Resource Allocation in Wireless Relay Networks

Transcription

1 Resource Aocation in Wireess Reay Networks By Udit Pareek B.Tech., Indian Institute of Technoogy (Guwahati), 007 THESIS SUBMITTED IN PARTIA FUFIMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPIED SCIENCE in the Schoo of Engineering Science Facuty of Appied Science Udit Pareek 0 SIMON FRASER UNIVERSITY Summer 0 A rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced, without authorization, under the conditions for "Fair Deaing". Therefore, imited reproduction of this work for the purposes of private study, research, criticism, review and news reporting is ikey to be in accordance with the aw, particuary if cited appropriatey.

2 APPROVA Name: Degree: Tite of Thesis: Udit Pareek Master of Appied Science Resource Aocation in Wireess Reay Networks Examining Committee: Chair: Dr. Rodney Vaughan Professor, Schoo of Engineering Science Dr. Danie C. ee Senior Supervisor Professor, Schoo of Engineering Science Dr. Pau Ho Supervisor Professor, Schoo of Engineering Science Dr. Ivan Bajic Interna Examiner Associate Professor, Schoo of Engineering Science Date Defended/Approved: May 9 0 ii

3 Partia Copyright icence

4 ABSTRACT The idea of using cooperating reays has been much discussed in the past decade. In a wireess communication system, reaying techniques can offer significant benefits in the throughput enhancement and range extension. On the other hand, cognitive radio is an interesting concept for soving the probem of spectrum avaiabiity by reusing the underutiized icensed frequency bands. In a cognitive radio network, reays can be particuary usefu for reducing the transmission power at the source and thus reduce the interference to the primary users. In this thesis, we study resource aocation probems for cognitive radio networks that empoy reays. In this work, the transmission power of the nodes (users and reays) is the resource that we wish to aocate. The power aocation probems are formuated as non-convex non-inear programs and they do not have a structure that coud guarantee the quaity of the soution. We present a method of transforming the proposed optimization probems to a new formuation so that ε-optima agorithms can be designed. In genera, the transformed probem exhibits certain properties, which enabe us to sove the optimization probems to a desirabe accuracy by appying known goba optimization techniques. We note that the goba optimization techniques require significant computations to sove our proposed optimizations. Therefore, we propose ow compexity heuristics that provide suboptima soutions to the given optimization probems. The simuation resuts show that the performance of the heuristics is cose to their respective optima soutions. Keywords: Cognitive radio, Cooperative communication, Two-Way Reay, Muti-Way Reay, Goba Optimization iii

5 DEDICATION To my famiy iv

6 ACKNOWEDGEMENTS I owe my deepest gratitude to my supervisor Professor Danie C. ee for his supervision, advice, and support throughout my graduate studies as we as giving me extraordinary experiences throughout my graduate studies. I gratefuy thank Professor Pau Ho, Professor Ivan Bajic and Professor Rodney Vaughan for being the members of my thesis defence committee. I am aso thankfu to Dr. Muhammad Naeem and Dr. Ajit Khosa, PhD aumni from the schoo of Engineering Science, for their guidance, encouragement and support on a aspects of my study and research. Specia thanks to Ravi, Saad and the members of RF and Communications ab. My deepest appreciations go out to my beoved famiy members. They have been a constant source of support and inspiration for me. v

7 TABE OF CONTENTS Approva... ii Abstract... iii Dedication... iv Acknowedgements... v Tabe of Contents... vi ist of Figures... viii ist of Tabes... ix ist of Abbreviations... x Chapter : Introduction.... Research Motivation.... Background..... Cognitive Radio System Spectrum sensing Dynamic Spectrum Access Cooperative Communication Thesis Overview Power aocation in OAF reay networks Power aocation in SAF reay networks Power aocation in Muti-Way reay networks....4 iterature Review....5 Organization of Thesis Chapter References... 6 Chapter : Power Aocation in Orthogona Two Way Reay Assisted Cognitive Radio Networks.... System Mode Probem Formuations Joint Sources and Reays Powers Optimization with Sum- Capacity Maximization Joint Sources and Reays Powers Optimization with Max- Min Fairness Proposed Approach to a Soution Preiminaries of Monotonic Optimization Definitions and Concepts of Monotonic Optimization Poybock Outer Approximation Agorithm vi

8 .5 ε-optima Soution based on Monotonic Optimization ε-optima Soution of Sum-Capacity Optimization ε-optima Soution of Max-Min Optimization Proposed Heuristics Greedy Power Aocation with Sum-Capacity Maximization Greedy Power Aocation with Max-Min Fairness Resuts Summary Chapter References Chapter 3: Power Aocation in Shared Band Two Way Reay Assisted Cognitive Radio Networks System Mode Probem Formuation Existing methods ε-optima Soution based on Monotonic Optimization Proposed Heuristic Resuts Summary Chapter References Chapter 4: Power Aocation in Muti-Way Reay Networks System Mode ε-optima Soution based on Monotonic Optimization Numerica resuts Summary Chapter References Chapter 5: Contributions and Future work Contributions Power aocation in Two-Way Reay assisted cooperative cognitive radio networks Power Aocation in Muti-Way Reaying Future work Resource aocation in cooperative CRS with imperfect CSI Power aocation in Two-Way Reay assisted cooperative cognitive radio networks Power aocation in Muti-Way Reaying Appendices Appendix A Appendix B... 0 Appendix C Appendix D Appendix E vii

9 IST OF FIGURES Fig.. Dynamic spectrum access strategies Fig.. Overay spectrum access Fig..3 Underay spectrum access Fig..4 Joint overay and underay spectrum access Fig.. Two-way reay assisted Cognitive Radio network... 4 Fig.. An Exempary Norma Set and Its Upper Boundary Fig..3 Projection on the Upper Boundary of the Norma Set Fig..4 Determination of Poybock P from P Fig..5 Outer Approximation of the Upper Boundary of the Feasibe Set Fig..6 Convergence Resuts Sum-Capacity Optimization Fig..7 Convergence Resuts Max-Min Optimization Fig..8 Sum Capacity vs. I, = m Fig..9 Minimum User Capacity vs. I, = m Fig..0 Minimum User Capacity vs.primary Users, = Fig.. Sum- Capacity vs.reays, M = Fig.. Minimum User Capacity vs.reays, M = Fig. 3. Two-way reay assisted Cognitive Radio network... 6 Fig. 3. Convergence Resuts Max-Min Optimization Fig. 3.3 Minimum User Capacity vs.primary Users, = Fig. 4. Convergence Resuts of Max-Min Optimization, P A B C 0 R A 0, P = P = P = P = P, P = watt and P tot = watt Fig. 4. Minimum Rate vs Transmit Power, P tot = watt P A B C 0 R A 0, P = P = P = P = P and P is varied from - to 4 db viii

10 IST OF TABES Tabe. IEEE 80. system parameters Tabe. Haf-Dupex One-Way Reaying Tabe.3 Haf-Dupex Two-Way Reaying Tabe.4 OAF Two-Way Reaying Tabe.5 SAF Two-Way Reaying Tabe.6 Muti-Way Reaying Tabe. Notations used in chapter Tabe. Pseudocode of poybock outer approximation agorithm Tabe.3 Bisection Search Based Projection Computation Tabe 3. Notations used in chapter Tabe 3. Bisection Search Based Power Aocation For SAF Two-Way Reaying ix

11 IST OF ABBREVIATIONS AF CCS CRS DSA FCC GeSI GPAMF GPASM GTSPA IEA ITU ICT JSRMF JSRSM MO PU SU WEO WRAN Ampify-And-Forward Cooperative Communication System Cognitive Radio System Dynamic Spectrum Access Federa Communications Commission Goba e-sustainabiity Initiative Greedy Power Aocation Max-Min Fairness Greedy Power Aocation Sum-Capacity Maximization Greedy Two-Step Power Aocation Internationa Energy Agency Internationa Teecommunication Union Information And Communication Technoogies Joint Source and Reay Power Aocation with Max-Min Fairness Joint Source and Reay Power Aocation with Sum- Capacity Optimization Monotonic Optimization Primary User Secondary User Word Energy Outook Wireess Regiona Area Network x

12 CHAPTER : INTRODUCTION. Research Motivation The idea of using cooperating reays has been much discussed in the past decade [], []. In a wireess communication system, reaying techniques can offer significant benefits in the throughput enhancement, and range extension []. Reaying protocos for one-way haf-dupex reays are considered in []. Recent research on cooperative communications has shown that haf-dupex two-way reaying is spectray more efficient [] than the conventiona haf-dupex one-way, [], reaying. In two-way reaying two users can exchange data with each other using a reay in two time sots. Recenty, the idea of two-way reay channe has been extended to muti-way reay channe in [3]. In this mode, mutipe users ( ) can exchange information with each other using a reay termina in two time sots. Cognitive radio [4], [5], [6] is an emerging technoogy intended to enhance the utiization of the radio frequency spectrum. A combination of cognitive radio with cooperative communication can further improve the future wireess systems performance. However, the combination of these techniques raises new issues in the wireess systems that need to be addressed. In particuar, in this thesis, we address the issue of aocating transmission power to the nodes (users and reays) subject to the constraints on the nodes transmit powers. We provide ow compexity heuristics to the proposed optimizations and compare them with their respective optima soutions. We aso study the rate and power aocation probem in a wireess reay network empoying muti-way reaying and provide an optima soution to the proposed optimization.

13 . Background In this section, we provide a brief overview of cooperative communication and cognitive radio... Cognitive Radio System Formay, a cognitive radio is defined as [7] A radio that changes its transmitter parameters based on the interaction with its environment The cognitive radio has been mainy proposed to improve the spectrum utiization by aowing unicensed (secondary) users to use underutiized icensed frequency bands [8] [9] [0]. In reaity, unicensed wireess devices (e.g., automatic garage doors, microwaves, cordess phones, TV remote contros etc.) are aready in the market [] []. The IEEE 80. standard for Wireess Regiona Area Network (WRAN) addresses the cognitive radio technoogy to access white spaces in the icensed TV band. In North America, the frequency range for the IEEE 80. standard wi be MHz, whie the 4 90MHz band wi be used in the internationa standard [9]. Tabe. shows the IEEE 80. system parameters, e.g., frequency range, bandwidth, moduation types, imum transmit power ratings, mutipe access schemes, etc. [3]. In the context of cognitive radio, the Federa Communications Commission (FCC) recommended two schemes to prevent interference to the teevision operations due to the secondary (unicensed) users. These are isten-before-tak and geo-ocation/database schemes [] []. In the isten-before-tak scheme, the secondary/unicensed device senses the presence of TV signas in order to seect the TV channes that are not in use. In geo-ocation/database scheme, the icensed/unicensed users have a ocation-sensing device (e.g., GPS receiver etc.) The ocations of primary and secondary users are stored in a centra database. The centra controer (aso known as spectrum manager) of the secondary/unicensed users has the access to the ocation database.

14 Tabe. IEEE 80. system parameters. Parameters Specification Remarks Frequency range MHz TV band Bandwidth Moduation Transmit power Mutipe access 6 MHz, 7 MHz, 8 MHz QPSK, 6-QAM, 64-QAM 4W OFDMA For USA, may vary in other reguatory domains The main functions of cognitive radio to support inteigent and efficient utiization of frequency spectrum are as foows:... Spectrum sensing Spectrum sensing determines the status of the spectrum and activity of the primary users [9] [4]. An inteigent cognitive radio transceiver senses the spectrum hoe without interfering with the primary users. Spectrum hoes are the frequency bands currenty not used by the primary users. Spectrum sensing is impemented either in a centraized or distributed manner. The centraized spectrum sensing can reduce the compexity of the secondary user terminas, since the centraized controer performs the sensing function. In distributed spectrum sensing, each mobie device (secondary user termina) senses the spectrum independenty. Both centraized and distributed decision-making is possibe in distributed spectrum sensing [9]. The centra controer (spectrum manager), based on the spectrum sensing information, aocates the resources for efficient utiization of the avaiabe spectrum. One major roe of the centra controer is to prevent overapped spectrum sharing between the secondary users [7] [9] [0]. 3

15 ... Dynamic Spectrum Access Dynamic spectrum access (DSA) is defined as rea-time spectrum management in response to the time varying radio environment e.g., change of ocation, addition or remova of some primary users, avaiabe channes, interference constraints etc [7] [0]. There are three DSA modes in the iterature, namey, excusive-use mode, common-use mode and shared-use mode [0]. Fig.. shows a hierarcha overview of DSA. Fig.. Dynamic spectrum access strategies. The excusive-use mode has two approaches, spectrum property rights and dynamic spectrum aocation. In spectrum property rights, owner of the spectrum can se and trade spectrum; and is free to choose the technoogy of interest. Dynamic spectrum aocation improves spectrum efficiency by expoiting the spatia and tempora traffic statistics of different services [0]. The European Union funded DRiVE (Dynamic Radio for IP Services in Vehicuar Environments) project is a cassica exampe of dynamic spectrum aocation [4]. It uses ceuar (e.g., GSM, GPRS, and UMTS) and broadcast technoogies (e.g., Digita Video Broadcast Terrestria, Digita Audio Broadcast) to enabe spectrum efficient vehicuar mutimedia services. 4

16 Fig.. Overay spectrum access. Fig..3 Underay spectrum access. Fig..4 Joint overay and underay spectrum access. 5

17 The common-use mode is an open sharing regime in which spectrum is accessibe to a users. The ISM (industria, scientific and medica) band and Wi- Fi are exampes of the commons-use mode. Spectrum underay and overay approaches are used in the shared-use mode [9] [0]. Spectrum overay or opportunistic spectrum access is shown in Fig... In spectrum overay, the secondary users first sense the spectrum and find the ocation of a spectrum hoe (vacant frequency band). After ocating the vacant frequency bands, the secondary users transmit in these frequency bands. In spectrum underay technique, the secondary users can transmit on the frequency bands used by the primary users as ong as they do not cause unacceptabe interference for the primary users. This approach does not require secondary users to perform spectrum sensing, however the interference caused by the secondary user s transmission must not exceed the interference threshod. Fig..3 shows the spectrum underay mode. In [5], a joint spectrum overay and underay method is proposed for better spectrum utiization. An iustration of joint spectrum overay and underay is shown in Fig..4. In joint spectrum overay and underay approach, the secondary users with the hep of spectrum sensing first try to find a spectrum hoe. If there is a spectrum hoe then the secondary users can use the spectrum overay technique. If there is no spectrum hoe then the secondary users wi use spectrum underay technique... Cooperative Communication We now provide a brief background of cooperative communications. Recenty the idea of cooperative communication has gained much attention. The cooperative communications expoit the broadcast nature of wireess channes. The basic idea is that the reay nodes can assist the transmissions of the source node by reaying a repica of the transmission of the source node that in turn expoits the inherent spatia diversities. Recent research in wireess communication systems shows that reaying techniques can offer significant 6

18 benefits in the throughput enhancement, and range extension []. A number of reaying schemes e.g., ampify-and-forward (AF), decode and forward (DF), incrementa reaying etc. for improving the performance of the wireess networks are in the iterature e.g., [], [6]. In a simpe AF reaying scheme, a reay ampifies the received signa and forwards it to the destination. In decode and forward reaying scheme, a reay first decodes the received signa and then transmits the re-encoded signa to the destination. Tabe. shows a simpe cooperative communication protoco. In this protoco, conveyance of each symbo from the source to the destination takes pace in two phases (two time sots). In the first phase, the source transmits its data symbo, and the destination and the reay(s) receive the signa carrying the symbo. In the second phase, the reay(s) forwards the data to the destination. Recent research on cooperative reaying has shown that haf-dupex twoway reaying is spectray more efficient [] than the conventiona haf-dupex oneway, [6], reaying. In two-way reaying, a pair of users exchanges information with each other using a reay using two time sots. The key idea is that a user can cance the interference (generated by its own transmission) from the signa it receives from the reay to recover the transmission of other terminas. Tabe.3 iustrates the two-way reaying. Haf-dupex protocos for two-way reaying using mutipe reays have been discussed in [7] and [8]. In this work, we study the power aocation probem for different types of two-way reaying protocos. In one of the protocos, which we wi refer to as orthogona ampify-and-forward (OAF) reaying, the transmissions of the reays are separated in time by aocating each reay a different time-sot band. In the other reaying protoco, which we wi refer to as shared-band ampify-and-forward (SAF) reaying, the reays share the same medium for their transmissions. We study the probem of jointy aocating power to the users and the reays for both OAF and SAF reaying protocos. Tabes.4 and.5 show OAF and SAF bidirectiona reaying protocos. 7

19 Recenty, the idea of two-way reaying has been extended to the case of mutipe users sharing a singe reay that is referred to as muti-way reaying [8]. In this thesis, we consider muti-way reaying where reay performs ampify and forward reaying. In this reaying scheme, in the first time-sot, the users broadcast their data and in the second time-sot, the reay broadcasts the ampified data. The capacity and achievabe rates for different reaying techniques (ampify-and-forward (AF), decode-and-forward and compress-andforward) for muti-way reay channe are discussed in [3]. Tabe.6 presents the muti-way reaying communication protoco. Tabe. Haf-Dupex One-Way Reaying. Time T Time T S D, S R R D Tabe.3 Haf-Dupex Two-Way Reaying. Time T Time T S, S R R S, S Tabe.4 OAF Two-Way Reaying. Time T Time T Time T 3 Time T 4 Time T + S, S (R, R,.., R ) R (S, S ) R (S, S ) R 3 (S, S ) R (S, S ) 8

20 Tabe.5 SAF Two-Way Reaying. Time T Time T S, S (R,R,..,R ) (R,R,..,R ) S, S Tabe.6 Muti-Way Reaying. Time T Time T (S, S...,S K ) R R (S, S...,S K ).3 Thesis Overview The main objective of this thesis is to determine power aocation in wireess reay networks. This thesis discusses three probems: ) Power aocation in OAF reay networks, ) Power aocation in SAF reay networks and 3) Power aocation in muti-way reay networks. In a three probems, we examine the effect of different system parameters (e.g. imum transmit power interference threshod eve, the number of primary users, the number of secondary users, reay power eves, etc.) on the performance of the proposed agorithms..3. Power aocation in OAF reay networks In this work, we study a cognitive radio network (comprising mutipe primary users) in which a pair of sources communicates with each other through mutipe reays that empoy two-way ampify-and- forward reaying. The reays use orthogona channes to transmit their data. We formuate optimization probems to adequatey decide the transmission powers of the nodes in such networks. We consider two optimization probems. In one probem, we consider imizing the minimum among the two sources capacities. In the other 9

21 probem, we consider imizing the sum capacity of the system. Our formuated optimization probems turn out to be non-convex and non-inear. For theoretica interest in deaing with these non-convex optimization probems for deciding the power eves, we show in this work that these optimization probems have a set of properties that guarantees ε-convergence if the monotonic optimization techniques are used. Then, we appy the monotonic optimization [9], [0] agorithm to obtain the optima soution of the proposed non-inear non-convex programming probems. Athough the monotonic optimization agorithm can guarantee convergence to a soution that has a performance arbitrariy cose (within an arbitrary number ε) to the optima performance, our experimentation with the monotonic optimization appied to this reay power aocation probem shows rather sow convergence and heavy computationa oad. Therefore, we propose a ow-compexity heuristics, which we name as Greedy Power Aocation with Max-Min Fairness (GPAMF) and Greedy Power Aocation with Sum Capacity Maximization (GPASM). The simuation resuts show that the proposed heuristics perform we in comparison with the respective optima soutions and have much ower computationa compexity than the monotonic optimization agorithm..3. Power aocation in SAF reay networks In this work, we consider a cognitive radio network (comprising mutipe primary users) in which a pair of sources communicates with each other through mutipe reays that empoy two-way ampify-and-forward reaying. The reays empoy SAF reaying, i.e., in the first sot the users broadcast their data and in the second sot, the reays simpy re-scae and re-transmit the received signa. We study the probem of aocating powers to the users and reays such that the minimum among the users SNRs is imized subject to the constraints on the transmit power of the nodes. The formuated optimization probem is nonconvex non-inear program and we do not see a specia structure that coud guarantee the quaity of a soution. We observe that we can transform the 0

22 probem into an equivaent probem (athough sti a non-convex non-inear program) which exhibit a specia property. In the transformed probems, we observe that the objective function and the constraints are increasing function of each optimization variabe when other variabes are fixed. This property enabes us to determine the goba optima soution to our optimization probems by appying the concepts of monotonic optimization agorithm [9]. Monotonic optimization agorithm guarantees convergence to a soution that has a performance arbitrariy cose (within an arbitrary number ε) to the optima performance. However, the appication of monotonic optimization techniques to sove the optimization probem requires significant computations. Therefore, we propose a ow-compexity heuristic. We perform simuations to examine the quaity of the soution obtained from the proposed heuristic and benchmark its performance using the optima soution obtained by using monotonic optimization techniques..3.3 Power aocation in Muti-Way reay networks In this work, we consider a muti-way reay channe comprising mutipe users and a singe reay. We assume that the reay termina uses AF reaying. For such systems, we study the probem of aocating power to the users and the reay termina such that the minimum among the users transmission rates is imized subject to the constraints on the transmission power of the nodes. The formuated optimization probem is a non-convex non-inear program and does not have a structure to guarantee the quaity of a soution. We observe that we can transform the probem into another equivaent probem (athough sti a non-convex non-inear program) which coud be soved to goba optimaity by appying the concepts of monotonic optimization agorithm [9]..4 iterature Review This section contains a iterature review for resource aocation strategies in wireess communication system. In particuar, we review the iterature

23 corresponding to the reay assignment and power aocation in reay assisted wireess networks. Tabe.3 summarizes the iterature review for the reay assignment strategies (RAS) in the wireess communication systems. The first coumn in Tabe.3 ists the objective functions as defined in the iterature. The succeeding coumns show the reaying type (one-way or two-way reaying), cognitive radio capabiity, protoco type (e.g. centraized, distributed or decentraized) and power aocation capabiity respectivey. There are three major casses of resource aocation in cooperative communications. The casses are, centraized resource aocation [-4] [8] [33-3], distributed resource aocation [5] [34], and decentraized resource aocation [6] [7] [33]. In [], joint bandwidth and power aocation strategies for a Gaussian reay network are investigated. Orthogona and shared-band AF and DF schemes are anayzed for joint bandwidth and power aocation. The main objective of joint bandwidth and power aocation is to imize the signa-tonoise ratio at the receiver using AF and DF schemes. The study in [] proposes a centraized framework that seects mutipe reays for transmission in a two-hop network. The aim of the mutipe reay seection is to imize the SNR at the destination using binary power aocation at the reays. An optima reay assignment and power aocation in a cooperative ceuar network is discussed in [3]. Using the sum-rate imization as a design metric, the authors proposed a convex optimization probem that provides an upper bound on performance. A heuristic water-fiing agorithm is aso suggested to find a near-optima reay assignment and power aocation. In [4], a inear-marking mechanism is investigated for reay assignment in a muti-hop network with mutipe sourcedestination pairs. The aim of the proposed inear-marking mechanism is to imize the worst user capacity. A distributed nearest neighbour reay seection protoco and its outage anaysis are presented in [5]. For the reay assignment in a mutiuser communication system, decentraized protocos are discussed in [6] and [30].

24 The decentraized framework in [6] uses decode and forward reaying and assigns reays without exercising power contro. In [30], decentraized ampify and forward protoco is used for joint reay assignment and power contro. The scheme imizes a harmonic mean-based approximate expression for the instantaneous received signa-to-noise ratio. The reay assignment and seection schemes described in [] [7] and [30] are not appicabe in the CRS because the interference caused by the reays to the primary users can exceed the prescribed interference imit. The reay seection scheme for a cognitive radio network has been considered in severa recent works [8] [34]. In [8], a mathematica formuation is proposed with the objective of minimizing the required network-wide radio spectrum resource for a set of user sessions. The proposed formuation is a mixed-integer non-inear program. The authors proposed a ower bound for the objective by reaxing the integer variabes and using a inearization technique. A near-optima agorithm is presented that is based on a sequentia fixing procedure, where the integer variabes are determined iterativey via a sequence of inear programs. In [3], reay seection in muti-hop CRS with the objective of minimizing the outage probabiity is proposed. The power aocation probem is soved using standard convex optimization techniques for both AF and DF protocos under Rayeigh fading conditions. A joint reay seection, spectrum aocation and rate contro (JRSR) scheme in CRS is proposed in []. A threestage sub-optima agorithm is proposed to address the JRSR probem. A noncooperative game based decentraized power aocation for primary and secondary users is considered in [33]. The two kinds of inks, one of which incudes the primary users and their reay, the other incudes the secondary users and their reay, are treated as payers of the non-cooperative game. Each payer competes against the other by choosing the power aocation strategy that imizes its own rate, subject to the QoS threshod of the primary system. A reay-assisted iterative agorithm is proposed to efficienty reach the Nash equiibrium. In [34], authors proposed both centraized and distributed power aocation schemes for muti-hop wideband CRS. The main objective is to 3

25 imize the output signa-to interference pus noise ratio (SINR) at the destination node of the CRS. The aforementioned work on reay networks cannot be appied to the bidirectiona reay networks. Reference [35], [36], [37] discussed power aocation for two-way reay networks with singe reay. In [35], a network comprising a singe reay and mutipe source-destination pairs is considered, and an optimization probem to decide transmission power of the reay was studied. Reference [35] does not consider jointy aocating power to the sources and the reay. In [36], a cognitive radio network comprising one source-destination pair, a singe reay, and a singe primary user is considered. For this system, the probem of aocating power to the source and determining optima beam-forming vectors of the reay is considered. In [37], a two-way reay network comprising a pair of users and mutipe reays is considered and the probem of seecting a singe reay and aocating power to it is considered. Power aocation for OAF bidirectiona reaying is considered in [7]. Reference [7] considers a two-way reay network comprising a pair of users and mutipe reays and performs joint source and reay power aocation. However, reference [7] presents a simper sub-optima power aocation by imizing the ower bound that serves as a good approximation ony at the high-snr region. Power aocation for NAF bidirectiona reaying is considered in [38]-[4]. Reference [39], [4] and [43] consider the optimization of ony reays transmit powers. Joint users and reays transmission powers aocation is considered in [0], [3], [34] where optimization probems are formuated to determine the transmission power of the users and the beam-forming vectors of the reay. However, the optimizations in [0], [3], [34] consider ony a singe sum-power constraint and the obtained soutions cannot be appied to the optimization probems that has both sum-power and mutipe individua power constraints. 4

26 Tabe.3 iterature Survey. Objective Reaying CR Protoco Power Contro Ref. [Ref Num, Name] Maximize the SNR of AF/DF shared bandwidth schemes One-Way No Centraized Yes [, I. Maric et. a] Seect the mutipe reays to imize the SNR in shared bandwidth AF scheme One-Way No Centraized Binary Power Contro [, Y. Jing et a.] Sum-rate imization One-Way No Centraized Yes [3, Kadoor et a.] Maximize the minimum capacity Protocos and outage anaysis One-Way No Centraized No [4, Y. Shi et a.] One-Way No Distributed No [5, Sadek et a.] Average sum-capacity One-Way No Decentraize No [6, P. Zhang et a.] Maximize the instantaneous received SNR Minimize the tota bandwidth Cosed-form expressions of detection probabiity Cooperation between primary user and secondary user.(secondary user act as reay for primary user) Minimize outage probabiity Maximize Average throughput Maximize the rate utiity function One-Way No Decentraize Yes [7, G. Farhadi et a.] One-Way Yes Centraized No [8, T. Hou et a.] One-Way Yes ---- No [9, J. Zhu et a.] One-Way Yes ---- Yes [30, R. Manna et a.] One-Way Yes Centraized Yes [3, Jayasinghe et a.] One-Way Yes Centraized Yes [3, H. Chun et a.] One-Way Yes Decentraize Yes [33, Xiaoyu et a.] Maximize SNR of RD ink One-Way Yes Distributed Yes [34, Mietzner et a.] Sum-Capacity Maximization for AF/DF reaying Two-Way No Centraized Yes [35, Chen et a.] 5

27 Sum-Capacity Maximization for OAF two-way reaying Sum-Capacity Maximization for SAF two-way reaying Beamforming in SAF Two-Way reaying Beamforming in SAF Two-Way reaying Singe reay seection and power aocation Two-Way No Centraized Yes [7, Zhang et. a] Two-Way No Centraized Yes [39, vaze et. a] Two-Way No Distributed Yes [38], [40],[4]-[43] Two-Way Yes Centraized Yes [36] Two-Way No Centraized Yes [37], [4].5 Organization of Thesis The structure of the thesis is as foows. Chapter describes the power aocation in two-way reay assisted cognitive radio networks where the reays empoy OAF reaying. Chapter 3 describes the power aocation in two-way NAF reaying subject to individua and sum-power constraints. Chapter 4 describes power aocation in muti-way reay channe..6 Chapter References [] J. N. aneman, D. N. C. Tse, and G. W. Worne, Cooperative Diversity in Wireess Networks: Efficient Protocos and Outage Behavior, IEEE Trans. Inform. Theory, vo. 50, no., pp , Dec [] Boris Rankov and Armin Wittneben, Spectra efficient protocos for hafdupex fading reay channes, IEEE Journa on Seected Areas in Communications, vo. 5, no., pp , Feb [3] Deniz Gunduz, Ayin Yener, Andrea J. Godsmith, and H. Vincent Poor, The muti-way reay channe, submitted in IEEE Trans. Inform. Theory, 00, avaiabe on 6

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29 [5] G. Bansa, O. Duva, and F. Gagnon, Joint Overay and Underay Power Aocation Scheme for OFDM-based Cognitive Radio Systems, In Proceeding of IEEE VTC spring 00, Taipei, Taiwan, 00. [6] J.N. aneman and G.W.Worne, Distributed space-time-coded protocos for expoiting cooperative diversity in wireess networks, IEEE Trans. Inform. Theory, vo. 49, no.0, pp , Oct [7] Xiao Juan Zhang and Yi Gong, Adaptive power aocation in two-way ampify-and-forward reay networks, in proceedings of IEEE Internationa Conference on Communications, pages 5, June 009. [8] Sang Joon Kim, Natasha Devroye, and Vahid Tarokh, Bi-directiona hafdupex protocos with mutipe reays, submitted in IEEE Trans. Inform. Theory, 008, avaiabe on [9] Hoang Tuy, Monotonic optimization: Probems and soution approaches, in SIAM Journa on Optimization, vo., no., pp , 000. [0] Hoang Tuy, Faiz A-Khayya, and Phan Thach, Monotonic optimization: Branch and cut methods, in Essays and Surveys in Goba Optimization, pages Springer US, 005. [] I. Maric and R. D. Yates, Bandwidth and Power Aocation for Cooperative Strategies in Gaussian Reay Networks, IEEE Trans. Inform. Theory, vo. 56, no. 4, pp , Apr. 00. [] Y. Jing and H. Jafarkhani, Singe and mutipe reay seection schemes and their achievabe diversity orders, IEEE Transactions on Wireess Communications, vo. 8, no. 3, pp , Mar [3] S. Kadoor and R. Adve, Optima Reay Assignment and Power Aocation in Seection Based Cooperative Ceuar Networks, IEEE Internationa Conference on Communications, 4-8 June, pp. -5, 009. [4] Y. Shi, S. Sharma, Y.T. Hou, and S. Kompea, Optima reay assignment for cooperative communications, In Proceedings of the 9th ACM internationa Symposium on Mobie Ad Hoc Networking and Computing, Hong Kong, China, pp. 3-,

30 [5] A. K. Sadek, Z. Han, and K. J. R. iu, Distributed Reay-Assignment Protocos for Coverage Expansion in Cooperative Wireess Networks, IEEE Transactions on Mobie Computing,, vo.9, no.4, pp , Apri 00. [6] P. Zhang, Z. Xu, F. Wang, X. Xie, and. Tu;, A Reay Assignment Agorithm With Interference Mitigation For Cooperative Communication, In Proceedings of IEEE Wireess Communications and Networking Conference, Apri 009. [7] G. Farhadi and N. C. Beauieu, A Decentraized Power Aocation Scheme for Ampify-And-Forward Muti-Hop Reaying Systems, In Proceedings of IEEE Internationa Conference on Communications (ICC), May 00. [8] Y. T. Hou, Y. Shi, and H. D. Sherai, Spectrum sharing for muti-hop networking with cognitive radios, IEEE Journa on Seected Areas of Communications, vo. 6, no., pp , Jan [9] J. Zhu, Y. Zou, and B. Zheng, Cooperative Detection for Primary User in Cognitive Radio Networks, EURASIP Journa on Wireess Communications and Networking, 009. [30] R. Manna, R.H.Y. ouie, Yonghui i, and B. Vucetic, Cooperative Ampify-and-Forward reaying in cognitive radio networks, In Proceedings of the Fifth Internationa Conference Cognitive Radio Oriented Wireess Networks & Communications (CROWNCOM),June 00. [3].K.S. Jayasinghe and N. Rajatheva, "Optima Power Aocation for Reay Assisted Cognitive Radio Networks," In Proceedings of 7nd IEEE Vehicuar Technoogy Conference, Sep. 00. [3] H. Chun, F. Zhiyong,.Z. Qixun,Z. Zhongqi and X. Han, A Joint Reay Seection, Spectrum Aocation and Rate Contro Scheme in Reay-Assisted Cognitive Radio System, In Proceedings of 7nd IEEE Vehicuar Technoogy Conference, Sept 00. [33] Q. Xiaoyu, T. Zhenhui, X. Shaoyi and J. i, Combined Power Aocation in Cognitive Radio-Based Reay-Assisted Networks, In Proceedings of IEEE Internationa Conference Communications Workshops (ICC), 00. 9

31 [34] J. Mietzner,. ampe and R. Schober, Distributed transmit power aocation for mutihop cognitive-radio systems, IEEE Transactions On Wireess Communications, vo. 8, no. 0, Oct 009. [35] Min Chen and A. Yener, Power aocation for f/tdma mutiuser two-way reay networks, IEEE Transactions on Wireess Communications, vo. 9, no., pp , February 00. [36] K. Jitvanichphaiboo, Ying-Chang iang, and Rui Zhang, Beamforming and power contro for muti-antenna cognitive two-way reaying, in proceedings of IEEE Wireess Communications and Networking Conference, 009. [37] ingyang Song, Reay seection for two-way reaying with ampify-andforward protocos, IEEE Transactions on Vehicuar Technoogy, vo. 60, no. 4, pp , May 0. [38] V. Havary-Nassab, S. Shahbazpanahi, and A. Grami, Optima network beamforming for bidirectiona reay networks, in proceedings of IEEE Internationa Conference on Acoustics, Speech and Signa Processing, pages 77 80, Apri 009. [39] R. Vaze and R.W. Heath, Optima ampify and forward strategy for twoway reay channe with mutipe reays, in proceedings of IEEE Information Theory Workshop on Networking and Information Theory, pages 8 85, June 009. [40] S. Shahbazpanahi and Min Dong, Achievabe rate region and sum-rate imization for network beamforming for bi-directiona reay networks, in proceedings of IEEE Internationa Conference on Acoustics Speech and Signa Processing (ICASSP), pages 50 53, March 00. [4] S. Tawar, Yindi Jing, and S. Shahbazpanahi, Joint reay seection and power aocation for two-way reay networks, IEEE Signa Processing etters, vo. 8, no., pp. 9 94, Feb. 0. [4] Rui Zhang, Ying-Chang iang, Chin Choy Chai, and Shuguang Cui, Optima beamforming for two-way muti-antenna reay channe with anaogue 0

32 network coding, IEEE Journa on Seected Areas in Communications, vo. 7, no. 5, pp , June 009. [43] M. Zeng, R. Zhang, and S. Cui, On Design of Distributed Beamforming for Two-Way Reay Networks, IEEE Transactions on Signa Processing, Vo. 59, No. 5, pp , May 0

33 CHAPTER : POWER AOCATION IN ORTHOGONA TWO WAY REAY ASSISTED COGNITIVE RADIO NETWORKS The conventiona one-way reaying protocos suffer from a oss in spectra efficiency due to the haf-dupex nature of the terminas. In order to increase the spectra efficiency of such a reay network, a bidirectiona (two-way) reay assisted communication protoco was suggested in [3]. In this chapter, we study a cognitive radio [] network (comprising mutipe primary users) in which a pair of sources communicates with each other through mutipe reays that empoy two-way ampify-and-forward reaying. The mutipe reays transmit in orthogona channes that can be achieved by assigning each reay a non-overapping timesot band for their respective transmissions as in [4]. We formuate optimization probems to adequatey decide the transmission powers of the nodes in such networks. We consider two optimization probems. In one probem, we consider imizing the minimum among the two sources capacities. In the other probem, we consider imizing the sum capacity of the system. Our formuated optimization probems turn out to be non-convex and non-inear. Power aocation in one-way reay networks has been we studied. Reference [6] presents a distributed singe and mutipe reay seection schemes with reay power aocation. In [7], a one-way wireess reay network comprising mutipe reays and a source-destination pair is studied and optima reay power aocation is determined. Joint source and reay power aocation is studied in [8]. Reference [8] performs joint optimization of the source and the reay power by using a high SNR approximation of the SNR at the destination. Unfortunatey, the power aocation schemes deveoped for one-way reays cannot be directy appied to the two-way reays, as the optimizations are very different.

34 Reference [4] deas with joint source and reay power aocation in twoway reay networks where the reays use orthogona channes. In [4], a high SNR approximation of the SNR at the two users is used to jointy determine the sources and reays transmit powers. However, the formuation in [4] is not reevant to cognitive radio network. Bidirectiona reaying in the context of cognitive radio has been considered in [5]. In [5], a cognitive radio network comprising one source-destination pair, a singe reay, and a singe primary user is considered. For this system, the probem of aocating power to the source and determining optima beam-forming vectors of the reay is considered. In this work, we provide an optima joint source and reay power aocation. We aso consider different cost functions (-min and sum-rate) and we provide ow-compexity heuristics to determine sub-optima soutions to our optimizations. For theoretica interest in deaing with these non-convex optimization probems for deciding the power eves, we show in this chapter that these optimization probems have a set of properties that guarantees ε-convergence if the monotonic optimization (MO) agorithm [9], [0] is used. We observe that our formuated optimizations have specific structures that enabe us to reduce the number of optimization variabes to ony two variabes. The resuting optimization probems are sti non-convex. However, we show that they can be transformed to equivaent optimizations that coud be soved to goba optimaity by using the methods of MO agorithm. Athough the MO agorithm can guarantee convergence to a soution that has a performance arbitrariy cose (within an arbitrary number ε) to the optima performance, our experimentation with the MO agorithm appied to this reay power aocation probem shows rather sow convergence and heavy computationa oad. Therefore, we propose a owcompexity heuristics, which we name as Greedy Power Aocation with Max-Min Fairness (GPAMF) and Greedy Power Aocation with Sum Capacity Maximization (GPASM). The simuation resuts show that the proposed heuristics perform we in comparison to the respective optima soutions and have much ower computationa compexity than the MO agorithm. 3

35 Tabe. Notations used in chapter. Symbo Definition M Number of primary users Number of reays s,s Source, source f Channe gain from source to the th reay g m, Channe gain from source to the th reay h Channe gain from th reay to the mth primary user h Channe gain from s to the mth primary user s, m h Channe gain from s to the mth primary user s, m ps p s p Transmission power of source, souece Transmission power of th reay p Maximum aowed transmission power of the th reay I m Maximum aowed interference at mth primary user n n R + ( ++ ) R Set of non-negative (positive > 0) integers f g h h s, m h s, m m, Fig.. Two-way reay assisted Cognitive Radio network 4

36 . System Mode We consider a two-way reay system with two sources and reays. Our system mode aso incudes M primary users, for which the transmission power of the cognitive radio nodes (secondary users) must be imited. Figure. depicts our system mode. The two sources wi communicate with each other with the hep of reays that use ampify-and-forward reaying. The reays, source (s), and source (s) are equipped each with a singe antenna. We assume that the transmission channes of the reays are orthogona to one another, which can be achieved by assigning the reays to non-overapping frequency bands or time sots. We denote by f the channe gain from s to the th reay, g the channe gain from s to the th reay, hs, m( hs, m) the channe gain from s (s) to the mth primary user and by h, m the channe gain from th reay to the mth primary user. For gaining simpe insights to the system, in this chapter we assume that each channe between a source and a reay is symmetric. It is aso assumed that transmissions from a nodes are perfecty synchronized. et p s, p s and p denote, respectivey, sources s s and s s transmission powers per dimension. We consider a two-step two-way ampify-and-forward (AF) scheme, as given in [4] for cooperative communication which we wi refer to as orthogona ampify and forward (OAF) reaying. In the first step the users (sources) send their data to the reays. The signa received by reay ( =,,.., ) is n y = ps f Xs + psg Xs + Z (.) where compex-vaued random variabes X s and X s represent the transmitted = =. Z is the compex- symbos and are normaized such that E( Xs ) E( Xs ) vaued white Gaussian noise at reay with E( Z ) No =. In the subsequent time-sots, reays,,, each transmits in its own non-overapping timesot/frequency band. Without oss of generaity, we define our indexing such that the th reay transmits at the + time sot and the sources transmit at the first time 5

37 sot of the frame. The th reay ampifies the signa received from sources s, s and transmits the ampified signa. The received signa at s and s from the th reay can be written as ( ) ( ) y = p f X + p g X + Z β f + Z s s s s s s, y = p f X + p g X + Z β g + Z s s s s s s, (.) where Z s, Z s are the i.i.d compex vaued white Gaussian noise at s and s with (, ) (, ) E Zs = E Zs = No and β is the ampification gain of the th reay. The ampification gain, β, is chosen such that the transmit power of the th reay is p, [0] i.e. β = p s s o p f + p g + N (.3) where p is the transmission power of the th reay. Notice that in (.), the received signa at s consists of a sef-interference term p fx β f. Since s s s knows the signa it transmitted and assuming perfect knowedge of the corresponding channe gains, s can subtract the interfering signa from its received signa. Simiary, s can aso subtract the interfering signa from its received signa. The received signas at s, s from the th reay after sefinterference canceation can be written as ( ) ( ) y = p g X + Z β f + Z s s s s, y = p f X + Z β g + Z s s s s, After sef-interference canceation [3]-[4], the received signas at s and s from the reays =,,.., can be written as 6

38 gf β β fz + Z s, ys = gf p β sxs + β fz + Zs, g f β β f Z + Z s, gf β β gz+ Z y = gf β p X + β gz+ Z g f β β g Z + Z s, s s s s, s, (.4) After ima ratio combining (MRC) SNRs at s and s are written as γ γ ps p f g s = = No p f ps f ps g No ( ) ps p f g s = = No p g ps f ps g No ( ), (.5). Probem Formuations In this section, we present our optimizations for aocating power to the sources and the reays. We consider two optimization probems. In one probem, we consider imizing the sum capacity of the system. In the other probem, we consider imizing the minimum among the two sources capacities. We sha refer to aforementioned optimizations as joint sources and reays powers optimization with sum capacity imization (JSRSM) and joint sources and reays powers optimization with -min fairness (JSRMF). 7

39 .. Joint Sources and Reays Powers Optimization with Sum-Capacity Maximization In this sub-section, we consider the optimization probem in which the sources and reays transmit powers that together imize the sum capacity of the system are sought. We denote by p the vector ( ) optimization probems as minimizing the cost function p, p,.., p. We formuate the + + (,, p) og ( + γ ) + og ( + γ ) s s s s f p p (.6) which is the sum capacity (in bits per degree of freedom). The optimization probem is formuated as f ( ps ps p) { p, p, p},,, s s subject to, m m C: p h I, m, C:0 p p, ( ) C3: p, p Y, where s s Y p p (, ) s s ps hs, m + ps hs, m Im, m, 0 ps, ps ps (.7) In the above optimization probem, constraint C ensures that the threshod of the reays interference to each PU is not exceeded. C represents each reay s imum transmission power constraints. C3 imits the sources transmission powers both from their own imitation p s and from the threshod of sources interference to every primary user. It shoud be noted that the objective function is not convex with respect to the variabes (p s, p s, p ). Thus, convex optimization techniques cannot be appied to determine the goba optima soution. In the seque, we wi refer to this probem as Joint Sources Powers and Reays Gains Optimization with Sum Capacity Maximization (JSRSM). 8