Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Resource allocation in wireless systems with relay-based cooperation and energy harvesting Arab Loodaricheh, Roya 2015

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2016_february_arabloodaricheh_roya.pdf [ 778.98kB ]
Metadata
JSON: 24-1.0221440.json
JSON-LD: 24-1.0221440-ld.json
RDF/XML (Pretty): 24-1.0221440-rdf.xml
RDF/JSON: 24-1.0221440-rdf.json
Turtle: 24-1.0221440-turtle.txt
N-Triples: 24-1.0221440-rdf-ntriples.txt
Original Record: 24-1.0221440-source.json
Full Text
24-1.0221440-fulltext.txt
Citation
24-1.0221440.ris

Full Text

gzsourxz Alloxvtion in lirzlzss hystzms fiithgzlvyBwvszy Xoopzrvtion vny Enzrgy HvrvzstingbyRoya Arab LoodarichehM.Sc., Amirkabir University of Technology (Tehran Polytechnic), 2012B.Sc., Isfahan University of Technology, 2009A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)December 2015c© Roya Arab Loodaricheh 2015AwstrvxtWireless communication networks are subject to exponential growth as a result of prolifer-ation of smart phones, diverse wireless services and Internet of Things (IoT) applications.This extensive growth of wireless networks can significantly increase energy consumption,and escalating environmental pollution and energy costs have already created an urge forgreen communication. Therefore, we need to be proactive in designing environment friendlycommunication technologies and efficient resource allocation solutions, which will potentiallydrive the future generation of wireless communication. In this thesis, we focus on two promis-ing communication technologies, namely cooperative relaying, which improves energy andspectral efficiency by providing spatial diversity, and energy harvesting technology, which canimprove sustainability by utilizing renewable energy sources. The objective of this thesis isto address a number of key challenges in the design of efficient resource allocation techniquesfor wireless systems based on these two communication technologies. Firstly, we addressthe problem of energy efficiency maximization for downlink orthogonal frequency divisionmultiple access (OFDMA)-based cooperative networks. The power and subcarrier allocationpolicies are jointly optimized with quality of service (QoS) provisioning. Afterwards, we in-vestigate frequency reuse in OFDMA device-to-device (D2D) cooperative systems in whichD2D pairs are classified based on the level of proximity with each other. We propose differentscenarios of downlink communications and provide efficient frequency allocation techniques.Moreover, resource allocation algorithms with low complexity and signaling overhead aredeveloped. Next, we focus on energy limitation of the relay nodes in cooperative systems.Using wireless energy harvesting to power the relay nodes, we propose an efficient resourceiiAwstrvxtallocation algorithm. As wireless energy harvesting technology is only effective for chargingsmall nodes in communication systems, finally, we focus on the issue of charging the wirelessnodes with renewable energy. We investigate the problem of resource allocation in energyharvesting systems considering the fact that the energy harvested from environment maynot be enough to satisfy the QoS of all users due to its random nature. Two different utilityfunctions are introduced and both offline and online schemes are devised to address thisproblem.iiierzfvxzPublications that have been resulted during the conduction of research in this thesis are asfollows:• S. Lohani, R. Arab Loodaricheh, S. Mallick, E. Hossain, and V. K. Bhargava, “Coop-erative networks with wireless energy harvesting,” submitted book chapter, lirzlzssBeofizrzy Communixvtion cztfiorksA VrxhitzxturzsA erotoxolsA vny Vpplixvtions , Cam-bridge University Press. (Linked to Chapter 4)• S. Mallick, R. Arab Loodaricheh, N. R. S. V. P. Koppisetti, and V. K. Bhargava,“Resource allocation for cooperative D2D communication networks,” submitted bookchapter, JG bowilz Communixvtions A Springer. (Linked to Chapters 2,3,4)• R. Arab Loodaricheh, S. Mallick, and V. K. Bhargava, “Resource allocation with QoSprovisioning for energy harvesting systems: A goal programming approach,” in eroxCof GEFJ IEEE ICC, pp.2791–2796. (Linked to Chapter 5)• R. Arab Loodaricheh, S. Mallick, and V. K. Bhargava, “Energy efficient resource al-location for OFDMA cellular networks with user cooperation and QoS provisioning,”IEEE irvnsC lirzlzss CommunC, vol. 13, no. 11, pp. 6132–6146, Nov. 2014. (Linkedto Chapter 2)• R. Arab Loodaricheh, S. Mallick, and V. K. Bhargava, “Resource allocation for OFDMAsystems with selective relaying and energy harvesting,” in eroxC of GEFI IEEE kiC(Fvll), pp. 1–5. (Linked to Chapter 4)iverefvxe• R. Arab Loodaricheh, S. Mallick, and V. K. Bhargava, “Joint resource optimizationfor OFDMA cellular networks with user cooperation and QoS provisioning,” in eroxCof GEFI IEEE lCcC, pp.1264–1269. (Linked to Chapter 2)• R. Arab Loodaricheh, S. Mallick, and V. K. Bhargava, “Distributed subcarrier pairingand relay selection for OFDM based cooperative relay networks,” in eroxC of GEF3IEEE lCcC, pp. 3557–3562. (Linked to Chapter 3)I am the primary researcher and author for all the research contributions made in thisthesis. I conducted the literature review and identified the research problems. Moreover, Iformulated the research problems and carried out the mathematical analysis and simulations.I also wrote the associated manuscripts for publication. The contributions of the coauthorsof my papers are as follows. Prof. V. K. Bhargava is a co-author for contributions made in allthe papers. He provided directions on identifying research problems and valuable commentson my research progress, and helped me by providing technical and editorial feedback duringthe preparation of associated manuscripts. Dr. S. Mallick is a post-doctoral fellow in ourgroup. I consulted him during all my research works, and he provided important comments,technical feedback and constructive suggestions. He also helped in editorial corrections whilewriting the associated manuscripts for publication.Some other research contributions not presented in the thesis but have been publishedduring my PhD program at UBC are listed in Appendix D.vivwlz of XontzntsAwstrvxt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iierzfvxz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivivwlz of Xontznts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viaist of ivwlzs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixaist of Figurzs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xaist of Awwrzvivtions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAxknofilzygmznts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvF Introyuxtion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Resource Allocation in Wireless Communication Systems . . . . . . . . . . . 21.2 Cooperative Relaying in Wireless Communication Systems . . . . . . . . . . 41.3 Energy Harvesting in Wireless Communication Systems . . . . . . . . . . . 71.4 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8G foh Afivrz vny Enzrgy Effixiznt gzsourxz Alloxvtion for Xoopzrvtivzlirzlzss Xommunixvtion hystzms . . . . . . . . . . . . . . . . . . . . . . . . 112.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . 112.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17viivwle of Contents2.4 Solution Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31H gzsourxz Alloxvtion for DGD gzlvying Xommunixvtion hystzms . . . . 393.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . 393.2 Resource Allocation for D2D Relaying Systems with Frequency Reuse . . . 403.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.2.2 D2D Relaying without Frequency Reuse . . . . . . . . . . . . . . . . 433.2.3 Buffer-Aided D2D Relaying with Frequency Reuse . . . . . . . . . . 473.2.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.5 D2D Relaying: Motivation for a General Scenario . . . . . . . . . . . 523.3 Low Complexity and Distributed Resource Allocation for Relaying Systems 533.3.1 System Model and Problem Formulation . . . . . . . . . . . . . . . . 543.3.2 Solution Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.3.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60I gzsourxz Alloxvtion for Xoopzrvtivz Xommunixvtion hystzms fiith lirzBlzss Enzrgy Hvrvzsting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . 664.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.4 Solution Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75J foh Afivrz gzsourxz Alloxvtion for Enzrgy Hvrvzsting Xommunixvtionhystzms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.1 Accomplished Works and Research Contributions . . . . . . . . . . . . . . . 795.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81viiivwle of Contents5.3 Best Effort Resource Allocation Problem . . . . . . . . . . . . . . . . . . . . 825.3.1 Offline Best Effort Resource Allocation . . . . . . . . . . . . . . . . . 845.3.2 Online Best Effort Resource Allocation . . . . . . . . . . . . . . . . . 865.4 Joint Admission Control and Power Allocation Problem . . . . . . . . . . . 905.4.1 Offline Admission Control and Power Allocation . . . . . . . . . . . 925.4.2 Online Admission Control and Power Allocation . . . . . . . . . . . 945.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996 Xonxlusions vny Futurz gzszvrxh Dirzxtions . . . . . . . . . . . . . . . . . 1076.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.2 Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Wiwliogrvphy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111AppznyixzsA eroof of thz xonvzxity for erowi . . . . . . . . . . . . . . . . . . . . . . . . . 121W Dzrivvtion of optimvl vuxilivry pofizrs . . . . . . . . . . . . . . . . . . . . . 123X eroof of thz totvlly unimoyulvrity for thz xonstrvint mvtrix . . . . . . . 125D aist of dthzr euwlixvtions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127viiiaist of ivwlzs1.1 Energy estimates of different EH sources . . . . . . . . . . . . . . . . . . . . 62.1 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1 Computational complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.1 Power transfer ranges for different types of mobile devices [78] . . . . . . . . 675.1 An example to show the drawback of Algorithm 9 . . . . . . . . . . . . . . . 955.2 Comparison of admission control and best effort schemes . . . . . . . . . . . 1055.3 Comparison of Algorithm 9 and Algorithm 10 . . . . . . . . . . . . . . . . . 105ixaist of Figurzs2.1 Figure shows cooperative (two time slots) and non-cooperative (one time slot)transmissions for destination node and relay nodes, respectively. . . . . . . . 142.2 Flowchart that summarizes our proposed iterative algorithm . . . . . . . . . 302.3 Convergence of Dinkelbach method . . . . . . . . . . . . . . . . . . . . . . . 322.4 Convergence of the dual decomposition technique . . . . . . . . . . . . . . . 332.5 Average system capacity versus emax for different number of nodes . . . . . . 342.6 Average energy efficiency versus emax for different number of nodes . . . . . 342.7 Average system capacity versus the number of subcarriers for different emax 352.8 Performance comparison of our proposed scheme with schemes that do notconsider pairing and relay selection . . . . . . . . . . . . . . . . . . . . . . . 362.9 QoS provisioning for different nodes comparing to the schemes with relaxedQoS constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.10 Probability of infeasible realizations . . . . . . . . . . . . . . . . . . . . . . . 372.11 Average system capacity versus emax for different data rate requirements . . 382.12 Average energy efficiency versus emax for different data rate requirements . . 383.1 System model for cellular wireless systems with cooperative D2D communi-cation. UEs with strong communication links from the BS can send/receivedata directly from the BS. However, UEs with bad communications links fromthe BS (for example, due to network blockage) can benefit from D2D commu-nication with relay UEs to send/receive the data from the BS. . . . . . . . . 41xaist of Figures3.2 Average system capacity versus BS power budget emax for different number ofUEs. Result shows significant improvement of system capacity when frequencyis reused in D2D links. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.3 Average system capacity versus number of subcarriers for emax = 35 dBmand K = 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.4 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.5 Average throughput of the system versus number of subcarriers for differentnumber of relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.6 Average of the relative error versus the number of subcarriers . . . . . . . . 643.7 CDF versus percentage of relative error for proposed scheme-2 with K = 2 . 643.8 Signaling overhead versus number of subcarriers . . . . . . . . . . . . . . . . 654.1 Downlink information relaying with energy harvesting in SWIPT network withone source (S), three relay nodes (R), three destination nodes (D), and fivesubcarriers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.2 Formation of the square matrix and a sample assignment solution . . . . . . 754.3 Convergence of our proposed algorithm for different number of subcarriers . 764.4 Average system capacity vs. emax for different number of subcarriers . . . . 774.5 Cooperation ratio vs. emax for different number of subcarriers . . . . . . . . 774.6 Average energy efficiency vs. emax for different number of subcarriers . . . . 785.1 Markov model for the channel gain . . . . . . . . . . . . . . . . . . . . . . . 995.2 Markov model for the harvesting energy . . . . . . . . . . . . . . . . . . . . 1005.3 Dissatisfaction in K time slots versus the EH rate (He) for c = 4 and K = 4. 1015.4 Maximum dissatisfaction ( max) versus the EH rate (He) for c = 4 and K = 4.1025.5 Throughput in K time slots (total transmitted bits) versus the EH rate (He)for c = 4 and K = 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103xiaist of Figures5.6 Comparison of power consumed by each user for our proposed schemes andno QoS provisioning scheme, for c = 4, K = 16, He = 10 joules, and foh1Pk= foh2Pk = 1.08 Mbits, foh3Pk = foh4Pk = 1.1 Mbits for all k. . . . . . . . . 1035.7 Comparison of power profile over time for the proposed schemes , for c = 1,K = 6, He = 2 joules, and foh1Pk={1P3P5} = 1.08 Mbits, foh1Pk={2P4P6} = 1.1Mbits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.8 Throughput in K time slots (total transmitted bits) versus the number oftime slots (K), for c = 4, He = 1 joules, and fohiPk = 0.4i Mbits. . . . . . . 106xiiaist of AwwrzvivtionsAF : Amplify-and-ForwardAP : Access PointAWGN : Additive White Gaussian NoiseBS : Base StationCDF : Cumulative Distribution FunctionCSI : Channel State InformationD2D : Device-to-DeviceDF : Decode-and-ForwardDP : Dynamic ProgrammingEH : Energy Harvestingi.i.d. : Independent and Identically DistributedKKT : Karush-Kuhn-TuckerMDP : Markov Decision ProcessMINLP : Mixed Integer Nonlinear ProgrammingNP hard : Non deterministic Polynomial time hardOFDM : Orthogonal Frequency-Division MultiplexingOFDMA : Orthogonal Frequency-Division Multiple AccessQoS : Quality of ServiceRF : Radio FrequencySNR : Signal-to-Noise RatioSWIPT : Simultaneous Wireless Information and Power Transferxiiiaist of AwwrevivtionsUE : User EquipmentWPC : Wireless Powered CommunicationxivAxknofilzygmzntsForemost, I would like to thank my supervisor, Professor Vijay K. Bhargava, for his guidance,support and patience. I am extraordinarily lucky to have had the chance to work with Prof.Bhargava. This thesis would not have been possible without his suggestions, advice andconstant encouragement.I would also like to thank Professor David Michelson, and Professor Lutz Lampe forserving as committee members during my PhD qualifying and departmental examinationsand for offering practical and constructive feedback.I am highly grateful to Dr. Shankhanaad Mallick, a senior member of our lab, for hisconstructive suggestions, contributions and helpful advice during my research.Furthermore, I would like to extend my deep gratitude to my lab mates for their invaluablesupport, friendship and all the fruitful discussions during my PhD program.I would like to express heartfelt thanks to my family. I owe much gratitude to myparents and my sister and brother for supporting me spiritually throughout my studies atthe University of British Columbia.Last but not the least, I would like to thank my loving husband Aref, who has beena constant source of support, care and encouragement during the challenges of graduateschool and life. He was always there cheering me up when the tasks seemed arduous andinsurmountable. Without him, I could not have completed this thesis.This work was supported by Natural Sciences and Engineering Research Council ofCanada (NSERC).xvXhvptzr FIntroyuxtionThe market of wireless communication networks has been experiencing exponential growthdue to the booming of the number of new users and applications over the past decade. Smartphones let people use social networks, read books, listen to audio and watch videos which leadto a massive data traffic demand. Moreover, this trend will continue as billions of devices willbe connected to the Internet of Things by 2020 [1]. Therefore, everyday, telecommunicationindustries are facing an increasing demand for higher capacity, lower latency, more deviceconnectivity and more efficient protocols.Finding a solution to cope with such exponential growth is challenging for research com-munities. The primary objective of wireless communication research has been to meet thisincreasing demand using available resources, such as bandwidth and transmit power. Coop-erative communication is a state-of-the-art technology which increases spectrum and energyefficiency in a resource-constrained wireless network. Therefore, cooperative communicationhas been considered as one of the promising technologies for standards such as 3GPP LongTerm Evolution-Advanced (LTE-A) and IEEE 802.16 [2].The extensive growth of wireless networks can significantly increase energy consumption.Escalating environmental pollution and energy costs have already created an urge for “green”wireless communications [3]. Green communications is defined as attempting to decrease theenergy costs while retaining the Quality of Service (QoS) of the system at the desired level [4].The main focus of “green” communication is to improve the energy efficiency and the batterylife of wireless devices. Information and communications technology (ICT) systems presentlyaccount for 10% of the overall energy consumption and 2% of global carbon emissions [5]. In1FCFC gesourxe Alloxvtion in lireless Communixvtion hystemsless than ten years, the power consumption of ICT is predicted to be equal to the total powergenerated today [5]. As a result, we need to be proactive in designing environment friendlyand efficient resource allocation solutions, which will potentially drive the future generationof wireless communication. The concept of renewable energy has been recently introducedin the context of wireless networks as an environmentally friendly approach with economicbenefits. Unlike the conventional energy sources, renewable energy, such as wind, solar, andthermal energy is sustainable with almost zero net carbon.In this chapter, we first present an overview of resource optimization in wireless commu-nication systems. Then we briefly go through the fundamentals of cooperative and energyharvesting wireless communication systems. Finally, we provide the outline of the thesis.FCF gzsourxz Alloxvtion in lirzlzss XommunixvtionhystzmsIn wireless communication systems, it is critical to allocate the resources to communicationnodes efficiently in order to achieve desirable performance of the network. Typically, re-source allocation problems are formulated as constrained optimization having resources asoptimization variables, with one objective function and a set of constraints which determinesthe feasible set of the problem. The feasible set is defined as the set of candidate solutionsthat satisfy all constraints. The optimization variables of resource allocation problem in wire-less systems are usually energy and spectrum. Energy and spectrum are important scarceresources whose optimal allocation poses various challenges in wireless communication sys-tems. Here, we discuss different elements of resource allocation in wireless communicationsystems.• dwjzxtivz funxtionsOObjective function in wireless communication systems is a satisfaction metrics of system2FCFC gesourxe Alloxvtion in lireless Communixvtion hystemsor users. A common performance metric is based on the Shannon capacity of thecommunication links. Different mappings can be applied on this metric to take variousaspects of the network into consideration. For example, for a system with multipledestinations, a social utility function can be defined as the summation of the rate overall the communication links. In addition, improving energy efficiency is considered tobe one of the most important factors in designing a communication network [6]-[7].The optimal resource allocation considering energy efficiency metric as the objectivefunction takes into account both the maximization of the system capacity and theminimization of power at the same time [8]-[11]. Other important design goals consist ofpower minimization, outage probability minimization, transmission time minimizationand fairness maximization.• XonstrvintsOThe power limitation of the communication nodes is represented by a set of constraints.Different power constraints are used in resource allocation problems. The total powerconstraint which limits the overall power consumption of all the nodes, gives insight onhow energy efficient the system is. However, the individual power constraints considerphysical limitations of wireless nodes. The power available for each node can be con-stant or variable over time. An example of dynamic power constraint is in the case ofenergy harvesting nodes where available energy changes over time due to the randomnature of the harvested energy.Considering a general application scenario, two types of receiver nodes exist in thesystem: delay sensitive and non-delay sensitive. The delay sensitive nodes have specificdata rate requirements due to the real time service they need (e.g. for mobile users,watching movies, playing online games, etc.), while the non-delay sensitive nodes haveflexible data rate requirements as they need non-real time services (e.g. downloadingfrom the internet). QoS provisioning for the delay sensitive nodes should be considered3FC2C Coopervtive gelvying in lireless Communixvtion hystemswhile optimizing the resources of the system. Therefore, QoS constraints are includedin resource allocation problems for communication systems with delay sensitive nodes.Other important constraint is the one which controls the interference of the system. Itis considered as posing a limit on transmission power to maintain the interference inan acceptable range. In addition, the interference mitigation can be taken into accountby allocating the radio frequency spectrum (e.g. allocating subcarriers to users in anOFDMA system) such that the orthogonality is preserved.In practical wireless communication systems, many limitations and opportunities arisein resource allocation according to the application. The examples of application dependentchallenges are: relay selection in cooperative communications, user association in heteroge-neous networks (HetNets), and satisfying causality power constraints in energy harvestingsystems.FCG Xoopzrvtivz gzlvying in lirzlzss XommunixvtionhystzmsCooperative communication is a novel technology for wireless networks which, compared tothe conventional systems, can provide higher spectral efficiency, larger coverage area andlonger network lifetime. The basic idea in cooperative communication is simple: a wirelesssource node transmits data to a destination node. A third node, named as relay, overhearsthis signal and relays it to the destination node. Finally, the destination node exploit thediversity by combining the two received signals.In a cellular network, two types of relay nodes exist: infrastructure (or fixed) relaysand mobile user relays. By introducing fixed relay stations, direct path transmission isdivided into shorter links, therefore destructive factors such as pathloss and shadowing be-come less dominant which results in a more efficient communication [12]-[13]. On the other4FC2C Coopervtive gelvying in lireless Communixvtion hystemshand, device-to-device (D2D) communication technology [14]-[20] makes it possible for de-vices in a multi-tier network to function as transmission mobile relays for one another [15].D2D communications can potentially improve the end-user experience by reducing networklatency, reducing power consumption, increasing peak data rates, and facilitating severalproximity-based services. By allowing relay-based communication, it is possible to improvenetwork coverage and quality of service. The idea of D2D relaying is particularly attractivefor the cell-edge users and for the users under coverage holes within the cells. Mobile userequipments (UEs) with strong communication links to the base station (BS) can help asrelays, via D2D communication, to other UEs with heavy blockage and shadowing at noadditional cost to the mobile operators. In other words, mobile relaying via D2D communi-cation can enhance the performance of cellular networks by taking advantage of “shadowingdiversity” [18]. The concept of D2D relaying has motivated researchers to investigate designmethods which jointly exploit the advantages of both D2D and relaying technologies.There are different relaying protocols among which decode-and-forward (DF) and amplify-and-forward (AF) are more popular [12]. In DF relaying, the relay receives the signal fromthe source, decodes it, and forwards it to the destination, while in AF relaying, the relaysimply amplifies the received signal from the source and forwards it to the destination.Cooperative communication systems can use higher degree of freedom to improve networkperformance. However, it is crucial to develop resource optimization schemes, which canguarantee to meet certain demands of users and enhance the performance of the networkconsidering the limited resources. There are several works on resource allocation, especiallycapacity maximization [21]-[22] and power minimization [23]-[24], for cooperative systems.Cooperative relaying technology greatly improves the energy efficiency of the system [25]. Forinstance, energy efficiency maximization problem has been studied for cooperative systemsin [26]. Recently, there has been significant interest for using OFDMA in cooperative systems.A large part of these research works include resource allocation, specifically, subcarrier andpower allocation and relay selection strategies for these systems [27]-[28]. For example,5FC2C Coopervtive gelvying in lireless Communixvtion hystemsin [22] and [29], resource optimization for OFDMA systems is studied for amplify-and-forwardand decode-and-forward relaying protocols, respectively. Moreover, optimal relay selectioncan improve the performance of the cooperative system; in [30]- [31], various optimal relayselection strategies are proposed.Availability of complete channel state information (CSI) at a central managing node isassumed in most of the existing works on resource allocation for cooperative systems. How-ever, this assumption may not be practical for a network with large number of subcarriersas it requires significant amount of CSI feedback and limits the scalability of the system. Inaddition, it leads to heavy computational load at the central node which may result in ex-tensive delay. Therefore, the centralized solutions may not be useful in practice. Distributedresource allocation, especially subcarrier pairing and relay selection for cooperative systemsis a highly challenging task. In [32], the authors address this problem using a model in whicheach relay sets a timer based on the channel condition and the timer of the relay with thebest end-to-end channel expires first. Therefore, the best relay can be selected without anyadditional feedback requirement. There are other research works on distributed cooperativesystems which are based on iterative algorithms, e.g. [21].Table 1.1: Energy estimates of different EH sourcesEH hource Hvrvzstzy eofizrViwrvtion/motion FEE W=cm3izmpzrvturz yiffzrznxz FE4 W=cm2aight FE5 W=cm2liny FE3 W=cm2gF trvnsmittzr fiith IW trvnsmission =NE2BN2M bHz) J W vt Jm6FCHC Energy Hvrvesting in lireless Communixvtion hystemsFCH Enzrgy Hvrvzsting in lirzlzss XommunixvtionhystzmsEnergy harvesting (EH) is a new technology which enables the wireless nodes to harvestenergy, such as wind, solar, vibrational and thermal energy from the environment. Energyharvesting in wireless networks not only brings environmental and economic benefits to thesystem, but also suggests an alternative solution to charge transceiver nodes for which it isimpossible to connect to power grids. In Table 1.1, the estimates of the harvested energyfrom different EH sources are listed [33]-[35].Various elements of a wireless communication network can be powered up using renewableenergy. BSs are one of the major contributors of carbon footprint in the ICT industry [3]-[5].BSs that can harvest solar/wind energy will reduce the energy cost and environmental im-pacts as well as the cost of maintenance requirements of the network [36]-[37]. In sensor net-works, the use of renewable energy will not only eliminate the need for battery replacementsbut also prolong the lifetime of the system [38]. In addition to harvesting renewable energiesfrom environment, radio frequency (RF) energy harvesting technique has also attracted sig-nificant attentions [39]. As RF waves transfer information and power simultaneously, part ofthe transmitting power can be harvested at the receiver for the purpose of communications.However, the harvested power using RF energy harvesting technology is so small that mightbe applicable only in wireless systems with very low power requirements such as body areanetworks.Resource allocation in EH systems faces numerous challenges. The most important one isthe random nature of harvested energy. The energy scavenged from renewable sources is notcontrollable as it changes with climate, time and location. In most of the cases, it is not easyto predict the amount of energy that can be harvested from environmental sources. In recentliterature, resource allocation techniques for wireless EH systems have been investigated.In [40], an optimal power allocation policy is proposed assuming that complete and non7FC4C dutline of ihesiscausal information about the harvesting energy is available. However, such assumptions aretoo optimistic for EH systems that rely only on natural sources of energy. In [41]-[42], a morerealistic scenario has been considered, where the authors assume that the amount of energythat will be harvested in the future is not completely known. In [43], it is assumed that someimperfect information about the energy that can be harvested in future is available and anenergy allocation policy for cooperative EH systems is proposed. The uncertain nature ofthe wireless channel and the lack of knowledge about harvesting energy have been discussedin [44]-[45]. The other challenging issue in resource allocation in EH systems is capacity andleakage of storage devices. Resource allocation for EH systems considering these challengeshave been discussed in [40],[43].Resource allocation policies for EH systems are proposed in the literature consideringdifferent objectives such as throughput maximization, outage probability minimization andtransmission time minimization [46]-[48]. In addition, QoS provisioning in EH system isdiscussed in [49], where it is assumed that the energy is sufficient to provide the requiredQoS to all the users. However, guaranteed QoS to all users may not be feasible for EHsystems, since the source energy is unpredictable and varies over time. In [50], an algorithmis proposed for EH systems that guarantees delay sensitive data to be delivered by a deadline.Given the aforementioned advantages, drawbacks and challenges of EH wireless commu-nications, they have drawn significant attention, and are expected to be abundantly used infuture.FCI dutlinz of ihzsisThe rest of this thesis is organized as follows:• In chapter 2, we consider a dowlink cooperative wireless communication in which therelay nodes not only relay the signals from source for some destination nodes, but alsoreceive their own messages from the source node. Joint relay selection, subcarrier allo-8FC4C dutline of ihesiscation and power allocation algorithms are developed with the objective of maximizingthe energy efficiency of the system considering the quality of service requirements of thereceiver nodes. The resource allocation problem is a mixed integer nonlinear program(MINLP), which is in general very difficult to solve in its original form. The energyefficiency metric is a fractional and nonlinear function, which complicates the prob-lem further. We provide novel optimization framework to solve such non-linear andnon-convex optimization problems. The proposed solution to this joint optimizationproblem is optimal and computationally efficient.• In chapter 3, we introduce device-to-device relaying as an example of the system modeldiscussed in chapter 2. Different challenges associated with cooperative D2D is studiedin this chapter. In section 3.2, we propose resource allocation techniques consideringfrequency reuse in OFDMA D2D communication. We consider two scenarios based onthe proximity of the D2D pairs. Firstly, we consider that D2D pairs are very closeto each other and their coverage areas overlap. In this case, we propose subcarrierallocation without frequency reuse in order to avoid the interference among the D2Dlinks. Next, we consider that the D2D pairs are far enough and their coverage areasare disjoint. In this case, we propose subcarrier allocation policy with full frequencyreuse with the help of buffer-aided relaying. We also provide motivation for resourceallocation in a general scenario where D2D pairs are randomly distributed in a cell, i.e.,the two aforementioned scenarios co-exist within the cell. Furthermore, we propose lowcomplexity distributed subcarrier and relay selection for relaying systems in section 3.3.We develop two suboptimal algorithms which are efficient in terms of signaling overheadand complexity reduction at the expense of a small degradation in performance.• Another challenge in the cooperative system modeled in chapter 2 is whether the relaydevices are interested to spend their own power for the purpose of relaying. In chapter4, we assume that the devices are capable of energy harvesting using “wireless power9FC4C dutline of ihesistransfer” technology and only the harvested energy is used for cooperation. The jointoptimization problem of power and subcarrier allocation and relay selection is providedusing dual decomposition approach. Numerical results demonstrate the effectivenessof the proposed scheme in terms of energy efficiency.• In chapter 4, we propose a resource allocation scheme using wireless power transfertechnology to charge the relay nodes with power limitations. However, this technologyis only effective for applications with small wireless devices. Therefore, in chapter 5,we consider a wireless communication network in which the nodes are charged withrenewable energy. We propose quality-of-service based resource allocation schemes forsuch energy harvesting systems. We consider a system model in which the transmitternodes harvest energy from the environment. Our goal is to develop efficient resourceallocation policies for EH systems when the harvested energy at the source node isuncertain and insufficient to satisfy the QoS of the users completely. To address thisproblem, two different schemes and resource allocation policies are developed. In thefirst scheme, we minimize the total dissatisfaction of the users over a period of timethrough goal programming approach. In the second scheme, we maximize the numberof admitted users over a period of time and provide guaranteed QoS to the admittedusers. For both schemes, we first develop offline algorithms assuming that perfect CSIand complete information about the harvested energy are available. Next, under theassumption of causal CSI and information about the harvested energy, we devise onlinealgorithms using dynamic programming.• Finally, chapter 6 provides the concluding remarks of the thesis and discusses somefuture research directions.10Xhvptzr Gfoh Afivrz vny Enzrgy Effixizntgzsourxz Alloxvtion for Xoopzrvtivzlirzlzss Xommunixvtion hystzmsIn this chapter, we investigate resource allocation problem for cooperative wireless communi-cation systems considering QoS provisioning and energy efficiency. The accomplished worksand research contributions of this chapter are briefly described in the following.GCF Axxomplishzy lorks vny gzszvrxh XontriwutionsIn this chapter, we consider an OFDMA cooperative system model with one source, multiplerelays and multiple destination nodes. We assume that the relay nodes receive their owndata from the source node while relaying the data for the destination nodes. We optimallysolve the joint subcarrier and power allocation and relay selection problem, considering thatboth in relay nodes and destination nodes there are some nodes with specific data raterequirements. Moreover, we incorporate the QoS provisioning for these receiver nodes whileoptimizing the energy efficiency of the system.The optimization problem of joint power and subcarrier allocation, subcarrier pairingand relay selection under QoS provisioning is MINLP, which is in general very difficult tosolve in its original form [51]. The energy efficiency metric is a fractional and nonlinearfunction, which complicates the problem further. To make the original optimization prob-112C2C hystem boyellem a tractable one, the MINLP problem is reformulated by relaxing the integer variablesand by introducing “Dinkelbach” method to take care of the fractional objective function.In most of the existing works in the literature, it is assumed that the same subcarrier isused for the source to relay and for the relay to destination links [30]-[31]. However, thisassumption limits the performance of the system, though it reduces the complexity of theproblem. In [22],[52]-[53], it is assumed that the system is flexible to use different subcarriersin the source node to relay and the relay to destination links. This concept, known as sub-carrier pairing, can improve the performance of the system considerably. In this work, weincorporate optimal subcarrier pairing in our resource allocation algorithm. As we considersubcarrier pairing, a “Hungarian” based algorithm is introduced to allocate the subcarriers.We prove that our proposed solution of the relaxed integer problem is optimal and has integervalues. To the best of our knowledge, the proof of optimality of the solution for such relaxedinteger problems in resource allocation, is still missing in the literature. In [21],[26],[54],similar MINLP resource allocation problems are solved using convex relaxation and dualdecomposition approach. However, no such proofs of the optimality are provided. Based onthe dual decomposition method, we propose an algorithm for the joint optimization problemwhich is optimal and computationally efficient in polynomial time.The remainder of this chapter is organized as follows. The system model is introducedin section 2.2. In section 2.3, the joint resource optimization problem is formulated. Thesolution approach is presented in section 2.4. The numerical results are demonstrated insection 2.5.GCG hystzm boyzlConsider an OFDMA cooperative network with one source, multiple relays and multipledestination nodes. The total available bandwidth is divided into c orthogonal subcarriers,each of them with a bandwidth of l . We assume the relay nodes receive their own data122C2C hystem boyelfrom the source node, while relaying the data for the destination nodes.The source node broadcasts the data and only the relays can receive it directly from thesource, since we assume the direct link channels from source to destination nodes are in deepfade. A complete communication with relays requires a single time slot. Unlike the relays, acomplete transmission to destination nodes requires two time slots. In the first time slot, thesource node transmits the data and the relays receive. In the second time slot, the selectedrelays amplify the received data and forward it to the destination nodes. The relays can actboth as destination node and relay at the same time.We have b relay nodes and K destination nodes. As the transmission to destinationnodes requires two time slots to receive a data from the source, we assume that the channelgains remain constant over two time slots and are estimated perfectly. We consider that therelay nodes are capable of full-duplex communication, which is realized when relays in thesecond time slot forward data for destination nodes, and also they receive their own datafrom the source simultaneously in different frequency bands. Note that the source does notsend any data targeted for the destination nodes in the second time slot. This is becausethe channel gains remain constant for two time slots and optimal resource allocation is notpossible as transmission is completed in the following time slot with unknown channel gains.The following simple example illustrates the system model. As depicted in Fig. 2.1, thesource node h transmits data for destination node k with the help of relay m1 over subcarrierpair (iP j), where i is the subcarrier used in the first time slot and j is the subcarrier used inthe second time slot. The cooperative transmission requires two time slots and is indicatedwith dashed line in the figure. Relays also can receive their own data from the source nodein both time slots. This direct transmission is completed in one time slot and shown withsolid lines in the figure. For example, relay nodes m2 and m1 receive their data from thesource node in the first time slot over subcarrier i′ and in the second time slot over j′,respectively. We assume that in each time slot each subcarrier is used only once in orderto avoid interference, for example, in this figure i ̸= i′ and j ̸= j′. Note that, relay m1 can132C2C hystem boyelBSm1km2Subcarrier: itime slot, T=1Subcarrier:j’time slot, T=2Subcarrier: i’time slot, T=1Subcarrier: jtime slot, T=2Figure 2.1: Figure shows cooperative (two time slots) and non-cooperative (one time slot)transmissions for destination node and relay nodes, respectively.receive his own data in the second time slot over subcarrier j′, and transmits data (act asrelay) for destination node k in the same time slot over subcarrier j simultaneously, wherej ̸= j′.For cooperative transmission, AF relaying is used. Each destination node can be assistedby different relays, and relay can help more than one destination node.The channel coefficient of the link from the source node h to relay m on subcarrier i, andthe coefficient from relay m to destination node k on subcarrier j are denoted as hihPm andhjmPk, respectively. The channel gains are defined as gihPm = |hihPm|2 and gjmPk = |hjmPk|2.As mentioned before, we have two types of transmission: cooperative (X) and non-cooperative (cX) or direct. We consider that in cooperative transmission, source nodecan communicate with destination node k ∈ {1P 2P OOOP K} with the assist of relay m ∈{1P 2P OOOPb}. In the first time slot, relay m receives a symbol m ik from source for destinationk in subcarrier i and is given byniP(CP1)hPm(k) =√eiP(CP1)hPm gihPmmik + oimP (2.1)where eiP(CP1)hPm is the transmission power of the source to relay m link, on subcarrier i and142C2C hystem boyelthe superscript (XP 1) denotes the first time slot of cooperative transmission. oim is AWGNwith variance of c0 received by relay m on subcarrier i with bandwidth of l .The received signal is amplified by the factor of√11 + eiP(CP1)hPm gihPm[12], and is sent todestination node k on subcarrier j. Switching the subcarriers from i to j results in a betterperformance [53]. The received signal at destination node k in the second time slot is givenbynjP(CP2)mPk =√ej;(C;2)R;P gjR;P1+eN;(C;1)S;R gNS;R(√eiP(CP1)hPm gihPmmik + oim)+ ojkP (2.2)where ejP(CP2)mPk and ojk are defined similarly for relay m to destination node k link. We assumethat the noise power on each subcarrier for all of the receivers is the same and is equal toc0l . Based on (2.2), the signal-to-noise ratio of the cooperative link is calculated asΓiPjP(C)mPk =ihPmeiP(CP1)hPm jmPkejP(CP2)mPk1 + ihPmeiP(CP1)hPm + jmPkejP(CP2)mPkP (2.3)where we define ihPm = gihPmR(c0l ) and jmPk = gjmPkR(c0l ). The capacity of the AFcooperative transmission is given bygiPjP(C)mPk =12log2(1 + ΓiPjP(C)mPk )P (2.4)where the factor 12comes from two time slot transmission. At high SNR, (2.3) can beapproximated and capacity can be written asgiPjP(C)mPk =12log2(1 +ihPmeiP(CP1)hPm jmPkejP(CP2)mPkihPmeiP(CP1)hPm + jmPkejP(CP2)mPk)O (2.5)The expression (2.5) under the assumption of high SNR is plausible for the next gener-ation wireless systems, due to multiuser and frequency diversity as well as introducing ap-propriate schedulers [55]-[56], which is used and justified in many works such as [21],[22],[26]152C2C hystem boyeland [57]. In [57], it is proved that even for the low SNR this expression can give result closeto the actual one.For non-cooperative transmission in the first and second time slot, the capacity of thelink from source to relay m over subcarrier i and j is given bygiP(cCP1)m =12log2(1 + ihPmeiP(cCP1)hPm )P (2.6)andgjP(cCP2)m =12log2(1 + jhPmejP(cCP2)hPm )P (2.7)respectively, where eiP(cCP1)hPm and ejP(cCP2)hPm are the transmission power of the source to relaym link in the first and second time slot over subcarrier i and j, respectively. We use thefactor 12in (2.6) and (2.7), because the time of non-cooperative transmission in our systemmodel is half of a complete time of the cooperative transmission.The average of the total capacity in a two time slot period is the sum of the capacity forcooperative and non-cooperative links and is calculated asgi =b∑m=1K∑k=1c∑j=1c∑i=1/iPjmPkgiPjP(C)mPk +b∑m=1c∑i=1iP(1)m giP(cCP1)m +b∑m=1c∑j=1jP(2)m gjP(cCP2)m O (2.8)In (2.8), /iPjmPk, iP(1)m and jP(2)m are indicator variables for subcarrier assignment. If thesource is transmitting to destination node k over subcarrier pairs (iP j) with the assistanceof relay m, /iPjmPk is one, otherwise it is zero. If the source is transmitting data to relay m oversubcarrier i in the first time slot, iP(1)m is one, otherwise it is zero. Similarly jP(2)m is definedfor non-cooperative transmission in the second time slot.Since our goal is to maximize the energy efficiency of the network, we need to estimatethe total power consumed in the system. The total power, consumed in source, relays and indestination nodes, consists of a constant term and a variable term [58]. The constant poweris independent of data transmission, and is consumed by the electronic devices when they162CHC erowlem Formulvtionare turned ON. This constant term is not negligible. Unlike the constant term, the variablepower depends on the data transmission and amplifier efficiency. The average of the totalpower consumed in our system for two successive time slots can be calculated asei = ehC +begC +KeDC+12[ b∑m=1K∑k=1c∑j=1c∑i=1/iPjmPk(ϵeiP(CP1)hPm + ϵejP(CP2)mPk)+ϵb∑m=1c∑i=1iP(1)m eiP(cCP1)hPm + ϵb∑m=1c∑j=1jP(2)m ejP(cCP2)hPm] (2.9)In (2.9), e hC , egC , and eDC are the constant powers consumed by the source node, relay node,and the destination node, respectively. ϵ is amplifier inefficiency constant, which is definedas the reciprocal of power amplifiers efficiency and has value greater than one, i.e., ϵ S 1.GCH erowlzm FormulvtionIn [3], the energy efficiency metric is defined as the ratio of the average of the total capacity,gi given in (2.8) and the average of the total consumed power, ei given by (2.9),energy =gi (eP h)ei (eP h)P (2.10)where e contains all of the power variables, and h contains all of the indicators.Our optimization objective is to maximize the energy efficiency defined in (2.10), subjectto total power constraint considering QoS provisioning for the delay sensitive nodes. Theproblem is joint optimization of power allocation, subcarrier assignment, subcarrier pairing172CHC erowlem Formulvtionand relay selection. The optimization problem can be formulated asmaximizeePhgi (eP h)ei (eP h)subject to :X1 : /iPjmPkP iP(1)m P jP(2)m ∈{0P 1}P ∀kPmP iP jX2 :b∑m=1K∑k=1c∑j=1/iPjmPk +b∑m=1iP(1)m = 1P ∀iX3 :b∑m=1K∑k=1c∑i=1/iPjmPk +b∑m=1jP(2)m = 1P ∀jX4 :b∑m=1K∑k=1c∑j=1c∑i=1/iPjmPk(eiP(CP1)hPm + ejP(CP2)mPk )+b∑m=1c∑i=1iP(1)m eiP(cCP1)hPm +b∑m=1c∑j=1jP(2)m ejP(cCP2)hPm ≤ emaxX5 : eiP(CP1)hPm P ejP(CP2)mPk P eiP(cCP1)hPm P ejP(cCP2)hPm ≥ 0P ∀kPmP iP jX6 :c∑i=1iP(1)m giP(cCP1)m +c∑j=1jP(2)m gjP(cCP2)m ≥ g(cC)Pminm P ∀m ∈b1X7 :b∑m=1c∑j=1c∑i=1/iPjmPkgiPjP(C)mPk ≥ g(C)Pmink P ∀k ∈ K1(2.11)In (2.11), X1 is an integer constraint which shows that the indicators for subcarrierassignment are binary variables. X2 and X3 are the orthogonality constraints which restricteach subcarrier to be used at most once in each time slot in order to avoid interference. X4 is ajoint power constraint with total maximum power emax. Ideally, the nodes have independentpower supplies for which individual transmit power constraints should be used. Unlike thesingle-carrier networks, individual power constraints for each node in OFDMA networksbecome coupled together and also with the orthogonality constraints due to the integervariables, which is common in all the constraints. These couplings make the convergenceof the dual decomposition algorithm (which will be discussed later) very tricky. Therefore,to obtain globally optimal solution with faster convergence and useful insight of the totalpower consumption of the system, we consider a joint power constraint. X5 is the non-negative power constraint. X6 and X7 are the QoS constraints, where the system needs tosatisfy specific data rate requirements for the delay sensitive nodes, b1 in relay nodes and182C4C holution ApprovxhK1 in destination nodes, respectively.In general, the problem can become infeasible when emax is not enough to satisfy the QoSconstraints. To overcome this problem, admission control techniques can be used, which arebeyond the scope of this chapter. In the following, we provide the solution approach assumingthat the problem is feasible.GCI holution ApprovxhThe optimization problem in (2.11) is a mixed-integer nonlinear program, which means thatthe feasible set of the problem has both nonlinear and discrete forms. The difficulty of theproblem arises mainly due to the coupled integer and continuous variables with nonlinearfunctions. Different methods like branch-and-bound, outer approximation and generalizedBender’s decomposition have been proposed to tackle MINLP [51]. The drawbacks of thesemethods are that they are effective only for small size problems. For example, in branch-and-bound method, the complexity increases exponentially as the problem size increases.In order to avoid the high complexity of the MINLP problems, we will first reformulateour problem to a more tractable one, such that it can be solved efficiently in polynomialtime complexity. The major concern for solving optimization problem in (2.11) is the inte-ger variables and constraints. We relax the optimization problem by replacing the binarysubcarrier assignment variables with continuous ones. However, the relaxed problem is stillnon-convex; therefore, we define new auxiliary variables to make the feasible set convex,the numerator and denominator of the objective function concave and affine, respectively.To tackle the fractional objective function, we then introduce an iterative algorithm namedDinkelbach [59]. In each iteration of the Dinkelbach algorithm, we solve a convex opti-mization problem via dual decomposition technique. Although we solve the relaxed integerproblem, we prove that our solution is optimal with integer values.The details of our proposed scheme are given in the following.192C4C holution ApprovxhAs mentioned before, the first step is to relax the binary subcarrier assignment variables,/iPjmPk , iP(1)m and jP(2)m to continuous variables in [0P 1] interval.The next step is to define auxiliary power variables e˜ ={e˜iP(CP1)hPm P e˜jP(CP2)mPk P e˜iP(cCP1)hPm P e˜jP(cCP2)hPm}ase˜iP(CP1)hPm = /iPjmPkeiP(CP1)hPm ; e˜jP(CP2)mPk = /iPjmPkejP(CP2)mPk ;e˜iP(cCP1)hPm = iP(1)m eiP(cCP1)hPm ; e˜jP(cCP2)hPm = jP(2)m ejP(cCP2)hPm O(2.12)After substituting the original power variables (e ) by auxiliary power variables (e˜ ), therelaxed optimization problem can be formulated as (2.13).maximizeee Phg˜i (e˜ P h)e˜i (e˜ P h)subject to :X˜1 : 0 ≤ /iPjmPkP iP(1)m P jP(2)m ≤ 1P ∀kPmP iP jX˜2 :b∑m=1K∑k=1c∑j=1/iPjmPk +b∑m=1iP(1)m ≤ 1P ∀iX˜3 :b∑m=1K∑k=1c∑i=1/iPjmPk +b∑m=1jP(2)m ≤ 1P ∀jX˜4 :b∑m=1K∑k=1c∑j=1c∑i=1(e˜iP(CP1)hPm + e˜jP(CP2)mPk )+b∑m=1c∑i=1e˜iP(cCP1)hPm +b∑m=1c∑j=1e˜jP(cCP2)hPm ≤ emaxX˜5 : e˜iP(CP1)hPm e˜jP(CP2)mPk P e˜iP(cCP1)hPm P e˜jP(cCP2)hPm ≥ 0P ∀kPmP iP jX˜6 :c∑i=1iP(1)m g˜iP(cCP1)m +c∑j=1jP(2)m g˜jP(cCP2)m ≥ g(cC)Pminm P ∀m ∈b1X˜7 :b∑m=1c∑j=1c∑i=1/iPjmPkg˜iPjP(C)mPk ≥ g(C)Pmink P ∀k ∈ K1(2.13)where g˜i and e˜i are the auxiliary total rate and power variables obtained by replacinge by e˜ Rh. For example, g˜iPjP(C)mPk is obtained asg˜iPjP(C)mPk =12log2(1 +ihPme˜iP(CP1)hPm jmPke˜jP(CP2)mPk/iPjmPk(ihPme˜iP(CP1)hPm + jmPke˜jP(CP2)mPk ))(2.14)Similarly, g˜iP(cCP1)m and g˜jP(cCP2)m are defined.202C4C holution ApprovxhThe new auxiliary rate and power variables make the relaxed problem more tractable.It can be easily shown that g˜i is concave, e˜i is affine, and the feasible set that reflectsthe constraints of the new problem is convex. Such properties, which did not exist beforeintroducing the new auxiliary variables, enable us to use an effective method to solve theproblem with fractional objective function.The optimization problem (2.13) has a fractional objective function and a convex feasibleset. In this part, we will show how to solve this type of problems efficiently.To tackle the fractional objective function of (2.13), we use the following theorem.ihzorzm F: Suppose C is the feasible set due to X˜1-X˜7, then there exists maximumenergy efficiency q∗ such thatq∗ =g˜i (e˜∗P h∗)e˜i (e˜ ∗P h∗)= max( ee Ph)∈Cg˜i (e˜ P h)e˜i (e˜ P h)P (2.15)if and only ifmax( ee Ph)∈C{g˜i (e˜ P h)− q∗e˜i (e˜ P h)}= g˜i (e˜∗P h∗)− q∗e˜i (e˜ ∗P h∗) = 0P(2.16)where (e˜ ∗P h∗) reflects the optimal power and subcarrier allocation solution.The proof of the theorem can be obtained similar to the proof given in [59]. The abovetheorem states that there exists an equivalent non-fractional form for the fractional objectivefunction.To find the optimal solution of the problem (2.13), an iterative algorithm known as“Dinkelbach method” can be used, which is given in the following.212C4C holution ApprovxhAlgorithm F : Dinkelbach methodgzquirzO  S 0 , q0 = 0 , i = 0 S 0 : maximum tolerance allowed for convergenceqi: Dinkelbach parameteri = 0: iteration indexfihilz qi − qi−1 S  yoSolve problem Probi :(e˜ ∗P h∗) = argmax ee Ph g˜i (e˜ P h)− qie˜i (e˜ P h)subject to: X˜1-X˜7.i = i+ 1 ;qi =g˜i (e˜∗P h∗)e˜i (e˜ ∗P h∗);zny fihilzrzturn e˜ ∗P h∗According toAlgorithm F, in each iteration i of the Dinkelbach method, an optimizationproblem should be solved for a given qi. We call this problem Probi. At the same iteration,qi is updated. The algorithm is terminated when qi converges. The convergence proof of thisalgorithm is similar to the proof given in [59].The optimization problem, Probi, is jointly concave with respect to the auxiliary powerand the relaxed subcarrier assignment variables. The proof is given in Appendix A.Since Probi is convex, it can be solved by available convex optimization algorithms [60].The convex problem Probi satisfies Slater’s condition; therefore, strong duality holds, andthe solution to the original problem can be obtained by solving the dual problem. TheLagrangian dual problem of Probi can be formulated asminPP≥0maxee Ph a(PPP e˜ P h)P (2.17)where the partial Lagrangian is defined in equation (2.18) for a given qi.222C4C holution Approvxha(PPP e˜ P h) = g˜i − qie˜i+(emax −b∑m=1K∑k=1c∑j=1c∑i=1(e˜iP(CP1)hPm + e˜jP(CP2)mPk )−b∑m=1c∑i=1e˜iP(cCP1)hPm −b∑m=1c∑j=1e˜jP(cCP2)hPm)+b∑m=1,m(∑ci=1 iP(1)m g˜iP(cCP1)m +c∑j=1jP(2)m g˜jP(cCP2)m −g(cC)Pminm)+K∑k=1k(b∑m=1c∑j=1c∑i=1/iPjmPkg˜iPjP(C)mPk −g(C)Pmink)(2.18)In (2.18), ,  = [1P 2P OOOP kP OOOP K ] and  = [,1P ,2P OOOP ,mP OOOP ,b ] are the non-negativeLagrange multipliers associated with X˜4, X˜6 and X˜7, respectively. We have set the minimumrate requirement to zero for non-delay sensitive nodes. The constraints X˜1, X˜2, X˜3 and X˜5,which are not considered in the partial Lagrangian, will be satisfied later.The dual problem given in (2.17) can be solved by the dual decomposition technique,which is iterative and in each iteration some subproblems and a master problem are solved.We start with an initial value for Lagrange multipliers. The subproblems find the optimalpower and subcarrier assignment variables for given Lagrange multipliers. Then the masterproblem updates the multipliers. This process is continued until the desired convergence isachieved. The details of the method to solve the dual problem are given in the following.holving suwprowlzmsIn each iteration t of the dual decomposition method, we can obtain all of the powervariables(e˜ ) and the indicators h given the Lagrange multipliers PP by solving the max-imization part of dual problem (2.17) asmaxee Ph a(PPP e˜ P h)P (2.19)232C4C holution Approvxhwhich can be reformulated as a two step maximization problem asmaxhmaxee a(PPP e˜ P h)O (2.20)We first focus on the maximization problem over power variables, i.e., maxee a(PPP e˜ P h),and we find the auxiliary power variables as a function of the indicators using KKT (Karush-Kuhn-Tucker) conditions [60]. KKT conditions state that the gradient is equal to zero atthe optimal points; therefore, we can write@a(PPP e˜ P h)@e˜iP(CP1)hPm| ee N;(C;1)S;R = ee N;(C;1)S;R = 0P (2.21)@a(PPP e˜ P h)@e˜jP(CP2)mPk| ee j;(C;2)R;P = ee j;(C;2)R;P = 0P (2.22)@a(PPP e˜ P h)@e˜iP(cCP1)hPm| ee N;(NC;1)S;R = ee N;(NC;1)S;R = 0P (2.23)@a(PPP e˜ P h)e˜jP(cCP2)hPm| ee j;(NC;2)S;R = ee j;(NC;2)S;R = 0O (2.24)The optimal auxiliary power variables as a function of the indicators and for the givenmultipliers in each iteration of the dual decomposition technique, have the following expres-sionse˜iP(CP1)∗hPm = /iPjmPk[(1+P)jR;Px2ln(2)(NS;R+xjR;P)(+12qNϵ)− (NS;R+xjR;P)xNS;RjR;P]+P (2.25)e˜jP(CP2)∗mPk = xOe˜iP(CP1)∗hPm P (2.26)242C4C holution Approvxhx =√ihPmjmPkP (2.27)e˜iP(cCP1)∗hPm = iP(1)m[(1 + ,m)2ln(2)(+ 12qiϵ)− 1ihPm]+P (2.28)e˜jP(cCP2)∗hPm = jP(2)m[(1 + ,m)2ln(2)(+ 12qiϵ)− 1jhPm]+O (2.29)The details of the derivation of (2.25)-(2.29) are given in Appendix B. While deriving,we have taken into account the non-negative power constraint given in X˜5, which was notconsidered in the partial Lagrangian by using [x]+ = max(0P x) notation.Once we have obtained the optimal auxiliary power variables as a function of the in-dicators, we can find the optimal subcarrier allocation policy, h. First, we plug optimalauxiliary power variables derived in (2.25)-(2.29) into equation (2.20). By rearranging, wecan show that the maximization problem (2.20) becomes a linear program with respect tothe indicator variables, i.e., /iPjmPk , iP(1)m and jP(2)m . Besides, we incorporate the constraints X˜1, X˜2 and X˜3 which were not considered before in the partial Lagrangian. After rearranging,(2.20) can be written asmaximizehb∑m=1K∑k=1c∑j=1c∑i=1/iPjmPkHiPjP(C)mPk +b∑m=1c∑i=1iP(1)m HiP(cCP1)m +b∑m=1c∑j=1jP(2)m HjP(cCP2)m+emax −K∑k=1kg(C)Pmink −b∑m=1,mg(cC)Pminm −qi(ehC +begC +KeDC )subject to : X˜1P X˜2 and X˜3(2.30)where HiPjP(C)mPk , HiP(cCP1)m and HjP(cCP2)m are given by252C4C holution ApprovxhHiPjP(C)mPk = (1 + k)giPjP(C)∗mPk − (+ 12qiϵ)e iP(CP1)∗hPm −(+ 12qiϵ)ejP(CP2)∗mPk PHiP(cCP1)m = (1 + ,m)giP(cCP1)∗m − (+ 12qiϵ)e iP(cCP1)∗hPm PHjP(cCP2)m = (1 + ,m)gjP(cCP2)∗m − (+ 12qiϵ)e jP(cCP2)∗hPm O(2.31)The linear program in (2.30) can be categorized as a modified “linear assignment prob-lem” [61]. The above formulation allows us to take non-integer values for /iPjmPk , iP(1)m andjP(2)m . However, we prove that the optimal solution of the relaxed problem has always integervalues if certain conditions are satisfied.ihzorzm G: A linear program with constraint Ax = b always has an integer optimalsolution if the constraint matrix A is totally unimodular and vector b is integer [62].The definition for totally unimodularity is given as follows.Dznition F : Matrix A with full row rank, is totally unimodular, if all entries are integerand each square sub-matrix of A has determinant ±1 or 0.In general it is not easy to show that a matrix is totally unimodular. In Appendix C,the totally unimodularity of the constraint matrix of linear program in (2.30) is proven.Therefore, we can conclude that the linear problem in (2.30) has an integer optimal solution.In the following, we solve the linear problem to obtain the optimal solution of the subcar-rier assignment policy h. Since the constraints X˜2 and X˜3 are not coupled with coordinatesm and k , we can simply maximize over m and k as given in hiEe F and hiEe G.The constraints X˜2 and X˜3 imply that firstly, only one of the cooperative or non-cooperativemodes can be used over each subcarrier pair, which is taken into account in hiEe H and sec-ondly, each subcarrier can be used only once in each time slot in order to avoid interference,which is incorporated in hiEe I. The detailed procedure is given in the following.hiEe FO For a cooperative transmission over each subcarrier pair (iP j), we find the bestrelay and best destination node using the following expression262C4C holution Approvxh(m∗1(iP j)P k∗(iP j)) = maxmPkHiPjP(C)mPk P ∀iP j (2.32)hiEe GO In addition, for a non-cooperative transmission over each subcarrier, we findthe best node from the relays for the first and second time slot respectively, using thefollowing expressionsm∗2(i) = maxmH iP(cCP1)m P ∀im∗3(j) = maxmHjP(cCP2)m O ∀j (2.33)hiEe HO We need to determine whether cooperative or non-cooperative mode is betterfor a subcarrier pair (iP j). If the following conditionHiPjP(C)m1(iPj)Pk(iPj)S HiP(cCP1)m2(i)+HjP(cCP2)m3(j)(2.34)holds, then it is better to use cooperative mode over subcarrier (iP j) than non-cooperativemode. The best destination node and relay are given by k∗(iP j) and m∗1(iP j) which can beobtained from equation (2.32). On the other hand, ifHiPjP(C)m1(iPj)Pk(iPj)Q HiP(cCP1)m2(i)+HjP(cCP2)m3(j)(2.35)then the non-cooperative mode is better for subcarrier pair (iP j). The nodes from relaysthat receive data on subcarrier i in the first time slot and subcarrier j in the second timeslot are m∗2(i) and m∗3(j), respectively, which can be obtained from (2.33).If both sides of (2.34) are equal, we randomly pick one of the above modes.hiEe IO In the previous steps, we have determined which transmission mode (cooper-ative or non-cooperative) should be used for subcarrier pair (iP j), and also which nodes are272C4C holution Approvxhselected for this transmission.In order to obtain which subcarriers should be paired, we form an c × c matrix A =[a(iP j)], such that if (2.34) holds, a(iP j) = HiPjP(C)m1(iPj)Pk(iPj). Otherwise if (2.35) holds, a(iP j) =HiP(cCP1)m2(i)+HjP(cCP2)m3(j).In addition, we save the information about the transmission mode and correspondingnodes in another matrix, W = [b(iP j)], such that if (2.34) holds, b(iP j) = (XPm∗1(iP j)P k∗(iP j)),which states that this is a cooperative mode with corresponding destination k∗(iP j) andrelay m∗1(iP j). Otherwise, if (2.35) holds, b(iP j) = (cXPm∗2(i)Pm∗3(j)), which states that anon-cooperative mode is selected for communication over subcarrier pair (iP j) with nodesm∗2(i) and m∗3(j) (from relays) receiving their own data in the first and second time slot,respectively.Next, we apply Hungarian method [61] on matrix A to find the subcarrier pairing. Hun-garian method is used to find the optimal solution for linear assignment problems with thecomplexity of d(c3). Using Hungarian method, we guarantee that each subcarrier is usedonly once in each time slot.We denote the result of Hungarian method as j(i)P ∀i, i.e., subcarrier j in the secondtime slot is paired by subcarrier i in the first time slot. Let us assume that all resourceallocation indicators h are initialized by zero. For subcarrier i in the first time slot, if thecorresponding entry b(iP j(i)) in matrix W states that it is a cooperative mode, then we set/iPj(i)k(iPj(i))Pm1(iPj(i))= 1; otherwise it is a non-cooperative mode and iP(1)m2(i)= 1 and j(i)P(2)m3(j(i))= 1.holving thz mvstzr prowlzmIn the master problem of the dual decomposition technique, we use the sub-gradient method [63]to update the Lagrange multipliers, which is given in (2.36)-(2.38), where 1(t) , 2(t) and3(t) are the step sizes, and t is the index of the iterations. Positive constant step sizeparameters are used which are optimized to obtain fast convergence rate. The convergenceproof of the sub-gradient method for constant step size is given in [64].282C4C holution Approvxh(t+ 1) =[(t)− 1(t)(emax −b∑m=1K∑k=1c∑j=1c∑i=1(e˜iP(CP1)hPm + e˜jP(CP2)mPk )−b∑m=1c∑i=1e˜iP(cCP1)hPm −b∑m=1c∑j=1e˜jP(cCP2)hPm)]+ (2.36),m(t+ 1) =[,m(t)− 2(t)(c∑i=1iP(1)m g˜iP(cCP1)m +c∑j=1jP(2)m g˜jP(cCP2)m −g(cC)Pminm)]+P ∀m ∈b(2.37)k(t+ 1) =[k(t)− 3(t)(b∑m=1c∑j=1c∑i=1/iPjmPkg˜iPjP(C)mPk −g(C)Pmink)]+P ∀k ∈ K(2.38)In this section, we have proposed a novel scheme that optimally allocates the resourcesto a cooperative OFDMA system while maximizing the energy efficiency taking into accountthe data rate requirements. The procedure is summarized in Fig. 2.2.The complexity of the proposed scheme in each iteration of the dual decomposition tech-nique is dominated by the subcarrier allocation algorithm and is given by d(bKc2 +c3).Therefore, the overall complexity of our proposed algorithm isd (IyualIDinkelbaxh(bKc2 +c3)),where Iyual and IDinkelbaxh is the number of iterations required for convergence of dual de-composition technique and Dinkelbach method, respectively. Considering the number ofnodes, i.e., b and K are in the order of d(√c), then the overall complexity becomesd(IyualIDinkelbaxhc3). The optimal solution obtained by exhaustive search approach has acomplexity of the order d(2bKc2+2bc), which is significantly higher than our proposedscheme.292C4C holution Approvxhq0=0 : Initialize Dinkelbachmethod’s parameter Initialize LagrangianmultipliersSolve sub-problems to find optimal resource allocation for given multipliers Convergence Solve the master Nodual decomposition technique of multipliers?Update qi according to Dinkelbach methodConvergence of Dinkelbachmethod?problem to update the multipliersOptimal resource allocationYesYesNoFigure 2.2: Flowchart that summarizes our proposed iterative algorithm302CJC cumerixvl gesultsGCJ cumzrixvl gzsultsIn this section, we conduct extensive simulation to evaluate the performance of our proposedresource allocation algorithm. We compare our proposed energy efficiency maximizationscheme with other existing schemes in the literature and demonstrate the effectiveness ofour method.We consider a circular area where the source node is located in its center. The relay anddestination nodes are randomly located inside this area with uniform distribution. There isa ring shape inner boundary. The radii of the outer and inner boundaries are 1 km and 0.5km, respectively. The relays are assumed to be in the inner boundary, while the destinationnodes are distributed between the inner and the outer boundary.The channel coefficients are independent and identically distributed (i.i.d.) circularlysymmetric complex Gaussian random variables.Unless stated elsewhere, one user from each group (relay group and destination group)is delay sensitive with gmin = 1 Mbits/sec, and the number of subcarriers is set as c = 16.Simulation parameters are summerized in Table 2.1.Table 2.1: Simulation parametershimulation parameter kaluehuwxvrrizr wvnyfiiyth 2E KHzcoisz pofizr spzxtrvl yznsity =c0) BFLI yWm/Hzevth loss xozffixiznt =) Ihtvtix pofizr xonsumption FEElZffixiznxy of thz pofizr vmplizrs for thz sourxz HM:cumwzr of xhvnnzl rzvlizvtions FEEEFig. 2.3 illustrates the average energy efficiency for different number of nodes versus theiteration indices of Dinkelbach algorithm for emax = 55 dBm. As shown in this figure, thealgorithm converges only in 4 iterations. We can also observe that the number of iterationsrequired for convergence is independent of the number of nodes which confirms the scalabilityof our proposed scheme.312CJC cumerixvl gesults1 2 3 4 5 6 7 8 9 1000.050.10.150.20.250.30.350.40.45I te rat i on indexAverageenergyefficiency[bits/Joule/Hz]  (M,K)=(2, 2)(M,K)=(8, 8)Figure 2.3: Convergence of Dinkelbach methodFig. 2.4 depicts the average of energy efficiency versus the iteration indices of the dualdecomposition technique for (M,K)=(8,8). This figure illustrates the convergence speed ofthe dual decomposition method. As mentioned before, in each iteration i of the Dinkel-bach method a convex optimization problem (Probi) is solved. This figure illustrates theconvergence for the first iteration of Dinkelbach method. Other iterations have a similarconvergence speed. As shown in the figure the dual decomposition method converges within50 iterations.Figs. 2.5 and 2.6 depict the average of total capacity and energy efficiency of the system,respectively versus the maximum of allowed total transmit power emax for different numberof nodes. The figures compare the performance of our proposed energy efficiency maximiza-tion scheme with the capacity maximization scheme. In Fig. 2.5, we see that the averagetotal capacity of the system increases with emax for the capacity maximization scheme. How-ever, for the energy efficiency maximization scheme the average total capacity of the systemincreases with emax upto a certain power level, i.e., emax = 35 dBm and after that it remainsconstant. In Fig. 2.6, we see that the energy efficiency of the capacity maximization scheme322CJC cumerixvl gesults10 20 30 40 50 60 70 80 90 1000.10.150.20.250.30.350.40.450.5I te rat i on indexAverageenergyefficiency[bits/Joule/Hz]Pmax=45dBmPmax=35dBmPmax=50dBmFigure 2.4: Convergence of the dual decomposition techniquedecreases rapidly when the maximum total allowed transmit power is high. In the energyefficiency maximization scheme, the energy efficiency is a non-decreasing function of emax.When the maximum available power is high, only a part of it is used in order to keep theenergy efficiency at its optimal point. The total power constraint X4 is not active for highemax for the proposed energy maximization scheme. We see that both the energy efficiencyand total capacity curves saturate at emax = 35 dBm. With the increase of the number ofnodes, both the average energy efficiency and total capacity increase due to the multiuserdiversity.In Fig. 2.7, the average system capacity versus the number of subcarriers c is shown fordifferent emax for capacity maximization scheme. As expected, the total system capacityincreases with the increase of the number of subcarriers. For example, with emax = 30 dBm,increasing the number of subcarriers from 16 to 32 and from 16 to 256 improves the averagesystem capacity by approximately 1O5× 107 bits/sec and 2O18× 108 bits/sec, respectively.In Fig. 2.8, we compare the performance of our proposed method with other resourceallocation schemes for (M,K)=(8,8). First we compare our proposed scheme with [54] that332CJC cumerixvl gesults0 10 20 30 40 50 6011.11.21.31.41.51.61.71.81.9x 107Pmax (dBm)Averagesystemcapacity[bits/sec]  Capac i ty max . (M,K)=(2, 2)Capac i ty max . (M,K)=(4, 4)Capac i ty max . (M,K)=(8, 8)EE max . (M,K)=(2, 2)EE max . (M,K)=(4, 4)EE max . (M,K)=(8, 8)Figure 2.5: Average system capacity versus emax for different number of nodes15 20 25 30 35 40 45 500.20.250.30.350.40.45Pmax (dBm)Averageenergyefficiency[bits/Joule/Hz]  Capac i ty max . (M,K)=(2, 2)Capac i ty max . (M,K)=(4, 4)Capac i ty max . (M,K)=(8, 8)EE max . (M,K)=(2, 2)EE max . (M,K)=(4, 4)EE max . (M,K)=(8, 8)Figure 2.6: Average energy efficiency versus emax for different number of nodes342CJC cumerixvl gesults16 32 64 128 25600.511.522.53x 108Number of sub carr i e rs (N )Averagesystemcapacity[bits/sec]  Pmax= 10 dBmPmax= 20 dBmPmax= 30 dBmPmax= 40 dBmPmax= 50 dBmFigure 2.7: Average system capacity versus the number of subcarriers for different emaxconsiders optimal resource allocation but assumes that same subcarriers are used in bothhops of cooperative transmission. Then, we compare our proposed scheme with the schemeproposed in [26], which do not consider subcarrier pairing and relay selection, i.e., in co-operative mode, the relays are assigned to destinations before the transmission is started.The figure shows that the proposed method outperforms both the existing schemes. Ourproposed scheme can obtain a reasonable performance gain compared to the no-pairing [54],and no-selection no-pairing [26] methods.In Fig. 2.9, our scheme is compared with the method that does not consider QoS provi-sioning for emax = 25 dBm and (M,K)=(4,2). As shown in the figure, our proposed optimalscheme satisfies the minimum rate requirements. However, for the schemes with relaxed QoSconstraints, the data rate requirements are not satisfied for some of the nodes.Fig. 2.10, shows the probability of infeasible realizations versus minimum rate require-ment gmin for our proposed algorithm. The probability that the problem is infeasible isdepicted for different emax values. For higher values of gmin, the power budget becomesinsufficient to meet the required QoS and probability of infeasibility increases. In addition,352CJC cumerixvl gesults15 20 25 30 35 401.21.251.31.351.41.451.5x 107Pmax (dBm)Averagesystemcapacity[bits/sec]  Optimalno pairingno pairing−no relay selectionFigure 2.8: Performance comparison of our proposed scheme with schemes that do notconsider pairing and relay selectionk1 k2 m1 m2 m3 m400.511.522.533.54x 106Use r i ndexAveragecapacity[bits/sec]  Minimum rate requi rement of use rOptimalUnconstrai ntedFigure 2.9: QoS provisioning for different nodes comparing to the schemes with relaxed QoSconstraints362CJC cumerixvl gesults2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.7500.10.20.30.40.50.60.70.80.91Rm in (Mbi ts/se c )ProbabilityofinfeasiblerealizationsPmax=0dBmPmax=20dBmPmax=10dBmPmax=30dBmPmax=40dBmPmax=50dBmPmax=60dBmFigure 2.10: Probability of infeasible realizationsas emax becomes larger, the problem becomes feasible for wider range of gmin. We selectedgmin = 1 or 2 Mbits/sec as our simulation parameter which is in the feasible region for theselected power budget.In Figs. 2.11 and 2.12, we show both the system capacity and energy efficiency versusthe maximum total allowed transmit power for two different QoS requirement scenarios for(M,K)=(8,8). As shown in the figures, both system capacity and energy efficiency decreasewith the increase of the data rate requirement. This result is not surprising because thesystem with a lower QoS requirement, i.e., gmin = 1 Mbits/sec is more relaxed and flexiblethan that with a higher QoS requirement of gmin = 2 Mbits/sec. The performance ofthe scheme with specific QoS constraints are upper bounded by the scheme with no QoSrequirements.372CJC cumerixvl gesults0 10 20 30 40 50 6011.21.41.61.822.22.4x 107Pmax (dBm)Averagesystemcapacity[bits/sec]  Re laxed QoS constrai nts , Capac i ty max .Rm in= 1 Mbi ts/se c , Capac i ty max .Rm in= 2 Mbi ts/se c , Capac i ty max .Re l ax ed QoS constrai nts , EE max .Rm in= 1 Mbi ts/se c , EE max .Rm in= 2 Mbi ts/se c , EE max .Figure 2.11: Average system capacity versus emax for different data rate requirements0 10 20 30 40 50 6000.050.10.150.20.250.30.350.40.450.5Pmax (dBm)Averageenergyefficiency[bits/Joule/Hz]  Re laxed QoS constrai nts , Capac i ty max .Rm in= 1 Mbi ts/se c , Capac i ty max .Rm in= 2 Mbi ts/se c , Capac i ty max .Re l ax ed QoS constrai nts , EE max .Rm in= 1 Mbi ts/se c , EE max .Rm in= 2 Mbi ts/se c , EE max .Figure 2.12: Average energy efficiency versus emax for different data rate requirements38Xhvptzr Hgzsourxz Alloxvtion for DGD gzlvyingXommunixvtion hystzmsIn this chapter, we investigate challenges in resource allocation problem for device-to-devicerelaying communication systems. The accomplished works and research contributions of thischapter are briefly described in the following.HCF Axxomplishzy lorks vny gzszvrxh XontriwutionsIn this chapter, we focus on challenges in design and resource allocation of D2D relayingcommunication systems. Frequency reuse in D2D communication networks can significantlyimprove the system performance. However, efficient schemes for reusing the channel resourcesare required to mitigate interference. Therefore, in section 3.2, we investigate resource al-location problem for downlink transmission in OFDMA-based D2D relaying networks. Wedevelop efficient algorithms to solve the problem of subcarrier allocation such that the sys-tem capacity is maximized. Since D2D is a short-distance based communication technology,sufficiently separated D2D links can simultaneously operate on the same frequency band,thereby facilitating dense spectral reuse across the network. We first classify the D2D pairsbased on the level of proximity with each other and propose different scenarios of downlinkcommunications. For each scenario the possibility of frequency reuse is discussed and anefficient frequency allocation technique is proposed. Another important challenge in D2Drelaying systems is designing low complexity and distributed resource allocation techniques.39HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geuseTherefore, in this section 3.3, we propose distributed subcarrier allocation and relay selec-tion for OFDM based cooperative systems. Our objective is to maximize the throughputof the network using minimal CSI feedback. Due to high signaling overhead and processingcomplexity of the optimal centralized solution, we propose two suboptimal distributed algo-rithms scalable and suitable for practical implementation. The first proposed algorithm isbased on Hungarian method and is efficient in terms of signaling overhead. The performanceof this algorithm is extremely close to the optimal solution for large number of subcarriers.To reduce the computational complexity and signaling overhead further, we propose anothernovel distributed algorithm. The signaling overhead becomes insignificant for this algorithmcompared to the other schemes at the expense of a small degradation in performance.The remainder of this chapter is organized as follows. In section 3.2, we study resourceallocation for D2D relaying systems considering frequency reuse. In section 3.3, low com-plexity and distributed resource allocation for cooperative systems is discussed. In both ofthe sections, the corresponding system model, problem formulation, solution approach andnumerical results are presented.HCG gzsourxz Alloxvtion for DGD gzlvying hystzmsfiith Frzquznxy gzuszIn this section, we study resource allocation problem for D2D relaying communication sys-tems with frequency reuse at D2D communication links.HCGCF hystzm boyzlWe consider the scenario in which BS cannot communicate with the destination UE due toheavy obstructions or shadowing as shown in Fig. 3.1 . Our goal is to establish indirect com-munication links between the BS and the UEs which are blocked from direct communication40HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geuseBSD2D CommunicationAssistedDLULRelay UEDestination UENetwork BlockageFigure 3.1: System model for cellular wireless systems with cooperative D2D communication.UEs with strong communication links from the BS can send/receive data directly from theBS. However, UEs with bad communications links from the BS (for example, due to networkblockage) can benefit from D2D communication with relay UEs to send/receive the datafrom the BS.41HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geusewith the BS. In this regard, some other UEs with fair connection to the BS can assist asrelays.Let us assume that all the mobile UEs which can directly communicate with the BSare interested in relaying. However, we opportunistically select few UEs for relaying basedon the performance gains they can offer to the system. The important fact in the D2Dcommunication is that the UEs can only communicate within short distances. Therefore,the relay-UEs (also referred to as relays interchangeably) and the UEs in coverage holes(also referred to as destination-UEs, interchangeably) must be in the coverage area of eachother. Also, to make the problem general, we assume that the destination-UEs can receiveassistance from multiple relays. Let c orthogonal subcarriers, each with bandwidth l beavailable for resource allocation in the system. Let K be the number of destination-UEs, i.e.,UEs requiring relay assistance. Further, let us denote the BS, relay-UEs and destination-UEsas B,R, and U, respectively. The set of the relays which can assist the kth UE is denotedby gk. The channel gain and the transmission power from the BS to relay mk ∈ gk oversubcarrier i at time slot t are denoted by gWPgkPmPPiPt and eWPgkPmPPiPt, respectively. Similarly, thechannel gain from relay mk ∈ gk to the kth UE over subcarrier j at time slot t is denotedby ggPjkPmPPjPt. The transmission power of any relay in the candidate set, i.e., gkP∀k, over anysubcarrier, i.e., ∀i ∈ {1P 2P O O O c}, is the same fixed value denoted by eg. We implement thepopular AF protocol for relaying.Specifically, we investigate D2D relaying for downlink transmission in OFDMA cellularnetworks. We first classify the D2D pairs based on the level of proximity with each other.Firstly, we consider a scenario where all the D2D pairs are very close to each other andtheir coverage areas overlap. In this case, since reusing the subcarriers among the D2D pairswill introduce significant interference to the D2D links, we do not attempt subcarrier reuseamong the D2D pairs. Next, we consider a scenario where the D2D pairs are far enoughfrom each other, and therefore their coverage areas are disjoint. In this case, full subcarrierreuse can be attempted with the help of buffer-aided relaying in all of the D2D pairs. We42HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geusediscuss relevant resource allocation problems and analyze the throughput gains achievablein both of the above scenarios. Later, we provide a general motivation on how frequencyreuse can be attempted for a general scenario where D2D pairs are randomly distributed ina cell, i.e., the two aforementioned scenarios co-exist simultaneously within the cell.HCGCG DGD gzlvying fiithout Frzquznxy gzuszWe start with the first case in which all the D2D pairs are close to each other and theircoverage areas overlap. As a result, frequency reuse may introduce excessive interference intothe system. Note that, due to indirect communication via relaying, downlink transmissionfrom the BS to a given destination-UE happens over two-time-slot intervals. During thefirst time slot, the BS transmits information to a relay-UE. This information is relayed bythe relay-UE to the destination-UE during the second time slot. We also assume that eachrelay-UE has a unit buffer size, i.e., if all the BS-to-relay transmissions occur in the tth timeslot, all the relay-to-destination-UE transmissions occur in the (t+ 1)th time sot. Under theAF relaying protocol, the achievable throughput gkPmPPi for downlink transmission from theBS to the kth UE via relay mk over subcarrier i is given bygkPmPPi =12log2(1 +eB;RP;RP;NeRgB;RP;RP;NgR;UP;RP;NeB;RP;RP;NgB;RP;RP;N+eRgR;UP;RP;NO 1c0l)P (3.1)where c0 is the noise variance assuming AWGN channels. In this orthogonal transmissioncase, the time index is omitted, e.g., gWPgkPmPPi is used in place of gWPgkPmPPiPt, because we assume theunit buffer size at all the relays. Using (3.1), we formulate the following resource allocation43HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geuseproblem to maximize the sum throughput in the systemmaximizeePhK∑k=1∑mP∈gPc∑i=1skPmPPigkPmPPisubject to :X1 :K∑k=1∑mP∈gPc∑i=1skPmPPieWPgkPmPPi≤ emaxPX2 : skPmPPi ∈{0P 1}P ∀iP kPmkPX3 :K∑k=1∑mP∈gPskPmPPi ≤ 1P ∀iPX4 : eWPgkPmPPi≥ 0P ∀iP kPmkP(3.2)where e = {eWPgkPmPPi} and h = {skPmPPi} denote the power allocation and subcarrier allocationpolicies, respectively.X1 is the power budget constraint with emax being the power budget for the BS. X2 showsthat the subcarrier assignment indicators skPmPPi are binary integer variables. skPmPPi = 1 ifBS is transmitting to the kth UE via relay mk over subcarrier i and skPmPPi = 0 otherwise.X3 ensures that the subcarriers are not reused in each time slot to avoid interference. X4ensures that the power allocation variables are non-negative.In simple terms, our goal in (3.2) is to allocate the BS transmission power and the csubcarriers such that the sum-throughput in the system is maximized. From an optimizationperspective, the problem in (3.2) is MINLP which, as discussed before, is difficult to solve inpolynomial time due to the coupled integer and continuous variables. Therefore, to obtain apolynomial time solution, we attempt a series of mathematical modifications and simplifica-tions. Similar to the solution proposed in the previous chapter, firstly, we relax the integerbinary variables, i.e., the subcarrier assignment indicators skPmPPi) into continuous variablesin the interval [0,1]. Using this relaxation, we introduce auxiliary power variables ase˜WPgkPmPPi = skPmPPieWPgkPmPPiO (3.3)44HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geuseWhen the original power variables in (3.2) are replaced by the auxiliary power vari-ables defined in (3.3), the optimization problem (3.2) is relaxed into the following convexoptimization problemmin≥0maxee Ph a(P e˜ P h)P (3.4)where a is a Lagrangian function and  is the associated Lagrangian multiplier. Therefore,efficient convex optimization algorithms can be used to solve the relaxed problem. The dualdecomposition technique, similar to the one used in previous chapter, can be adopted to solve(3.4) by allowing the master problem to update s and the sub-problems to find optimalpower and subcarrier assignment for a given .We begin with the following definition of the Lagrangian functiona(P e˜ P h) =K∑k=1∑mP∈gPc∑i=1skPmPPi12log2(1 +ePB;RP;RP;NgB;RP;RP;NsP;RP;NN0WeRgR;UP;RP;NePB;RP;RP;NgB;RP;RP;NsP;RP;N+eRgR;UP;RP;N)+(emax −K∑k=1∑mP∈gPc∑i=1e˜WPgkPmPPi)P(3.5)where we consider the power constraint X1 only and initialize the Lagrangian multiplier with a non-negative value. Constraints X2P X3P X4 are not considered in (3.5) but will besatisfied in subsequent steps. By applying KKT conditions to (3.5), we can derive optimalauxiliary power variables e˜ ∗WPgkPmPPiand the corresponding throughput g˜∗kPmPPi in terms of thesubcarrier assignment indicators skPmPPi and the Lagrangian multiplier . In the derivationprocess, constraint X4 can be satisfied by offsetting negative e˜ ∗WPgkPmPPivalues to zero. Pluggingback e˜ ∗WPgkPmPPiand g˜∗kPmPPi into the sub-problem (3.5) and re-arranging the equations, weobtain the simplified problemmaximizehK∑k=1∑mP∈gPc∑i=1skPmPPiHkPmPPi + emaxsubject to : X3P(3.6)45HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geusewhere we haveHkPmPPi = g˜∗kPmPPi − e˜ ∗WPgkPmPPiO (3.7)Upon inspection, one may observe that (3.6) is a linear programming problem [60] withrespect to skPmPPi, i.e., it is a linear subcarrier assignment problem. Applying totally uni-modularity theorem [62] shows that the problem (3.6) has integer optimal values even if theoptimization variables h = {skPmPPi} span over the continuous interval [0,1]. Optimal solutionto the linear subcarrier assignment problem (3.6) can be obtained using simple algorithmssuch as Algorithm 2.Algorithm G : Subcarrier Allocation Algorithm IF: Find the best user-relay pair for each subcarrier as(k∗Pm∗k) = maximizekPmPHkPmPPiP∀i.2: rzturn h∗Note that, constraint X3 can be satisfied while implementing Algorithm 2. Also, sinceAlgorithm 2 yields optimal solutions, constraint X2 is satisfied inherently due to totallyunimodularity theorem. Since the optimal power allocation and subcarrier assignment valuesare now available, the master problem of updating the Lagrange multiplier  can be solvedusing standard sub-gradient methods [63] as follows(l + 1) =[(l)− (emax − K∑k=1∑mP∈gPc∑i=1e˜WPgkPmPPi)]+P (3.8)where  is a constant step size parameter, l is the iteration index.The master problem and the sub-problems are solved iteratively until we observe a con-vergence in the Lagrangian multiplier, i.e., , values. The complexity of the proposed algo-rithm is polynomial in time and is significantly lower than the brute-force exhaustive searchmethod.46HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geuseHCGCH WuffzrBAiyzy DGD gzlvying fiith Frzquznxy gzuszWe now consider the second scenario wherein the D2D pairs are far enough from eachother such that their coverage areas do not overlap. Therefore, frequency reuse can now beattempted to fully utilize the available spectrum. The resource allocation scheme proposedin the previous subsection, i.e., for orthogonal transmission, may not be spectrally efficientfor this system because frequency reuse was not considered. Note that, frequency reuse isnot possible in the first time slot, as the BS is broadcasting the messages. However, inthe second time slot, frequency reuse can be attempted to establish D2D communicationbetween relay-UEs and destination-UEs. To exploit the benefits of frequency reuse, wepropose a communication protocol using buffer-aided relaying.As a motivational example, let us consider a system with two D2D pairs and two subcar-riers. During the first time slot, the BS broadcasts two packets, i.e., one to each relay-UE,over the two subcarriers. During the second time slot, the BS broadcasts another two packetsover the two subcarriers. Therefore, at the end of the second time slot, we have four packetsat the relay-UE buffers, i.e., two packets at each relay-UE. Since the coverage areas of thetwo D2D pairs do not overlap, both the relay-UEs can use the two subcarriers simultaneouslyfor D2D communications. That is, during the third time slot, each relay-UE can forward itstwo packets over the two subcarriers without causing any interference to other relay-UEs.Therefore, using buffer-aided relaying with full frequency reuse, four packets are transmittedto two destination-UEs in three time slots. On the other hand, the orthogonal transmission,i.e., without frequency reuse, scheme discussed previously in Section 3.2.2 requires four timeslots to transfer the same four packets from the BS to the two destination-UEs.To understand the benefits of frequency reuse, we now formulate a resource allocationproblem similar to (3.2) wherein the objective is to maximize the sum throughput in thesystem. Similar to the previous scenario, we have K destination UEs and c subcarriers. Weassume that the BS broadcasts messages to the relay-UEs over i time slots and that therelay-UEs forward these messages to destination-UEs during time slot i + 1. Thereby, the47HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geusefollowing resource allocation problem can be formulated.maximizeePhK∑k=1∑mP∈gPc∑i=1c∑j=1i∑t=1skPmPPiPjPtgkPmPPiPjPtsubject to :X1 :K∑k=1∑mP∈gPc∑i=1c∑j=1skPmPPiPjPteWPgkPmPPiPt≤ emaxP ∀tPX2 : skPmPPiPjPt ∈{0P 1}P ∀iP jP kPmkP tPX3 :K∑k=1∑mP∈gPc∑j=1skPmPPiPjPt ≤ 1P ∀iP tPX4 :i∑t=1∑mP∈gPc∑i=1skPmPPiPjPt ≤ 1P ∀kP jPX5 :i∑t=1∑mP∈gPc∑i=1c∑j=1skPmPPiPjPt ≤ cP ∀kPX6 : eWPgkPmPPiPt≥ 0P ∀iP kPmkP tP(3.9)where e = {eWPgkPmPPiPt} and h = {skPmPPiPjPt} denote the power allocation and subcarrier allo-cation policies, respectively. Here, X1 is the power budget constraint for the BS and emax isthe maximum power budget for the BS. X2 shows that the subcarrier assignment indicatorsskPmPPiPjPt are binary integer variables. skPmPPiPjPt = 1 if the BS is transmitting messages to arelay mk over subcarrier i during time slot t, and the relay mk forwards these messages tothe kth UE over subcarrier j during time slot (i + 1). skPmPPiPjPt = 0 otherwise. X3 impliesthat the BS cannot reuse any subcarrier within a given time slot for broadcasting to avoidinterference. X4 implies that the subcarriers cannot be reused during a given time slot forcommunication within a D2D pair to avoid interference. X5 implies that each relay-UE canhave a buffer length upto c because a maximum of c messages, i.e., using all the c subcar-riers, can be forwarded by a given relay-UE in a given time slot. X6 ensures that the powervariables are non-negative.In simple terms, our goal in (3.9) is to allocate the BS power and assign the c subcarrierssuch that the total system throughput is maximized. The achievable throughput gkPmPPiPjPtfor downlink transmission from BS to UE k, via the relay mk, over subcarrier i and j in the48HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geusetth and (i + 1)th time slots , respectively, is given bygkPmPPiPjPt =1i + 1log2(1 +eB;RP;RP;N;teRgB;RP;RP;N;tgR;UP;RP;j;T+1eB;RP;RP;N;tgB;RP;RP;N;t+eRgR;UP;RP;j;T+1O 1c0l)O (3.10)Similar to the scenario in the previous subsection, the original problem is MINLP. Asthe problem is complex, the optimal approach used previously is not possible. Therefore,we first find the subcarrier assignment policy for equal power allocation. Then, we allocatethe power for the optimal subcarrier allocation. As encountered in the previous solutionapproach, we are required to solve a linear integer programming problem so as to obtainsubcarrier assignment policy. Therefore, we propose Algorithm 3 to solve the subcarrierassignment problem in polynomial time.Algorithm H : Subcarrier Allocation Algorithm IIF: For each subcarrier, find the relay-UE with the best channel gain to each destination-UE:m∗k = maximizemPggPjkPmPPjPi+1P ∀kP j.2: Count the number of subcarriers assigned to each relay-UE and denote it as a(mk).H: for i = 1 : cI: for t = 1 : iJ: For each subcarrier i used by the BS to broadcast messages to the relay-UEs, find theD2D pair with the best channel gain at time slot t:(k∗Pm∗k) = maximizekPmPgWPgkPmPPiPt.K: a(m∗k) = a(m∗k)− 1;L: if a(m∗k) ≥ 0, assignment (iP tP k∗Pm∗k) is valid.zlsz assignment (iP tP k∗Pm∗k) is not valid and relay-UE m∗k is omitted from the relayselection pool.M: znyN: znyFE: For each relay mk, implement an ordered subcarrier pairing [22].FF: rzturn h∗Algorithm 3 begins with finding the best relay-UE for all the subcarriers i used by the BSfor broadcasting messages and all the subcarriers j used by the relay-UEs for forwarding thosemessages. Here, the subcarriers are guaranteed to be used at most once in each broadcastingtime slot, i.e., constraint X3 is satisfied. However, subcarrier reuse is permitted in the secondtime slot because the D2D pairs are far apart and their coverage areas do not overlap, i.e.,49HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geuseconstraint X4 is satisfied. We also ensure that each relay receives and transmits over thesame number of subcarriers. In the process, constraint X5 is also satisfied. Towards the end,we use ordered subcarrier pairing [22] such that the subcarrier with the greatest channelgain among the BS-relay communication links is assigned to the subcarrier with the greatestchannel gain among the relay to destination-UE communication links. Similarly, subcarrierswith the second largest gains are paired, and so on. Such a subcarrier pairing is known tomaximize the system throughput [22]. Note, however, that an optimal subcarrier assignmentcan not be found in polynomial time and that the discussed subcarrier assignment algorithm,although sub-optimal, provides a polynomial time solution.Now that we found the subcarrier allocation policy, we refine the power by applyingdual decomposition method for the given sub-optimal subcarrier assignments. That is, theMINLP problem in (3.9) reduces to a convex power allocation problem as h∗ is alreadyobtained. This completes our discussion on resource allocation for D2D relaying systemswith frequency reuse.HCGCI cumzrixvl gzsultsIn this section, we present two numerical results to illustrate and compare the performancegains achieved by the proposed resource allocation methods. We consider a circular area withradius of 1 km where the AP is located in its center. The destination-UEs are randomlylocated inside this area with uniform distribution. The propagation model for the channelfrom AP to destination-UEs is similar to the one used in previous chapter. The simulationsetup comprises three candidate relays for each UE. The distance between the relay anddestination nodes varies between 30 to 60 meters. The transmission power for each relayover each subcarrier (eg) is set to 0.1 Watt. The channels for D2D links are modeled asWINNER II propagation model [65]. D2D channel models are based on outdoor to indoorscenario with the path loss model as ea[dW] = 36O8log10(d) + 43O8. The standard deviationof shadow fading is set as 4 dB. We do not consider small scale fading for D2D links.50HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geuse20 25 30 35 400.70.80.911.11.21.31.41.5x 107Pmax(dBm)Averagesystemcapacity[bits/sec]Dashed line: D2D with frequency reuseSolid line: D2D without frequency reuseK from 2 to 8K from 2 to 8Figure 3.2: Average system capacity versus BS power budget emax for different number ofUEs. Result shows significant improvement of system capacity when frequency is reused inD2D links.Fig. 3.2 shows average system capacity versus emax for different number of UEs (K)considering c = 16 subcarriers. We show the achievable performance of a scenario wherefrequency reuse is possible, i.e., when D2D pairs are far enough from each other with disjointcoverage area. We compare the two cases of with and without frequency reuse. Significantsystem capacity improvement is observed for resource allocation schemes with frequencyreuse. With the increase of number of UEs, i.e., K, the frequency reusing factor improvesand as a result, the capacity gain increases.In Fig. 3.3, we show average system capacity versus number of subcarriers (c) for emax =35 dBm and K = 4. As expected the system capacity increases with the increase of thenumber of subcarriers. Here, we show the performance of the resource allocation schemewith frequency reuse for different values of i , where i is the number of time slots forbroadcasting. We notice that by increasing i from 3 to 4, the system capacity increases.However, the system capacity decreases when we change i from 4 to 5. The reason is wheni is greater than the number of D2D pairs, the number of messages are greater than the sizeof the buffer at the relays. Therefore, some of the messages are discarded which will resultin having lower system capacity than expected.51HC2C gesourxe Alloxvtion for D2D gelvying hystems with Frequenxy geuse4 8 16 32 64 1280246810x 107Number of subcarriers (N )Averagesystemcapacity[bits/sec]  frequency reuse, T=4frequency reuse, T=3frequency reuse, T=5no frequency reuseFigure 3.3: Average system capacity versus number of subcarriers for emax = 35 dBm andK = 4.HCGCJ DGD gzlvyingO botivvtion for v Gznzrvl hxznvrioIn the discussions so far, we have considered two theoretically extreme scenarios in thecontext of D2D relaying. In the first scenario, the D2D pairs are close to each other andtheir coverage areas overlap. Therefore, since frequency reuse cannot be attempted, weproposed resource allocation algorithms considering the orthogonality of the subcarriers. Inthe second scenario, the D2D pairs are far enough from each other and their coverage areasare disjoint. Therefore, we proposed resource allocation which fully reuse the subcarriers forD2D communication.However, in a practical setup, D2D pairs would be distributed randomly in the cell. As aresult, both the scenarios discussed in the previous sections can co-exist simultaneously. Thatis, few D2D pairs would experience coverage overlap with each other, while few other D2Dpairs would be disjoint from each other. Resource allocation for such a general scenario canbe attempted by developing an analogy based on the conventional frequency reuse patternsused in cellular networks.In conventional cellular systems, the available frequency spectrum is generally reused insufficiently separated cells. While adjacent cells use different frequencies to reduce inter-cell52HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsinterference, the available set of frequencies are usually exhausted within a cluster of cells dueto limited spectrum. However, the same frequencies can be reused in adjacent cell-clusters.A more aggressive and effective approach from an interference perspective is the fractionalfrequency reuse (FFR) technique, where the cells are in-turn partitioned into smaller spatialregions and the available frequency spectrum is reused over these regions.Similar frequency reuse ideas can be applied in the context of D2D relaying networks.The cellular operator can reserve a dedicated in-band spectrum for D2D communications.Since D2D communications occur over short distances, ultra-dense frequency reuse can beattempted. In other words, several clusters of D2D pairs, with each cluster fully exhaustingthe available frequency resources, can co-exist within each cell. The D2D pairs in the samecluster should use orthogonal frequencies, i.e., resource allocation as per the first scenario(c.f. Section 3.2.2) should be attempted. On the other hand, D2D pairs in different clusterscan reuse the same set of available frequencies, i.e., resource allocation as per the secondscenario (c.f. Section 3.2.3) should be attempted. On a slightly advanced note, intelligentFFR techniques can also be adopted for D2D communications (for example, see [66]) tominimize interference in the system.HCH aofi Xomplzxity vny Distriwutzy gzsourxzAlloxvtion for gzlvying hystzmsIn this section, we propose distributed subcarrier pairing and relay selection for cooperativenetworks. Our objective is to maximize the throughput of the network using minimal CSIfeedback. We focus on a single source-destination OFDM system and propose two subop-timal, low complexity and distributed algorithms suitable for practical implementations ofcooperative systems.53HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsSource (S) Destination (D) Relay 2Relay kRelay 1 Relay K 3514 7264652173First Hop Second  HopSubcarrier iSubcarrier jFigure 3.4: System modelHCHCF hystzm boyzl vny erowlzm FormulvtionConsider a half-duplex single antenna multi-relay OFDM system with a single source-destinationpair as depicted in Fig. 3.4, in which K relay nodes help the source using AF protocol tocommunicate with the destination node. As before, the available bandwidth is divided intoc orthogonal subcarriers. The transmission protocol consists of two phases. In the firstphase, the source transmits the messages on all of the subcarriers and the relays listen. Weassume that the direct link between the source and the destination is in deep fade and hencethe destination can not hear the source during the first phase. In the second phase, the relaysamplify the received messages and forward them to the destination while the source is silent.For example, in the first phase, relay k ∈ {1P 2P OOOP K} receives a message on subcarrier ifrom the source, amplifies it and forwards it to the destination on subcarrier j in the secondphase. Therefore, a communication between the source and the destination is established viarelay k on subcarrier pair (iP j). Note that i and j can be different subcarriers and each relaycan assist more than one subcarrier pair. However, depending on the channel conditions,some relays may not get any subcarrier pairs. In order to avoid interference, each subcarrieris used only once in each phase of transmission and hence the frequency orthogonality ispreserved.54HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsLet us assume that subcarrier pair (iP j) is assigned to relay k. The channel gains onsubcarrier i ∈ {1P 2P OOOP c} in the first hop and on subcarrier j ∈ {1P 2P OOOP c} in the secondhop are denoted as giPkP1 and gjPkP2, respectively, and the capacity of the link (iP j) assistedby relay k is denoted as giPjPk.Our objective is to maximize the throughput, subject to some constraints on subcarrierpairing and relay selection. The problem is formulated as:maximize{N;j;P}K∑k=1c∑i=1c∑j=1/iPjPkgiPjPksubject to :X1 : /iPjPk ∈ {0P 1} ∀iP jP kPX2 :K∑k=1c∑j=1/iPjPk = 1 ∀iPX3 :K∑k=1c∑i=1/iPjPk = 1 ∀jP(3.11)where /iPjPk is an indicator for the relay selection and subcarrier pairing. /iPjPk equals to oneonly if the source transmits to relay k in the first hop on subcarrier i and relay k transmitsto the destination on subcarrier j in the second hop, otherwise /iPjPk = 0. X2 and X3 aresubcarrier allocation constraints which are imposed to guarantee that each subcarrier willbe used at most once in each hop. In this section, we focus only on subcarrier pairing andrelay selection methods and consider equal power allocation at all the subcarriers.HCHCG holution ApprovxhIn this section, we first present the optimal centralized solution for the problem given in(3.11). The centralized method assumes that complete CSI is available at the central man-aging node. However, availability of full CSI may not be practical for many applications.Also, it requires significant CSI feedback which increases the size of signaling overhead.To overcome the problem, we propose two suboptimal distributed schemes. Our proposedschemes are superior to the optimal one in terms of signaling overhead at the expense of a55HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsvery small degradation in performance.dptimvl Xzntrvlizzy holutionFor centralized case, it is assumed that complete CSI is known by a central manager. If weconsider that the central managing node can measure its associated channel gains using pilotsignals, then channel gains associated with the other nodes should be reported to the centralmanager. For example, if the destination is the central manager, it can measure the channelgains of the second hop, therefore, full CSI of first hop needs to be sent to the destination.If each channel gain can be quantized in b bits, then for a system with K relays and csubcarriers, it requires cKb bits signaling overhead in total.In this method, for each subcarrier pair (iP j) , we find relay k that maximizes the ca-pacity giPjPk and denote it by k(iP j). In order to perform subcarrier pairing, we make atwo dimensional matrix of giPjPk(iPj) for i ∈ {1P 2P OOOP c} and j ∈ {1P 2P OOOP c}. Hence, wehave a two dimensional linear assignment problem which can be optimally solved using theHungarian method. The details of the algorithm are given below.Algorithm I : Centralized optimal method for subcarrier pairing and relay selectiongzquirzO complete CSI at the central managing node.{hiEe FO Finy thz wzst rzlvys for zvxh suwxvrrizr pvir }F: for i = 1 : c yo2: for j = 1 : c yoH: Calculate k(iP j) = argmaxk∈{1P2:::PK}giPjPkI: zny forJ: zny for{hiEe GO huwxvrrizr pviring }K: Apply Hungarian method on matrix giPjPk(iPj)L: rzturnhuwBdptimvl Distriwutzy hxhzmzBFThe signaling overhead for the optimal scheme is too high, especially for large number ofsubcarriers and relays. In the following, we propose a suboptimal distributed scheme to56HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsreduce the signaling overhead. We keep the same assumption regarding CSI as before, i.e.,the source can measure all giPkP1 and the destination can measure all gjPkP2.In this scheme, for each subcarrier i in the first hop, the source finds relay k that maxi-mizes the channel gain giPkP1 and denote it by k(i). Then giPk(i)P1 is reported to the destination.Based on this information, the destination then makes a two dimensional matrix of giPjPk(i)(for i ∈ {1P 2P OOOP c} and j ∈ {1P 2P OOOP c}) and apply Hungarian method to find the relayselection and subcarrier pairing. The details of the algorithm are given below.Algorithm J : Distributed scheme-1 for subcarrier pairing and relay selectiongzquirzO giPkP1 at the source; giPk(i)P1 and gjPkP2 at the destination.{hiEe FO Finy thz wzst rzlvy for zvxh suwxvrrizr of thz rst hop }F: for i = 1 : c yo2: Calculate k(i) = argmaxk∈{1P2:::PK}giPkP1H: zny for{hiEe GO huwxvrrizr pviring }I: Apply Hungarian method on matrix giPjPk(i)J: rzturnIn this scheme, we just need to send the maximum of the channel gains for each subcarrierof the first hop in order to obtain the assignment matrix at the destination. Therefore, theoverhead is cb (bits) which is K times lower than the optimal method. A significant amountof savings in terms of feedback is possible with our proposed scheme-1 as compared to theoptimal method for large number of relays in the system. Also, we can observe in section 3.3.3that the performance is extremely close to optimal method especially for large number ofsubcarriers.huwBdptimvl Distriwutzy hxhzmzBGAlthough the sub-optimal distributed scheme-1 reduces the signaling overhead, the feedbackis still very high for large number of subcarriers. In addition, both centralized and distributedscheme-1 use Hungarian method. Hungarian method has a complexity of O(c3), which isconsidered high for many practical applications. To reduce the computational complexity57HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsand overhead further, we propose another distributed algorithm.In this scheme, we assume that the source can measure all giPkP1 and the destination canmeasure all gjPkP2 and each relay knows only its own links from the source and from thedestination. Our goal is not to feedback any channel gains of the first hop to the secondhop and vice-versa. The optimization problem can be divided in three steps and each stepis solved considering the available information without any CSI feedback.In the first step, our objective is to find the best relay for each subcarrier of the first hop.This step is done at the source based on the available channel gains giPkP1 only. The solutionis to assign each subcarrier in the first hop to the relay that has the highest channel gain onthat subcarrier. The selected relay for subcarrier i in the first hop is denoted by k1Pi. Wesave these subcarrier to relay assignments in a set C as (iP k1Pi) to use them later for pairing.In the second step, the objective is to find the best relay for each subcarrier of the secondhop. This step is done at the destination based on the available channel gains gjPkP2. However,the restriction for pairing is that the number of subcarriers assigned to each relay in bothhops should be the same. Therefore, only this information from the first step is requiredto be sent to the destination. To obtain the solution of this part, we follow a “greedy”approach. Let us assume that the number of subcarriers assigned to relay k in the first hopis denoted by n(k). Consider that a set A contains channel gains of the second hop, gjPkP2for all k ∈ {1P 2P OOOP K}, j ∈ {1P 2P OOOP c} and sort it in a descending order (↓). Then we dothe following steps until set A becomes empty.First we check whether n(k) is zero and update A by removing (−) the channel gainsgjPkP2 from it for all j ∈ {1P 2P OOOP c} and for all k. Then we select the maximum of theset A by taking the first element (first element(A)) of the sorted set A and add (∪) thecorresponding subcarrier and relay index given by (j′P k2Pj′) in set B. We again update A byremoving the channel gains gj′PkP2 for all k. Then we decrease n(k2Pj′) by one and repeat thesteps.Note that we have taken care of having the same number of subcarriers in each relay for58HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsboth hops and also the constraint to guarantee that each subcarrier will be used at mostonce in each hop. At the end of step two, we have subcarrier to relay assignments of bothhops saved in C and B.Algorithm 6 : Distributed scheme-2 for subcarrier pairing and relay selectiongzquirzO giPkP1 at the source;gjPkP2 and n = [n(1)P OOOP n(k)P OOOn(K)]i at the destination;Each relay knows only its own links from the source and from the destination.F: Consider the sets C = ϕ and B = ϕ{hiEe FO Finy thz wzst rzlvy for zvxh suwxvrrizr of thz rst hop }2: for i = 1 : c yoH: Calculate k1Pi = argmaxk∈{1P2:::PK}giPkP1I: Denote C = C ∪ {(iP k1Pi)}J: zny for{hiEe GO Finy thz wzst rzlvy for zvxh suwxvrrizr of thz szxony hop }K: Denote A = {gjPkP2P ∀kP ∀j}L: Denote A ← Sort ↓ AM: fihilz A ̸= ϕ yoN: for k = 1 : K yoFE: if n(k) == 0 thznFF: Update A ← A− {gjPkP2P ∀j}F2: zny ifFH: zny forFI: Find (j′P k2Pj′) = first element(A)FJ: Update B ← B ∪ {(j′P k2Pj′)}FK: Update A ← A− {gj′PkP2P ∀k}FL: n(k2Pj′) = n(k2Pj′)− 1FM: zny fihilz{hiEe HO huwxvrrizr pviring }FN: for k = 1 : K yo2E: Denote Bk = {(a2P b) ∈ B|b = k}, Ck = {(a1P b) ∈ C|b = k}2F: Denote B′k ← Sort ↓ Bk and C ′k ← Sort ↓ Ck22: Denote Dk = {(a1′P a2′P k)|(a1′P k) ∈ C ′kP (a2′P k) ∈ B′k}2H: zny for2I: rzturn DkP ∀kIn step three, the objective is to pair the assigned subcarriers to each relay. It is provedthat ordered subcarrier pairing is optimal for single relay AF networks [27]. Therefore, foreach relay the assigned subcarrier of both hops can be coupled in sorted way. For example,for each relay the strongest assigned channel gain in the first hop is paired with the strongest59HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsTable 3.1: Computational complexityAlgorithms Computational complexityOptimal centralized scheme O(c3)Proposed distributed scheme-1 O(c3)Proposed distributed scheme-2 O(cK log(cK))assigned channel gain in the second hop, and then the second strongest assigned channel gainin the first hop with the second strongest assigned channel gain in the second hop and so on.Since it is assumed that each relay knows about its own channel gains, this step is performedat the relays as follows.In sets Bk and Ck, we get the elements from the sets B and C, respectively such thatthe index corresponding to relay is k. Then after sorting the sets in a descending order, weobtain the paired subcarriers assigned to relay k in the set Dk. The details of the algorithmare given in Algorithm 6.The only feedback requirement in this method is the number of assigned subcarriers toeach of the relays by the source in the first hop. The maximum number of subcarriers assignedto each relay is c , which can be represented by log2(c) bits. Therefore, in this algorithm,the required signaling overhead in the worst case is K log2(c) bits. The complexity of thismethod is dominated by the second step. Since we use sorting algorithm on all subcarriersat this step, the complexity of this algorithm is O(cK log(cK)). Table 3.1 shows thecomputational complexity of the optimal and the proposed algorithms.HCHCH cumzrixvl gzsultsWe have conducted extensive simulations considering different system parameters to analyzeand compare the performances of our proposed distributed schemes. We have assumeduniform power allocation across subcarriers. The signal to noise ratio on each subcarrier ofeither hops is set at 10 dB. Each of the complex channel coefficients is generated as i.i.d.circularly symmetric complex Gaussian random variables with zero mean and unit variance.The results are averaged over 1000 independent channel realizations.60HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsAs a benchmark, we compare the performance of our proposed schemes with the optimalone and three other methods existing in the literature. The first method is “symbol based”relay selection which selects a single relay node that maximizes the capacity over all of thesubcarriers [22]. In this method, for each relay node, the subcarriers are sorted in each hopand the subcarrier with highest channel gain in the first hop is paired with the subcarrier withthe highest channel gain in the second hop. Then the subcarrier with second highest channelgain in the first hop is paired with the subcarrier with second highest gain in the secondhop and this pairing process continues until all the subcarriers are paired. As mentionedbefore, this method is proved to be optimal for single relay OFDM based AF cooperativesystems [27]. Then the total capacity of each relay is computed. Finally, the relay thatmaximizes the total capacity is selected. The second benchmark method does not considersubcarrier pairing [30]. In this “no pairing” scheme, it is assumed that the ith subcarrierin the first hop is paired with the same (ith) subcarrier in the second hop. Then the bestrelay is selected in terms of the capacity for each (iP i) subcarrier pairs. The third methodis “random” selection method. The subcarriers are assigned to the relays a-priori and thepairing is done without considering the CSI.Fig. 3.5(a) compares the average throughput (bits/sec/Hz) over each subcarrier of dif-ferent schemes for different number of subcarriers. The results are shown for K = 2 re-lays in the network. The number of subcarriers are taken as power of 2, for example,(c = 2P 4P 8P OOOP 256). From these results, we observe that both distributed schemes tend tooptimal method as the number of subcarriers increase. The performance of our proposeddistributed scheme-1 is extremely close to the optimal one for large number of subcarriersand is slightly better than that of the proposed distributed scheme-2. However, the signalingoverhead and computational complexity of the first method is more than the second one.Therefore, depending on the applications and requirements, one of the proposed schemesmight have a preference over the other. Results show that the performance of our proposedschemes are significantly better than the schemes that do not have subcarrier pairing. Our61HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystemsproposed schemes also outperform the symbol based and random selection methods.Fig. 3.5(b) shows the increment in throughput with the increase of the number of relaysfromK = 2 toK = 8. The performance of our proposed schemes are very close to the optimalone for large number of subcarriers and proposed scheme-1 performs better than proposedscheme-2. Results show the superiority of our schemes compared to the three benchmarkmethods. Note that the schemes designed without considering the number of relays, forexample, symbol based and random selection methods, do not provide any performancegains with the increase of the number of relays.In Fig. 3.6, we observe the average of relative error for different number of subcarriers.Relative error is defined as (Ropt − Rprop)RRopt, where Ropt and Rprop are the throughput ofthe optimal and proposed schemes, respectively. We can see that the relative error decreasesfor both schemes as the number of subcarrier increases. For proposed scheme-1, the relativeerror approaches to zero very fast but for proposed scheme-2, it decreases slowly as comparedto scheme-1. However, we can observe that the relative error for scheme-2 is less than 1%for c = 256 and K = 2.Although the relative error for scheme-2 decreases slowly compared to the first scheme,in this experiment, we show that the probability of having an error that is more than somemaximum relative error is approximately zero. Fig. 3.7 represents cumulative distributionfunction (CDF) of the percentage of relative error for the proposed scheme-2 when K = 2.We observe that as the number of subcarriers increases, the CDF approaches to 1 in a lowerpercentage of relative error. It appears that with the increase of the number of subcarriers,the probability of having higher error is zero. For example, when c = 128, the probabilityof having relative error more than 4% is zero.Fig. 3.8 shows the signaling overhead in bits of the proposed schemes for different numberof subcarriers. We assume that b = 10 bits are required to transmit each channel gain. Asshown in the figure, the signaling overhead is much lower for the proposed distributed scheme-1 compared to the optimal method and the overhead does not depend on the number of relays.62HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystems0 50 100 150 200 2501.31.41.51.61.71.8Number of subcarrie rsAveragethroughput(bits/sec/Hz)  OptimalProp osed - 1Prop osed - 2No pairingSymb ol - basedRandom=v) Vvzrvgz throughput vsC numwzr of suwxvrrizrs for K R 20 50 100 150 200 2501.41.61.822.2Number of subcarrie rsAveragethroughput(bits/sec/Hz)  OptimalProp osed - 1Prop osed - 2No pairingSymb ol - basedRandom=w) Vvzrvgz throughput vsC numwzr of suwxvrrizrs for K R MFigure 3.5: Average throughput of the system versus number of subcarriers for differentnumber of relays63HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystems0 50 100 150 200 25000.020.040.060.080.10.120.14Number of subcarrie rsAverageofrelativeerror  Prop osed - 1,K=2Prop osed - 2,K=2Prop osed - 1,K=8Prop osed - 2,K=8Figure 3.6: Average of the relative error versus the number of subcarriers10 20 30 40 50 60 70 80 90 1000.40.50.60.70.80.91Percentage of re lat ive errorCumulativedistributionfunction(CDF)N=128N=64N=32N=16N=8N=4N=2Figure 3.7: CDF versus percentage of relative error for proposed scheme-2 with K = 264HCHC aow Complexity vny Distriwutey gesourxe Alloxvtion for gelvying hystems0 50 100 150 200 25000.20.40.60.811.21.41.61.82x 104Number of subcarrie rsSignalingoverhead(bits)  Optimal ,K=2Proposed-1,K=2Proposed-2,K=2Optimal ,K=8Proposed-1,K=8Proposed-2,K=8Figure 3.8: Signaling overhead versus number of subcarriersResults show that the proposed scheme-2 is extremely efficient. The signaling overhead ofthis scheme is almost negligible compared to the optimal method and the proposed scheme-1.The ratio of signaling overhead between proposed scheme-2 and optimal centralized methodisK log2(c)cKb=log2(c)cb, which is approximately zero for any practical cooperative network.65Xhvptzr Igzsourxz Alloxvtion for XoopzrvtivzXommunixvtion hystzms fiithlirzlzss Enzrgy HvrvzstingIn this chapter, we investigate the resource allocation problem for cooperative communicationsystems in which the relays are powered with wireless energy harvesting. The accomplishedworks and research contributions of this chapter are briefly described in the following.ICF Axxomplishzy lorks vny gzszvrxh XontriwutionsRecently, wireless power transfer technology [39], [67]-[69] has been introduced for energyharvesting in wireless systems. Wireless EH technology is studied in two different paradigmsof wireless communication network. One is wireless powered communication (WPC) in theuplink [70]-[72] and the other is the simultaneous wireless information and power transfer(SWIPT) in downlink [73]-[75]. In WPC, some fraction of uplink transmission durationis dedicated for downlink energy transmission from the access point (AP) to UEs. Theharvested energy during this time is utilized by UEs to power their uplink informationtransmission to AP in the remaining fraction of time. However, SWIPT technique is usedto supply wireless energy to the UEs whilst making information transmission to them in thedownlink at the same time. Since current information receiver circuits are not able to harvestenergy, the receiver nodes should have a separate energy harvesting circuit, thus different664CFC Axxomplishey lorks vny gesevrxh Contriwutionsprotocols, such as power splitting and time switching [8], [76]-[77], are defined to share thesignal between information receiver and energy harvesting circuit.One important challenge in wireless power transfer technology is the high propagationloss. Table 4.1, from [78], shows numerical results (based on calculations) for maximumpossible power transfer range for charging different types of devices. Details of simulationsetup can be found in [78].Table 4.1: Power transfer ranges for different types of mobile devices [78]iransmit power oigWzz hmvrt phonzs ivwlzt xomputzrs avptop xomputzrsFE l J m J m H m BHE l N m M m L m BJE l FE m FE m N m I mFEE l FI m FI m FH m K mTable 4.1 shows that, considering practical issues, power transfer range for chargingdifferent wireless devices varies from 3 to 14 meters depending on transmit power. Thesedistances are still significantly shorter than the typical cell radii. The maximum possibleenergy that can be harvested from ambient RF is on the order of 1 l . Therefore, RFenergy scavenging is only applicable for small node wireless communications with micropower requirements.With the ability of wireless power transfer along with information transfer, there aredifferent ways of cooperation in wireless energy harvesting networks. In the network whererelay nodes are energy constrained and require energy harvesting to elongate their batterylife, hence unwilling to contribute their own energy cooperation, they can be designed toperform simultaneous information and energy relaying to enhance the performance of thesystem. As RF signals transfer both information and power, part of the transmitting powercan be harvested in the receiver for the purpose of relaying. In this chapter, we have focusedon SWIPT protocol for charging the relay nodes, and among the various kinds of receiversproposed in the literature, we focus on energy splitting receivers. In an energy splittingreceiver, the signal received by a node is splitted into two streams, in which one of them674C2C hystem boyelis used for decoding the information and the other one is used for harvesting. We assumethat the relay nodes are capable of energy splitting, and they use the harvested energy forforwarding the information. In such a case, relay node needs to first harvest energy fromthe information it is going to relay, and then forward that information with the harvestedenergy which provides an incentive for relaying.In this chapter, we consider an OFDMA multi-relay SWIPT system, and we optimallyallocate the subcarrier, power, as well as the power splitting factors and perform optimalrelay selection. Selective relaying is considered for our cooperative communications in thischapter. In other words, relays cooperate only when it is more beneficial than direct trans-mission for the system. This improves the performance further in terms of energy efficiencyand spectral efficiency [23].The rest of the chapter is organized as follows. In Section 4.2, the system model andassumptions are introduced. In Section 4.3 and 4.4, the problem formulation and solutionapproach are discussed. In Section 4.5, the numerical results are presented.ICG hystzm boyzlSimilar to the previous chapters, we consider an OFDMA network with c orthogonal sub-carriers, each of them with a bandwidth of l as shown in Fig. 4.1. We have one source,multiple relays, and multiple destination nodes. When cooperation is beneficial for the des-tination nodes, they get help from relays. DF relaying protocol is used when cooperation isbeneficial. The source decides whether to cooperate or not based on the channel conditions.We denote the relays by m, and the destinations by k. The transmission modes corre-sponding to cooperative and non-cooperative are superscripted with (X) and (cX), respec-tively. The channel gains from source h to relay m, and from relay m to destination node kare defined as giP(CP1)hPm and giP(CP2)mPk , respectively. The superscript iP (XP 1) and iP (XP 2) indicatethe cooperative transmission mode over subcarrier i in time slot one and two, respectively.684C2C hystem boyelFigure 4.1: Downlink information relaying with energy harvesting in SWIPT network withone source (S), three relay nodes (R), three destination nodes (D), and five subcarriers.Similarly, the channel gain for the non-cooperative (direct) link is defined as giP(cC)hPk .We assume that each node has two sources of power, one from the battery and theother from the harvested energy. We assume that the relay nodes use the energy fromRF signal sent from the source to receive information and harvest energy. The harvestedenergy is received by the power splitting operation. Particularly, in the case of cooperativetransmission, relays split the received signal from the source into two streams: one forharvesting the energy (Z), and the other for decoding the information (I) with the ratios of/iP(E)mPk and /iP(I)mPk , respectively. The harvested energy is used by the relays only to forward thedata for the destination nodes. Therefore, relay nodes do not spend their own batteries forthe purpose of relaying.Fig. 4.1 shows the SWIPT system model with three relays, three destinations, and fivesubcarriers. The subcarriers are allocated such that the total capacity of the system ismaximized. Selective relaying is used in this protocol, i.e., relaying is used only when it isbeneficial in terms of system capacity maximization. For example, D3 is close to the S and694CHC erowlem Formulvtionas a result, it does not need any assistance of relays. However, D2 is far from the S anddue to high attenuation and blockage, a direct link to the S cannot be established. D2 isassisted by two relays, R2 and R3. D1 utilizes both relaying and direct communications.In subcarrier 1 relaying is beneficial, whereas in subcarrier 2, direct transmission is morefavorable for D1.ICH erowlzm FormulvtionIn this section, we formulate the resource optimization problem, where the objective is tomaximize the total capacity of the system. The capacity of the DF cooperative link can becalculated asgiP(C)mPk =12min{log2(1 +1c0lgiP(CP1)hPm /iP(I)mPk eiP(C)hPm )Plog2(1 +1c0lgiP(CP2)mPk giP(CP1)hPm /iP(E)mPk eiP(C)hPm )}P(4.1)where eiP(C)hPm is the transmission power of the source h on subcarrier i over the cooperativelink to send the data for relay m. This power attenuated by the fading channel in the firsthop is received by relay m as giP(CP1)hPm eiP(C)hPm . The relay splits the received signal into twopower streams with the ratios of /iP(I)mPk and /iP(E)mPk , where /iP(I)mPk and /iP(E)mPk are used for decodingthe information and for harvesting, respectively. In the second time slot, the relay will usethe harvested power given by giP(CP1)hPm /iP(E)mPk eiP(C)hPm to forward the data for destination node k.It is assumed that all the energy harvested in first time slot in the relay will be used forforwarding the information in the second time slot.If the direct link is better than the cooperative link, the source directly transmits datato the destination node. The capacity of the direct link is calculated asgiP(cC)k = log2(1 +1c0lgiP(cC)hPk eiP(cC)hPk )P (4.2)where eiP(cC)hPk is the transmission power of source h on subcarrier i over the direct link to704CHC erowlem Formulvtiondestination node k.Our objective is to maximize the total capacity of the system subject to the power con-straint of the source. The joint optimization problem of subcarrier assignment, power allo-cation, transmission mode (cooperative or non-cooperative) and relay selection is formulatedasmaximizeePhPK∑k=1b∑m=1c∑i=1siP(C)mPk giP(C)mPk +K∑k=1c∑i=1siP(cC)k giP(cC)ksubject to :X1 :K∑k=1b∑m=1c∑i=1siP(C)mPk eiP(C)hPm +K∑k=1c∑i=1siP(cC)k eiP(cC)hPk ≤ emaxX2 : siP(C)mPk P siP(cC)k ∈{0P 1}P ∀iP kPmX3 :K∑k=1b∑m=1siP(C)mPk +K∑k=1siP(cC)k ≤ 1P ∀iX4 : /iP(I)mPk + /iP(E)mPk = siP(C)mPk P ∀iP kPmX5 : eiP(C)hPm P eiP(cC)hPk P /iP(I)mPk P /iP(E)mPk ≥ 0P ∀iP kPmX6 :K∑k=1c∑i=1siP(C)mPk ≤ nmP ∀mX7 : giP(CP1)hPm /iP(I)mPk = giP(CP1)hPm giP(CP2)mPk /iP(E)mPk P ∀iP kPm(4.3)where e , / and h denote the power allocation, power splitting factors and subcarrier alloca-tion policy, respectively. X1 is the power constraint, where emax is the power budget of thesource. X2 shows that siP(C)mPk and siP(cC)k are binary integer variables (indicators). If sourceis transmitting to destination node k with the assistance of relay m over subcarrier i, siP(C)mPkis one, otherwise it is zero. Similarly siP(cC)k is defined for non-cooperative transmission. X3implies that each subcarrier can be used only once to avoid interference. It also states thatover each subcarrier either cooperative or non-cooperative mode can be used. X4 indicatesthat the sum of the power splitting ratio in each subcarrier should be equal to one if thatsubcarrier is selected for cooperation, i.e., the splitter is not producing any energy and powerwastage is ignored. X5 states that the power and splitting variables are non-negative. X6indicates that each relay can only assist over nm subcarriers due to the limitation of thepower splitter and energy harvester, where nm is known a-priori. To avoid information loss714C4C holution Approvxhand wastage of power at the relays, we have incorporated X7 into our formulation.ICI holution ApprovxhThe problem stated above is MINLP, and is very difficult to solve in general. In this sectionwe show how to solve this problem optimally.First, we obtain the power splitting ratios for each cooperative link from X4 and X7 as/iP(I)∗mPk =giP(CP2)mPk1 + giP(CP2)mPkP/iP(E)∗mPk =11 + giP(CP2)mPkO(4.4)Since we have optimally obtained the splitting factors in (4.4), the variables of the optimiza-tion problem in (4.3) are reduced to (eP h), i.e., transmission power and subcarrier allocationpolicy.The major concern for solving problem (4.3) is the integer subcarrier assignment variablesand constraints. Similar to the previous chapters, we relax the indicators h in [0,1] intervaland define auxiliary power variables. The relaxed optimization problem is convex withrespect to (e˜ P h) and strong duality holds, i.e., the duality gap is zero. Therefore, wecan solve the Lagrangian dual problem and still obtain the optimal solution of the relaxedproblem. The partial Lagrangian for the relaxed problem is given bya(P e˜ P h) =K∑k=1b∑m=1c∑i=1siP(C)mPk12log2(1 +gN;(C;1)S;R N;(I)R;Pee N;(C)S;Rc0lsN;(C)R;P)+K∑k=1c∑i=1siP(cC)k log2(1 +gN;(NC)S;Pee N;(NC)S;Pc0lsN;(NC)P)+(emax −K∑k=1b∑m=1c∑i=1e˜iP(C)hPm −K∑k=1c∑i=1e˜iP(cC)hPk)P(4.5)where  is the non-negative Lagrangian multiplier. We solve the dual problem (4.5) withdual decomposition technique. The details of the dual decomposition algorithm for this724C4C holution Approvxhproblem are given in the following.holving thz huwprowlzmsSolving the subproblems, we obtain the optimal power and subcarrier allocation policy fora given multiplier.Using KKT conditions, we obtain the optimal power allocation policy as follows. Sincethe gradient is equal to zero at the optimal points, the auxiliary power variables (e˜ ) in termsof (h) in iteration t of the dual decomposition technique can be derived ase˜iP(C)∗hPm = siP(C)mPk[ 12ln(2)− c0lgiP(CP1)hPm /iP(I)∗mPk]+Pe˜iP(cC)∗hPk = siP(cC)k[ 1ln(2)− c0lgiP(cC)hPk]+(4.6)To obtain the optimal subcarrier allocation policy (h), we use the optimal power solutione˜iP(C)∗hPm and e˜iP(cC)∗hPk of (4.6) into the Lagrangian (4.5). After rearranging, the problem canbe written as a linear function in terms of (h) given bymaximizehK∑k=1b∑m=1c∑i=1siP(C)mPk HiP(C)mPk +K∑k=1c∑i=1siP(cC)k HiP(cC)ksubject to : X3P X6(4.7)where HiP(C)mPk and HiP(cC)k are given byHiP(C)mPk =12log2(1 +1c0lgiP(CP1)hPm /iP(I)∗mPk[12ln(2)− c0lgN;(C;1)S;R N;(I)R;P]+)−[12ln(2)− c0lgN;(C;1)S;R N;(I)R;P]+PHiP(cC)k = log2(1 +1c0lgiP(cC)hPk[1ln(2)− c0lgN;(NC)S;P]+)−[1ln(2)− c0lgN;(NC)S;P]+O(4.8)We have satisfied constraints X4 and X7 to obtain optimal power splitting ratios in (4.4), and734C4C holution ApprovxhX1 and X5 in (4.6) to obtain optimal power allocation policy. The rest of the constraints areincorporated in (4.7) to obtain the optimal subcarrier allocation policy. Note that, (4.7) is amodified linear assignment problem which can be solved with available integer programmingalgorithms. Next, we propose an optimal subcarrier allocation policy in each iteration ofdual decomposition technique as follows.htzp FO For non-cooperative mode, find the best destination node (kcCi ) for each sub-carrier i as:k(cC)i = argmaxkHiP(cC)k ∀iO (4.9)htzp GO Similarly, for cooperative mode, find the best destination node for each subcar-rier relay pair (iPm) as:k(C)iPm = argmaxkHiP(C)mPk ∀iPmO (4.10)htzp HO Now we form a matrix with c columns such that:-For each relay m, we incorporate nm similar rows (to satisfy X6) each of them occupiedwith HiP(C)mPk(C)N;Rfor all i ∈ {1P OOOP c}. Therefore we haveb∑m=1nm rows corresponding to thecooperative transmission.-For the direct link, we have c similar rows, each of them occupied with HiP(cC)k(NC)Nfor alli ∈ {1P OOOP c}.htzp IO The matrix formed in step 3 has the size of (c +b∑m=1nm) × c which is non-square. We make the matrix square by addingb∑m=1nm zero columns to solve the assignmentproblem.htzp JO For optimal solution of (4.7), we apply Hungarian algorithm [61] on the squarematrix obtained in htzp I. The algorithm satisfies X3 and X6, and hence, optimal subcarrierallocation (h∗) in each iteration of dual decomposition technique is obtained.Fig. 4.2 shows the formation of the square matrix and a sample assignment solution forour proposed algorithm for number of subcarriers c = 2, number of relays b = 2, numberof destination nodes K = 1 and nm = 2P 1 for m = 1P 2. The figure states that the capacity744CJC cumerixvl gesultsFigure 4.2: Formation of the square matrix and a sample assignment solutionis maximized if relay m = 1 forwards the data in subcarrier i = 1 and the other subcarrieri = 2 is used for direct communication.holving thz bvstzr erowlzmUsing subgradient method [63], we update the multiplier as(t+ 1) =[(t)− (t)(emax − K∑k=1b∑m=1c∑i=1e˜iP(C)hPm −K∑k=1c∑i=1e˜iP(cC)hPk)]+P (4.11)where (t) is a constant step size parameter.In this section, we have proposed a novel method to solve the joint resource allocationproblem of power and subcarrier allocation, and relay and transmission mode selection op-timally. The complexity of our proposed method is polynomial, which is much lower thanthe exponential complexity of the brute-force method.ICJ cumzrixvl gzsultsIn this section, we demonstrate the simulation results to show the effectiveness of our pro-posed protocol and optimization method. The nodes are randomly located inside the circular754CJC cumerixvl gesults0 5 10 15 20 25 30 35 4000.511.522.5x 105I te rat ion indexAveragesystemcapacity[bits/sec]  N=16N=32N=64Figure 4.3: Convergence of our proposed algorithm for different number of subcarriersarea with uniform distribution. The relay nodes are located inside and the destination nodesare distributed outside the inner circle. The noise power spectral density (c0) and band-width of each subcarrier (l ) are assumed to be 5×10−5 Watt/Hz and 20 KHz, respectively.The energy harvesting efficiency of the relay nodes is  = 50%. The channel coefficientsare independent and identically distributed (i.i.d.) circularly symmetric complex Gaussianrandom variables, with the path loss coefficient set as  = 4. The number of relay anddestination nodes is 8, i.e., b = K = 8 and number of subcarriers for each relay (nm) is 4.All the simulation results are averaged over 1000 independent channel realizations.Fig. 4.3, illustrates the convergence of our proposed algorithm based on dual decompo-sition technique for emax = 50dWm. The figure shows that the algorithm converges within25 iterations and proves the effectiveness of the proposed scheme.Fig. 4.4, depicts the average system capacity in terms of the power budget of the source(emax) for different number of subcarriers. As shown in the figure, the total capacity of thesystem grows both with the increase of emax and the number of subcarriers.Fig. 4.5, depicts the cooperation ratio in terms of emax for different number of subcarriers.Cooperation ratio is defined as the fraction of subcarriers used for cooperative transmission.As shown in the figure, by increasing emax, the cooperation ratio decreases, because there764CJC cumerixvl gesults45 50 55 60024681012141618x 105Pmax (dBm)Averagesystemcapacity[bits/sec]  N=8N=16N=32N=64Figure 4.4: Average system capacity vs. emax for different number of subcarriers30 35 40 45 50 55 6000.20.40.60.8Pmax (dBm)Cooperationratio  N=8N=16N=32Figure 4.5: Cooperation ratio vs. emax for different number of subcarriers774CJC cumerixvl gesults40 45 50 55010002000300040005000600070008000Pmax (dBm)Averageenergyefficiency[bits/Joule]  N=16N=32N=64Solid line : No harvest ing scenarioDashed line : Proposed scenarioFigure 4.6: Average energy efficiency vs. emax for different number of subcarriersis enough power for the transmitters to transmit over the direct link. In addition, as thenumber of subcarriers increases the cooperation ratio improves.Fig. 4.6, shows the energy efficiency in terms of emax for different number of subcarriers.The energy efficiency is defined as giRei , where gi is the total system capacity and ei isthe total power consumed in the system. ei contains both the transmission and the constantpower of all the nodes. We assume that the constant power consumption for the source is20l and and the one for relay and destination nodes is 5l . We compare our proposedscheme with a scenario that there is no energy harvesting. As shown in the figure, theperformance of our proposed scheme is close to that of “No harvesting” scenario in termsof energy efficiency. It is worth to mention that our proposed energy harvesting schemeoutperforms the “No harvesting” scenario in terms of fairness, since the relay nodes do notspend their energy for the purpose of relaying.78Xhvptzr Jfoh Afivrz gzsourxz Alloxvtion forEnzrgy Hvrvzsting XommunixvtionhystzmsIn this chapter, we investigate resource allocation problem for energy harvesting wirelesscommunication systems considering QoS provisioning. The accomplished works and researchcontributions of this chapter are briefly described in the following.JCF Axxomplishzy lorks vny gzszvrxh XontriwutionsWe consider an EH system model with single source and multiple destination nodes, inwhich the source harvests energy from environment. For example, the source can be a BSor an access point that harvests solar energy and the destination nodes can be wireless userequipments. We consider that the harvesting energy at the source node is uncertain andinsufficient to satisfy the QoS of the users thoroughly. Consequently, existing throughputmaximization based algorithm [41] may not provide efficient solution and fairness amongthe users. To address this problem, we propose two different utility functions and developresource allocation algorithms with QoS provisioning to users and show the implications ofuncertain and limited harvesting energy on resource allocation policy.At first, we define the utility function in terms of dissatisfaction of the users, and developresource allocation algorithm such that total user dissatisfaction over a period of time is79JCFC Axxomplishey lorks vny gesevrxh Contriwutionsminimized. Since the optimization objective is to minimize the total user dissatisfactionover a period, we denote it as “best effort” resource allocation problem, in which QoS isnot satisfied for all users at all instances. We formulate the resource optimization problemusing goal programming approach and provide an upper bound for optimal solution assumingthe availability of complete and non causal information of CSI and energy arrival process.We denote this upper-bound solution as “offline”. We obtain closed form analytical powerallocation solution based on dual decomposition technique. Next, we consider a more realisticscenario, in which only causal information regarding CSI and harvesting energy is available.We develop an efficient algorithm based on dynamic programming (DP) to obtain the optimalsolution of “best effort” resource allocation problem, and denote this solution as “online”.Next, our goal is to maximize the number of admitted users over a certain period andprovide guaranteed QoS to the admitted users. Unlike the “best effort” scheme, our objectiveis to satisfy some of the users at their desired QoS requirements once they are admittedconsidering limited and uncertain harvesting energy. Joint admission control and powerallocation problem for EH system under practical constraints is non-polynomial (NP) hardand has not been addressed in the literature. To address this problem, at first, we developefficient sub-optimal “offline” admission control scheme assuming the availability of completeand non causal information of CSI and harvesting energy. Next, we consider the practicalscenario with causal information and develop sub-optimal “online” admission control andpower allocation algorithm. We compare our proposed DP-based algorithm with a “naive”admission control algorithm based only on instantaneous information.The rest of the chapter is organized as follows. In Section 5.2, the system model is pre-sented. In Section 5.3 and 5.4, the problem formulations and “offline” and “online” resourceallocation algorithms are developed for the “best effort” and “admission control” resourceallocation problems, respectively. In Section 5.5 we conduct comprehensive simulations todemonstrate the effectiveness of our proposed schemes.80JC2C hystem boyelJCG hystzm boyzlWe consider a general EH system model with one source node and c destination nodes.The source node harvests energy from the environment which is renewable. We assume thatthe source of energy is available over a certain period of time, for example, solar energy isonly available during the day. We consider that the process of energy harvesting and datatransmission occur in limited number of time slots. We consider a transmission block size ofK time slots, where in each time slot the source node transmits to the users in orthogonalfrequency channels. We also assume that the harvested energy needs to be utilized by theend of Kth time slot. Without loss of generality, the duration of each time slot is assumed tobe 1 sec. Therefore, the energy and the power terms will be used interchangeably in the restof this chapter. Let us denote the indexes for time slot by k and for user by i, respectively.We also denote the channel gain (or, channel power gain) from the source node to user i atkth time slot by hiPk. We further assume that the channel gain remains constant in each timeslot. We consider that each user has different QoS requirements denoted by fohiPk, whichvaries over time. The amount of energy harvested at source node in kth time slot is denotedby Hk and the amount available at initial time k = 0, is denoted by H0. In typical scenarios,the harvesting energy has a slow variation over time [79] and therefore, we assume that it isconstant in each time slot. For simplicity, we assume that the battery has infinite capacity.Resource allocation for EH systems considering the capacity limitation of the battery havebeen discussed in [40],[43].We assume that the available energy is insufficient to satisfy the QoS requirements of allthe users at all the instances. For the case where energy is sufficient to satisfy the QoS of allthe users, system capacity maximization problem with QoS constraints is feasible and canbe solved similar to [49]. For our case, the desired QoS of users are conflicting objectives.This is because increasing the rate of one user may result in decreasing the rate of others, asthe power is not sufficient to satisfy the QoS of all the users. The motivation of this study is81JCHC West Effort gesourxe Alloxvtion erowlemto show the influence of uncertain and limited harvesting energy on QoS provisioning basedresource allocation policy.We formulate the resource optimization problem for two different cases considering twodifferent objective functions. In the first case, we assume all the users receive some data inall time slots, however due to the power limitation, their required QoS may not be satisfied.We call this problem “best effort”, since the objective is to minimize the total dissatisfactionof all the users over K time slots, i.e., to satisfy the users as much as possible given the powerbudget. In the second case, we formulate the problem considering admission control, i.e., ineach time slot only some of the users are admitted and receive their data with guaranteedQoS. The non-admitted users will not receive anything in that particular time slot. In thiscase, the objective is to jointly maximize the number of admitted users with guaranteed QoSand maximize the system throughput considering the limited power budget. We denote it as“admission control” problem. In the following sections, we formulate the two optimizationproblems discussed above and provide efficient solution approaches.JCH Wzst Effort gzsourxz Alloxvtion erowlzmIn this problem, we assume that all the users are admitted and receive data from the sourcenode in all the time slots. Due to insufficient power, it is not possible to satisfy the QoS ofall the users completely. Goal programming is a suitable method to address such problems,in which the QoS of users are the targets or goals, and the objective is to minimize the totaldissatisfaction of the users. Dissatisfaction of user i at time k is defined as the deviationfrom its required QoS, and is denoted by iPk. We call this problem “best effort” resourceallocation, since the goal is to satisfy the users as much as possible with the insufficient82JCHC West Effort gesourxe Alloxvtion erowlempower. We formulate the problem through goal programming [80] asminimizeN;PPeN;PK∑k=1c∑i=1iPksubject to :X1 : l log2(1 +eN;PhN;Pc0l) + iPk = fohiPkP ∀iP kX2 :k∑l=1c∑i=1eiPl ≤k−1∑l=0HlP k = {1P 2P OOP K}X3 : eiPkP iPk ≥ 0P ∀iP k(5.1)where eiPk is the transmit power of source node to send the message for user i at timek. c0 is the receiver noise which is assumed to be AWGN, and l is the bandwidth of thechannel.In (5.1), X1 shows that iPk is the deviation of the achieved rate for user i at time k fromthe desired QoS given by fohiPk. X2 is the causality constraint, which states that the totalpower that can be used for transmission at time k should be less than the harvested energyminus the energy consumed until time slot k − 1. Note that X2 can also be written asc∑i=1eiPk ≤k−1∑l=0Hl −k−1∑l=1c∑i=1eiPlO (5.2)X3 is the non-negative constraints on iPk and eiPk. iPk is assumed to be non-negative.This is because we do not want some users to have surplus rates when some others have notyet met their requirements as power is insufficient to satisfy all QoS.Next, we provide a framework to solve problem (5.1). Based on the availability of infor-mation, we consider two scenarios: offline and online resource allocation. In the offline case,we assume that we have complete information about the harvesting energy (Hk), and thechannel gains (hiPk) prior to transmission and resource allocation. Although this assumptionis very optimistic, it provides the upper bound of the solution of problem (5.1) when onlycausal information is available. It also gives insight into the resource allocation policy andis useful for predictable environments. The second scenario is the online resource allocation,83JCHC West Effort gesourxe Alloxvtion erowlemwhere we assume that only causal information about the harvesting energy and channel gainis available. We provide optimal online solution using DP considering causal information.JCHCF dfflinz Wzst Effort gzsourxz AlloxvtionThe optimization problem discussed before, assuming all the parameters are deterministicand known in advance, is a convex problem with respect to the optimization variables,therefore convex optimization algorithms and tools [60] can be used to solve the problem.Since the problem is convex, Slater’s condition, and therefore, strong duality holds; theduality gap is zero and we can obtain the optimal solution of the primal problem by solvingits dual problem. We first re-write the problem by substituting X1 into the objective function.minimizeeN;PK∑k=1c∑i=1[fohiPk −l log2(1 + eN;PhN;Pc0l )]subject to :X2 :k∑l=1c∑i=1eiPl ≤k−1∑l=0HlP k = {1P 2P OOP K}X3 : 0 ≤ eiPk ≤ c0lhN;P (2QTSN;PW − 1)O ∀iP k(5.3)In (5.3), X3 is modified to consider iPk ≥ 0. The objective function can be furthersimplified tomaximizeeN;PK∑k=1c∑i=1log2(1 +eN;P:hN;Pc0l) (5.4)Now, the Lagrangian function can be defined asa(PP ) =K∑k=1c∑i=1log2(1 +eN;PhN;Pc0l) +K∑k=1k[ k−1∑l=0Hl −k∑l=1c∑i=1eiPl]P (5.5)where  = [1P 2P OOOP kP OOOP K ] is the Lagrangian multiplier vector associated with X2. Pis the vector of all eiPk. Constraint X3, which is not incorporated in (5.5), will be consideredlater.The dual problem can be solved via dual decomposition method. The detail of the84JCHC West Effort gesourxe Alloxvtion erowlemsolution is given below.holving thz suwprowlzmsIn each iteration of the algorithm, we find the optimal value of the primal variable P for agiven multiplier  using KKT conditions as follows. The first order necessary condition is@a(PP )@eiPk|eN;P=eN;P∗ = 0P (5.6)which can be calculated as@a(PP )@eiPk=hN;Pc0lln(2)(1 +eN;PhN;Pc0l)−K∑l=klO (5.7)Therefore, we can find the optimal value of eiPk incorporating the constraint X3 of (5.3) ase ∗iPk =[1ln(2)K∑l=kl− c0lhiPk]N0WhN;P(2QTSN;PW −1)0P (5.8)where the notation [x]ba is defined as[x]ba =a if x Q ax if a ≤ x ≤ bb if x S b.The optimal power allocation policy in (5.8) has the form of water-filling solution [60].In order to find the optimal values of deviations ∗iPk, the optimal values of e∗iPk need to beplugged in the equation of X1 in (5.1).85JCHC West Effort gesourxe Alloxvtion erowlemholving thz mvstzr prowlzmIn the subproblems, the optimal values of the primal variables are obtained for given multi-plier . In the master problem, we update the Lagrange multipliers using the sub-gradienttechnique ast+1k =[tk − tk( k−1∑l=0Hl −k∑l=1c∑i=1eiPl)]+P (5.9)where tk are the positive step sizes, and t is the iteration index.In general, it is not reasonable to assume the availability of non causal and completeknowledge of harvesting energy (Hk) and the channel gain (hiPk). In the following, we consideronly causal information for these parameters and provide solution for the resource allocationproblem.JCHCG dnlinz Wzst Effort gzsourxz AlloxvtionIn this section, we propose a solution for the problem in (5.1) assuming only causal infor-mation of harvesting energy (Hk) and the channel gain (hiPk) are available. This scenariois more realistic, since in most of the practical cases, it is not possible to achieve perfectinformation of upcoming Hk and hiPk. In this section, we model harvesting energy (Hk)and the channel gain (hiPk) as a joint random process and formulate the resource allocationproblem as Markov decision process (MDP) in finite-horizon, and provide an optimal onlinealgorithm via DP.We assume that the channel information is available in each time slot, i.e., at time slotk we know about hiPk. Moreover, the amount of energy harvested (Hk) at time k is notknown until the end of the time slot, i.e., we know about Hk at time k + 1. Here, a firstorder Markov model is assumed for the channel gains (hiPk). Experimental measurementsand mathematical analysis show that the first order Markov model is a valid assumptionfor Rayleigh fading channels [81]-[82]. The energy arrival process (Hk) is also assumed tohave first order Markovian model. In [83], using empirical measurements with supporting86JCHC West Effort gesourxe Alloxvtion erowlemanalysis, the suitability of using stationary Markov models for harvesting solar energy isvalidated. The first order Markov models for both CSI and energy arrival process are provedto be valid models in practice and make the analysis and implementation mathematicallytractable. We assume that harvesting energy and the channel gain are independent and wedenote their transition probability as p(Hk|Hk−1) and p(hiPk|hiPk−1). We also assume thatthese transition probabilities are independent of time and have joint pdf given byp(Hk−1P hk) = p(Hk−1|Hk−2)c∏i=1p(hiPk|hiPk−1)P (5.10)where we have assumed that the channel gain from the source node to different users areindependent. The joint distribution can be obtained via long-term measurements.Let us define the available energy at source node at time k as Wk. Therefore, X2 of (5.1)can be re-written asX2 :c∑i=1eiPk ≤ WkP ∀k (5.11)where Wk is given byW1 = H0Wk =k−1∑l=0Hl −k−1∑l=1c∑i=1eiPl= Wk−1 +Hk−1 −c∑i=1eiPk−1O k = {2P OOP K}(5.12)Since Wk is only dependent on Wk−1, it also follows first order Markov model.Let us define the state of the system at time slot k ashk = (WkP Hk−1P hk)O (5.13)The state of the problem hk consists of the available energy Wk at the source node at currenttime k, the harvested energy Hk−1 at previous time k − 1 and the channel gains hk of thecurrent time slot. hk is the vector of channel gains from source node to all the users at time87JCHC West Effort gesourxe Alloxvtion erowlemk, i.e., hk = {h1PkP h2PkP OOOP hcPk}. Having the state of the system hk, we can decide how muchpower the source node can spend to send the information to the users. The feasible set ofactions for the transmission power .k at time k is.k = {(e1PkP e2PkP OOOP ecPk)|eiPk ≥ 0Pc∑i=1eiPk ≤ Wk}O (5.14)A feasible policy is defined as the sequence of decisions from feasible set of actions. Let usdenote the set of feasible policy as Π.Our goal is to find an optimal and feasible policy which minimizes the dissatisfaction ofthe users over K time slots. For a given initial state h0, the optimal value can be calculatedas ∗ = minimizex∈ΠK∑k=1Z{c∑i=1iPk|xP h0}P (5.15)where Z{O} denotes the statistical expectation with respect to the channel gains and har-vesting energies.To obtain optimal online solution, we introduce Bellman’s equations [84]. Assuminginitial state is known, the minimum cost can be recursively obtained through Bellman’sequation asJK(hK) = minimize.Kc∑i=1iPK (5.16)and for k = {1P 2P OOP K − 1}Jk(hk) = minimize.Pc∑i=1iPk + J¯k+1(hkP ek)P (5.17)where ek =c∑i=1eiPk andJ¯k+1(hkP ek) = ZH˜PPh˜P+1{Jk+1(Wk − ek + H˜kP H˜kP h˜k+1)|Hk−1P hk}P (5.18)88JCHC West Effort gesourxe Alloxvtion erowlemin which H˜k and h˜k+1 are random variables demonstrating the harvested energy and thechannel gains at the present time slot. ZH˜PPh˜P+1{O} can be calculated using the joint pdf inequation (5.10).Bellman’s equations provide the optimal online solution given the causal and incompleteinformation. The proof is given in [84]. In order to solve the problem optimally in an onlinemanner, we develop Algorithm 7 with two phases: planning and transmission. The planningphase is done before transmission is started. In this phase, we find optimal power allocationpolicy for all possible values of available energy Wk, harvesting energy Hk−1, and channelgain hk. We start with the last time slot, where all the available energy at source node shouldbe utilized, i.e.,c∑i=1eiPK = WK . We solve (5.16) for all possible values of WK , and hK . Then,for k = {1P 2P OOP K−1}, we recursively solve (5.17) for all possible Wk, Hk−1 and hk. We savethe optimal values of transmission power for different values of Wk, Hk−1 and hk in a lookuptable to use them when the transmission starts. Second phase is the transmission phase, inwhich information is transmitted to the users using optimal power allocation policy. At timeslot k, Wk, hk, and Hk−1 become known. Therefore, we can select the appropriate values forthe transmission power (eiPk) from the look up table prepared in the planning phase.Algorithm L : Optimal online best effort resource allocation algorithmF: elvnning phvsz O2: Calculate JK(hK) using equation (5.16), ∀WK P hKH: for k = K − 1 : 1 yoI: Calculate Jk(hk) using equation (5.17), ∀WkP hkP Hk−1J: zny forK: irvnsmission phvsz OL: Available information at time slot k : {WkP hkP Hk−1}M: for k = 1 : K yoN: From the planning phase find .∗k that maximizes Jk(hk) for given {WkP hkP Hk−1}.FE: Consume .∗k amount of energy to transmit information to users.FF: Update the available energy (Wk+1) in the battery using equation (5.12).F2: zny forFH: rzturn .∗k, ∀k89JC4C Joint Aymission Control vny eower Alloxvtion erowlemJCI Joint Aymission Xontrol vny eofizr AlloxvtionerowlzmIn the previous section, we proposed “best effort” resource allocation schemes with theobjective of minimizing the total dissatisfaction of all the users, however the QoS of allusers are not guaranteed due to scarcity of power. In this section, we want to develop an“admission control” scheme with the objective of maximizing the number of admitted usersover K time slots with guaranteed QoS. In each time slot, some users will receive datawith guaranteed QoS from the source, and the rest will not receive anything. The primarygoal of the admission control algorithm is to maximize the number of admitted users withguaranteed QoS.In conventional systems, the source power is connected to a grid and is constant over time.Therefore, the existing admission control algorithms for conventional systems [85]-[86] seekto admit as many users as possible in each time slot. However, developing admission controlalgorithms for EH systems is more challenging. This is because the amount of availableenergy can vary over time due to the causality constraints of the harvesting energy. As aresult, admitting as many users as possible in each time slot may not be the best idea. If wereserve more energy for upcoming time slots, we may admit more users in overall K timeslots, due to lower data rate requirements or better channel gains at future time slots.In the best effort problem, the goal is to minimize the overall dissatisfaction of users.Since the power is not enough to satisfy the QoS of all the users, we do not allocate morepower to a user than the amount it requires to satisfy the QoS. However, in admissioncontrol problem, the primary goal is to admit the maximum possible number of users withguaranteed QoS subject to limited available power. Therefore, the dissatisfaction of theadmitted users is zero. After the admitted users set is determined, it may happen that theoverall harvested energy is more than the sum of the power required to satisfy the QoS of theadmitted users. The next question is how to utilize the unused power? For our admission90JC4C Joint Aymission Control vny eower Alloxvtion erowlemcontrol scheme, we have chosen the secondary objective to be the maximization of the sumrate so that the remaining power is not wasted.The objective of this optimization problem is to jointly maximize the number of admittedusers over K time slots and the sum rate for the admitted users. It can be formulated as atwo-stage problem given in (5.19) and (5.20) [85]-[86].maximizeA⊆{1P2P::Pc}×{1P2P::PK}|A|subject to :X1 : l log2(1 +eN;PhN;Pc0l) ≥ fohiPk ∀(iP k) ∈ AX2 :k∑l=1∑{i|(iPl)∈A}eiPl ≤k−1∑l=0Hl k = {1P 2P OOP K}X3 : eiPk ≥ 0 ∀(iP k) ∈ A(5.19)maximizeeN;P∑(iPk)∈Ajlog2(1 +eN;PhN;Pc0l)subject to :X1 : l log2(1 +eN;PhN;Pc0l) ≥ fohiPk ∀(iP k) ∈ AjX2 :k∑l=1∑{i|(iPl)∈Aj}eiPl ≤k−1∑l=0Hl k = {1P 2P OOP K}X3 : eiPk ≥ 0 ∀(iP k) ∈ Aj(5.20)In the first stage problem in (5.19), our objective is to maximize the number of admittedusers over time. The set of admitted users over time is denoted by A and |A| denotes thecardinality of the set. We determine the users that can be admitted to the system in eachtime slot such that the total number of users over K time slots are maximized. However,we may not utilize all the harvested energy by allocating the minimum power required tosatisfy the QoS of the admitted users. In order to utilize all the power, we solve the secondstage problem (5.20). In the second stage problem, the sum rate is maximized for the setof admitted users with guaranteed QoS provisioning. In the first stage, there can be severalsets A1 , A2 , ... which are the optimal solutions for (5.19). Therefore, in the second stage,91JC4C Joint Aymission Control vny eower Alloxvtion erowlemamong these sets the one which gives the highest value of problem (5.20) will be selected.Problem (5.19) is very difficult to solve as it falls in the class of NP hard problem. Dueto the limitation of the available power, if all the users are admitted in all time slots, theirQoS cannot be guaranteed and the problem in (5.20) becomes infeasible. Therefore, in eachtime slot, some of the users should be rejected. There are different criteria for rejectingusers in admission control problems. In the schemes proposed here, the rejection criterionis based on the power required to satisfy the QoS of users; i.e., the users with less requiredpower are admitted first, so that more users can be admitted to the system. Once the setof admitted users are obtained, the sum rate maximization problem in (5.20) is convex andconvex optimization techniques can be used to derive the solution.The two-stage problem can be formulated as a single-stage multi-objective problem [86],however the problem is still NP hard. Obtaining the optimal solution for admission controlproblem is extremely difficult, if possible and therefore, efficient sub-optimal solutions arerequired. Next, we propose sub-optimal offline and online schemes to solve the admissioncontrol problem for EH systems.JCICF dfflinz Aymission Xontrol vny eofizr AlloxvtionIn this section, we propose sub-optimal offline resource allocation policy for admission controlproblem.First, we find the set of users in each time slot that can be admitted. To do so, thepower required to satisfy the QoS of each user in each time slot is calculated. Then, we willsort these powers in an increasing order and admit the users with lower power requirements.In this way we can admit more users and fulfill our primary objective of maximizing thenumber of admitted users. However, when admitting a user, we have to check whether thecausality constraints on power are satisfied. If not, we should not admit that user.Once the set of admitted users are obtained, it may happen that the sum of requiredpower to guarantee the QoS is less than the total available power. Therefore, in the second92JC4C Joint Aymission Control vny eower Alloxvtion erowlemstage, sum rate maximization problem (5.20) is solved subject to causality constraints onpower. Using techniques similar to the offline “best effort” scheme discussed in the previoussection, a water-filling solution can be obtained for problem (5.20). The Lagrangian functionof problem (5.20) is defined asa(PP ) =∑(iPk)∈Ajlog2(1 +eN;PhN;Pc0l) +K∑k=1k[ k−1∑l=0Hl −k∑l=1c∑i=1eiPl]P (5.21)Using KKT conditions, a water-filling solution for the optimal values of power eiPkP ∀(iP k) ∈Aj can be derived ase ∗iPk =[1ln(2)K∑Q=PQ− c0lhN;P]∞N0WhN;P(2QTSN;PW −1)P (5.22)in which we can update the Lagrangian multipliers with sub-gradient method given byt+1k =[tk − tk( k−1∑l=0Hl −k∑l=1c∑i=1eiPl)]+P (5.23)where tk are the positive step sizes, and t is the iteration index.The offline algorithm to solve the joint admission control and power allocation problemis given as follows.Algorithm M : Offline admission control and power allocation algorithmF: For all (iP k) pairs, find the eiPk such that the rate is equal to the desired QoS:eiPk =c0lhiPk(2QTSN;PW − 1)O2: For all (iP k) pairs, sort eiPk in an increasing order and denote the sequence by h ={sj|j = {1P 2P OOOP cK}}. Set j = 1. Denote set A = {} for admitted users.H: Check the causality constraint for admitted users A = A||{(iP k)|sj = eiPk}, where || isthe concatenation symbol. If the constraints are satisfied, update the admitted users setby A = A||{(iP k)|sj = eiPk}.I: If j = cK go to step 5, zlsz j = j + 1 and go to step 3.J: For admitted users set A, find e ∗iPk using equations (5.22) and (5.23).K: rzturn A and e ∗iPk.93JC4C Joint Aymission Control vny eower Alloxvtion erowlemJCICG dnlinz Aymission Xontrol vny eofizr AlloxvtionIn this section, we propose an online solution for the joint admission control and powerallocation problem. As mentioned earlier, online resource allocation is more realistic thanthe offline scheme, since in most of the cases, achieving perfect information of upcoming Hkand hiPk is impossible. For online solution, we assume only causal information of harvestingenergy Hk and the channel gain hiPk. Since DP is a well-known technique to solve problemswith causal models, we propose our sub-optimal online solution based on DP.Before introducing our DP-based algorithm, we first propose a naive online techniquebased on instantaneous information. In this method, we find the maximum number of usersthat can be admitted in each time slot without considering the future time slots. We startrejecting the user that requires highest amount of power to satisfy its QoS so that the problembecomes feasible with minimum number of user removal. The algorithm is equivalent to theoffline scheme algorithm 9, when the number of time slot equals to one. The details of themethod in given in algorithm 9.Algorithm N : Naive admission control and power allocation algorithm for each time slot kF: At time slot k for all users, find the eiPk(hk) such that the rate is equal to the desiredQoS:eiPk(hk) =c0lhiPk(2QTSN;PW − 1)O2: For all users at time slot k, sort eiPk(hk) in an increasing order and denote the sequenceby h = {sj|j = {1P 2P OOOP c}}. Set j = 1. Denote set Ak(hk) = {} for admitted users.H: Check the causality constraint for admitted users Ak(hk) = Ak(hk)||{(iP k)|sj =eiPk(hk)}, where || is the concatenation symbol. If the constraint is satisfied, updatethe admitted users set by Ak(hk) = Ak(hk)||{(iP k)|sj = eiPk(hk)}.I: If j = c go to step 5, zlsz j = j + 1 and go to step 3.J: rzturn Ak(hk) , eiPk(hk).Although our proposed naive algorithm 9 is simple, in the following, we provide an intu-itive example in Table 5.1 to show why algorithm 9 is not efficient and DP-based techniquesare required. Let us assume that we have a system with c = 4 users and the transmission94JC4C Joint Aymission Control vny eower Alloxvtion erowlemis done within K = 4 time slots. The harvesting energy and the required power to satisfythe QoS of each user in each time slot is shown in the table. Using algorithm 9, we findthe number of admitted users in each time slot. As algorithm 9 does not consider the infor-mation of the future time slots, it will consume all of the available power at each time slot.From the table, we can see the total number of admitted users based on algorithm 9 is 7.However, “Case A”, a heuristic but more efficient admission control scheme admits one moreuser (total 8), while the causality constraints of power is still satisfied. The performancecomparison of “Case A” with algorithm 9 is shown in Table 5.1.Table 5.1: An example to show the drawback of Algorithm 9Inyzx of timz slot k R 1 k R 2 k R H k R 4Hk−1 =Joulzs) H F ECJ ECJZnzrgy rzquirzy to svtisfy thz foh of thz uszrs ∀i =Joulzs) F ECJ ECJ ECJcumwzr of vymittzy uszrs wvszy on vlgorithm N H 2 F Feofizr xonsumption of wvszy on vlgorithm N H F ECJ ECJcumwzr of vymittzy uszrs B Cvsz V 2 H 2 Feofizr xonsumption of uszrsB Cvsz V 2 FCJ F ECJNote that by admitting lower number of users than |Ak(hk)| at time slot k, “Case A”scheme admits more users at the following time slots. The reason can be better channelcondition or lower required QoS at the future time slots. The above example, shows thatAlgorithm 9 is not efficient over K time slots as it is only based on instantaneous informationand motivates us to look for an intelligent online approach which takes into account thepossible scenarios of the future time slots. The question is how to incorporate the unknownnon causal information for a better sub-optimal technique? In the following, we propose aDP-based admission control algorithm which takes into account the possible forecast of thefuture time slots.The maximum number of users that can be admitted to the systems in time slot k atstate hk is |Ak(hk)|, which can be derived from algorithm 9. The cardinality of the feasible95JC4C Joint Aymission Control vny eower Alloxvtion erowlemset of actions for the number of admitted users in time slot k at state hk isj = 0 : |Ak(hk)|P (5.24)which indicates that up to |Ak(hk)| users1 can be admitted. Depending on the channelquality or lower QoS requirements of the future time slots, it may happen that if we admitnumber of users lower than |Ak(hk)| at time slot k, we can admit more users at the followingtime slots. Therefore, in order to maximize the number of admitted users over time, weconsider all possible number of admitted users j, starting from 0 to |Ak(hk)| and calculatethe expected value of the admitted users from time slot k to the last time slot K. We choosethat number of admitted user in time slot k which maximizes the total number of admittedusers over K time slots. Mathematically, it can be achieved by maximizing the followingBellman’s equation which shows the expected value of number of admitted user from timeslot k to the last time slot (K):ajk(hk) = j + a¯jk+1(hk) (5.25)where a¯jk+1(hk) is defined asa¯jk+1(hk) = ZH˜PPh˜P+1{ajˆk+1(Wk − e jk (hk) + H˜kP H˜kP h˜k+1) |hkP Hk−1} (5.26)and e jk (hk) is the total power consumed when the number of admitted users is j. As discussedin the offline case, if we allocate only the minimum power required to meet the QoS, we mighthave some unused power at the end. Once the users are admitted with guaranteed QoS, thenext step is to optimally utilize the unused power to maximize the sum rate. Therefore,1It is plvusiwlz to vssumz thvt fihzn vymitting lofizr numwzr of uszrs thvn thz mvximum possiwlz numwzr|Ak=Sk)|A fiz rzjzxt thz onzs fiith highzr rzquirzy pofizr to vymit morz uszrsC96JC4C Joint Aymission Control vny eower Alloxvtion erowlemtransmission power .∗k(hk) policy can be obtained by maximizing Bellman’s equation asJk(hk) = maximize.P∑(iPk)∈Ajlog2(1 +eN;PhN;Pc0l) + J¯k+1(hkP ek)P (5.27)where .k is defined as.k = {(e1PkP e2PkP OOOP ecPk)|eiPk ≥ c0lhiPk(2QTSN;PW − 1)P ek =∑(iPk)∈AjeiPk ≤ Wk}P (5.28)and J¯ is defined asJ¯k+1(hkP ek) = ZH˜PPh˜P+1{Jk+1(Wk − ek + H˜kP H˜kP h˜k+1)|Hk−1P hk}O (5.29)It is worth mentioning that the set of admitted users for the last time slot is calculatedusing Algorithm 9, as there is no upcoming time slots and we want to consume all theavailable power. In addition, we can find the transmission power policy for the last time slotusing equations (5.22) and (5.23). The details of the DP-based online algorithm is providedin the following.Similar to Algorithm 7, in order to solve the problem optimally in an online manner,we have two phases: planning and transmission, where the planning phase is done beforetransmission is started. In planning phase, we find the admitted users A∗k(hk) and powerallocation policy .∗k(hk) for all possible states of the problem. Recall that the state hkconsists of the available energy Wk at current time k, the harvesting energy Hk−1 at previoustime slot k−1 and the channel gains hk of time k. Having the state of the system hk, we candecide which users to admit in each time slot and how much power the source node shouldspend to send the information to the admitted users. We start planning from the last timeslot, and we find the admitted users and power allocation policy for all possible values ofWK , and hK . Then, for k = {1P 2P OOP K − 1}, we recursively find the admitted users A∗k(hk)and power allocation policy .∗k(hk) for all possible Wk, Hk−1 and hk. We save the optimal97JC4C Joint Aymission Control vny eower Alloxvtion erowlemvalues of .∗k(hk) and A∗k(hk) in a lookup table to use them when the transmission starts.In the transmission phase, once we know the actual Wk, Hk−1 and hk we use the lookuptable to find the optimal power allocation policy and admitted users for each time slot.The algorithm to obtain online admission control and power allocation policy is given inalgorithm 10.Algorithm FE : Online admission control and power allocation algorithmF: elvnning phvsz O2: Find A∗K(hK) using Algorithm 9 and .∗K(hK) using equations (5.22) and (5.23), ∀WK P hK .H: for k = K − 1 : 1 yoI: Find Ak(hk) and eiPk(hk) using Algorithm 9, ∀WkP hkP Hk−1J: for j = |Ak(hk)|+ 1 : 1 yoK: ajk(hk) = j + a¯jk+1(hk)L: Ajk(hk) = Ak(hk)M: Ak(hk) = Ak(hk) \ {i|i = argmax{eiPk(hk)}}N: zny forFE: jˆ(hk) = argmax{ajk(hk)}FF: A∗k(hk) = Ajˆ(hP)k (hk)F2: Find the optimal power allocation .∗k(hk) for admitted users set A∗k(hk) using equation(5.27).FH: zny forFI: irvnsmission phvsz OFJ: Available information at time slot k : {WkP hkP Hk−1}FK: for k = 1 : K yoFL: From the planning phase find the admitted users A∗k and it corresponding transmitpower .∗k for given hk = {WkP hkP Hk−1}.FM: Consume .∗k amount of energy to transmit information to admitted users (A∗k).FN: Update the available energy (Wk+1) in the battery using equation (5.12).2E: zny for2F: rzturn A∗k and .∗k , ∀kIn the following numerical results section, we show that DP-based online algorithm,i.e., Algorithm 10, achieves significant performance improvement in terms of the numberof admitted users, dissatisfaction and throughput over Algorithm 9, which supports thediscussions and analysis of this section. In addition, we show that our proposed DP-basedonline algorithm performs notably close to the offline algorithm.98JCJC cumerixvl gesultsA BPAAPABPBAPBBPCCPCBPBCCFigure 5.1: Markov model for the channel gainJCJ cumzrixvl gzsultsIn this section, we conduct extensive simulations to evaluate the performance of EH systemswith QoS provisioning. We compare the performance of our proposed DP-based onlineschemes, i.e., best effort and admission control, with offline schemes considering differentsystem parameters. In addition, we compare the performance of our proposed resourceallocation schemes to the one proposed in [41] with no QoS provisioning. The bandwidthof the channel is l = 20 KHz and the noise power density is c0 = 5 × 10−25 WattRHz.We consider a three state Markov model for the channel gain as depicted in Fig. 5.1. Thevalues of the states A, W, and X are 0O5× 10−4, 1× 10−4, and 1O5× 10−4, respectively. Thetransition matrix of the channel gain is given by [87]-[88]eAA eAW eACeWA eWW eWCeCA eCW eCC =0O3 0O7 00O25 0O5 0O250 0O7 0O3For simplicity, we assume finite number of states for harvesting energy, which is shownin Fig. 5.2. The set of values for states are {H1P H2P H3P H4} = {0O25HeP 0O5HeP 0O75HeP He}.We vary He to show the impact of the EH rate on the performance of the system. Thetransition probability for given EH states is considered as99JCJC cumerixvl gesults0.25 He0.5 He1/21/21/31/31/31/30.75 HeHe1/31/31/21/2Figure 5.2: Markov model for the harvesting energyeH1PH1 eH1PH2 eH1PH3 eH1PH4eH2PH1 eH2PH2 eH2PH3 eH2PH4eH3PH1 eH3PH2 eH3PH3 eH3PH4eH4PH1 eH4PH2 eH4PH3 eH4PH4=12120 013131300 1313130 0 1212Fig. 5.3 shows the total dissatisfaction in K time slots versus the EH rate He. Wecompare the performance of “best effort” scheme with “admission control” for different datarate requirements. For both schemes, the system with lower data rate or QoS requirementhas less dissatisfaction as it is less constrained. Also, we can see that the “best effort”scheme outperforms “admission control” scheme in terms of total dissatisfaction. This isbecause for admission control, the system is required to satisfy the QoS of the admitted userscompletely and ignores the dissatisfaction of non-admitted users, which doesn’t permit thesystem to achieve the lowest possible overall dissatisfaction. As expected, in both schemes,by increasing the EH rate He, available energy at the source node increases, which in turndecreases the total dissatisfaction of the users.Fig. 5.4 shows the maximum dissatisfaction (max) of users for our proposed schemes.We define the maximum dissatisfaction asmax =maxi(K∑k=1iPk)K∑k=1c∑i=1fohiPkO (5.30)100JCJC cumerixvl gesults10 15 20 25 30 35 40024681012x 106HeDissatisfactioninKtimeslots[bits]  Bes t effor t s cheme, , QoS i , k= 0.3 i Mbit sBes t effor t s cheme, , QoS i , k= 0.4 i Mbit sAdmis s ion cont r ol s cheme, , QoS i , k= 0.4 i Mbit sAdmis s ion cont r ol s cheme, , QoS i , k= 0.3 i Mbit sFigure 5.3: Dissatisfaction in K time slots versus the EH rate (He) for c = 4 and K = 4.In Fig. 5.4 we observe similar trends to that of Fig. 5.3. We consider four users and the QoSrequirement is proportional to the index of the users. For the admission control scheme withlower values of He, user 4 is not admitted in any of the time slots as it has the highest QoSrequirement and gives the highest dissatisfaction of 0.4. As He increases and the power isenough to admit more users, the system admits user 4 in one of the time slots which reducesmax to 0.3.Fig. 5.5 depicts the throughput in K time slots (total transmitted bits) versus He fordifferent data rate requirements. Also, the throughput maximization based scheme thatdoes not consider QoS provisioning [41] is included as a benchmark. As expected, in all theschemes, by increasing He, the total throughput of the system improves. Interestingly, thethroughput comparison is not as straightforward as the one for dissatisfaction factor. Forexample, one may expect that the “best effort” scheme with lower data rate requirementswill perform better than the one with higher data rate but we observe the opposite. Thereason is that the goal of the best effort scheme is not to maximize the total throughputbut to minimize the total dissatisfaction; and increasing the data rate requirement doesnot necessarily shrink the feasible region. Besides, “admission control” scheme with higher101JCJC cumerixvl gesults10 15 20 25 30 35 4000.050.10.150.20.250.30.350.4Heδmax  Bes t effor t s cheme, QoS i , k= 0.3 i Mbit sBes t effor t s cheme, QoS i , k= 0.4 i Mbit sAdmis s ion cont r ol s cheme, QoS i , k= 0.4 i Mbit sAdmis s ion cont r ol s cheme, QoS i , k= 0.3 i Mbit sFigure 5.4: Maximum dissatisfaction ( max) versus the EH rate (He) for c = 4 and K = 4.QoS can perform either better or worse than the one with lower QoS requirement basedon the number of admitted users and power requirement of users. In addition, either ofthe proposed “admission control” or “best effort” scheme can give better total throughputperformance based on the specifications of the system. Therefore, general comments aboutspectral efficiency comparison is not valid, and the performance is highly dependent on thesystem parameters.In Fig. 5.6, we provide comparison of our proposed schemes with the scheme that does notconsider QoS provisioning [41]. For each of the schemes, we compare the energy consumptionof the source to transmit data for each user. The required energy at the source node tosatisfy the QoS of each user over K time slots is demonstrated as a benchmark. As the totalharvesting energy is not sufficient, we observe that none of the schemes can distribute thepower such that the QoS of all users are satisfied. However, we can see that the best effortscheme can only satisfy two of the users completely whereas the admission control schemethree of the user are satisfied in all K time slots.Fig. 5.7 shows the power profile of a single user over time for a particular realizationof channel gain and harvesting energy. The shaded area shows the energy required in each102JCJC cumerixvl gesults10 15 20 25 30 35 400.811.21.41.61.8x 107HeThroughputinKtimeslots[bits]  Bes t effor t s cheme, QoS i , k= 0.3 i Mbit sAdmis s ion cont r ol s cheme, QoS i , k= 0.3 i Mbit sBes t effor t s cheme, QoS i , k= 0.4 i Mbit sAdmis s ion cont r ol s cheme, QoS i , k= 0.4 i Mbit sNo QoS provis ion ingFigure 5.5: Throughput in K time slots (total transmitted bits) versus the EH rate (He) forc = 4 and K = 4.1 2 3 40102030405060User indexEnergyinKtimeslots  Energy r equ ir ed t o sat is fy QoSNo QoS provis ion ingBes t effor t s chemeAdmis s ion cont r ol s chemeFigure 5.6: Comparison of power consumed by each user for our proposed schemes and noQoS provisioning scheme, for c = 4, K = 16, He = 10 joules, and foh1Pk = foh2Pk = 1.08Mbits, foh3Pk = foh4Pk = 1.1 Mbits for all k.103JCJC cumerixvl gesults1 2 3 4 5 600.511.522.533.544.5Time s lot indexEnergy  Energy r equ ir ement t o sat is fy QoSBes t effor t s chemeAdmis s ion cont r ol s chemeFigure 5.7: Comparison of power profile over time for the proposed schemes , for c = 1,K = 6, He = 2 joules, and foh1Pk={1P3P5} = 1.08 Mbits, foh1Pk={2P4P6} = 1.1 Mbits.time slot to satisfy the QoS of the user. We observe that the “best effort” scheme allocatespower in all of the time slots to minimize the overall dissatisfaction. In addition, it doesnot allocate more power than that required to satisfy the QoS. It is obvious from the figurethat in “best effort” scheme, the user is not satisfied in all of the time slots. In “admissioncontrol” scheme, in the time slots when the user is not admitted (for this example, in timeslot 2 and 6), no power is allocated. However, when the user is admitted, the allocated poweris enough to satisfy the QoS of the user on that time slot. Unlike the “best effort” scheme,in “admission control” scheme, we allocate more power than that required to satisfy the QoSin some of the time slots. That is because when the user is admitted, there might be someexcess power after satisfying the QoS. However, that amount is not enough to admit the userin any other time slot. Since we want to utilize all the harvested energy by the end of lasttime slot, the remaining power is allocated following a water-filling pattern.In Table 5.2, we compare different performance aspects of our proposed QoS provision-ing based schemes. The simulation parameters are the same as the one used in Fig. 5.6.104JCJC cumerixvl gesultsTable 5.2: Comparison of admission control and best effort schemesBest effort scheme Vdmission control schemeiotvl numwzr of vymittzy uszrs ovzr K timz slots KI KEiotvl numwzr of svtiszy uszrs ovzr K timz slots H2 KEiotvl yissvtisfvxtion ovzr K timz slots =wits) F:FJ× FE6 I:I× FE6max L:MM× FE−4 E:EKHFJvin's fvirnzss inyzx ECIM EC2JComparing the two schemes in Table 5.2, we observe that the “admission control” schemesignificantly outperforms the “best effort” scheme in terms of the number of satisfied users.However, the “best effort” scheme performs better in terms of dissatisfaction and fairnessamong the users. To compute fairness, we have used Jain’s fairness on dissatisfaction factors,which is defined asJ =(K∑k=1c∑i=1iPk)2cKK∑k=1c∑i=12iPkO (5.31)In Table 5.3, we show a comparison between Algorithm 9 and Algorithm 10. As mentionedbefore, Algorithm 9 is naive and only uses instantaneous information about the channel andharvesting energy to allocate the resources, whereas in Algorithm 10, stochastic informationabout future time slots is used. For this experiment, the simulation parameters are c = 6,K = 6, He = 5 joules, and ∀i fohiPk={1P2P3} = 1.14 Mbits, fohiPk={4P5P6} = 1.08 Mbits. Weobserve that by using Algorithm 10, a larger number of users are admitted to the systemin overall K time slots since the stochastic information of upcoming time slots is takeninto account. In addition, Algorithm 10 outperforms Algorithm 9 in terms of throughputand dissatisfaction. However, it is clear that Algorithm 10 is more complex as we need toconstruct a look-up table based on Bellman’s equations before transmission starts. Therefore,as far as complexity is concerned, Algorithm 9 is a better candidate.Table 5.3: Comparison of Algorithm 9 and Algorithm 10Vlgorithm 9 Vlgorithm 1Eiotvl numwzr of vymittzy uszrs ovzr K timz slots N FKiotvl yissvtisfvxtion ovzr K timz slots =wits) H:E2× FE7 2:2L× FE7iotvl throughput ovzr K timz slots =wits) N:ME× FE6 F:LH× FE7105JCJC cumerixvl gesults10 15 20 25 30 35 4002468101214x 107Number of t ime slots (K )ThroughputinKtimeslots[bits]  Offl ine no QoS provisioningOffl ine best effort schemeOffl ine admission control schemeOnline no QoS provisioningOnline best effort schemeOnline admission controlFigure 5.8: Throughput in K time slots (total transmitted bits) versus the number of timeslots (K), for c = 4, He = 1 joules, and fohiPk = 0.4i Mbits.Next, we compare the performance of our proposed online and offline schemes. Fig. 5.8shows the throughput in K time slots (total transmitted bits) versus the number of timeslots K. The figure shows that the performance of online and offline schemes are very closefor both “best effort” and “admission control” algorithms. We also demonstrate the offlineand online performances of the scheme proposed in [41] with no QoS provisioning in orderto show that, the differences between our proposed QoS based offline and online schemes arecomparable to the existing scheme [41]. The performance of the offline scheme is slightlybetter than that of the online scheme because of the availability of the complete and noncausal CSI and harvesting energy information, whereas in the online schemes, only causaland incomplete information are available. Moreover, we have discretized Wk in the planningphase of online algorithms for the simulation, as we need to calculate Jk(hk) for all possibleWk. We also observe that in both online and offline schemes, by increasing the number oftime slots the throughput increases, since the total harvesting energy increases with K.106Xhvptzr 6Xonxlusions vny Futurz gzszvrxhDirzxtionsIn section 6.1 of this chapter, we briefly review the main results and highlight the contribu-tions made in this thesis. In section 6.2, we propose directions for future research.6CF XonxlusionsDifferent resource allocation schemes have been developed in this thesis for cooperative andEH communication systems. We considered user cooperation, in which the relay nodes areuser equipments which are powered by constant energy sources or the energy harvested fromthe environment.The main results of each chapter are summarized as follows:In chapter 2, we addressed the problem of energy efficiency maximization for the downlinktransmission of an OFDMA cooperative network. The relay nodes receive their own datafrom the source node while relaying the data for the destination nodes. The power andsubcarrier allocation policies are jointly optimized considering total power constraint andQoS requirements of the destination and relay nodes. The optimization problem is MINLP,which is very difficult to solve in its original form. The energy efficiency metric is a fractionaland nonlinear function, which complicates the problem further. The optimization problemwas reformulated by relaxing the integer problem and by introducing “Dinkelbach” method totackle the fractional objective function. We modified the joint relay selection and subcarrier1076CFC Conxlusionsallocation problem to a linear problem and proved that our proposed solution of the relaxedinteger problem is optimal with integer values. We proposed a novel algorithm to obtainthe optimal subcarrier assignment solution based on the Hungarian method. We developeda computationally efficient scheme to obtain both optimal power and subcarrier allocationpolicies for cooperative OFDMA systems via dual decomposition method.In chapter 3, we introduced D2D relaying systems as an example of the OFDMA-basedsystem model of chapter 2. Firstly, we investigated frequency reuse in such relaying sys-tems. We classified the D2D pairs based on the level of proximity with each other andproposed efficient subcarrier allocation techniques considering different scenarios of down-link communications. Next, we proposed distributed subcarrier pairing and relay selectionschemes for OFDM based cooperative relay networks. We maximized the throughput of thenetwork using minimal signaling overhead and provided low complexity distributed resourceoptimization techniques.In chapter 4, we focused on energy limitation factor of the relay nodes in OFDMA-basedcooperative system of chapter 2. We considered SWIPT EH protocol to power the relaynodes, and proposed resource allocation algorithm with selective relaying. We assumed thatthe relay node equipments are capable of power splitting and only the harvested power isused for the relaying purpose. A novel scheme is proposed to solve the joint optimizationproblem of power and subcarrier allocation, and relay and transmit mode selection in thisOFDMA cooperative system.As wireless EH technology is only efficient to charge small nodes in communication sys-tems, in chapter 5, we focused on renewable energy sources for charging the wireless nodes.We investigated the problem of resource allocation in EH systems with QoS provisioning tothe users. Note that the energy harvested from environment may not be enough to satisfythe QoS of all users due to its random nature. To address this problem, two different resourceallocation policies were proposed. The first scheme is defined as “best effort”, in which theobjective is to minimize the total dissatisfaction of users over a period of time. We developed1086C2C Future gesevrxh Dirextionsoptimal offline and online resource allocation policies for this problem. The offline resourceallocation problem assumes the availability of complete knowledge of CSI and harvestingenergy and is efficiently solved using dual decomposition algorithm. We proposed an algo-rithm based on DP to obtain the online optimal solution considering causal and incompleteinformation of CSI and harvesting energy. Secondly, we proposed an “admission control”scheme, in which the objective is to maximize the number of admitted users with guaranteedQoS. As the admission control problem is NP hard, sub-optimal online and offline solutionsare proposed. We provided extensive numerical analysis to demonstrate the effectiveness ofour proposed schemes.6CG Futurz gzszvrxh DirzxtionsIn this section, we provide some possible research directions that can be followed from thisthesis:• In the context of QoS provisioning for EH systems, we have proposed two QoS awareschemes to allocate the resources. As we have assumed energy limitation at the sourcenode, the QoS of users can not be satisfied thoroughly. The two utility functions rep-resent the total satisfaction of the system rather than the happiness of each individual.In other words, it may happen that QoS of some users is always satisfied over time,whereas such allocation result in starvation of expensive users. Therefore, designingmore comprehensive optimization framework with the objective of attaining fair QoSaware resource allocation in EH systems is a possible future research work.• In our research on resource allocation for EH systems, we have assumed same rate ofchanges for harvesting energy and channel gain. However, in a typical EH wirelesscommunication system, channel gains fluctuate faster than harvesting energy. Thechannel changes on the order of milliseconds while the harvesting energy changes onthe order of seconds or minutes [79]. As a possible future research direction, resource1096C2C Future gesevrxh Dirextionsallocation in EH systems under different timescales of channel gain and harvestingenergy can be considered.• In the context of resource allocation for cooperative wireless EH systems, we haveassumed that the two hops of the cooperative transmission have the same duration.However, due to the attenuation of power, the harvested energy at relays may notbe sufficient for a reliable communication. Therefore, similar to WPC systems [70],allocating more time to the first hop (power transfer operation) than the second one(information transfer operation) may result in a better system performance. In this re-gard, joint optimization of time and power splitting factor in SWIPT energy harvestingsystems can be considered as a future research work.• In our research on D2D relaying systems, we proposed low complexity resource alloca-tion schemes with frequency reuse at D2D pairs. In this work, we have assumed thatD2D pairs operate on half duplex mode and a dedicated band is assigned to them. Fullduplex interference coordination for D2D cooperative communication is an interestingfuture research direction.• The resource allocation scheme developed for D2D relaying systems does not consideruncertainty, fluctuations, and estimation errors of channels. This assumption is toooptimistic especially for the channel between the D2D pairs and the effect of ignoringthese issues is illustrated in [89]. Therefore, design of robust resource allocation forD2D relaying systems is a possible future research work.110Wiwliogrvphy[1] LM Ericsson, “More than 50 billion connected devices,” Feb. 2011.[2] Y. Yang, H. Hu, J. Xu, and G. Mao, “Relay technologies for WiMax and LTE-advancedmobile systems,” IEEE CommunC bvgC, vol. 47, no. 10, pp. 100–105, Oct. 2009.[3] Z. Hasan, H. Boostanimehr, and V.K. Bhargava, “Green cellular networks: A survey,some research issues and challenges,” IEEE Communixvtions hurvzys vny iutorivls,vol. 13, no. 4, pp.524–540, Fourth Quarter, 2011.[4] A. He, et al. “Green communications: A call for power efficient wireless systems,”Journvl of Communixvtions vol. 6, no. 4, pp. 340–351, 2011.[5] C. Han et al., “Green radio: radio techniques to enable energy-efficient wireless net-works,” IEEE CommunC bvgC, vol. 49, no. 6, pp. 46–54, 2011.[6] 3GPP TR 32.826, Telecommunication management; Study on en-ergy savings management (ESM), (Release 10), Mar 2010. Vvvilvwlz:http://www.3gpp.org/ftp/Specs/html-info/32826.htm[7] G.Y. Li, et. al. “Energy-efficient wireless communications: tutorial, survey, and openissues,” IEEE irvnsC lirzlzss CommunCA vol. 18, no. 6, pp. 28–35, Dec. 2011.[8] D. W. K. Ng, E. S. Lo, and R. Schober, “Wireless information and power transfer:Energy efficiency optimization in OFDMA systems,” IEEE irvnsC lirzlzss CommunC,vol. 12, no. 12, pp. 6352–6370, Dec. 2013.111Wiwliogrvphy[9] G. Miao, N. Himayat, and Y. Li, “Energy-efficient link adaptation in frequency-selective channels,” IEEE irvnsC CommunCA vol. 58, no. 2, pp. 545–554, Feb. 2010.[10] G. Miao, N. Himayat, Y. Li, and D. Bormann, “Energy-efficient design in wirelessOFDMA,” in eroxC GEEM IEEE ICC, pp. 3307–3312.[11] Z. Hasan, G. Bansal, E. Hossain, and V.K. Bhargava, “Energy-efficient power allo-cation in OFDM-based cognitive radio systems: A risk-return model,” IEEE irvnsClirzlzss CommunCA vol. 8, no. 12, pp. 6078–6088, Dec. 2009.[12] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wirelessnetworks: efficient protocols and outage behavior,” IEEE irvnsC InformC ihzory, vol.50, no. 12, pp. 3062–3080, Dec. 2004.[13] R. Pabst, et. al., “Relay-based deployment concepts for wireless and mobile broadbandradio,” IEEE CommunC bvgC, vol. 42, no. 9, pp. 80–89, Sep. 2004.[14] G. Fodor, et al., “Design aspects of network assisted device-to-device communications,”IEEE CommC bvgC, vol. 50, pp. 170–177, 2012.[15] A. Asadi, Q. Wang, and V. Mancuso, “A survey on device-to-device communication incellular networks,” IEEE Communixvtions hurvzys vny iutorivls, vol. 16, no. 4, pp.1801–1819, Fourth Quarter, 2014.[16] K. Doppler, et al., “D2D communications underlaying an LTE cellular network,” IEEECommC bvgC, vol. 7, no. 12, pp. 42–49, 2009.[17] L. Chen, et al., “Mobile Relay in LTE-Advanced Systems,” IEEE CommC bvgC, vol.51, no. 11, pp. 144–151, 2013.[18] N. Bhushan, et al., “Network densification: the dominant theme for wireless evolutioninto 5G,” IEEE CommC bvgC, vol. 52, no. 2, pp. 82–89, 2014.112Wiwliogrvphy[19] S. Mumtaz and J. Rodriguez, hmvrt yzvixz to smvrt yzvixz xommunixvtion, SpringerInternational Publishing, 2014.[20] L. Song, D. Niyato, Z. Han, and E. Hossain, lirzlzss yzvixzBtoByzvixz xommunixvtionsvny nztfiorks, Cambridge University Press, 2015.[21] D. W. K. Ng and R. Schober, “Cross-layer scheduling for OFDMA amplify-and-forwardrelay networks,” IEEE irvnsC kzhC izxhnolC, vol. 59, no. 3, pp. 1443–1458, Mar. 2010.[22] W. Dang, M. Tao, H. Mu, and J. Huang, “Subcarrier-pair based resource allocationfor cooperative multi-relay OFDM systems,” IEEE irvnsC lirzlzss CommunC, vol. 9,no. 5, pp. 1640–1649, May 2010.[23] S. Mallick, R. Devarajan, M. Rashid, and V.K. Bhargava, “Resource allocation forselective relaying based cellular wireless system with imperfect CSI,” IEEE irvnsCCommunC, vol. 61, no. 5, pp. 1822–1834, May 2013.[24] K. Vardhe, D. Reynolds, and B.D. Woerner, “Joint power allocation and relay selectionfor multiuser cooperative communication,” IEEE irvnsC lirzlzss CommunC, vol. 9, no.4, pp. 1255–1260, Apr. 2010.[25] E. Hossain, D. I. Kim, and V. K. Bhargava, Eds., Coopzrvtivz xzllulvr fiirzlzss nztfiorks.Cambridge University Press, 2011.[26] K.T.K Cheung, S. Yang, and L. Hanzo, “Achieving maximum energy-efficiency inmulti-relay OFDMA cellular networks: A fractional programming approach,” IEEEirvnsC CommunC, vol. 61, no. 7, pp. 2746–2757, Jul. 2013.[27] Y. Li, W. Wang, J. Kong, and M. Peng, “Subcarrier pairing for amplify-and-forwardand decode-and-forward OFDM relay links,” IEEE CommunC azttzr, vol. 13, no. 1,pp. 209–211, Apr. 2009.113Wiwliogrvphy[28] L. Vandendorpe, R.T. Duran, J. Louveaux, and A. Zaidi, “Power allocation for OFDMtransmission with DF relaying,” in eroxC IEEE ICC, May 2008, pp. 3795–3800.[29] L. Weng, and R.D. Murch, “Cooperation strategies and resource allocations in mul-tiuser OFDMA systems,” IEEE irvnsC kzhC izxhnolC, vol. 58, no. 5, pp. 2331-2342,Jun. 2009.[30] M. Kaneko, K. Hayashi, P. Popovski, K. Ikeda, H. Sakai, and R. Prasad, “Amplify-and-forward cooperative diversity schemes for multi-carrier systems,” IEEE irvnsClirzlzss CommunC, vol. 7, no. 5, pp. 1845–1850, May 2008.[31] B. Gui, L. Dai, and L.J. Cimini, “Selective relaying in cooperative OFDM systems:Two-hop random network,” in eroxC GEEM IEEE lCcC, pp. 996–1001.[32] A. Bletsas, A. Khisti, D.P. Reed, and A. Lippman, “A simple cooperative diversitymethod based on network path selection,” IEEE JC hzlzxtC Vrzvs CommunC, vol. 24,no. 3, pp. 659–672, Mar. 2006.[33] J. A. Paradiso, and T. Starner, “Energy scavenging for mobile and wireless electronics,”IEEE ezrvvsivz Computing, vol. 4, no. 1, pp. 18–27, 2005.[34] “Powercast,” [Online] Available: http://www.powercastco.com[35] M. Raju, and M. Grazier, “ULP meets energy harvesting”, lhitz evpzr, Texas In-struments, 2008.[36] M.A. Marsan, et al., “Towards zero grid electricity networking: Powering BSs withrenewable energy sources,” in eroxC GEF3 IEEE ICC.[37] Motorola, “Alternative power for mobile telephony base stations,” holutions evpzr,2007.114Wiwliogrvphy[38] S. Sudevalayam, P. Kulkarni, “Energy harvesting sensor nodes: Survey and impli-cations,” IEEE Communixvtions hurvzys vny iutorivls, vol. 13, no. 3, pp. 443–461,Third Quarter 2011.[39] L. Liu, R. Zhang, and K.C. Chua, “Wireless information transfer with opportunisticenergy harvesting,” IEEE irvnsC lirzlzss CommunC, vol. 12, no. 1, pp. 288-300, Jan.2013.[40] O.Ozel, J. Yang and S. Ulukus, “Optimal broadcast scheduling for an energy har-vesting rechargeable transmitter with a finite capacity battery,” IEEE irvnsC lirzlzssCommunC, vol. 11, no. 6, pp. 2193–2203, 2012.[41] C. K. Ho and R. Zhang, “Optimal energy allocation for wireless communications withenergy harvesting constraints.” IEEE irvnsC hignvl eroxzssC, vol. 60, no. 9, pp. 4808–4818, 2012.[42] J. Xu and R. Zhang, “Throughput optimal policies for energy harvesting wirelesstransmitters with non-ideal circuit power,” IEEE JhVC, vol. 32, no. 2, pp. 322–332,2014.[43] I. Ahmed, A. Ikhlef, D.W.K. Ng, and R. Schober, “Power allocation for a hybrid energyharvesting relay system with imperfect channel and energy state information,” in eroxCGEFI IEEE lCcC.[44] D. Gunduz, K. Stamatiou, N. Michelusi, and M. Zorzi, “Designing intelligent energyharvesting communication systems,” IEEE CommunC bvgC, vol. 52, no. 1, pp. 210–216,2014.[45] O. Ozel, K. Tutuncuoglu, J. Yang, S. Ulukus, and A. Yener, “Transmission with energyharvesting nodes in fading wireless channels: optimal policies,” IEEE JC hzlC VrzvsCommunC, vol. 29, pp. 1732–1743, 2011.115Wiwliogrvphy[46] C. Huang, R. Zhang, and S. Cui, “Throughput maximization for the Gaussian relaychannel with energy harvesting constraints,” IEEE JhVC, vol. 31, no. 8, pp. 1469–1479,2013.[47] C. Huang, R. Zhang, and S. Cui, “Optimal power allocation for outage probabilityminimization in fading channels with energy harvesting constraints,” IEEE irvnsClirzlzss CommunC, vol. 13, no. 2, pp. 1074–1087, 2014.[48] J. Yang, S. Ulukus, “Transmission completion time minimization in an energy harvest-ing system,” in eroxC GEFE IEEE CIhh.[49] D.W.K. Ng, E.S. Lo, and R. Schober, “Energy-efficient resource allocation in OFDMAsystems with hybrid energy harvesting base station,” IEEE irvnsC lirzlzss CommunC,vol. 12, no. 7, pp. 3412–3427, 2013.[50] X. Chen, et al., “Provisioning quality-of-service to energy harvesting wireless commu-nications,” IEEE CommunC bvgC, vol. 53, no. 4, pp. 102–109, 2015.[51] J. Lee, and S. Leyffer , Eds., bixzy intzgzr nonlinzvr progrvmming. Series: The IMAVolumes in Mathematics and its Applications, vol. 154, 2012.[52] H. Boostanimehr, and V. K. Bhargava, “Selective subcarrier pairing and power alloca-tion for DF OFDM relay systems with perfect and partial CSI,” IEEE irvnsC lirzlzssCommunC, vol. 10, no. 12, pp. 4057–4067 , Dec. 2011.[53] Y. Wang, X. Qu, T. Wu, and B. Liu, “Power allocation and subcarrier pairing algorithmfor regenerative OFDM relay systems,” in eroxC GEEL IEEE kiC, pp. 2727–2731.[54] M. S. Alam, J. W. Mark, and X. Shen, “Relay selection and resource allocation formulti-user cooperative OFDMA networks,” IEEE irvnsC lirzlzss CommunC,vol. 12,no. 5, pp. 2193–2205, May 2013.116Wiwliogrvphy[55] “Air interface for fixed and mobile broadband wireless access systems,”IEEE 802.16e working group, tech. rep., Dec. 2005. [online] Available:http://standards.ieee.org/getieee802/download/802.16e-2005.pdf[56] O. Oyman, “Opportunistic scheduling and spectrum reuse in relay-based cellular net-works,” IEEE irvnsC lirzlzss CommunCA vol. 9, no. 3, pp. 1074–1085, Mar. 2010.[57] J. Tang, and X. Zhang, “Cross-layer resource allocation over wireless relay networksfor quality of service provisioning,” IEEE JC hzlC Vrzvs CommunCA vol. 25, no. 4, pp.645–656, May 2007.[58] O. Arnold, F. Richter, G. Fettweis, and O. Blume, “Power consumption modeling ofdifferent base station types in heterogeneous cellular networks,” in eroxC GEFE IEEEFuturz cztfiork vny bowilz hummit, pp. 1–8.[59] W. Dinkelbach, “On nonlinear fractional programming,”bvnvgzmznt hxiznxz, vol. 13,pp. 492–498, Mar. 1967.[60] S. Boyd, and L. Vandenberghe, Convzx optimizvtion. Cambridge University Press,2004.[61] H. W. Kuhn, “The Hungarian method for the assignment problem,” cvvvl gzszvrxhaogistix fuvrtzrly, vol. 2, pp. 83–97, 1955.[62] S. O. Krumke, Intzgzr progrvmmingC eolyhzyrv vny vlgorithms. Draft: January 4, 2006.[63] S. Boyd, L. Xiao, and A. Mutapcic, “Subgradient methods,”cotzs for EE3NGo htvnforyUnivzrsity Vutumn, 2003–2004.[64] N. Z. Shor, binimizvtion mzthoys for nonByiffzrzntivwlz funxtions. Springer series incomputational mathematics. Springer, 1985.[65] WINNER II D1.1.2, “WINNER II channel models,” Sept. 2007. Vvvilvwlz:https://www.istwinner.org/deliverables.html117Wiwliogrvphy[66] H. Zhu and J. Wang, “Device-to-device communication in cellular networks with frac-tional frequency reuse,” in eroxC GEFI IEEE ICC, pp. 5503–5507.[67] L. Varshney, “Transporting information and energy simultaneously,” in eroxC GEEMIEEE IhIi, pp. 1612–1616.[68] H. Jabbar, Y. Song, and T. Jeong, “RF energy harvesting system and circuits forcharging of mobile devices,” IEEE irvnsC Consumzr Elzxtronixs, vol. 56, no. 1, pp.247–253, 2010.[69] D. Mishra, et al., Smart RF energy harvesting communications: challenges and oppor-tunities, IEEE CommC bvgC, vol. 53, no. 4, pp. 70–78, 2015.[70] H. Ju, and R. Zhang, “Throughput maximization in wireless powered communicationnetworks,” IEEE irvnsC lirzlzss CommunC, vol. 13, no. 1, pp. 418–428, 2014.[71] X. Kang, C. K. Ho; S. Sun, “Optimal time allocation for dynamic-TDMA-based wire-less powered communication networks,” in eroxC GEFI IEEE GadWECdb, pp. 3157–3161.[72] X. Kang, C. K. Ho; S. Sun, “Charging and transmission time minimization for wirelesspowered communication networks,” in eroxC GEFI IEEE GadWECdb, pp. 1436–1441.[73] X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and power transfer: Archi-tecture design and rate-energy trade-off,” IEEE irvnsC CommunC, vol. 61, no. 11, pp.4754–4767, 2013.[74] K. Huang, and E. Larsson, “Simultaneous information and power transfer for broad-band wireless systems,” IEEE irvnsC hignvl eroxzssC, vol. 61, no. 23, pp. 5972–5986,2013.118Wiwliogrvphy[75] R. Zhang, and C. K. Ho, “Mimo broadcasting for simultaneous wireless informationand power transfer,” IEEE irvnsC lirzlzss CommunC, vol. 12, no. 5, pp. 1989–2001,2013.[76] A. Nasir, et al., “Relaying protocols for wireless energy harvesting and informationprocessing,” IEEE irvnsC lirzlzss CommunC, vol. 12, no. 7, pp. 3622–3636, 2013.[77] A. Nasir, et al., “Wireless-powered relays in cooperative communications: Time-switching relaying protocols and throughput analysis,” IEEE irvnsC CommunC, vol.63, no. 5, pp. 1607–1622, 2015.[78] K. Huang, and X. Zhou, “Cutting the last wires for mobile communications by mi-crowave power transfer,” IEEE CommunC bvgC, vol. 53, no. 6, pp. 86–93, 2015.[79] H. Li, et al., “A general utility optimization framework for energy harvesting basedwireless communications,” IEEE CommunC bvgC, vol. 53, no. 4, pp. 79–85, 2015.[80] S.M. Lee, Govl progrvmming for yzxision vnvlysis. Philadelphia: Auerbach, 1972.[81] H.S. Wang, and P. Chang, “On verifying the first-order Markovian assumption fora Rayleigh fading channel model,” IEEE irvnsC kzhC izxhnolC, vol. 45, no. 2, pp.353–357, May 1996.[82] P. Sadeghi, R. Kennedy, P. Rapajic, and R. Shams, “Finite-state Markov modeling offading channels - a survey of principles and applications,” IEEE hignvl eroxzssC bvgC,vol. 25, no. 5, pp. 57–80, Sep. 2008.[83] C. K. Ho, P. D. Khoa, and P. C. Ming, “Markovian models for harvested energy inwireless communications,” in eroxC GEFE IEEE ICCh.[84] D. P. Bertsekas, Dynvmix progrvmming vny optimvl xontrol. vol. 1, no. 2, Belmont,MA: Athens Scientific, 1995.119Wiwliogrvphy[85] E. Matskani, et al., “Convex approximation techniques for joint multiuser downlinkbeamforming and admission control,” IEEE irvnsC lirzlzss CommunC, vol. 7, no. 7,pp. 2682–2693, 2008.S. Mallick, R. Devarajan, M.M. Rashid, and V.K. Bhargava, “Resource allocation forselective relaying based cellular wireless system with imperfect CSI,” IEEE irvnsCCommunC, vol. 61, no. 5, pp.1822–1834, 2013.[86] K. T. Phan, T. Le-Ngoc, S. A. Vorobyov, and C. Tellambura, “Power allocation inwireless multi-user relay networks,” IEEE irvnsC lirzlzss CommunC, vol. 8, no. 5, pp.2535–2545, 2009.[87] H.S. Wang, and N. Moayeri, “Finite-state Markov channel-a useful model for radiocommunication channels,” IEEE irvnsC kzhC izxhnolC, vol. 44, no. 1, pp. 163–171,1995.[88] S. Mao, M.H. Cheung, and V.W.S. Wong, “Joint energy allocation for sensing andtransmission in rechargeable wireless sensor networks,” IEEE irvnsC kzhC izxhnolC,vol. 63, no. 6, pp. 2862–2875, 2014.[89] S. Mallick, R. Devarajan, R. Arab Loodaricheh, and V.K. Bhargava,“Robust resourceoptimization for cooperative cognitive radio networks with imperfect CSI,” IEEEirvnsC lirzlzss CommunC, vol. 14, no. 2, pp. 907–920, 2015.120Appznyix Aeroof of thz xonvzxity for erowiIn this section, we prove that Probi is jointly concave with respect to the power variablesand indicators.First, we prove the concavity of giPjP(C)mPk . We definef(eiP(CP1)WPm P ejP(CP2)mPk ) = 1 +iWPmeiP(CP1)WPm jmPkejP(CP2)mPkiWPmeiP(CP1)WPm + jmPkejP(CP2)mPkO (A.1)In order to show that f(eiP(CP1)WPm P ejP(CP2)mPk ) is concave, we need to prove that the Hessian off(eiP(CP1)WPm P ejP(CP2)mPk ), which can be calculated asH(f) =2N2B;Rj2R;P(NB;ReN;(C;1)B;R +jR;Pej;(C;2)R;P )3× −e jP(CP2)2mPk e iP(CP1)WPm e jP(CP2)mPkeiP(CP1)WPm ejP(CP2)mPk −e iP(CP1)2WPm P(A.2)is negative semidefinite. The eigenvalues of the Hessian matrix H(f) are given bye1 = 0Pe2 =−2i2WPmj2mPk(eiP(CP1)2WPm + ejP(CP2)2mPk )(iWPmeiP(CP1)WPm + jmPkejP(CP2)mPk )3P(A.3)where both the eigenvalues e1 and e2 are non-positive. Therefore, the Hessian matrix H(f)is negative semidefinite and f(eiP(CP1)WPm P ejP(CP2)mPk ) is concave.Since log(.) is an increasing concave function, giPjP(C)mPk is concave. It is proven in [60] that121Appenyix AC eroof of the xonvexity for erowithe perspective function of f(x), which is defined as g(xP t) = tf(xRt), is concave if f(x)is concave. Therefore, /iPjmPkg˜iPjP(C)mPk , iP(1)m g˜iP(cCP1)m and jP(2)m g˜jP(cCP2)m are concave due to theperspective operation. We can conclude that g˜i is concave with respect to (e˜ P h).It is obvious that e˜i is affine with respect to e˜ , and therefore, the objective function ofProbi, i.e., (g˜i (e˜ P h)− qie˜i (e˜ P h)), is concave. The convexity of the feasible set formed bythe constraints can be proved in a similar way.122Appznyix WDzrivvtion of optimvl vuxilivry pofizrsThe optimal auxiliary powers given in (2.25)-(2.29) are derived in this section. Using KKTconditions in (2.21) and (2.22) we obtainUa(PPP ee Ph)U ee N;(C;1)B;R =N;jR;P(1+P)@eΓN;j;(C)R;P@ ePN;(C;1)B;R2ln(2)(1+eΓN;j;(C)R;P ) − (+ 12qiϵW) = 0P(B.1)Ua(PPP ee Ph)U ee j;(C;2)R;P =N;jR;P(1+P)@eΓN;j;(C)R;P@ ePj;(C;2)R;P2ln(2)(1+eΓN;j;(C)R;P ) − (+ 12qiϵjE) = 0O(B.2)After re-arranging the above equations, we obtain/iPjmPk(1 + k)UeΓN;j;(C)R;PU ee N;(C;1)B;R2ln(2)(1 + Γ˜iPjP(C)mPk )= (+12qiϵW)P (B.3)/iPjmPk(1 + k)UeΓN;j;(C)R;PU ee j;(C;2)R;P2ln(2)(1 + Γ˜iPjP(C)mPk )= (+12qiϵjE)O (B.4)By dividing (B.3) by (B.4), we have@Γ˜iPjP(C)mPk@e˜iP(CP1)WPm@Γ˜iPjP(C)mPk@e˜jP(CP2)mPk=+ 12qiϵW+ 12qiϵjEP (B.5)where@Γ˜iPjP(C)mPk@e˜iP(CP1)WPmand@Γ˜iPjP(C)mPk@e˜jP(CP2)mPkcan be calculated as123Appenyix WC Derivvtion of optimvl vuxilivry powers@Γ˜iPjP(C)mPk@e˜iP(CP1)WPm=iWPmj2mPke˜jP(CP2)2mPk/iPjmPk(iWPme˜iP(CP1)WPm + jmPke˜jP(CP2)mPk)2 P (B.6)@Γ˜iPjP(C)mPk@e˜jP(CP2)mPk=i2WPmjmPke˜iP(CP1)2WPm/iPjmPk(iWPme˜iP(CP1)WPm + jmPke˜jP(CP2)mPk)2 O (B.7)By substituting (B.6) and (B.7) in (B.5), we can derivee˜jP(CP2)mPke˜iP(CP1)WPm=√√√√ (+ 12qiϵW)iWPm(+ 12qiϵjE)jmPk= xO (B.8)By substituting e˜jP(CP2)mPk = xOe˜iP(CP1)WPm in (B.3), the auxiliary power variables for cooperativetransmission can be derived as given in (2.25) and (2.26), respectively.The non-cooperative auxiliary power variables e˜iP(cCP1)WPm and e˜jP(cCP2)WPm can be obtaineddirectly from (2.23) and (2.24), respectively.124Appznyix Xeroof of thz totvlly unimoyulvrity forthz xonstrvint mvtrixConsidering the problem in (2.30), we can re-write the constraints X˜2 and X˜3 as Xh = F,where h is a [(c2Kb + 2cb)× 1] vector of all the indicators, i.e., {/iPjmPkP iP(1)m P jP(2)m P ∀k ∈[1P OOOP K]Pm ∈ [1P OOOPb ]P i ∈ [1P OOOP c ]P j ∈ [1P OOOP c ] }, F is a [2c × 1] vector of all ones, andX is the [2c × (c2Kb + 2cb)] constraint matrix given byX = [KM times︷ ︸︸ ︷X1P OOOPX1PM times︷ ︸︸ ︷I2c×2c P OOOP I2c×2c ]P (C.1)where I is the identity matrix and X1 is a (2c ×c2) matrix, which is given byX1 =N times︷ ︸︸ ︷11OOO11N times︷ ︸︸ ︷11OOO11. . .N times︷ ︸︸ ︷11OOO11Ic×c Ic×c OOO Ic×cOIt is proved in [62] that a matrix m is totally unimodular if and only if (m,I) is totallyunimodular. Therefore, to prove that the constraint matrix X is totally unimodular, we onlyneed to prove that m = [X1P OOOP X1︸ ︷︷ ︸KM times] is totally unimodular.ihzorzm (ICFI) of [62], that proves a sufficient condition for totally unimodularity, is125Appenyix CC eroof of the totvlly unimoyulvrity for the xonstrvint mvtrixgiven in the following:Consider a matrix mm×n with entries{0,-1,+1}in which any column has at most twonon zero entries. If there exist a partition of rows (b1 ∪b2 = 1P OOOPm) in m, where eachcolumn j with two non zero entries has the following property:∑i∈b1xij =∑i∈b2xijPthen matrix m is totally unimodular.For the considered problem (2.30), matrixm = [KM times︷ ︸︸ ︷X1P OOOP X1] obviously satisfies the sufficientcondition. The partition of rows in matrix X1 is shown by a dashed line. We conclude thatm and therefore, the constraint matrix X are totally unimodular.126Appznyix Daist of dthzr euwlixvtionsSome other research contributions not presented in the thesis but have been published duringmy PhD program at UBC are as follows:• S. Mallick, R. Devarajan, R. Arab Loodaricheh, and V. K. Bhargava, “Robust re-source optimization for cooperative cognitive radio networks with imperfect CSI,”IEEE irvnsC lirzlzss CommunC, vol. 14, no. 2, pp. 907–920, Feb. 2015.• S. Lohani, R. Arab Loodaricheh, E. Hossein, and V. K. Bhargava, “On multiuserresource allocation in relay-based wireless-powered uplink cellular networks,” IEEEirvnsC lirzlzss CommunC, to appear.• S. Lohani, R. Arab Loodaricheh, E. Hossein, and V. K. Bhargava, “Relay-basedharvest-then-transmit protocol for uplink cellular networks,” in eroxC of GEFI IEEEGadWECdb, pp. 912–917.127

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0221440/manifest

Comment

Related Items