1490 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 62, NO. 5, MAY On Achievable Rate and Ergodic Capacity of NAF Multi-Relay Networks with CSI

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1 190 IEEE TRASACTIOS O COMMUICATIOS, VOL. 62, O. 5, MAY 201 On Acievable Rate and Ergodic Capacity of AF Multi-Relay etworks wit CSI Tuyen X. Tran, Student Member, IEEE, gi H. Tran, Member, IEEE, Hamid Reza Barami, Member, IEEE, and Sivakumar Sastry, Senior Member, IEEE Abstract Tis paper investigates te acievable rate and ergodic capacity of a non-ortogonal amplify-and-forward AF alf-duplex multi-relay network were multiple relays exploit cannel state information CSI to cooperate wit a pair of source and destination. In te first step, for a given input covariance matrix at te source, we derive an optimal power allocation sceme among te relays via optimal instantaneous power amplification coefficients to maximize te acievable rate. Given te nature of broadcasting and receiving collisions in AF, te considered problem in tis step is non-convex. To overcome tis drawback, we propose a novel metod by evaluating te acievable rate in different sub-domains of te vector cannels. It is ten demonstrated tat te globally optimal solution can be derived in closed-form. In te next step, we establis te ergodic cannel capacity by jointly optimizing te input covariance matrix at te source and te power allocation among te relays. We sow tat tis is a bi-level non-convex problem and solve it using Tammer decomposition metod. Tis approac allows us to transform te original optimization problem into an equivalent master problem and a set of sub-problems aving closed-form solutions derived in te first step. Te cannel capacity is ten obtained using an iterative water-filling-based algoritm. Finally, we analyze te capacity-acieving input covariance matrix at te source in ig and low signal-to-noise ratio SR regimes. At sufficiently ig SRs, it is sown tat te transmit power at te source sould be equally distributed in all broadcasting and cooperative pases. On te oter and, in low SR regions, te source sould spend all its power in te broadcasting pase associated wit a relay aving te strongest cascaded source-relay and relay-destination cannels. Index Terms Acievable rate, cannel state information, distributed water-filling, ergodic capacity, multiple relays, nonortogonal amplify-and-forward, power adaptation, relay cannel. I. ITRODUCTIO DUE to cannel impairments suc as fading, interference, and noise, te wireless cannels fluctuate randomly over time. Tis makes it callenging to design a wireless communications system wit guaranteed performance. One effective way to enance te reliability and data rate of wireless systems is is to employ intermediate network nodes Manuscript received July 31, 2013; revised December 6, 201. Te editor coordinating te review of tis paper and approving it for publication is D. Gunduz. Te autors are wit te Department of Electrical & Computer Engineering, te University of Akron, Akron, OH, USA txt2@zips.uakron.edu, {ngi.tran, rb, ssastry}@uakron.edu. Tis work was supported in part by Te University of Akron under a Startup Grant and a Firestone Fellowsip Award. A part of tis work was presented at te IEEE International Conference on Communications ICC, Budapest, Hungary, June ]. Digital Object Identifier /TCOMM /1$31.00 c 201 IEEE tat assist eac oter by relaying transmissions 2] 5]. In general, relaying strategies can be categorized as decode-andforward DF 6], 7], compress-and-forward CF 8], 9], and amplify-and-forward AF 5], 10] 1]. Wile DF and CF relaying usually require ig decoding complexity, te AF sceme is very simple to implement, since te relay only needs to transmit a scaled version of te signal. As suc, AF relaying is of practical interest and in fact, it as been adopted in major wireless standards 15]. Wile early researc on AF relaying as mainly devoted to dual-op and multi-op AF relaying systems were te direct link between te source and destination is not taken into account see for example 16] 21] and references witin, tere as been a growing interest in cooperative scemes tat make use of te direct link. It is because by considering te source to destination link, cooperative AF networks can furter exploit te degrees of freedom of te cannel and provide rate as well as diversity advantages 3], 5], 10] 1]. For suc scemes, te intermediate nodes relays receive signal from te source during te broadcasting pases and ten transmit te noisy amplified version of tat signal to te destination during te cooperative pases. Different AF relaying protocols wit direct link can be classified into te ortogonal AF OAF protocol and te non-ortogonal AF AF protocol 3], ]. In OAF, te source and relays use separate time slots or ortogonal cannels to transmit signals, i.e., te source only transmits in te broadcasting pase and remains silent in te cooperative pase. On te oter and, in AF, te source-destination link is exploited in bot broadcasting and cooperative pases wic maximizes te degrees of broadcasting and receiving collisions. Specifically, in te cooperative pase, te source attempts to transmit a new symbol wen te relays forward te received symbols in te previous pase. In fact, te AF protocol is considered to be favorable over oter AF scemes, not only from an information-teoretic point of view 10] 12], 1], but also in terms of diversity performance 22], 23]. However, due to te complexity of broadcasting and receiving collisions, te analysis and optimization of non-ortogonal networks are more callenging and ave received less attention tan te OAF counterpart 10], 1]. In AF relaying, depending on te availability of te cannel state information CSI, a relay simply amplifies te noisy version of te received signal using a suitable amplification coefficient. For example, by assuming tat a relay can only obtain te cannel distribution information CDI of te sourcerelay cannel, te received signal at te relay is scaled by

2 TRA et al.: O ACHIEVABLE RATE AD ERGODIC CAACITY OF AF MULTI-RELAY ETWORKS WITH CSI 191 a constant-gain coefficient before being transmitted to te destination 3], 1], 22]. Wen te relay as an instantaneous knowledge of te source-relay cannel, te cannel inversion CI tecnique can be used to amplify te received signal at a desired power level ], 10]. Recently, motivated by te benefit offered by te cooperation between te relay and destination, references 2] and 25] ave examined AF and OAF single-relay systems in wic te relay acquires complete CSI of te source-destination and source-relay links via a feedback cannel from te destination. By assuming a fixed covariance matrix at te source, it was sown in 2] and 25] tat wit CSI, te acievable rate can be significantly improved over wat could be acieved using CDI and CI. Te idea as been recently extended to AF multi-relay networks in 26] for furter improvements, but only for te OAF protocol. Extending te idea of using CSI at te relays wit a suitable power allocation at te relays and te source to enance te performance of an AF multi-relay system presents many callenges. First, different from a single-relay system, we need to take into account power budget constrained on te nodes globally and locally. Second, te broadcasting and receiving nature of AF makes it difficult to analyze and optimize te fundamental limits. For example, for a fixed input covariance matrix, obtaining an optimal power saring sceme among te relays and te corresponding acievable rate for te AF networks in closed-form are already callenging. Finding a capacity-acieving strategy is even more difficult, since one needs to simultaneously optimize te input covariance matrix at te source and te power saring strategy among te relays. Motivated by te above discussions, tis paper addresses te acievable rate and ergodic cannel capacity for AF multi-relay systems wit full CSI available at te relays. We adopt te multi-relay protocol originally proposed in 10], 27] were te relays take turns to transmit. Tis multirelay protocol as been widely considered in te literature 10], 1], 27], 28]. We sall consider bot a Total Average ower Constraint TAC and an Individual Average ower Constraint IAC imposed on te relay nodes. First, for a given input covariance matrix, we identify te optimal power saring sceme among te relays by means of te optimal instantaneous power amplification coefficients to maximize te acievable rate. Due to te nature of te AF protocol, te considered problem is not convex. Our metod is to modify te problem by evaluating te acievable rate in different subdomains of te vector cannels. It is ten sown tat te obtained closed-form solution is indeed te globally optimal solution of te original problem, wic can be understood as an extended water-filling sceme wit te vessels aving bot te bottoms and lids. Furtermore, we investigate te capacity limit of te considered AF system by jointly examining te optimal power allocation sceme at te relays and te optimal input covariance matrix at te source. Te optimization problem in tis step is a bi-level non-convex problem for wic it is not feasible to derive a closed-form solution. As an alternative, we effectively utilize te Tammer decomposition metod 29] to transform te original problem to an equivalent master problem and a set of sub-problems. It is ten demonstrated tat te sub-problems ave te same closed-form solution as obtained in te first step. Te ergodic capacity can ten be obtained via an iterative water-filling-based algoritm. Finally, we analyze te capacity-acieving input covariance matrix at te source in ig and low signal-to-noise ratio SR regimes. Specifically, we sow tat at sufficiently ig SRs, te transmit power at te source sould be equally distributed in all broadcasting pases to acieve te capacity. On te oter and, in low SR regimes, it is demonstrated tat te source spends all its power in te broadcasting pase associated wit a relay aving te strongest cascaded source-relay and relaydestination cannels. Te rest of tis paper is organized as follows. Section II introduces te considered AF system. Optimal power saring scemes at te relays for a given input covariance matrix are derived in Section III. In Section IV, we address te optimal power saring at te relays and te optimal input covariance matrix at te source simultaneously to acieve te cannel capacity. Section V analyzes te capacity-acieving input covariance matrix at te source and te corresponding capacity at ig and low SRs. umerical results are provided in Section VI to illustrate te gains of te proposed power adaptation scemes. Finally, Section VII concludes te paper. II. SYSTEM MODEL A. AF Multi-Relay rotocol Te alf-duplex AF multi-relay system sown in Fig. 1a consists of relay nodes, R 1,...R, tat assist te transmissions between a source S and a destination D via multiple cooperation frames as proposed in 10], 27]. Te instantaneous complex cannel gains of te S-D, S-R n and R n -D links are denoted, respectively, as SD, SRn and RDn. Signals are transmitted from te source to te destination via a sequence of cooperative frames, eac consisting of 2 time-slots as illustrated in Fig. 1b. In eac cooperative frame, a relay will only be active in two consecutive timeslots to assist te transmission from S to D wile oter relays remain silent or participate in oter transmissions. Wile te adopted protocol migt not be te best multi-relay strategy, it as been demonstrated in 10], 28] tat tis protocol provides superior performance over oter AF protocols from te diversity-multiplexing tradeoff DMT perspective and as te potential to acieve full diversity. Also, by using tis protocol, interference among te relays can be avoided witin te considered systems. Furtermore, in practice, a relay node can engage in oter transmissions wen its relaying function is inactive 10], 27]. Suc benefits make tis multirelay protocol fundamentally different from oter multi-relay protocols tat allow te relays to transmit simultaneously 23], 30]. For te considered protocol, eac cooperative frame is divided into two -time-slot pases, te broadcasting pases and te cooperative pases. Eac broadcasting pase is carried out in te 2n 1t time-slots, 1 n. Foragiven 2n 1t time slot, only te relay R n stays active and te source S sends te signal x n,1 to bot D and R n.te received signals at R n and D can be written, respectively, as r n = E s SRn x n,1 +w n,andy 2n 1 = E s SD x n,1 +v n,1, were E S is a constant related to te transmitted power; w n,v n,1 are te i.i.d zero-mean circularly symmetric Gaussian noises wit variance 0, denoted as C0, 0.

3 192 IEEE TRASACTIOS O COMMUICATIOS, VOL. 62, O. 5, MAY 201 S SD SR1 RD1 R 1 SR2 RD2 D S R 1 R 2 x1,1 x1,2 x2,1 2,2 r 1 br 11 r 2 x x,1 x,2 br 2 2 SR R 2 RD R r br R D y1 y2 y3 y y2 1 y 2 Fig. 1. a Te alf-duplex AF multi-relay system. b Te frame structure of te AF multi-relay protocol; te solid boxes denote te transmitted signals and te dased boxes denote te received signals. Te cooperative pase appens in te 2nt time-slots, 1 n 3]. In particular, te source S transmits a new signal x n,2 to D, wile R n forwards te amplified version of r n to D. Te received signal at D in te 2nt time-slot is given by y 2n = E s SD x n,2 + RDn b n E s SRn x n,1 + w n +v n,2, were v n,2 C0, 0 and b n is te amplification coefficient at te relay R n. Witening te noise component, te AF system can be written as y = E S Hx + n, were x = x 1,1,x 1,2,x 2,1,x 2,2,..., x,1,x,2 ] T, y = y 1,y 2,..., y 2 ] T, te equivalent noise n C0, 0 and H is a 2 2 block diagonal cannel matrix given by H = diagh ] 1, H 2,..., H, wit H n = SD 0,andα α nb n RDn SRn α n n = 1 is te SD 1+b 2 n RDn 2 noise witening factor. B. CSI and ower Constraints Te cannels between different nodes in te system are assumed to be constant during at least one cooperative frame, and teir magnitudes are independently Rayleig distributed, i.e., SD C0,φ SD, SRn C0,φ SRn and RDn C0,φ RDn,wereφ SD, φ SRn and φ RDn are te cannel variances. Following references 5], 10] 1], we also assume tat D as perfect knowledge of te gains of all links. In addition, as recently considered in 2], suc complete CSI can be made available at eac relay using a feedback cannel from te destination. Suppose tat te source S uses Gaussian input signal and as no CSI knowledge; it as been sown in 1] tat te optimal input covariance matrix is a diagonal matrix given ] qn1 0 as Q = diag Q 1, Q 2,...Q n,wereq n =, 0 q n2 and q n1 = E x n,1 2], q n2 = E x n,2 2]. Hence, q n1 E S and q n2 E S, 1 n, can be interpreted as te average transmit power of te source in te broadcasting pase and te cooperative pase, respectively. Te average transmit power constraint at te source can ten be expressed as tr Q = tr Q n = q n1 + q n2 S. 1 Furtermore, let = SD, SR1, SR2,..., SR, RD1, RD2,..., RD ] T be te vector cannels and μ n E S be te instantaneous power allocated to te relay R n in one cooperative frame. Using te full CSI knowledge, te relays can adjust teir instantaneous transmit power in order to adapt to te current cannel conditions. Tus, te instantaneous value of μ n depends on and witout loss of generality, we can write μ n = μ n. Suc a variation is reflected in te use of an instantaneous power amplification coefficient b n at eac relay R n,wicis given as b n = μ n ρ SRn 2 q n1 ρ +1, 2 wit ρ = E S / 0 being te normalized SR. We consider two types of power constraint, te TAC on all te relays and te IAC on eac relay, wic can be written, respectively, as TAC : μ n f d R, 3 IAC : μ n f d n,,..., were f is te probability density function of te cannel state, R is te total average power available for all relays, and n is te average power limit on eac relay R n, n = 1,... Te assumption of total power constraint is feasible, due to te fact tat te relays and te destination can be managed directly by te service provider. As suc, te relays and te destination can cooperate to sare te total power constraint. In addition, a network wit suc a constraint can serve as a system bencmark to any system wit only individual power constraints due to te constraint on eac individual RF cain. Finally, it sould be noted tat wen te relays only ave te knowledge of te CDI of te S-R n link, te amplification coefficient at relay R n is 3], 1], 22]: b CDI ρ R n = E SRn 2 ]q n1 ρ +1, 5

4 TRA et al.: O ACHIEVABLE RATE AD ERGODIC CAACITY OF AF MULTI-RELAY ETWORKS WITH CSI 193 On te oter and, wen only te CSI of te S-R n link is available at te relays, eac relay R n can use te cannel inversion CI sceme wit te following amplification coefficient ], 10]: b CI ρ R n = SRn 2 q n1 ρ C. Acievable Rate and Ergodic Cannel Capacity Given te CSI knowledge at te destination, te sourcedestination instantaneous mutual information can be expressed as Ix, y = log deti 2 + ρh HQ], 7 were denotes te Hermitian operator and log. is te base- 2 logaritm. Tus, for a given input covariance matrix Q, te maximum acievable rate in bits per cannel use of te AF system can be defined as R Q = 1 2 max μ n,, I x, y f d. 8 ote tat te normalization factor of 1/2 is used in 8 to account for te fact tat eac transmission from te source to destination associated wit an active relay requires two cannel uses. By furter optimizing te input covariance matrix at te source and te power allocation at te relays simultaneously, one can acieve te ergodic capacity of te system, wic is expressed as C = 1 max I x, y f d, 9 2 Q 0,trQ S, μ n,, In te following, we sall present te solutions to te acievable rate R Q in 8, and te ergodic capacity C in 9. In particular, by first considering a fixed input covariance matrix Q, we derive te closed-form optimal power allocation solutions at te relays to maximize te acievable rate in 8. Tese closed-form solutions will be used in Section IV to obtain te ergodic capacity. III. ACHIEVABLE RATE AD OTIMAL OWER ALLOCATIO AT THE RELAYS In tis section, we sall develop te optimal power saring scemes among te relays to maximize te acievable rate RQ. For te sake of convenience, let x n = RDn 2, y = SD 2, z n = SRn 2. Using 7 we obtain Ix, y = were log det I 2 + ρh ] nh n Q n = logγ n, Γ n = ρ2 y 2 q n1 q n2 1+b 2 n x n 10 + ρ q n1 y + q n1b 2 n x nz n + q n2 y 1+b 2 n x +1. n 11 From 2 and 11, we get Γ n = Γ n μ n ] = Γn1μn] Γ, wit n2μ n] Γ n1 μ n ] = μ n ρq n1 y + ρq n1 z n +1ρx n +ρ 3 qn1 2 q n2z n y 2 + ρ 2 q n1 q n2 y 2 + ρ 2 qn1 2 z ny + ρ 2 q n1 q n2 z n y +ρq n1 z n + ρq n1 y + ρq n2 y +1, 12 and Γ n2 μ n ] = ρμ n x n +ρq n1 z n Under bot TAC and IAC, te set of optimal instantaneous power allocated at te relays {μ n} to maximize te acievable rate RQ can be obtained by solving te following optimization problem max μ n 0, s.t. I x, y f d μ n f d R, μ n f d n. 1 Let Ix, y =Iµ were µ =μ 1,...,μ ]. Differentiating te objective function in 1 wit respect to μ n we ave I μf d μ n = log Γ n μ n ] f d 15 μ n = log Γ n μ n ]f d. μ n Since 15 is a functional derivative of te inner product of log Γ n μ n ] and f, it follows from 31] tat: I μf d = log Γ nμ n ] f 16 μ n μ n A n = ln2c n μ 2 f, 17 n+d n μ n +E n ] were A n = ρ 2 x n ρq n1 z n +1ρq n1 q n2 y 2 + q n2 y q n1 z n, C n = ρ 2 x 2 n ρq n1y + ρq n1 z n +1, D n = ρx n ρq n1 z n + 12ρq n1 y + ρq n2 y + ρq n1 z n + ρ 2 q n1 q n2 y 2 +2, E n =ρq n1 y +1ρq n2 y +1ρq n1 z n Similarly, te second derivatives can be calculated as: 2 μ 2 n I μf d and 2 μ m μ n A n2c nμ n+d n] = f, ln2c nμ 2 n +Dnμn+En]2 I μf d =0, m n. 19 It can be verified tat wile C n, D n and E n are always positive, A n migt be positive, negative or zero depending on te SR, power allocation at S, and te instantaneous cannel gains. Hence, te problem in 1 is not concave.

5 19 IEEE TRASACTIOS O COMMUICATIOS, VOL. 62, O. 5, MAY 201 As a consequence, te Karus-Kun-Tucker KKT conditions cannot be applied directly. To overcome tis drawback, in te following, we propose a novel approac by evaluating te acievable rate in different sub-domains of te vector cannels and sow tat te globally optimal solution can be obtained. To tis end, let define te feasible set for te problem in 1 as F = {µ R μ n 0, μ n f d R }. Furtermore, let γ n = ρq n1 q n2 y 2 + q n2 y q n1 z n. For eac relay R n, we divide te domain of into two disjoint regions, n = { γ n 0} and n = { γ n < 0}. In te domain n we ave A n 0, making te first derivative in 17 non-positive, tus, Iµ is a decreasing function of μ n. Furtermore, let µ n be a vector obtained by replacing te element μ n in µ by zero. It is straigtforward to see tat I µ Iµ n, n. In addition, for any µ F and n =1, 2,...,, weave I µf d = I µf d + I µf d n n I µf d + I µ n 20 f d. n n Hence, te objective function in 1 can ten be upperbounded as I µf d 1 n I µf d + n I µ n f d, 21 and one acieves te equality wen μ n = 0 n,n =1,...,. Using 21, we ten ave te following modified optimization problem: 1 max μ n 0, + s.t. n n I µ n f d n I µf d μ n f d R. 22 Given tat te second term of te objective function in 22 does not depend on μ n and te fact tat A n < 0 in te sub-domain n, te Hessian matrix of te objective function in 22 is diagonal wit strictly negative elements. Tus, 22 is now a concave optimization problem and any solution in te form of μ n =μ n is globally optimal. Te problem in 22 can ten be solved using te KKT conditions. Specifically, te Lagrangian can be written as Lµ,λ= 1 I µf d n + I µ n f d n λ R λ n n n n μ n f d μ n f d. Differentiating te Lagrangian in 23 we obtain Lµ,λ = μ n λ + λ n f 1 μ n 0, n I µf d, n n 23, 2 By equating te gradient of te above Lagrangian to zero and solving for μ n, te globally optimal instantaneous power allocation μ n for te AF system under bot TAC and IAC is finally expressed as μ n = D Dn+ 2n Cn E n+ 0, A n 0 + An ln2 λ +λ n, A n < 0 2C n 25 were we ave ignored te oter root since it violates te non-negativity of μ n. In 25, we ave Dn 2 A C n E n + n ln2λ +λ n > 0. Terefore, te values of μ n are always real. In addition, λ 0 and λ n 0 are te constants satisfying μ n f d R, λ R μ n f d =0, μ n f d 26 n, λ n n μ n f d =0, λ + λ n > 0. Te two parameters λ and λ n depend on te cannel distribution f, tesrρ, and te average power constraints R and { n }, and tey can be found numerically using bisection. Te solution in 25 is an extended water-filling based sceme over time and space wit te vessels aving bot bottoms and lids. It can also be observed tat te average power allocated to a particular relay not only depends on its related links but also depends on all te oter links involved in te system. Hereafter, we sall refer to tese scemes as OA-R scemes.

6 TRA et al.: O ACHIEVABLE RATE AD ERGODIC CAACITY OF AF MULTI-RELAY ETWORKS WITH CSI 195 From 1, it is easy to see tat as long as n < R, TAC is always satisfied and one needs to consider IAC only. If it is te case, te conditions on λ and λ n can be simplified to: λ =0, μ n f d n, λ n n 27 μ n f d =0. On te oter and, wen n R, one needs to take into account TAC and IAC simultaneously, wic is certainly of more interest. Finally, it is noted tat if only TAC is assumed, te optimal solution μ n is simplified to μ n,t A C = D Dn+ 2n Cn 0, A n 0, + E n+ An ln2λ, A n < 0, 2C n were λ > 0 is a constant tat satisfies μ nf d = R. IV. CHAEL CAACITY 28 In te preceding section, given te diagonal input covariance matrix Q, we derived te maximum acievable rate RQ of te AF systems by optimizing te instantaneous power allocation at te relays. In tis section, we investigate te ergodic capacity of te system by simultaneously optimizing te diagonal input covariance matrix at te source and te instantaneous power allocations at te relays. Unless oterwise stated, we will focus on te case of using bot te TAC and IAC were n R, wic implies tat TAC and IAC need to be taken into account simultaneously. Te ergodic capacity of te AF system can be expressed as C = 1 2 s.t. max Q 0,trQ S, μ n,, I x, y f d μ n f d n, μ n f d R, q n1 + q n2 S. 29 In general, it is not possible to obtain te closed-form solution of 29 due to te complexity and non-convexity of te problem. However, we observe tat tis problem belongs to te class of bi-level non-convex optimization problems wit separable objective functions. In particular, we can consider eac μ n as a local variable tat appears only in one block and Q as te global variable tat appears in all te blocks. Exploiting tis property, te Tammer decomposition metod proposed in 29] can be used to effectively address tis problem. Te main idea of Tammer decomposition metod is to transform an original optimization problem wit ig complexity into an equivalent master problem and a set of subproblems wit significantly lower complexity. In our case, if we temporarily fix te global variable Q, te problem in 29 can be separated into multiple sub-problems wose solutions can be verified to be te same as tat of te maximizing te acievable rate problem derived in te previous section. Te capacity can ten be obtained by solving te master problem via an iterative water-filling-based algoritm. Te decomposition process is described in detail in te following. First, for convenience, let Λ n Q n,μ n = log det I 2 + ρh n H ] nq n f d = log Γ n μ n ]f d. 30 Ten from 10, we can rewrite te objective function in 29 as follows I x, y f d = Λ n Q n,μ n. 31 Following Tammer decomposition metod, solving te problem in 29 is equivalent to solving te following master problem max Λ n Q n s.t. tr Q n S, 32 Q n,, were Λ n Q n is te optimal-value function corresponding to te nt sub-problem, and it can be written as Λ n Q n= max Λ n Q n,μ n μ n 0 μ n f d n, s.t. μ n f d R. 33 Te sub-problems in 33 are obtained by setting Q to a fixed value and tey are subject to a global constraint and multiple individual constraints. Terefore, instead of solving te sub-problems separately as in 29], we need to solve tem simultaneously. It is straigtforward to verify tat eac subproblem in 33 as te same solution as te problem in 1; te solution to tis problem is sown in 25. Our approac is to solve te sub-problems and ten use te information obtained from teir optimal solution {μ n} to determine te optimal value of Q. To solve te master problem, our metod is to apply te line searc tecnique using a penalty function M k 32] to convert te constrained master problem in 32 into an unconstrained problem as follows 2 max Λ n Q n M k S tr Q n. Q n,, 3

7 196 IEEE TRASACTIOS O COMMUICATIOS, VOL. 62, O. 5, MAY 201 Let Λ Q = 2 Λ n Q n M k S tr Q n, 35 in wic te optimal-value function Λ n Q n in eac iteration is obtained by solving te sub-problems wit te closedform solutions given in 25. All te sub-problems in eac iteration are solved and te solutions are used to determine te new searc direction. Te value of Q will also be adjusted accordingly. ote tat te sub-problem in 33 is feasible for all values of Q n satisfying Q n 0 and tr Q n S. Te iterative algoritm, wic is referred to as master solver MASSOL, to solve te master problem can ten be summarized as follows: MASSOL Algoritm 1 Initialization Initialize te penalty parameter M k := M 0 and te optimality tolerance ɛ := ɛ 0. 2 Starting point Set Q := Q wit Q being an initial point. Solve all te sub-problems in 33 to obtain Λ Q and te gradient Λ Q. 3 Line searc wile Λ Q >ε 0 : Generate te descent direction vector p = Λ Q. Set te initial step lengt τ := 1 and ˆQ = diag ˆq 11, ˆq 12,..., ˆq n1, ˆq n2 were ˆq n1 = q n1 + τp 2n 1 and ˆq n2 = q n2 + τp 2n, wit p 2n 1 and p 2n being te 2n 1t and 2nt elements of p, respectively. Solve all te sub-problems in 33, verify te sufficient decrease condition SDC and adjust te step lengt τ until we find ˆQ tat satisfies te SDC. Ceck convergence condition and update penalty function if ˆq n1 q n1 2 + ˆq n2 q n2 2 >ɛ 0 - Update M k := M k+1.setq = ˆQ. - Solve all te sub-problems in 33 to obtain Λ Q and Λ Q. -GotoStep3. else Stop. ote tat in te MASSOL algoritm, te gradient Λ Q is calculated as Λ Q = Λ q 11,q 12,..., q n1,q n2 36 Λ T Q =, Λ Q,..., Λ Q, Λ Q, 37 q 11 q 12 q n1 q n2 were Λ Q = Λ q 11,q 12,.., q nj + θ,...q n1,q n2 ] Λ Q, q nj θ 38 for j =1, 2 and θ is an incremental step set to 10 3.Te penalty function M k is determined suc tat te sequence {M k }, k =0, 1,.., tends to infinity wen k increases and M k+1 >M k > 0 33]. In addition, wile te starting point M 0 sould be relatively small to avoid numerical computation difficulties, te sequence {M k } needs to grow quickly to a large value in order to provide a converged solution 33]. In our implementation, via extensive numerical results, we observe tat using ɛ 0 =10 3, M k =10 k,andθ =10 3 yields a good convergence. For te MASSOL algoritm, witin eac iteration, te solutions of te sub-problems are obtained from 25 and tey are globally optimal. Terefore, during te line searc, te feasible condition of te sub-problems is always satisfied. As a result, te proposed iterative algoritm is guaranteed to converge to a local minimizer 29]. In addition, as we sow in Appendix A, Λ n Q n,μ n in 30 is a concave function of Q n. Since te optimal-value function Λ n Q n in 33 is te point-wise maximum of Λ n Q n,μ n, Λ n Q n is also a concave function of Q n 3]. It is furter noted tat te constraint in 32 is convex in te space of positive semi-definite matrices 35]. Terefore, te master problem in 32 is a concave optimization problem of {Q n } and te local solution is a globally optimal solution. As a result, te MASSOL algoritm leads to te globally optimal solution. It sould be noted tat tis property olds for any initial point Q 0. Before closing tis section, it is wort mentioning about te complexity of te proposed iterative water-filling algoritm. It can be seen tat in eac iteration, te solution of te subproblem given in 25 requires te calculation of λ and λ n, n =1,..., using bisection metod. Te complexity terefore grows linearly wit te number of relays 36]. To solve te master problem, te iterative process in te algoritm increases te running time but not te complexity of te algoritm 37]. Terefore, we can conclude tat te complexity of te proposed iterative water-filling algoritm increases linearly wit. Tis property is important for a system wit a large number of relays. V. CAACITY AD CAACITY-ACHIEVIG IUT COVARIACE AT LOW AD HIGH SRS As presented in previous section, te ergodic capacity of te multi-relay AF system can be calculated effectively using iterative water-filling algoritms. In tis section, under te assumptions of ig and low SRs, we furter analyze te capacity-acieving input covariance matrices and te beavior of te considered system, and obtain te capacity in closedform. A. Hig SR Regime At sufficiently ig SRs, i.e., wen ρ = E S / 0 is sufficiently large, te function Γ n in 11 is dominated by te term ρ 2. Tus, we obtain te following approximation ρ 2 y 2 q n1 q n2 log Γ n log 1+b 2 nx n =log ρ 2 y 2 q n1 q n2 log 1+ ρμ n x n 39 1+ρq n1 z n

8 TRA et al.: O ACHIEVABLE RATE AD ERGODIC CAACITY OF AF MULTI-RELAY ETWORKS WITH CSI 197 log ρ 2 y 2 q n1 q n2 log 1+ μ n x n. 0 q n1 z n Recall tat A n = ρ 2 x n ρq n1 z n +1ρq n1 q n2 y 2 + q n2 y q n1 z n. Terefore, wen ρ is sufficiently large, we ave μ n =0= A n > 0 1, 1 It ten follows tat E log 1+ μ ] n x n 0. 2 q n1 z n Ten by combining 10, 0, 2, we ave E I x, y ] E log ] ρ 2 y 2 q n1 q n2 E log ] q n1z n 1+ μnxn E log ] ρ 2 y 2 q n1 q n2 ρy q n1+q n2 E 2 log =2 log ρφsd S In 3, te second inequality is obtained by applying Caucy- Scwarz inequality and te equality is acieved wen q n1 = q n2 = S 2, n = 1,... In addition, te tird equality comes from te fact tat q n1 + q n2 = S and E y] = E SD 2] = φ SD. Terefore, te equal power allocation at te source over all te transmission pases, referred to as te EA-S sceme, is optimal. For convenience, let q s = S 2. Te optimal input covariance matrix is simply a scaled identity matrix, and can be expressed as Q = Q EA S = q s I 2.Te cannel capacity can ten be simplified to C = R Q EA S = 1 max I x, y f d. 2 μ n,, Q=q si 2 ote tat te capacity in can be acieved by incorporating te EA-S sceme at te source and te OA-R sceme at te relays. By substituting q n1 = q n2 = q s into 25 we obtain te optimal power allocation at te relays to acieve te capacity in as μ n = D n+ were D 2n C n Ē n+ 0, Ā n 0, + Ān ln2 λ + λ n, Ā n < 0, 2 C n 5 Ā n = ρ 2 x n q s ρq s z n +1ρq s y 2 + y z n, C n = ρ 2 x 2 n ρq sy + ρq s z n +1, D n = ρx n ρq s z n + 13ρq s y + ρq s z n + ρ 2 q 2 sy 2 +2, Ē n =ρq s y +1 2 ρq s z n +1 2, 6 and λ and λ n satisfying μ n f d R, λ R μ n f d =0, μ n f d n, λ n n μ n f d =0, λ 0, λ n 0, λ + λ n > 0. 7 Given te above results, te capacity for te considered system at ig SRs can ten be obtained in closed-form as C = 1 2 ρ log ρ 2 y 2 q 2 s 1+ b 2 n xn + q s y + qs b 2 n xnzn+qsy 1+ b 2 n xn +1 ] f d, 8 were bn = ρ μ n z n q s ρ +1, 9 wit μ n given in 5. B. Low SR Regime In tis subsection, we sall investigate te system tat operates at low SR regimes, i.e., wen ρ is small. From 10 and 11, for a given input covariance matrix, te unconditional mutual information can be calculated as I x, y =E Ix, y ] = E log 1+ ρ2 y 2 q n1q n2 1+b n xn ρ q n1 y + qn1b2 n xnzn+qn2y 1+b 2 n xn ] For convenience, let F n = ρ2 y 2 q n1 q n2 1+b 2 + ρ q n1 y + q n1b 2 nx n z n + q n2 y nx n 1+b nx n Wen ρ is very small, by ignoring te terms containing ig orders of ρ, we obtain te following approximation: 1 + F n 1+ F n. 52 It ten follows from 50 tat ] I x, y E log 1+ F n = E log 1+ρy + q n1 + ρ 2 y 2 q n1q n2+ρq n1b 2 n xnzn qn2 1+b 2 n xn 1+b 2 n xn ] E log 1 + ρy S + ] ρ 2 y 2 q n1q n21+ρq n1z n+q n1μ nx nz n 1+ρq n1z n+ρμ nx n. 53 Te inequality in 53 comes from te fact tat q n1 + q n1 + q n2 = S and we qn2 1+b 2 n xn

9 198 IEEE TRASACTIOS O COMMUICATIOS, VOL. 62, O. 5, MAY 201 acieve te equality wen eiter q n2 = 0 or E b n ] = 0 for eac relay R n, n =1,... ote tat E b n ]=0means te relay R n is inactive. All scemes acieving te equality in 53 can ten be categorized in two cases as follows. i All te relays are inactive. In tis case, te system becomes a direct cannel, i.e., we ave only a direct transmission from te source to te destination. It ten follows tat ] I x, y E 1+ρy S + ρ 2 y 2 q n1 q n2. 5 It can be easily verified tat te unconditional mutual information in 5 is maximized wen q n1 = q n2 = S 2, n =1,... Ten for tis case, te maximum information rate can be expressed as I x, y = 1 ] 2 2 E log 1+ρ 2 y 2 S + ρy S 2 = 1 2 E 2 log 1+ρy ] S E ρy S log e]. 55 ii At least one relay is active. In tis case, witout loss of generality, let K be te set of te active relays. For tese relays, we ave It follows from 53 tat I x, y = E log E b k ] 0 and q k2 =0, k K ρy S + ρ 2 k K ] q k1 μ k x k z k 1+ρq k1 z k +ρμ k x k. 57 Observe tat log 1 + x x log e wen x 0. Terefore, wen ρ is sufficiently small, we ave I x, y E ρy S + ρ ] 2 q k1 μ k x k z k log e 1+ρq k1 z k + ρμ k x k k K E ρy S + ρ ] 2 q k1 μ k x k z k log e k K = E ρy S + ] Ψ k q k1 log e 58 k K were Ψ k q k1 =ρ 2 q k1 μ k x k z k. 59 By comparing 55 and 58, it can be seen tat te direct transmission is suboptimal. Terefore, for a capacity-acieving sceme, at least one relay must be active. We now consider an arbitrary pair of relays R i, R j in K suc tat R j as a stronger cascaded S-R and R-D cannels, i.e., E x j z j ] E x i z i ]. We ten ave te following Lemma. Lemma 1. For te same amount of power q allocated to te broadcasting pases at te source associated wit R i and R j in K, we ave E Ψ j q] E Ψ i q]. roof: Let off k =rμ k =0], k = i, j, be te probability tat te relay R k is silent at a given cooperative frame. Te probability of te relay R k being active in tat cooperative frame is terefore on k = rμ k > 0] = 1 off k.for simplicity, assume tat te IAC is te same for all relays. Te average power Ēμ k ] allocated to relay R k can ten be expressed as { E μ Ē μ k ] = k ] E μ k ] k, 60 k E μ k ] > k, were E μ k ] is te average power allocated to relay R k under TAC. Observe from 28 and 62 tat under TAC, te relay R k remains silent at a given frame if and only if Dk 2 C A k k E k + ln 2 λ D k. 61 It follows from 56 tat A k = ρ 2 qx k z k ρqz k +1 0 k = i, j. 62 Hence, 61 is equivalent to ρ 2 qx k z k λ ln2, 63 wen ρ ] is sufficiently ] small. Furtermore, since E ρ 2 qx j z j > E ρ 2 qx i z i, we ave j on > on. i As a result, E μ j ] E μ i ]. Combining tis wit 60, we ave Ēμ j ] > Ēμ i ] for te system under bot TAC and IAC. From te above analysis, it turns out tat we always ave E ρ 2 qμ j x j z j ] > E ρ 2 qμ i x i z i ]. 6 Terefore, E Ψ j q] E Ψ i q]. Using Lemma 1, it is ten easy to sow tat for a given total power allocated to te broadcasting pases at te source associated wit a pair of relays R i and R j aving E x j z j ] E x i z i ], it is more beneficial to allocate all te power to te broadcasting pase associated wit R j.teresult can be straigtforwardly extended to any number of relays. In particular, for a system aving relays, if R o as te strongest cascaded S-R and R-D cannels, te optimal power allocation at te source to acieve te capacity at low SRs will be q o1 = S, q n1 =0 n =1,..., n o, 65 q n2 =0 n =1,... Tis power allocation sceme is optimal at low SR regimes and it is referred to as te selective power allocation sceme at te source, denoted as SA-S. By using tis sceme, one sould allocate all te power to te relay aving te strongest cannel cascaded by te source-relay and relaydestination links and keep all oter relays silent. As a result, te cannel capacity can be simplified to C = 1 2 max I x, y f d, and can be easily calculated. In μ o particular, te optimal power adaptation solution at te relay R o can be expressed as 0, A o 0, μ + D o = Do+ 2o Co E o+ Ao ln2λ o 2C o, A o < 0, 66

10 TRA et al.: O ACHIEVABLE RATE AD ERGODIC CAACITY OF AF MULTI-RELAY ETWORKS WITH CSI CSI CDI CI CSI CDI CI Acievable Rate b/s/hz Acievable Rate b/s/hz Fig. 2. cannel SR db Te acievable rate of different AF systems over te symmetric SR db Fig. 3. Te acievable rate of different AF systems over te asymmetric cannel. wile μ n =0, n =1,..., n o, wit A o = ρ 2 S x o z o ρ S z o +1, C o = ρ 2 x 2 oρ S y + ρ S z o +1, D o = ρx o ρ S z o + 12ρ S y + ρ S z o +2, E o =ρ S y +1ρ S z o +1 2, 67 and λ o > 0 is te constant satisfying μ o f d min o, R Terefore, te system ergodic capacity at low SRs under bot TAC and IAC can be written as C = 1 ρ 2 S μ ] o x o z o 3.5 log 1+ρy S ρ S z o + ρμ f d o x o SR db 69 Fig.. Te acievable rate of te AF system wit full CSI under bot TAC and IAC and under TAC only over te asymmetric cannel. VI. ILLUSTRATIVE RESULTS In tis section, numerical results are presented to illustrate te acievable rate and ergodic capacity obtained by our derived power allocation scemes using CSI. We will only focus on te systems aving tree relays, but te results can be obtained for any number of relays. Unless oterwise stated, te distance-dependent pat-loss cannel model 38] is adopted suc tat te cannel variances depend on te patloss exponent, i.e., φ SD = d v SD, φ SR n = d v SR n, φ RDn = d v RD n were v = 3 is cosen as te pat-loss exponent. We consider bot te symmetric cannel in wic we set d SD = d SRn = d RDn =1, n =1, 2, 3; and te asymmetric cannel in wic we set d SD = 1, d SR1 = d RD1 = 2, d SR2 = d RD2 =0.5, d SR3 = d RD3 = 1. In all cases, it is assumed tat S = R =6and 1 = 2 = 3 =0. R. A. Acievable Rate: CSI vs. CDI/CI In tis subsection, we sall illustrate te gain in terms of acievable rate provided by aving full CSI at te relays. Te two conventional systems using CDI and CI will be used as bencmarks for comparison wit our OA-R sceme using Acievable Rate b/s/hz TAC TAC + IAC CSI. Fig. 2 first plots te acievable rate of te CSI, CDI, and CI systems in te symmetric configuration. ote tat all te considered systems use te equal power allocation at te source and ave te same TAC at te relays. Observe from Fig. 2 tat te CSI system significantly outperforms te CDI and CI systems. Te gains acieved by te CSI system over te CDI and CI systems are around 0.8dB and 1dB, respectively. Te gain offered by CSI is sligtly larger in te asymmetric configuration. In particular, Fig. 3 provides te acievable rate of te CSI, CDI, and CI systems in te asymmetric configuration. ote from Fig. 3 tat te gains are as muc as 1.1dB and 1.dB over te CDI and CI systems, respectively. Again, tis gain comes from te flexibility in saring te TAC among tree relays, tanks to te knowledge of CSI. Finally, Fig. compares te acievable rate of te two AF systems using OA-R wit full CSI and equal power allocation at te source under bot TAC and IAC and under only TAC over te asymmetric cannel. As expected, tere is a small penalty by imposing individual power constraint on eac relay. Te loss is of about 0.2dB at various SR regions.

11 1500 IEEE TRASACTIOS O COMMUICATIOS, VOL. 62, O. 5, MAY Acievable Rate & Ergodic Capacity b/s/hz OA S EA S SA S A S Acievable Rate & Ergodic Capacity b/s/hz OA S EA S SA S A S SR db SR db Fig. 5. Te acievable rate and ergodic capacity of te AF systems over te asymmetric cannel in medium and ig SR regimes. Fig. 6. Te acievable rate and ergodic capacity of te AF system over te asymmetric cannel in low SR regimes. B. Effects of ower Allocation at te Souce In tis subsection, given te OA-R sceme at te relays, we sall examine te impact of power allocation at te source. In particular, we sall consider te systems wit OA-R sceme at te relays incorporating wit four power allocation scemes at te source as follows: i OA-S - a capacity-acieving system wit optimal power allocation at te source using our derived results from te MASSOL algoritm. ii EA-S - a system wit equal power allocation at te source in all te transmission pases, i.e., q n1 = q n2 =1, n =1, 2, 3. As demonstrated in Section V, tis system is optimal at ig SR regimes. iii SA-S - a system using only te relay aving strongest cascaded source-relay and relay-destination cannels. In our configuration, relay R 2 is used wile relay R 1 and R 3 keep silent. Te power allocation at te source is: q 11 = q 12 = q 22 = q 31 = q 32 =0,q 21 =6. Tis sceme was sown to be optimal at low SR regimes in Section V. iv A-S - a system were te transmit power at te source is pre-selected as q 11 = 2,q 12 = 1,q 21 = q 22 = 0.5,q 31 = q 32 =1. For brevity of te presentation, we only present te results for te asymmetric cannel under bot TAC and IAC. Similar results can be obtained for oter scenarios. We first examine te four considered systems at medium and ig SR regimes. Specifically, te acievable rates of te four AF systems are plotted in Fig. 5. It can be seen tat te OA-S system as te best performance since it is te capacity-acieving sceme. Te OA-S system provides significant gains over te SA-S and A-S systems in a wide range of SRs and sligtly outperforms te EA-S in medium SR regions. At sufficiently ig SRs, te acievable rate of te EA-S system approaces te cannel capacity acieved by te OA-S system, wic confirms our analysis about te optimality of te EA-S sceme at ig SR regimes. Ergodic Capacity b/s/hz TAC TAC + IAC SR db Fig. 7. Te ergodic capacity of te AF system under bot TAC and IAC and under TAC only over te asymmetric cannel. Fig. 6 compares te maximum acievable rates of te four considered systems at low SR regions. Given tat te OA-S system is optimal, it can be seen tat te OA-S system acieves te best performance. Different from te ig SR scenario, te OA-S system provides a gain ranging from 0.5dB to 2dB over te EA-S system. Wen te SR decreases, we can see tat te SA-S system acieves te same rate as tat of te optimal OA-S system, wic is consistent wit our analysis about te optimality of SA-S at low SRs in Section V. C. Cannel Capacity under bot TAC and IAC and under TAC only Finally, in Fig. 7, we compare te capacity limits of two OA-S scemes under bot TAC and IAC and under TAC only over te asymmetric cannel. Similar to te acievable rate, we also observe tat te rate decreases by imposing te individual power constraint on eac relay. Te loss is of about 0.1dB in a wide range of SRs.

12 TRA et al.: O ACHIEVABLE RATE AD ERGODIC CAACITY OF AF MULTI-RELAY ETWORKS WITH CSI 1501 VII. COCLUSIO Tis paper addressed te acievable rate and ergodic capacity of an AF multi-relay network wit CSI at te relays by examining te optimal power allocation scemes at te relays OA-R and at te source OA-S to maximize te acievable rate. At first, for a given power allocation sceme at te source, te OA-R solutions were derived for te systems under bot TAC and IAC. It was ten sown tat te proposed OA-R scemes wit CSI at te relays significantly outperform te conventional systems wit CDI and CI. Furtermore, by jointly investigating te OA-R and OA-S scemes, we establised te ergodic capacity for te considered systems. We also demonstrated tat at ig SR regions, te equal power allocation sceme at te source EA-S incorporated wit te OA-R sceme acieves te capacity. On te oter and, at low SR regimes, it was sown tat te capacity can be acieved by using only te relay wit te strongest cascaded source-relay and relay-destination cannels wile te source spends all of its transmit power in te broadcasting pase associated wit tat relay. Finally, it is noted tat tis paper considered an idealized i.i.d cannel. It is certainly of practical interest to investigate a more realistic cannel model suc as te spatial cannel model 39], 0]. Under tis cannel model, one needs to take into account spatial information suc as te angle of departure, angle of arrival, and te spacing between te transmitter and receiver. Extending te results in tis paper to suc a realistic model is terefore a promising researc direction. AEDIX A COCAVITY OF Λ n Q n,μ n From 30, it can be seen tat we need to sow log det ] I 2 + ρh nh n Q n is a concave function of Qn.Using det I + AB =deti + BA, weave: log det I 2 + ρh n H nq n =logdet I2 + ρh n Q n H n. 70 Observe tat I 2 + ρh n Q n H n is Hermitian. Furtermore, given a positive semi-definite matrix Q n, for any non-zero vector u we ave u I 2 + ρh n Q n H n u = u 2 + ρ H n u Qn H n u Tus, I2 + ρh n Q n H n is Hermitian and positive semidefinite. Using Teorem in 1], we can ten conclude tat log det. is a concave function of I 2 + ρh n Q n H n. As a result, for any two given 2 2 positive semi-definite matrices A and B and for all α 0, 1 we obtain log det α ] I 2 + ρh nah n +1 α I2 + ρh nbh n α log det I 2 + ρh nah n +1 αlogdet I2 + ρh nbh n. 72 Equivalently, we ave log det ] I 2 + ρh n αa +1 α B H n α log det I 2 + ρh nah n +1 αlogdet I2 + ρh nbh n. 73 Tus, log det ] I 2 + ρh nh n Q n is te concave function of Q n over te set of positive semi-definite matrices. 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Aazang, Outage minimization and optimal power control for te fading relay cannel, in roc. 200 IEEE Information Teory Worksop, pp ] 3rd Generation artnersip roject 3G, Spatial cannel model for multipe input multiple output MIMO simulations 3G TR version release 6, ETSI, Tec. Rep., ] J. Salo, G. D. Galdo, J. Salmi,. Kyosti, M. Milojevic, D. Laselva, and C. Scneider, MATLAB implementation of te 3G Spatial Cannel Model 3G TR Available: ttp:// Jan ] R. A. Horn and C. R. Jonson, Matrix Analysis. Cambridge University ress, Tuyen X. Tran received te B.Eng. degree Honors rogram in Electronics & Telecommunications from Hanoi University of Tecnology, Vietnam in 2011, and te M.Sc. degree in Electrical & Computer Engineering from te University of Akron, OH, USA in His researc interest lies in te areas of information teory, cooperative wireless communications and MIMO networks. He received te Dean s Fellowsip Award in recognition of outstanding graduate work and researc acievement from te University of Akron in gi H. Tran received te B.Eng. degree from Hanoi University of Tecnology, Vietnam in 2002, te M.Sc. degree wit Graduate Tesis Award and te.d. degree from te University of Saskatcewan, Canada in 200 and 2008, respectively, all in Electrical & Computer Engineering. From May 2008 to July 2010, e was at McGill University as a ostdoctoral Scolar under te prestigious atural Sciences and Engineering Researc Council of Canada SERC ostdoctoral Fellowsip. From August 2010 to July 2011, Dr. Tran was at McGill University as a Researc Associate. He also worked as a Consultant in te satellite industry. Since August 2011, Dr. Tran as been an Assistant rofessor in te Department of Electrical and Computer Engineering, University of Akron, OH, USA. Dr. Tran s researc interests span te areas of signal processing and communication and information teories for wireless systems and networks. Dr. Tran as been serving as a TC member for a number of flagsip IEEE conferences. He is a TC co-cair of te Worksop on Trusted Communications wit ysical Layer Security for IEEE GLOBECOM 201. Hamid Reza Barami is currently an Assistant rofessor at te Department of Electrical and Computer Engineering at Te University of Akron, OH, USA. His main area of researc includes wireless communication, information teory, and applications of signal processing in communication. He received is.d. degree in electrical engineering from McGill University, Montreal, Canada in From 2007 to 2009 and prior to joining te University of Akron, e was a scientist at Wavesat Inc. Montreal, Canada. Dr. Barami as B.Sc. and M.Sc. degrees bot in Electrical Engineering from Sarif University of Tecnology and University of Teran, Iran, respectively. He as served as te Editor for Transactions on Emerging Telecommunications Tecnologies, and as te Tecnical rogram Committee member of numerous IEEE conferences including IEEE GLOBECOM and International Conference on Communications ICC. He is currently a member of te IEEE, te IEEE Communications Society, and te IEEE Veicular Tecnology Society. Dr. Sivakumar Sastry received is.d. degree in Computer Engineering and Science from Case Western Reserve University. He earned an M.Sc.Engg degree from Indian Institute of Science and an MS Computer Science degree from University of Central Florida. He as extensive industry experience in software engineering and automation systems and is an expert in grap algoritms and modeling. His current interests are in sensor-actuator systems for automation, provable adaptation, diagnostics and prognostics, and predictable monitoring. He is currently an Associate rofessor at University of Akron. Here, e leads te Complex Engineered Systems Lab. rior to joining Akron, e was Senior Researc Scientist and Advisory Software Developer wit Rockwell Automation. Dr. Sastry is senior member of IEEE.