigure 3.3: Throughput versus α for the TSR and the hybrid protocols and versusρ for the PSR protocol1 2 3 4 5 6 7 8 9 100.10.20.30.40.50.60.70.8PI Throughput, τds  Sim., α=0.2− TSRPI and PsSim., α=0.2− TSRPs onlySim., ρ=0.7− PSRPI and PsSim., ρ=0.7− PSRPs onlySim. ρ=0.5, α=0.2− HybridPI and PsSim. ρ=0.5, α=0.2− HybridPs onlyFigure 3.4: Throughput versus PI for the TSR, PSR and the hybrid protocols423.6. Numerical Results1 2 3 4 5 6 7 8 9 100.350.40.450.50.550.60.650.70.75Ps Throughput, τds  Sim., α=0.2− TSRPI and PsSim., α=0.2− TSRPs onlySim., ρ=0.5− PSRPI and PsSim., ρ=0.5− PSRPs onlySim., ρ=0.5, α=0.2− HybridPI and PsSim., ρ=0.5, α=0.2− HybridPs onlyFigure 3.5: Throughput versus Ps for the TSR, PSR and the hybrid protocolsThe throughput of each of the studied relaying protocols versus the source powerPs, is shown in Fig. 3.5. It can be observed that the performance improvement forall relaying protocols when harvesting energy from the interference signal is verysmall compared to that when energy harvesting from the interference signal is notconsidered.In Figs. 3.6 and 3.7 we show the throughput of each of the studied relayingprotocols versus the S−R internode distance d3, and the R−D internode distanced4, respectively. From Figs. 3.6 and 3.7, it can be seen that the throughput for eachof the relaying protocols are nearly the same with and without harvesting RF energyfrom the interference.433.6. Numerical Results0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.10.20.30.40.50.60.70.8d3 Throughput, τds  Sim., α=0.2PI and PsSim., α=0.2Ps onlySim., ρ=0.7PI and PsSim., ρ=0.7Ps onlySim., α=0.2, ρ=0.7PI and PsSim., α=0.2, ρ=0.7Ps onlyFigure 3.6: Throughput versus d3 for the TSR, PSR and the hybrid protocols0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.10.20.30.40.50.60.7d4 Throughput, τds  Sim., α=0.2− TSRPI and PsSim., α=0.2− TSRPs onlySim., ρ=0.7− PSRPI and PsSim., ρ=0.7− PSRPs onlySim., α=0.2, ρ=0.7− HybridPI and PsSim., α=0.2, ρ=0.7− HybridPs onlyFigure 3.7: Throughput versus d4 for the TSR, PSR and the hybrid protocols443.7. SummaryIn summary it can be seen from Figs. 3.3-3.7, that the throughput improve-ment achieved due to including harvesting energy from the interference signal isvery small. This is due to our assumed system configuration which makes the RFenergy harvested from the source signal larger than that harvested from the in-terference signal. The improvement would have been more significant in case theharvested energy from the interference signal was comparable or much larger thanthat harvested from the source signal.3.7 SummaryIn this chapter we extended the study in Chapter 2, by considering the case whereRF energy is harvested from both the interference and information signals. Wederive expressions for the outage probability and throughput in the delay-sensitivemode for this general case. Using the same system parameters and configurations asin Chapter 2, we compare the throughput performance with the case studied previ-ously, in which the relay’s harvested energy from the interference signal is neglected.Our results show that there is only a slight performance improvement in terms ofthroughput and outage probability. However, this improvement is insignificant dueto our assumed system configuration, which makes the RF energy harvested by therelay from the source signal much larger than that harvested from the interferencesignal.45Chapter 4Power Allocation in a DFWireless Relay Network withRF Energy HarvestingIn this chapter, we study different power allocation schemes for a two-hop DF WRNconsisting of multiple source-destination pairs and a single relay harvesting energyfrom the source transmissions under Rayleigh fading. We state the motivation andcontributions, followed by the system model description. First we consider a non-shared power allocation scheme, then four different shared power allocation schemesare studied. All schemes are compared in terms of outage probability, throughputand fairness. Performance evaluation results are provided and finally, a summary isgiven at the end of this chapter.4.1 MotivationRelays are employed in wireless networks to split the path from the source to thedestination into shorter hops, in order to improve the energy efficiency of the networkand prolong its lifetime. In the previous chapters, we studied the outage probabilityand the throughput in the delay-sensitive transmission mode of a DF WRN with onesource-destination pair. In this chapter, we study the case when we have multiple464.1. Motivationsource-destination pairs assisted by one energy-constrained relay which harvests RFenergy from the source transmissions.The main problem when having a scenario with multiple source-destination pairsand one relay, is to allocate the relay’s power among the different relay-destinationlinks, so as to achieve some desired objective. SWIPT is studied in a cooperativeclustered WSN in [30], where energy-constrained relays harvest RF energy from thesource node transmissions to prolong its lifetime. The optimal transmission power,relay selection and PS ratio are determined so as to maximize the energy efficiencyof the system. In [31] the authors study the power allocation problem in a DFWRN with multiple source-destination pairs and one RF energy harvesting relay.Two centralized allocation schemes based on equal power allocation and sequentialwaterfilling are studied, as well as an auction-based allocation strategy to realize dis-tributed power allocation. The focus in [31] is to distribute the RF energy harvestedby the relay among the different relay-destination links to minimize the outage prob-ability of the system. The study in [32] focused on maximizing the data rate per unitenergy in both AF and DF cooperative networks with multiple source-destinationpairs and one energy harvesting relay. A closed-form solution for the optimal powerallocation scheme is obtained for the non-cooperative case, i.e. when the relay har-vests energy and forwards information from the i-th source to the i-th destination.While an energy cooperation scheme is applied at the relay node to find the optimalPS ratio for the cooperative transmission case. The problem in [32] is a non-convexoptimization problem, and is solved by proposing an iterative algorithm where theupdate in each iteration consists of a group of convex problems with a continuousparameter. It is shown in [32] that the solution can have fast convergence to theoptimum, and the results show that the proposed algorithm can enhance the systemsum rate compared with the non-cooperative scheme. The spatial randomness of474.2. Contributionsuser locations is taken into account in [33] when the outage probability is derived fora cooperative network with multiple source-destination pairs communicating witheach other via an energy harvesting relay. Efficient power allocation schemes formulti-user AF WRNs are developed in [34] according to several different objectives:(1) the minimum SNR among all users is maximized, (2) the maximum transmitpower over all sources is minimized and (3) the network throughput is maximized.Moreover a joint admission control and power allocation algorithm for the system isproposed. Power allocation schemes to maximize the minimum rate among all usersas well as to maximize the weighted-sum of rates have been proposed in [35] forwireless multi-user AF relay networks. A distributed algorithm was also developedusing the dual decomposition approach for the problem of maximizing the weighted-sum of rates. The study in [36] considers a multi-user single-relay AF network, anduses game theory to derive the power allocation of the relay power among the users.However, energy harvesting is not considered in [34]-[36].4.2 ContributionsIn this chapter we consider a cooperative DF WRN with multiple source-destinationpairs, one energy harvesting relay and one interferer node. Shared and non-sharedallocation schemes are studied to allocate the relay’s harvested power among dif-ferent relay-destination transmissions. Our main figures of merit are the outageprobability, throughput in the delay-sensitive mode and fairness.The main contributions of this chapter are summarized as follows:• The single source-destination pair model studied in Chapter 2 is extendedto the multiple source-destination pairs, in which the relay harvests RF en-ergy and forwards information from the i-th source to its corresponding i-thdestination.484.3. System Model• An equal power allocation scheme [31] is studied as one of the shared allocationschemes, such that the relay divides the harvested power from all the sourcesevenly among the relay-destination pairs.• A power allocation scheme is proposed and studied, in which the relay allocatesthe minimum power required for the user with the best channel condition first,followed by the user with the second best channel condition if there is anypower left at the relay, and so on. If the relay has energy left over after allusers have been allocated their minimum required powers, the residual energyis equally divided between relay-destination links.• Other criteria to distribute the relay’s harvested power are examined. First weconsider a power allocation which maximizes the minimum rate of all relay-destination links, followed by a weighted-sum-rate maximization of all relay-destination links.The remainder of this chapter is organized as follows, the system model is pre-sented in Section 4.3. The outage probability and the throughput of the non-sharedpower allocation scheme as well as of the different shared allocation schemes areanalyzed in Sections 4.4 and 4.5 respectively. Numerical results and discussion arepresented in Section 4.6, followed by a summary in Section 4.7.4.3 System ModelWe consider a wireless cooperative network with N source-destination pairs denotedas Si −Di, i = 1, ..., N , and one energy harvesting relay R as shown in Fig. 4.1.There is no direct link between the source-destination pairs, so each source com-municates with its intended destination via the relay. The cooperative transmissiondivides the transmission time slot into two halves, each of duration T2 . The first494.3. System ModelFigure 4.1: System ModelT2 is for the source-relay pair communication and the remainingT2 is for the relay-destination pair communication. Each source communicates with its correspondingdestination in a different mini-slot TN , than the other adopting the orthogonalityprinciple; the first T2N is for Si−R communication while the remaining T2N is forR−Di communication, as illustrated in Fig. 4.2. All link gains are assumed to beindependent and each experiences Rayleigh block fading [37]-[39]. The relay har-vests RF energy from the source transmissions based on the PSR protocol since itwas found to outperform the TSR protocol [19].In the PSR protocol, the relay splits the power of the received signal from the i-thtransmitter, i.e., Ps,i, into two streams throughout its dedicated mini-slotT2N . Theportion ρiPs,i is used for energy harvesting, while the remaining portion (1− ρi)Ps,iis used for information decoding, where ρi is the PS ratio of the i-th user pair. Thepower required at the relay for information processing is assumed to be negligible504.3. System ModelFigure 4.2: Time Slot Structurecompared to the power required for signal transmission from the relay to the requireddestination [13].The channel gains from the sources to the relay and from the relay to the desti-nations are denoted by hi, each with a mean parameter λi, and gi, each with meanparameter ωi, respectively. The link gain from interferer I and relay R is denotedby f0, with a mean parameter ν0, while the link gains to the different destinationsare denoted by fi, each with a mean parameter νi, where i = 1, ..., N . The distancebetween I and R is denoted by d1, while the distance between I and the destinationDi is denoted by d2,i. On the other hand the distance between the source Si and Ris given by d3,i, and the distance between R and the destination Di is given by d4,i.We neglect the effect of noise in our model as the interference power is assumed tobe much higher than the noise power.The portion of the received signal from the source node Si, which is used forinformation decoding at the relay node is given byyr,i =√(1− ρi)Ps,idm3,ihixs,i, (4.1)where Ps,i is the transmission power of the i-th source and xs,i is the signal trans-mitted by the i-th source where |xs,i|2 = 1. The data rate from the i-th source to514.4. Non-Shared Power Allocation Scheme (NSPA)the relay R can be given asRi,r =12log(1 +(1− ρi)Ps,i|hi|2dm1dm3,iPI |f0|2), (4.2)where PI is the interferer transmit power. Assuming R is the minimum achievabledata rate at the relay, then the parameter ρi can be adjusted to satisfy Ri,r = R asρ∗i = 1−dm3,iPI |f0|2(22R − 1)Ps,i|hi|2dm1. (4.3)From (4.3), if the PS ratio ρi is chosen such that ρi > ρ∗i , there will not beenough power for information decoding leading to unsuccessful decoding at therelay. Therefore to ensure successful decoding at the relay, we need to ensure thatρi ≤ ρ∗i , given that the statistical CSI is available at the relay. The total energyharvested by the relay should be allocated to different users to achieve a certainoverall objective for the relay network. The chosen objective aims at enhancing adesired performance measure, which in turn results in a certain power allocationscheme that has its own effect on the system performance. This will be studied inthe following sections. First we consider a non-shared power allocation scheme thenwe study several shared allocation schemes, followed by a performance comparisonfor each of the considered schemes.4.4 Non-Shared Power Allocation Scheme (NSPA)The simplest way to use the relay’s harvested energy is to consider that there isno cooperation between the different source-destination pairs. Then, the energyharvested from the i-th source is used by the DF relay as its transmit power forinformation transmission to the i-th destination, i.e., the relay transmit power for524.4. Non-Shared Power Allocation Scheme (NSPA)the i-th destination is given asPr,i =ηρiPs,i|hi|2dm3,i, (4.4)where the transmit powers of all sources are assumed to be the same, i.e. Ps,i = Ps.This extends the case we studied in Chapter 2 where we had only one source-destination pair, to having N source-destination pairs. For notational simplicity wedefine Xi = |Hi|2, Yi = |Gi|2, Zi = |Fi|2 and Z0 = |F0|2 where |hi|2, |gi|2, |fi|2 and|f0|2 are realizations of the rv’s |Hi|2, |Gi|2, |Fi|2 and |F0|2 respectively. The SIR atthe relay and at each of the destinations can be expressed asΓR,i =Ps (1− ρi) |hi|2dm1dm3,iPI |f0|2=ρRiXiZ0, (4.5)ΓD,i =Pr,i|gi|2dm2,idm4,iPI |fi|2=ρDiXiYiZi, (4.6)where we assume that d2,i = d2, d3,i = d3 and d4,i = d4 throughout this chapter tosimplify our expressions.The outage probability for the DF relay network is expressed asPout = 1− Pr {ΓR,i ≥ γth,ΓD,i ≥ γth, } . (4.7)Using the same approach as in Chapter 2, the outage probability and the throughputin the delay-sensitive transmission mode using the PSR protocol can be expressedasPout,i =ciλieciλiE1(ciλi)− ciλi eaiciE1 (aici) + 1aiλi , (4.8)τds,i =T/2NT Rds(1− Pout,i) = 12NRds(1− Pout,i), (4.9)534.5. Shared Power Allocationwhere ρRi =Ps(1−ρi)β1,3PI , ρDi =ηρiPsβ2,4dm3 PI, β1,3 =dm1dm3, β2,4 =dm2dm4, ci =νiγthρDiωi=γthνidm3 PIηρiPsβ2,4ωiand ai =ρRiγthν0+ 1λi =Ps(1−ρi)β1,3PIγthν0 +1λi. Moreover, the optimal PS ratiofor the Non-Shared Power Allocation (NSPA) scheme can be found by solving thefollowing problemmaxρiRtot =N∑i=1Ris.t. 0 ≤ ρi ≤ 1 (4.10)where Ri = min(12 log2 (1 + ΓR,i) ,12 log2 (1 + ΓD,i)), and is defined as the systemrate for the i-th user pair. Therefore the optimal solution is when the Si−R rateis equal to the R−Di rate since all user pairs are independent of each other. Theoptimal PS ratio for the non cooperative transmission is found as12log2 (1 + ΓR,i) =12log2 (1 + ΓD,i)Ps(1− ρ∗i,NSPA)Xiβ1,3PIZ0=ηρ∗i,NSPAPsXiYiβ2,4dm3 PIZiρ∗i,NSPA =β1,3Z0β1,3Z0+ηβ2,4Yidm3 Zi. (4.11)4.5 Shared Power AllocationIn the shared power allocation schemes the relay harvests energy from the N sourcessuch that the total energy harvested at the relay node and the relay transmit powerare given respectively asEhr =N∑i=1ηρiPs,i|hi|2dm3× T2, (4.12)Pr =EhrT/2=N∑i=1ηρiPs,i|hi|2dm3, (4.13)544.5. Shared Power Allocationgiven that Ps,i = Ps for all N sources and ρi ≤ ρ∗i expressed in (4.3) to ensuresuccessful information decoding at the relay. We wish to study how the total powerat the relay should be distributed among the various R−D links available. Wewill consider (1) an equal power allocation scheme, (2) a power allocation schemewhich assigns powers to each R−D link based on its strength, (3) a power alloca-tion scheme which maximizes the minimum R−D rate and (4) a power allocationscheme which maximizes the weighted-sum-rate of all R−D links.4.5.1 Equal Power Allocation (EPA)In equal power allocation (EPA), the relay distributes the energy harvested from allsource transmissions equally among all R−D links. The relay transmit power forany of the R−D links is expressed asPr =EhrT/2× 1N=1NN∑i=1ηρPs|hi|2dm3, (4.14)where we assume that the different S−R channel gains are independent and iden-tically distributed, i.e. λi = λ. Compared to the NSPA scheme, this scheme canensure that the R−D links with poor channel conditions can experience reducedchances of outages without having to know the R−D channel information. From(4.3), we find the optimal PS ratio ensuring successful decoding at the relay is thesame for all S−R links. The SIRs at the relay and each of the destinations areΓR,i =Ps (1− ρ) |hi|2β1,3PI |f0|2 =ρRXiZ0, (4.15)ΓD,i =Pr,i|gi|2β2,4PI |fi|2 =1N× ηρPs|gi|2β2,4dm3 PI |fi|2×N∑i=1|hi|2= ρDYiWZi, (4.16)554.5. Shared Power Allocationwhere W =∑Ni=1 |hi|2, and the sum of N independent exponential rv’s has a chi-square distribution. Assuming λ1 = λ2 = ... = λi = λ, the PDF and the CDF of Ware given respectively asfW (w) =wN−1e−wλΓ (N) (λ)N, (4.17)FW (w) =Γ(N, wλ)Γ(N), (4.18)where Γ(.) denotes the complete gamma function and Γ(., .) denotes the incompletegamma function [28]. From (4.15) and (4.16), we see that in the EPA schemeΓR,i and ΓD,i are independent. Hence the outage joint probability in (4.7) can beexpressed asPout,i = 1− (Pr {ΓR,i ≥ γth} × Pr {ΓD,i ≥ γth}) . (4.19)An expression for the outage probability can be found asIR,i = Pr{ρRXiZ0≥ γth}=ρRλiγthν0 + ρRλi, (4.20)ID,i = Pr{ρDYiWZi≥ γth}= 1Γ(N)aN∫∞0WNW+ci× e−aWdW, (4.21)where the probability expression in (4.20) is evaluated similarly as in (3.7), ci =γthνiρDωiand a = 1λ . The integral in (4.21) can be approximated as follows [27]ID,i = 1Γ(N)aN×[(−1)N−1cNi eciaEi(−cia) +N∑k=1(k − 1)!(−ci)N−ka−k]. (4.22)The outage probability expression is obtained by substituting (4.20) and (4.22)into (4.19). The achievable throughput for the delay-sensitive transmission mode564.5. Shared Power Allocation(refer to Subsection 2.4.2) can be expressed asτds,i =T/2NTRds(1− Pout,i) = 12NRds(1− Pout,i). (4.23)4.5.2 R−D Channel Dependent Power Allocation (RDCD)In the R−D channel dependent (RDCD) scheme the relay’s harvested power isdivided among its links to the different destinations unequally, such that the powerallocated for the i-th link depends on the R−Di channel gain as well as the corre-sponding interference channel gain, i.e., |gi|2 and |fi|2 respectively. In this schemewe assume that the statistical CSI is available at the relay. The data rate at thei-th destination isRi,d =12log2 (1 + ΓD,i) =12log2(1 +Pr,i|gi|2β2,4PI |fi|2). (4.24)For a minimum achievable data rate, Ri,d = R, the minimum required power,Pr,i, for the R−Di channel is given byPr,i =(22R − 1) PI |fi|2β2,4|gi|2 . (4.25)Assuming that the N sources are capable of delivering information to the relayreliably, and that the SIR at D1 is better than the SIR at D2 on average, allthe way till DN , then the minimum required relay transmission power for the Ndestinations can be expressed as(22R − 1) PI |fN |2β2,4|gN |2 ≥ · · · ≥(22R − 1) PI |f1|2β2,4|g1|2 . (4.26)In the RDCD scheme, the relay allocates the minimum required power to the574.5. Shared Power Allocationbest R−D channel, i.e., the one with strongest channel gain and lowest interfer-ence on average, by allocating a power of(22R−1)PI |f1|2β2,4|g1|2 to it, assuming the averagechannel gains are available at the relay node. This process is repeated for the nextbest R−D channel until either destination DN is allocated its minimum requiredpower, or until there is not enough energy left at the relay. In case the relay hassome energy after allocating the minimum required powers to each destination, theresidual energy at the relay will be equally distributed between all R−D channels.Distributing the residual energy increases the SIR among the different R−D links,which helps to reduce the outages at the corresponding R−D links. To derive anexpression for the outage probability, we first express the SIRs at the relay due tothe source Si’s transmission, as well as at the destination Di respectively asΓR,i =Ps (1− ρ) |hi|2dm1dm3 PI |f0|2=ρRXiZ0, (4.27)ΓD,i =Pr,i|gi|2dm2dm4 PI |fi|2=Pr,iρDYiZi. (4.28)Since ΓR,i in (4.27) and ΓD,i in (4.28) are independent, the outage probability andthe throughput in the delay-sensitive transmission mode are given respectively byPout,i = 1− (Pr {ΓR,i ≥ γth} × Pr {ΓD,i ≥ γth})= 1−({ρRλiγthν0 + ρRλi}×{Pr,iρDωiγthνi + Pr,iρDωi}), (4.29)τds,i =T/2NTRds(1− Pout,i) = 12NRds(1− Pout,i). (4.30)4.5.3 Max-Min R−D Rate Power allocation (MMRD)In the max-min R−D rate (MMRD) scheme, the relay’s harvested power is un-equally divided among its links to the different destinations, in such a way that theminimum destination SIR is maximized, i.e. the worst R−D rate is maximized.584.5. Shared Power AllocationThis can be expressed asmaxθi,i=1,...,Nmini=1,...,N {Ri,d}s.t.∑Ni=1 θi = 1 (4.31)whereRi,d =12log2 (1 + ΓD,i) , (4.32)andΓD,i =θiPr|gi|2dm2dm4 PI |fi|2=θiηρPsWYiβ2,4dm3 PIZi=θiρDWYiZi. (4.33)The parameter θi is the fraction of the total relay transmit power Pr allocated toits corresponding R−Di link. It is obtained by solving the optimization problemin (4.31). In order to get a closed-form expression for the optimization variable θi,we solve the previous optimization problem as follows [40]maxθi,i=1,...,Nts.t. t ≤ Ri,d∑Ni=1 θi = 1 , i = 1, ..., N.Since our aim is to maximize t, then the maximum will occur when the first in-equality constraint becomes an equality, i.e. t = Ri,d =12 log2 (1 + aiθi), whereai =ηρPsβ2,4WYidm3 PIZi. Thereforeθi =22t − 1ai, (4.34)then by substituting the expression for θi in the equality constraint, we get an594.5. Shared Power Allocationexpression for t and θ∗i ast =12log2(1 +1∑Ni=11ai), (4.35)θ∗i =1ai(∑Ni=11ai) . (4.36)Now we want to derive an expression for the outage probability. Note that theSIR at the relay as a result of the source Si’s transmission is the same as that definedin (4.27), while the SIR at the destination Di is given by (4.33). Since W =∑Ni=1Xiis the sum of N exponential rv’s, its pdf is given by (4.17). Therefore ΓR,i and ΓD,iare independent and the outage probability can be obtained asIR,i = Pr{ρRXiZ0≥ γth}= ρRλiγthν0+ρRλi , (4.37)ID,i = Pr{θiρDYiWZi≥ γth}= 1Γ(N)aN∫∞0WNW+ci× e−aWdW= 1Γ(N)aN×[(−1)N−1cNi eciaEi(−cia) +∑Nk=1(k − 1)!(−ci)N−ka−k],(4.38)Pout,i =ρRλiΓ(N)aN (γthν0 + ρRλi)×[(−1)N−1cNi eciaEi(−cia) +N∑k=1(k − 1)!(−ci)N−ka−k],(4.39)where ci =γthνiθiρDωiand a = 1λ . The throughput is obtained by substituting theexpression of Pout,i in (4.39) in (4.30). Note that the MMRD power allocationscheme achieves the highest fairness of all schemes at the cost of improving theperformance of the worst user only, which may lead to the degradation of the totalnetwork throughput.604.5. Shared Power Allocation4.5.4 Weighted-Sum-Rate Maximization of all R−D links PowerAllocationIn the weighted-sum-rate maximization (WSRM) scheme, the relay’s total harvestedpower is unequally divided among its links to the different destinations, in such away that the weighted-sum-rate of all the R−D links is maximized. The WSRMcan achieve certain fairness for different R−D links by allocating large weights tolinks with bad channel conditions, while maintaining good network performance,and it can be formulated as followsmaxθi,i=1,...,N∑Ni=1 µiRi,ds.t.∑Ni=1 θi = 1 (4.40)where µi denotes the weight allocated to the link R−Di. The optimization vari-able θi is the fraction of the total harvested power by the relay allocated to thelink R−Di, and Ri,d is the achieved rate at the link R−Di, which is expressedin Subsection 4.5.3 in (4.32) and (4.33). Now we rewrite the above optimizationproblem in terms of the variable θi asmaxθi,i=1,...,N∑Ni=1µi2 log2 (1 + aiθi)s.t.∑Ni=1 θi = 1 (4.41)where ai =ηρPsβ2,4WYidm3 PIZi.The objective function in (4.41) is concave and the constraint is affine in termsof the optimization variable θi thus it is a convex problem. The Lagrangian function614.5. Shared Power Allocation[40] is thus given byL (θi, λ) = 12N∑i=1µi log (1 + aiθi)− λ(N∑i=1θi − 1). (4.42)Since the problem is convex, we can find its optimal solution by using Karush-Kuhn-Tucker (KKT) conditions which aredL (θi, λ)dθi=(µi2 × ai1+aiθi)−λ = 0, (4.43)N∑i=1θi = 1. (4.44)After some mathematical manipulations we get an expression of θ∗i asθ∗i =µi(1 +∑i1ai)∑Ni=1 µi− 1ai. (4.45)Since θ∗i > 0, then by looking at (4.45) the weights should be chosen such thatµi∑Ni=1 µi>1ai(1 +∑i1ai) . (4.46)The choice of µi’s can be fixed and chosen such that channels with unfavorableconditions have larger µi’s than those with better conditions as discussed earlier. Wealso examine the dynamic assignment of µi’s to the different R−D links accordingto some criteria. The criteria we use for choosing the weights is dividing the sum ofrates achieved at all R−D links by the rate achieved at the intended R−Di link,given that the condition in (4.46) is satisfied. The dynamic weights are assigned asfollowsµi =∑Ni=1Ri,dRi,d, (4.47)which shows that R−D links achieving lower rates are assigned larger weights than624.6. Numerical ResultsR−D links achieving higher rates.The outage probability and the throughput using the WSRM scheme are evalu-ated similarly as in the MMRD scheme. The outage probability is given in (4.39).We then substitute Pout,i in (4.30) to evaluate the throughput, i.e., τds,i =12NRds(1−Pout,i). The similarity between the MMRD and the WSRM schemes can be observedsince ΓR,i and ΓD,i are the same for both schemes, and are given by (4.27) and (4.33)respectively. The only difference is in evaluating the variable θi, i.e., the power al-located for each R−Di link, which is different for each scheme since the WSRMobjective is different than the MMRD objective in (4.31). It would also be interest-ing to look at performance measures other than the outage probability/throughputsuch as the fairness which can be measured in terms of the fairness index given by[41]FI =(∑Ni=1Ri,d)2N ×∑Ni=1R2i,d . (4.48)4.6 Numerical ResultsIn this section, we compare the performances of the five different power allocationschemes discussed in Sections 4.4 and 4.5, in terms of their outage probabilities,throughputs, and the fairness. To simplify our expressions, we assumed that thedistances between all source nodes and the relay node are equal, the distances be-tween the relay node and all destination nodes are equal, and the distances betweenthe interferer node and all destination nodes are equal. The number, N , of source-destination pairs is set to 5, and we assume that the R−Di channel quality isnon-increasing with i ∈ {1, 2, ..., 5}, i.e., the R−D5 channel has the worst quality.The channel gains from the sources to the relay are assumed to be independent andidentically distributed, i.e, λ1 = λ2 = ... = λ5 = λ. The energy harvesting efficiency634.6. Numerical Resultsη = 1 and the SIR threshold value γth = 0 dB. We ensure that the power-splitratio ρi ≤ ρ∗i throughout this section for the different studied allocation schemes toensure successful information decoding at the relay node (as required in (4.3)). Theparameter values used in our simulation results are summarized in Table 4.1.Parameter Valueη 1m 4γth 0 dBPs 2 dBmd1 3 md2 2 md3 1.5 md4 1 mTable 4.1: Simulation parameter valuesA plot of the outage probability versus ρ for the NSPA and the EPA schemesis shown in Fig. 4.3 for all 5 S−R−D links. It can be seen that there is amatch between the simulation results and the analytical results. The results showthat the EPA scheme has a lower outage probability than the NSPA scheme forall 5 S−R−D channels. This shows that R−D links with poor channels willexperience reduced outage probabilities when considering the EPA scheme versusthe NSPA scheme. The observed performance improvement can be achieved withoutthe need to know the R−D statistical channel CSI for the EPA scheme, making itan attractive power allocation scheme.644.6. Numerical Results0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.10.20.30.40.50.60.7ρ Outage Probability,  Pout  Sim.S1−R−D1− NSPASim.S2−R−D2− NSPASim.S3−R−D3− NSPASim.S4−R−D4− NSPASim.S5−R−D5− NSPASim.S1−R−D1− EPASim.S2−R−D2− EPASim.S3−R−D3− EPASim.S4−R−D4− EPASim.S5−R−D5− EPAFigure 4.3: Outage Probability versus ρ for the NSPA and the EPA schemesIn Fig. 4.4, we compare the outage probability of the EPA and the RDCDschemes as discussed in Subsections 4.5.1 and 4.5.2 respectively. It can be seen thatthe channels with high SIRs experience nearly the same outage probability with thetwo schemes. On the other hand, the RDCD scheme outperforms the EPA schemein terms of outage probability for channels with low SIRs. This comes at the costof higher complexity since the RDCD scheme requires the relay or another centralcontroller node to know the statistical CSI of all wireless links.654.6. Numerical Results0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.050.10.150.20.250.30.350.40.45 ρ Outage Probability,  Pout  Sim.S1−R−D1− EPASim.S2−R−D2− EPASim.S3−R−D3− EPASim.S4−R−D4− EPASim.S5−R−D5− EPASim.S1−R−D1− RDCDSim.S2−R−D2− RDCDSim.S3−R−D3− RDCDSim.S4−R−D4− RDCDSim.S5−R−D5− RDCDFigure 4.4: Outage Probability versus ρ for the EPA and the RDCD schemesIn Fig. 4.5, we show the outage probabilities of the MMRD and the RDCDschemes. Recall that the MMRD is a max-min rate scheme. As expected, theMMRD scheme results in the same outage probability for all 5 S−R−D links.Note that using the MMRD scheme results in a lower outage probability for theS5−R−D5 link only, i.e., worst channel, while the remaining Si−R−Di linksexperience increased outage probabilities. Therefore the MMRD rate scheme isshown to be the fairest scheme so far but this may come at the cost of increasedoutage probability.664.6. Numerical Results0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.050.10.150.20.250.30.35 ρ Outage Probability,  Pout  Sim.S1−R−D1 − RDCDSim.S2−R−D2 − RDCDSim.S3−R−D3 − RDCDSim.S4−R−D4 − RDCDSim.S5−R−D5 − RDCDSim.S1−R−D1− MMRDSim.S2−R−D2− MMRDSim.S3−R−D3− MMRDSim.S4−R−D4− MMRDSim.S5−R−D5− MMRDFigure 4.5: Outage Probability versus ρ for the MMRD and the RDCD schemesSince the RDCD scheme outperforms all other schemes considered so far, interms of reduced outage probability, we compare it against the WSRM scheme inFig. 4.6. Recall that in WSRM the weights change dynamically as proposed in(4.47). Fig. 4.6 shows that the RDCD scheme is still superior in terms of outageprobability. However, the WSRM scheme achieves a better performance than theNSPA, EPA and MMRD schemes. Comparing Figs. 4.6 and 4.4 it can be seen thatthe EPA scheme yields better outage probability than the WSRM scheme for thehigh SIR links, namely S1−R−D1 and S2−R−D2.674.6. Numerical Results0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.050.10.150.20.250.30.350.4 ρ Outage Probability,  Pout  Sim.S1−R−D1− RDCDSim.S2−R−D2− RDCDSim.S3−R−D3− RDCDSim.S4−R−D4− RDCDSim.S5−R−D5− RDCDSim.S1−R−D1− WSRMSim.S2−R−D2− WSRMSim.S3−R−D3− WSRMSim.S4−R−D4− WSRMSim.S5−R−D5− WSRMFigure 4.6: Outage Probability versus ρ for the RDCD and the WSRM schemesIn order to illustrate the effect of using constant weights versus dynamic weightsin the WSRM scheme, we compare their outage probabilities in Fig. 4.7. The choiceof the constant weights values is done such that larger weights are assigned to linkswith worse channel conditions to reduce their outage probability. This comes at thecost of increased outage probabilities for links with lower weights. From extensivesimulation results, we found the constant weights which achieve an average outageprobability ±0.01 to ±0.04 compared to other schemes are, µ1 = 1, µ2 = 1.5, µ3 = 2,µ4 = 2.5 and µ5 = 3. We also use those values as the initial values for the dynamicweights which are then updated using (4.47). Fig. 4.7 shows that using constantµi’s yields a slightly lower outage probability than using dynamic µi’s for links with684.6. Numerical Resultsbad channel conditions, and slightly higher outage probability for links with betterchannel conditions.0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.050.10.150.20.250.30.350.4 ρ Outage Probability,  Pout  Sim.S1−R−D1− WSRM const. µiSim.S2−R−D2− WSRM const. µiSim.S3−R−D3− WSRM const. µiSim.S4−R−D4− WSRM const. µiSim.S5−R−D5− WSRM const. µiSim.S1−R−D1− WSRM dynamic µiSim.S2−R−D2− WSRM dynamic µiSim.S3−R−D3− WSRM dynamic µiSim.S4−R−D4− WSRM dynamic µiSim.S5−R−D5− WSRM dynamic µiFigure 4.7: Outage Probability versus ρ for the WSRM with dynamic andconstant µi’sFrom Figs. 4.4 - 4.7, we observe that the RDCD scheme yields the best outageprobability performance, followed by the WSRM scheme with dynamic weights witha slightly increased performance than the WSRM using constant weights for the linkswith high SIR, while for the links with low SIR the WSRM with constant weightsoutperforms the one with dynamic weights. Finally the EPA scheme comes at theend with the highest outage probability for low SIR links, however, it has a similarperformance as the RDCD scheme for links with high SIRs.694.6. Numerical Results1 2 3 4 5 6 7 8 9 100.080.0850.090.0950.1 Ps Worst User Throughput [bps/Hz]  MMRDWSRM− Const. µiRDCDWSRM− Dynamic µiEPANSPAFigure 4.8: Worst user throughput versus PsFig. 4.8 shows the throughput of the worst user as a function of the sourcepower, Ps, for the five power allocation schemes. It is observed that the MMRDscheme results in the highest worst user throughput. This is expected since it triesto maximize the worst R−D rate. The NSPA scheme has the lowest worst userthroughput. The next lowest worst user throughput is achieved by the EPA scheme,due to the fact that it allocates an equal amount of power to each link regardless ofthe channel condition. The RDCD scheme and the WSRM scheme with dynamic andconstant weights have similar performance in terms of the worst user throughput.704.6. Numerical Results1 2 3 4 5 6 7 8 9 100.4550.460.4650.470.4750.480.4850.490.495 Ps Total Throughput,  Σ i=1N τ ds,i  [bps/Hz]  RDCDEPAMMRDWSRM− Const. µiWSRM− Dynamic µiNSPAFigure 4.9: Total network throughput versus PsIn Fig. 4.9, we show the total network throughput, i.e.,∑Ni=1 τds,i, as a functionof the source power, Ps, for the five power allocation schemes. It can be seen thatthe NSPA scheme yields the worst network throughput. The next worst networkthroughput is achieved by the MMRD scheme, as its objective is to enhance theworst user performance. The best network throughput is achieved by the RDCDscheme. The next best performance is achieved by the WSRM scheme with a slightlylower network throughput than the RDCD scheme.In practice, it is important to look at other performance measures for the pre-sented power allocation schemes, such as the fairness index as defined in (4.48) andplotted in Fig. 4.10 versus ρ. As expected, the MMRD scheme is the fairest among714.6. Numerical Resultsall schemes at the cost of a lower throughput. The next best allocation schemeachieving fairness is the WSRM with constant µi’s first, followed by the WSRMwith dynamic µi’s. On the other hand the least fair scheme is the EPA. Table 4.2shows the rankings of the different shared allocation schemes in terms of throughput,fairness and outage probability. Note that the performance of the WSRM schemedepends on the choice of the weights, which we have chosen to achieve a reasonableaverage outage probability compared to other schemes.0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.850.90.951 ρ Fairness Index,  F I  MMRDWSRM− Const. µiWSRM− Dynamic µiRDCDEPAFigure 4.10: Fairness Index versus ρ724.7. SummarySchemeTotalThrough-putFairnessOutage forhigh SIRlinksOutage forlow SIRlinksAverageOutageEPA Poor Worst Good Worst PoorRDCD Best Poor Best Best BestMMRD Worst Best WorstBest (forlowest SIRonly)WorstWSRM dy-namic µiAverage Average Average Average AverageWSRMconstant µiGood Good Poor Good GoodTable 4.2: Comparison between different shared allocation schemes - NSPA worstof all4.7 SummaryDifferent power allocation schemes for a DF WRN have been studied, where mul-tiple source-destination pairs communicate via an energy-constrained relay whichharvests RF energy from the source transmissions. Expressions for the outage prob-ability and the throughput in the delay-sensitive transmission mode have been de-rived for each power allocation scheme. Shared power allocation schemes have beenfound to outperform the non-shared allocation scenario. Moreover fairness has beenconsidered as a performance measure to compare between different shared allocationschemes. Numerical results show an interesting tradeoff between the throughput andthe fairness of the different shared allocation schemes. The RDCD scheme achievedthe highest throughput at the cost of decreased fairness, while the MMRD schemeachieved the best fairness at the cost of overall throughput degradation. In con-clusion it is important to decide which performance measure is of higher prioritywhen designing resource allocation schemes, otherwise one can choose an allocationscheme which achieves the best balance between the different considered perfor-mance measures.73Chapter 5Conclusions and Future WorkIn this chapter we summarize our contributions and main findings in Section 5.1.In Section 5.2, we outline some possible directions for future work.5.1 ConclusionsIn this thesis we studied RF energy harvesting in wireless cooperative networks inthe presence of interference. Our main figures of merit are the outage probabilityand the throughput for delay-sensitive transmission.• In Chapter 2, we studied the performance of different energy harvesting re-laying protocols in a DF WRN in the presence of an interfering signal. TheDF relay is energy-constrained, and harvests RF energy from the source sig-nal using the TSR and the PSR protocols. Based on the TSR and the PSRprotocols, we proposed a new hybrid TSR-PSR protocol. We derived closedform expressions for the outage probability, upper and lower bounds, as well asthe throughput in the delay-sensitive transmission mode for all three relayingprotocols. The results show that the PSR protocol has a better throughputthan the TSR for high SIRs. Our proposed hybrid protocol generally yields abetter throughput performance than the TSR or PSR protocols when the TSand PS ratios are chosen properly.• In Chapter 3, we generalized the study in Chapter 2, by considering the effect745.2. Future Workof harvesting RF energy by the relay node from both the information signal andthe interference signal. We derived the outage probability and the throughputof the three relaying protocols studied. The performance degradation dueto neglecting harvesting energy from the interference was examined. Thenumerical results show that there is a slight performance improvement in termsof throughput and outage probability for the assumed system configuration,in which the RF energy harvested from the source signal is larger than thatharvested from the interference signal.• In Chapter 4, we considered a cooperative WRN where multiple source-destinationpairs communicate via a DF relay which harvests energy from the source trans-missions in the presence of an interfering signal. The goal is to efficiently dis-tribute the relay’s power among different R−D links. The outage probabil-ity and the throughput in the delay-sensitive transmission mode were derivedfor several power allocation schemes. Numerical results show that the stud-ied shared allocation schemes outperform the non-shared allocation schemein terms of outage probability and throughput. Different shared allocationschemes were compared against each other in terms of outage probability,throughput and fairness. The RDCD and the WSRM schemes achieve thebest outage and throughput performances but require the knowledge of sta-tistical CSI at the relay node. The results illustrate the tradeoff between thethroughput and the fairness of the different shared allocation schemes.5.2 Future WorkWe now outline some possible directions for future research:• In Chapter 2, we presented a sensitivity analysis to illustrate how the perfor-755.2. Future Workmance of the proposed hybrid TSR-PSR protocol changes depending on thechoice of the TS and PS ratios. Our results demonstrate that when the TS andthe PS parameters are well chosen, the hybrid protocol outperforms both TSRand PSR protocols. Further research on the optimization of these parameterswould be useful. For example, analytical expressions for the optimal TS andPS ratios of the hybrid protocol, will provide more insight into its performanceadvantage over the TSR and PSR protocols.• The system model in Chapter 2, can be extended to include multiple energyharvesting relay nodes and multiple interferer nodes. The effect of differentrelay selection schemes on the system performance can then be investigated.• In Chapter 4, we studied shared allocation schemes which require the relaynode to have knowledge of the statistical CSI. This may incur some overheadspecially when the system has a large number of users. It would be interest-ing to study distributed power allocation schemes for cases of imperfect CSIavailability, and the tradeoff between the system performance and complexity.The case when instantaneous CSI is available can also be studied, in order toassess the potential performance gain.• Another interesting future research direction is to consider buffer-aided relay-ing in the design of energy harvesting cooperative networks [42]. In buffer-aided relaying, the relays adaptively transmit or receive packets in a giventime slot based on the instantaneous CSI of the S−R and R−D channels.In conventional relaying, the relay receives in one time slot and forwards thereceived information to the destination in the following time slot, regardless ofthe instantaneous CSI of the S−R and R−D channels. This rigid schedul-ing may lead to performance degradation due to the inability of the relay to765.2. 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