IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012 3615

Power Allocation and Group Assignmentfor Reducing Network Coding Noisein Multi-Unicast Wireless Systems

Zahra Mobini, Student Member, IEEE, Parastoo Sadeghi, Senior Member, IEEE,Majid Khabbazian, Member, IEEE, and Saadan Zokaei

Abstract—In this paper, we consider physical-layer networkcoding (PNC) in a multi-unicast wireless cooperative networkwith a single relay. We aim to deal with the NC noise, i.e., anadditional noise term due to applying NC, with the objective ofimproving the network data rate. Our approaches are based onrelay power-allocation and group-allocation techniques. To thisend, we provide a mathematical framework for the achievableinformation rate of the system with the notion of power as-signment at the relay. Based on this framework, we present anovel power-allocation scheme to maximize the total informationrate among all the source–destination communication sessions inthe network. Further, we provide a closed-form solution for thetwo-unicast case. Simulation results show that the proposed relaypower allocation can significantly help alleviate the adverse effectsof NC noise. Next, we propose a group-allocation scheme to assignsessions to different groups for performing PNC at the relay.We combine power allocation and group allocation to furtherimprove performance. The formulated joint optimization problemis NP-hard. Therefore, a suboptimal heuristic algorithm is pro-posed and implemented at the relay to solve this problem. Fromthe simulation results, the proposed joint group assignment andpower-allocation scheme achieves up to 64% overall data rate gainfor the multi-unicast system compared with a single-group systemwith no relay power assignment. This observation shows that PNCcan be efficiently harnessed in a multi-unicast cooperative networkby exploiting proposed approaches.

Index Terms—Cooperative communications, group assignment,multi-unicast wireless systems, network coding (NC), NC noise,power allocation.

I. INTRODUCTION

I T HAS been shown that network coding (NC) can signifi-cantly improve the throughput and robustness of both wired

and wireless networks [1], [2]. The key feature of either digital

Manuscript received November 8, 2011; accepted June 11, 2012. Date ofpublication July 10, 2012; date of current version October 12, 2012. Thiswork was supported in part by the Australian Research Council’s DiscoveryProjects funding scheme under Project DP0984950 and in part by the IranTelecommunication Research Center. The review of this paper was coordinatedby Dr. C. Yuen.

Z. Mobini and S. Zokaei are with the Department of Electrical andComputer Engineering, K.N. Toosi University of Technology, Tehran, Iran(e-mail: z.mobini@ee.kntu.ac.ir; szokaei@eetd.kntu.ac.ir).

P. Sadeghi is with the Research School of Engineering, The Australian Na-tional University, Canberra, ACT 0200, Australia (e-mail: parastoo.sadeghi@anu.edu.au).

M. Khabbazian is with the Department of Electrical and Computer En-gineering, University of Alberta, Edmonton, AB T6G 2E1, Canada (e-mail:mkhabbazian@gmail.com).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2012.2207439

Fig. 1. Multi-unicast system with K source–destination pairs.

NC [2] or physical-layer NC (PNC [3], [4]) is to encourage theintermediate nodes in the network, which are known as relays,to forward the combination of their observations. This, alongwith the broadcast nature of radio propagation, makes PNCa promising candidate for multiuser cooperative communica-tions, enabling high-data-rate ad hoc networks.

Successful application of PNC, however, depends on thecommunication scenario. For example, PNC has been appliedto multiway relaying, where multiple transceivers with no directlink between them wish to communicate with all others usingthe help of a single relay node. In this case, interference cance-lation (an important requirement for PNC) can be successfullyaccomplished. In recent works [5]–[10], it has been shownthat PNC can significantly enhance the throughput performancein multiway relay networks. Moreover, PNC has been studiedfor communication scenarios, where multiple sources are com-municating with a common destination (multiple-access relaychannels), and has been shown to be effective to improve thesum of users’s information rates, or sum rate for short, andoutage probability performances [11], [12]. The advantage ofusing PNC in cooperative communication, which is referred toas network-coded cooperative communication (NC-CC), is notrestricted to multiway or multiple-access relay channels. Forexample, consider PNC in a multi-unicast cooperative networkwith K source–destination pairs as shown in Fig. 1. In thisnetwork, after each source node takes turn to transmit its in-formation to the corresponding destination, which is overheardby other destinations and the relay, the relay amplifies andforwards the linear combination of all the K overheard signalsin the previous time blocks in a single time block. This exampleshows that PNC can provide a significant data-rate performance

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3616 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

enhancement in a multi-unicast scenario by requiring (K +1) time blocks to complete the transmission, in comparisonwith conventional cooperative communication, e.g., amplify-and-forward cooperative communication (AF-CC) [13], thatrequires 2K time blocks.

However, bringing the promising benefits of PNC to themulti-unicast scenario is not free of cost. In [14] and [15], itwas shown that even with the perfect knowledge of channelinformation, there will be a nonnegligible noise introducedduring the signal extraction at destinations, which was coinedNC noise. The NC noise originates from inherently imperfector noisy cancelation of other users’ signals at a given destina-tion. Moreover, the data rates of source–destination pairs arehighly dependent on the NC noise and can even be lower thanthe conventional cooperative scheme [14]–[16]. Accordingly,the advantages of using PNC can notably decrease or evendisappear if the effect of NC noise is not taken into accountin the system analysis and design. The design of transmissionschemes that deal with this noise is, therefore, of paramountimportance and is one main goal of this paper. To the best ofour knowledge, this is largely an unaddressed problem.

Power allocation has long been regarded as an effective wayof improving the wireless cooperative system performance [17],[18]. Some efforts have been recently made to exploit powerallocation with NC in cooperative networks [5], [19]–[22].Optimal relay power allocation has shown to improve the sumrate, the sum of users’ bit error rate (BER) [5], and the weightedsum rate [19] for a multiuser scenario in PNC two-way relaying.Most of the work involving power allocation in NC-CC systemto date, however, is limited to two-way relaying schemes, andpower allocation for multiway or multi-unicast relay-assistedsystems has not received much attention. Therefore, an inter-esting question would be whether relay power allocation canalso help alleviate the detrimental effects of NC noise in themulti-unicast NC-CC system. This is one of the questions thatwe will address in this paper.

The second half of this paper recognizes the fact that evenwhen optimal power allocation is used, the performance ofthe multi-unicast NC-CC system is fundamentally limited byincreasing the number of source–destination pairs1 that sharethe same relay node. This is due to the higher NC noise atthe destination nodes for higher number of users and highercomplexity for power allocation and signal extraction, as willbe indicated in Section III. To deal with this problem, this paperintroduces a multigroup NC-CC transmission scheme in whichsource–destination pairs are grouped into different sets forperforming PNC at the relay. Grouping nodes in collaborativesets, i.e., the so-called cooperative clusters, has been proposedin conventional cooperative networks with no NC to reduce theresource management complexity [23]. Moreover, cooperativegrouping and partner selection have been developed in [24] and[25] to answer the issue of “who helps whom” in cooperativeresource-allocation problems. In [24], partner and subcarrierallocation was investigated in cooperative multiuser orthogonalfrequency-division multiplexing (OFDM) networks. Nosratinia

1In this paper, we use the terms session and source–destination pairinterchangeably.

and Hunter [25] have proposed a cooperative partner assign-ment to minimize the average outage probability over all usersin a cooperative network. The underlying networks in [24] and[25] are conventional cooperative networks with no NC and arevery different from ours.

To the best of our knowledge, [26] is the only work thatstudied group assignment and relay selection in the multi-unicast NC-CC system. Sharma et al. [26] proposed an onlinegroup-allocation algorithm based on an iterative scheme wheresource nodes select the best group among all offers from theneighboring relays. This algorithm is suitable for the case wherenetwork dynamics are unknown a priori. In this paper, however,by properly formulating the assignment problem, we determinegroup allocation at the relay node for a known network topol-ogy. Moreover, we present a joint grouping and relay power-allocation scheme, whereas Sharma et al. [26] do not addressthe problem of relay power allocation.

In this paper, we aim at developing a novel multi-unicast NC-CC scheme that efficiently deals with NC noise while takingadvantage of the inherent benefits of power allocation andgroup assignment. The main contributions of this paper are asfollows.

• We introduce power assignment in a single-group NC-CCsystem with NC noise and derive achievable informationrates.

• We formulate the optimal relay power-allocation problemwith the objective of sum-rate maximization. A closed-form solution for the two-user case is derived, and aneffective numerical algorithm is proposed for the multi-unicast case. We investigate the effectiveness of the pro-posed power allocation and show that it can significantlyhelp alleviate the adverse effects of NC noise comparedwith [14]. It is also shown that the performance of the NC-CC system degrades as the number of source–destinationpairs is increased. To deal with this, we introduce groupallocation into NC-CC and then reformulate the derivedachievable rates for the multigroup NC-CC system.

• To further enhance the performance of the NC-CC system,we combine group assignment and relay power allocation.The joint optimization problem is NP-hard. Therefore,we devise a suboptimal greedy algorithm to solve thejoint problem. The proposed relay power allocation andgrouping schemes are implemented at the relay and onlyrely on long-term channel statistics. Nevertheless, they areshown to be effective to alleviate the impact of NC noiseand to notably enhance data rates in the NC-CC system.Furthermore, the relay node needs to notify only thedestination nodes of the grouping and power allocation,instead of feeding back this information to all sources anddestinations.

II. SYSTEM MODEL

The wireless multi-unicast NC-CC network of interest herecompromises K mobile sources communicating with K mobiledestinations through one fixed relay using an AF protocol andPNC in the presence of the source-to-destination links, as inFig. 1. Let Sk denote the kth source, Dk the corresponding

MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3617

destination, and R denote relay node. Note that we use smallsubscripts sk, dk, and r to refer to nodes Sk, Dk, and R, re-spectively. We consider frequency-nonselective Rayleigh blockfading channels. That is, the realization of the fading channelin each link stays constant during transmission of a block ofsymbols and changes to an independent value in the next block.We assume all nodes operate in half-duplex mode using time-division multiplexing. Thus, transmissions from sources and therelay occur in different time blocks. In each block, N symbolsare transmitted in N -symbol time slots of duration TS each.

For three cooperative transmission strategies (single-groupNC-CC, multigroup NC-CC, and AF-CC) discussed in thispaper, a cooperation round consists of two phases: the broadcastphase where each source sends its own data to the destinationthat is also overheard by the relay and all other destinations, andthe relay phase where relay helps forward an additional copy ofthe data to destinations. Detailed description of the transmissionscenarios in the single-group NC-CC and AF-CC systems areprovided as follows. System description for each group in amultigroup NC-CC is similar to the single-group NC-CC caseand is omitted for brevity.

A. Multi-unicast Single-Group NC-CC

In this scheme, the overall transmission can be divided into(K + 1) blocks: K blocks in the broadcast phase and oneblock in relay phase. In the first K blocks, each source S�,where � = 1, . . . ,K, sends its own block of N symbols withtransmission power Ps� , to the relay and all destination nodesin a preassigned time block. The corresponding received signalsby the destination node Dk, where k = 1, . . . ,K, and the relayat the nth time slot can be expressed, respectively, as2

ys�dk=hs�dk

x� + zs�dk(1)

ys�r =hs�rx� + zs�r (2)

where x� is the transmitted signal such that E{|x�|2} = Ps�

(E{·} is the statistical expectation), and zs�,dkand zs�,r repre-

sent zero-mean complex-valued additive white Gaussian noise(AWGN) with variances σ2

s�,dkand σ2

s�,rduring the S� trans-

mission at destination Dk and at relay R, respectively. Inaddition, hs�,dk

and hs�,r denote the coefficients of the channelsbetween source S� and destination Dk and between sourceS� and relay R, respectively. We assume that channel coeffi-cients hs�,dk

and hs�,r follow a zero-mean complex Gaussian(ZMCG) distribution with variances σ2

hs�,dk= 1/das�,dk

and

σ2hs�,r

= 1/das�,r, respectively, where ds�,dkand ds�,r are the

S� to Dk and S� to R distances, and a is the path loss exponent[27]. This channel model includes both long-term path loss andshort-term fading. Dropping the indices, the long-term path lossσ2h determines the strength of the short-term fading, i.e., the

variance of the fading channel h or the mean of |h|2.In the final block, i.e., the (K + 1)th block, the relay per-

forms PNC by mixing the analog received signals. In particular,in contrast with [14] and [15] in which the relay mixes the

2Time index n is omitted in equations to simplify notations.

received signals without optimization of power allocation, ouraim is to use power assignment at the relay where each receivedsignal from a source is weighted by a power-allocation coeffi-cient, such that the sum-rate performance criterion is optimized.The processed signal at the relay can be expressed as

xr =

K∑�=1

αs�ys�r =

K∑�=1

αs�(hs�rx� + zs�r) (3)

where αs� is the relay power-allocation coefficient for S� suchthat 0 ≤ αs� ≤ 1, and

∑K�=1 α

2s�

= 1. The relay amplifies xr

with an amplification factor, i.e.,

A =

√Pr∑K

�=1 α2s�

(Ps� |hs�r|2 + σ2

s�,r

) (4)

to maintain a constant power Pr at the relay output and thenbroadcasts the resulted signal to all destination nodes. Thereceived signal at the destination Dk can be written as

yr,dk=Ahr,dk

xr + zr,dk

=Ahr,dkαskysk,r

+Ahr,dk

K∑�=1,� �=k

[αs�(hs�rx� + zs�r)] + zr,dk(5)

where zr,dkrepresents AWGN with variance σ2

r,dkat the

destination Dk during the transmission from R, and hr,dkis

the fading channel between relay R and destination Dk withZMCG distribution and variance σ2

hr,dk= 1/dar,dk

, where dr,dk

is the distance from R to Dk.Accordingly, destination node Dk receives one copy of signal

xk in the first transmission phase. Further, it obtains anothercopy of xk in the second phase as follows. Using the overheardsignals from S�, where � �= k, at Dk (1), we can write x� =(ys�,dk

− zs�,dk)/hs�,dk

. Using this notation in the receivedsignal from S� at the relay in (2), we can rewrite yr,dk

in (5) as

yr,dk=Ahr,dk

αskysk,r

+Ahr,dk

K∑�=1,� �=k

αs�hs�,r

hs�,dk

[ys�,dk− zs�,dk

]

+Ahr,dk

K∑�=1,� �=k

αs�zs�,r + zr,dk. (6)

The multi-unicast NC-CC system requires that completechannel state information (CSI), i.e., hs�,r, hr,dk

, and hs�,dk,

where � = 1, . . . ,K be available at the destination node Dk tocancel the unwanted terms [14], [15]. Moreover, the relay has tosend control bits to the destinations to indicate power-allocationcoefficients. This creates some overheard for signaling. Here,we assume that the mobility of the source and destination nodesis low so that the channel conditions are stable for sufficientlylong time; therefore, the frequency to update the channelinformation and power-allocation coefficients is low. However,the manner in which the destination obtains this information

3618 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

is beyond the scope of this paper. To remove ys�,dk, where

� = 1, . . . ,K and � �= k, Dk multiplies signal ys�,dkby factor

(Ahr,dkαs�hs�,r/hs�,dk

) and subtracts it from (6). Note thatthe destination node Dk needs to repeat this cancelation for allthe (K − 1) overheard signals ys�,dk

. The resulting signal atdestination node Dk, which is denoted by y∗r,dk

, is obtained as

y∗r,dk= yr,dk

−Ahr,dk

K∑�=1,� �=k

αs�hs�,r

hs�,dk

ys�,dk

=Ahr,dkαskysk,r −Ahr,dk

K∑�=1,� �=k

αs�hs�,r

hs�,dk

zs�,dk

+Ahr,dk

K∑�=1,� �=k

αs�zs�,r + zr,dk. (7)

From (7), it is observed that instead of zr,dk, we now have a new

noise term in this constructed signal as znewdk= zNC

dk+ zr,dk

,where

zNCdk

= −Ahr,dk

K∑�=1,� �=k

αs�hs�,r

hs�,dk

zs�,dk

+ Ahr,dk

K∑�=1,� �=k

αs�zs�,r (8)

is the NC noise at destination node Dk. It can be shown thatznewdk

has a zero mean and variance

σ2znewdk

= A2|hr,dk|2

K∑�=1,� �=k

[α2s�

(|hs�,r|2|hs�,dk

|2σ2s�,dk

+ σ2s�,r

)]

+ σ2r,dk

. (9)

B. Achievable Rate in Multi-unicast Single-Group NC-CC

Here, we will analyze the achievable information rate forthe multi-unicast single-group NC-CC system employing relaypower assignment. Let us derive the mutual information for theSk−Dk pair, which is denoted by Isk,dk

. By substituting ysk,rfrom (2) into (7), we have

y∗r,dk= Ahr,dk

αsk(hsk,rxk + zsk,r) + znewdk. (10)

Now, (1) (for � = k) and (10) present the appropriate channelmodel for an NC-CC scheme with AF relaying and a directpath from source Sk. We can rewrite these equations in vectorform as

Y = Hxk +BZ (11)

where

Y =

[ysk,dk

y∗r,dk

], H =

[hsk,dk

Ahr,dkαskhsk,r

]

B =

[0 1 0

Ahr,dkαsk 0 1

], Z =

zsk,rzsk,dk

znewdk

.

As it was discussed in [13], the AF cooperative protocol with adirect path produces an equivalent one-input two-output com-plex Gaussian noise channel with different noise levels in theoutputs. Therefore, it can be easily shown that for the givenchannel, Isk,dk

is given by

Isk,dk=

W

K + 1log det

(I2×2 + (PskHH†)

×(BE[ZZ†]B†)−1

)(12)

where W is the available bandwidth, det(·) is the determi-nant function, I2×2 is the identity matrix of size 2, † sym-bolizes the complex conjugate transposition, and E[ZZ†] =diag(σ2

sk,r, σ2

sk,dk, σ2

znewdk

) is the covariance matrix of noise.

Note that in (12), the factor 1/(K + 1) signifies that it takes(K + 1) time blocks to complete the Sk −Dk session. Afteralgebraic manipulations on (12) and substituting σ2

znewdk

from

(9), we have (13), shown at the bottom of the page. Threeobservations are worth mentioning here: 1) From (9), the newnoise variance is larger than the original noise variance σ2

r,dk

and is a function of power-allocation coefficients αs� , where� = 1, . . . ,K; 2) mutual information on each pair is dependenton all power-allocation coefficients; and 3) from (9) and (13),as the number of sessions K is increased, the NC noise variancewill increase, and the mutual information will decrease.

C. AF-CC

Let us briefly go over the AF-CC, against which NC-CCwill be compared. In the AF cooperative wireless network inFig. 1, each source Sk communicates with destination Dk viaa direct link and through one AF relay (without performingPNC) in a predetermined time block. In phase 2, the relayindividually amplifies and forwards the signal ysk,r, wherek = 1, . . . ,K, received from each source in phase 1. Therefore,communication occurs in 2K time blocks, and the achievablerate of kth session, i.e., IAF

sk,dk, can be obtained as [13]

IAFsk,dk

=W

2Klog

(1 +

Psk |hsk,dk|2

σ2sk,dk

+PskA

2AF|hsk,r|2|hr,dk

|2A2

AF|hr,dk|2σ2

sk,r+ σ2

r,dk

)(14)

Isk,dk=

W

K + 1log

1 +

Psk |hsk,dk|2

σ2sk,dk

+PskA

2α2sk|hsk,r|2|hr,dk

|2

A2|hr,dk|2(∑K

�=1 α2s�σ2s�,r

+∑K

�=1� �=k

α2s�

|hs�,r|2

|hs�,dk|2σ

2s�,dk

)+ σ2

r,dk

(13)

MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3619

where

AAF =

√Pr

Psk |hsk,r|2 + σ2sk,r

is the relay amplification gain in the AF-CC scheme.

III. RELAY POWER ALLOCATION IN A SINGLE-GROUP

NETWORK-CODED COOPERATIVE

COMMUNICATION SYSTEM

Here, we are interested in employing relay power allocationin the NC-CC system with the main purpose of alleviating theadverse effects of NC noise. Our objective is to find the optimalrelay power allocation that leads to the maximization of thesystem total data rate. We first analyze the general multi-unicastNC-CC system while incorporating the relay power allocationin our design considerations. We also provide the analyticalsolution for the special case of two-unicast. Note that, here, wefocus on single-group transmission. The grouping issue will beaddressed in Section IV.

A. Optimization of Power-Allocation Coefficients in aMulti-unicast System

Let us define α = [αs1 , . . . , αsK ] as the relay power-allocation vector for the multi-unicast NC-CC system. With theobjective of maximizing the sum rate (sum of information rates)of K sessions, denoted by Rsum, we formulate the followingpower-allocation optimization problem:

Maximize

αRsum(α) =

∑Kk=1 Isk,dk

s.t.∑K

k=1 α2sk

= 1s.t. 0 ≤ αsk ≤ 1, for k = 1, . . . ,K

(15)

where the dependence of Rsum on α is explicitly shown. Thisproblem is complex to solve directly because the objectivefunction is non-convex and also hard to be transformed intoa convex form [28]; therefore, classical convex optimizationtechniques cannot be used to find a closed-form expression forthe power allocation. There are some standard numerical meth-ods for nonlinear multivariable optimization such as conjugate-gradient, Powell, or simplex [29] that can be used to solvethis problem. However, these algorithms can be easily trappedin local maxima. Therefore, instead of using random initialvalues, we will use a robust optimization method by initialsampling of the parameter space with the help of Sobol quasi-random sequences [29]. In particular, we apply an improvedvariation of the Matlab fmincon function, which offers efficientcomputations within a polynomial time, as will be discussed inmore detail in Section III-C.

In a practical NC-CC system, relay power-allocation co-efficients can be calculated at the relay and sent via a low-

rate control channel to the destinations (assuming that blocklengths are sufficiently large). The destinations then extractthe received signal from the relay path based on the receivedpower coefficients. Later, in Sections III-C and V, we discussreplacing instantaneous CSI with long-term channel variancesfor power allocation, which will reduce the communicationoverhead between the relay and destinations.

B. Analytical Solution for Optimal Power Allocation in aTwo-Unicast System

Based on the derived mutual information for the multi-unicast case, we can readily obtain the achievable rates forthe special case of two-unicast. If we substitute K with twoin (13), we can find the mutual information between S1 andD1, i.e., Is1,d1

, in (16) shown at the bottom of the page, whereA2 is the relay amplification for the two-unicast case, whichis obtained from (4) by substituting K = 2. The mutual infor-mation between S2 and D2, i.e., Is2,d2

, can be easily derivedwith appropriate changes of indices. Using Is1,d1

, Is2,d2, and

α2s1

+ α2s2

= 1, we write Rsum(αs1 , αs2) in terms of αs1 (orαs2 ) as

Rsum(αs1) =W

3

[log2

(C7 +

C1α2s1

C2α2s1

+ C3

)

+ log2

(C8 +

C4

(1 − α2

s1

)C5α2

s1+ C6

)](17)

where 0 ≤ αs1 ≤ 1 and Ci, where i = 1, . . . , 8, are defined inAppendix A. Now, the maximum point of (17) can be calculatedby finding the zeros of its derivative. If we differentiate (17)with respect to αs1 and let it be equal to zero, then we have thefollowing quadratic equation to solve

Aα2 +Bα+ C = 0 (18)

where α∆= α2

s1, and A, B, and C are functions of channel gains,

relay and source power values, and noise variances, respec-tively, and defined in Appendix A. Fortunately, by solving (18),we obtain a closed-form solution for power allocation. Let Sdenote the set of the square roots of the real roots of (18) thatbelong to the open interval (0, 1). The optimum value of αs1 ,denoted by αs1,opt, is found among the elements of S or at theboundary points 0 and 1. Therefore

αs1,opt = argmaxαs1

∈{0,1}⋃

S(Rsum(αs1)) (19)

and then, using the condition α2s1

+ α2s2

= 1, we have

αs2,opt =√

1 − α2s1,opt

. Note that, in the case that S = ∅,

where ∅ is the empty set, dRsum(αs1)/dαs1 �= 0 and is strictlypositive or negative in the range αs1 ∈ (0, 1). Hence, the endpoints of the range, i.e., αs1 = 0 and αs1 = 1, should be tested.

Is1,d1=

W

3log

1 +

Ps1 |hs1,d1|2

σ2s1,d1

+Ps1A

22α

2s1|hs1,r|2|hr,d1

|2

A22|hr,d1

|2(α2s1σ2s1,r

+ α2s2σ2s2,r

+|hs2,r |2|hs2,d1

|2α2s2σ2s2,d1

)+ σ2

r,d1

(16)

3620 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

Fig. 2. Two-unicast network topology. p1 and p2 present two relay positions.

C. Simulation Results

Here, we study the adverse impact of NC noise on the NC-CC performance and then the efficiency of the proposed powerallocation in alleviating the effect of this noise. In what follows,the simulation results for the two-unicast NC-CC system areillustrated first, and those for the multi-unicast system arepresented next. Two transmission methods are compared: EPASG-NC is a single-group NC-CC scheme with equal relaypower allocation (EPA), i.e., the relay mixes the signals withequal power-allocation coefficients αsk = 1/

√K, where k =

1, . . . ,K; OPA SG-NC is a single-group NC-CC scheme withoptimal relay power allocation using (19) and (15) for two-unicast and multi-unicast cases, respectively.3

For all the simulations in this paper, we assume that thepath-loss exponent is a = 4, and without loss of generality,assume that all the AWGN variances are equal to 10−10 W.4

We consider a carrier frequency of 2.5 GHz and a bandwidthof W = 10 kHz, which is suitable for mobile WiMAX, i.e.,IEEE 802.16e [31]. In our numerical results, correlated mobile-to-fixed channel coefficients, i.e., sources-to-relay and relay-to-destinations channels, are generated according to Clarke’smodel [32]. In addition, correlated mobile-to-mobile channelcoefficients, i.e., source-to-destination channels, are generatedusing the method of exact Doppler spread [33]. We usenormalized Doppler frequency (i.e., fDTS , where fD is theDoppler frequency shift and where TS is the symbol dura-tion) of 0.003 corresponding to the mobile speed of 13 km/h.Note that in simulation results, we provide a mean sum rate,which is obtained by averaging the sum rate over 105 channelrealizations.

1) Two-Unicast NC-CC System: We investigate two scenar-ios based on various relay positions and source power valuesfor the topology shown in Fig. 2. Moreover, the AF-CC schemeand direct transmission are presented for comparison; wherein the latter, a source directly transmits its data to the corre-sponding destination without help from the relay. Fig. 3 showsthe average sum rate of the two-unicast system for varying

3Strictly speaking, since (15) is solved numerically, global optimality ofthe solution cannot be guaranteed. However, as will be shown in Fig. 5, thenumerically found solutions are almost indistinguishable from the optimalsolutions. Hence, we will use the term OPA SG-NC to refer to our proposedpower allocation.

4Although the formulation in this paper is derived for distinct noise variancesat each node, in simulation modeling, similar to [14]–[16], [24]–[26], and [30],we assume for the purpose of exposition that all the AWGN variances are thesame.

Fig. 3. Average sum rate of the two-unicast NC-CC system versus relayposition. Different transmission schemes with Ps1 = Ps2 = Pr = 0.4 W arecompared.

relay positions (from s1 to s2 on the dotted line in Fig. 2).Three main observations that follow from this simulation areas follows. First, the EPA NC-CC scheme without consideringthe NC noise, which is represented by “ideal NC-CC,” hasthe best sum-rate performance for most of the relay positions.However, in reality, when NC noise is present, the performanceof EPA SG-NC is severely degraded in comparison with idealEPA NC-CC. Second, the OPA SG-NC significantly mitigatesthe effect of NC noise. Third, the sum-rate performance of theideal NC-CC scheme similar to AF-CC is highly dependenton relay position [based on (17)]. When the relay node is notpositioned midway between the source and destination nodes,the sum rate is noticeably lower [15].5 However, in this case,power optimization offers more gain. For example, OPA SG-NC can even perform better than EPA ideal NC-CC when therelay is close to one of the sources.

In Fig. 3, it is also notable that direct transmission providesgreater average sum rate for some regions. For example, whenthe relay node is close to the source or destination node, theperformance of direct transmission is the best. Two intuitivereasons behind this phenomena are as follows. First, as afore-mentioned, the performance of NC-CC generally worsens asthe relay moves closer to or farther from the source. It isexpected that this will translate to poorer performance of OPASG-NC compared with direct transmission when the relay isreally close to one source node, even when nonequal powerallocation is used. Second, direct transmission in a two-unicastsystem has a higher spectral efficiency factor of 1/2 comparedwith 1/4 in (14) and 1/3 in (16) for the AF-CC and NC-CCtransmissions, respectively. However, it is known that directtransmission offers poorer outage probability due to diversityorder of 1 compared with 2 when relay is used [17].

5As can be seen from the figure, when the relay is positioned midwaybetween the source and destination, AF-CC and ideal NC-CC achieve theiroptimum performance, which worsens as the relay moves closer to or fartherfrom the source. This phenomenon is consistent with previous results presentedin [34] and [35], where it was shown that if the power allocation to the sourceand relay is equal, the optimum relay location is just in the middle with respectto the source and destination.

MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3621

Fig. 4. Average sum rate of the two-unicast NC-CC systems versus source s1power. Different transmission schemes with Ps1 = Ps2 = Pr are compared.

Fig. 4 demonstrates the average sum rate for different powervalues for source s1. In this simulation, we focus on the positionp1 for the relay (which is presented in Fig. 2). We see thatthe proposed OPA SG-NC outperforms other schemes for allsource power ranges. When the node power values are high,OPA SG-NC can achieve, respectively, up to 7.92% and 19.48%sum-rate gain in comparison with EPA SG-NC and AF-CCschemes. We note that, in this setup, OPA SG-NC outper-forms ideal NC-CC, which uses an equal power-allocationscheme.

2) Multi-unicast NC-CC System: Here, results for the multi-unicast system with a general random network topology arepresented. We consider 100 randomly generated network in-stances. For each instance, K source and destination nodes andone relay are distributed in a 2-D rectangular region of size450 m × 450 m. The relay is fixed at coordinate (225, 225),i.e., at the center of the square. The source–destination pairs arerandomly located with a uniform distribution in a square regionsuch that the relay is placed in the region between each pair. Theclosest distance between any two nodes is limited to 30 m. Wealso assume that all sources have equal power and Pr = 1 W.For each plot shown, the results are averaged over 100 networkinstances.

Note that the power-allocation problem (15) depends on theinstantaneous CSI. Therefore, to avoid the need for changingpower-allocation coefficients for each block transmission, wereplace the square of magnitude of channels, i.e., |h|2, withtheir means σ2

h. We will compare the difference in performancebetween using |h|2 and σ2

h in Section V. Moreover, to calculatethe power-allocation coefficients, we have solved (15) using theimproved variation of Matlab fmincon, which is initially givena budget, in terms of the number of objective function (Rsum)calls. Within the initial budget, fmincon evaluates the objectivefunction using the Sobol sequence and initializes a subspace,which is constructed from points with the maximum sum rate.The Sobol sequence ensures that we can progressively samplethe parameter space in a virtually uniform fashion. Intuitively,if the budget is large enough, the subspace can sufficiently closein on the global maximum to allow successful execution of theoptimization algorithm [36].

Fig. 5. Relay power-allocation coefficients found by the proposed numericalmethod and analytical solution (19) versus relay position.

Fig. 6. Average sum rate of the six-unicast NC-CC system versus sourcepower.

Unlike most optimization methods that start with a singlepoint in space, using the Sobol sequence allows us to start froma region of space that can be arbitrarily made close to the globalmaximum by increasing the initial budget. We set the initialbudget as 1000 objective function calls for the following sim-ulations. The effectiveness of the proposed numerical methodis shown in Fig. 5 for the multi-unicast NC-CC system withK = 2, where the simulation settings are the same as those inFig. 3.6 In particular, the power-allocation coefficients foundvia the improved version of fmincon using the Sobol sequenceare compared with those obtained using (19) for varying relaypositions. One can see that the results of the proposed numericalscheme are almost identical to the optimal power-allocationcoefficients.

Fig. 6 compares the average sum rate of the two schemesfor a six-unicast NC-CC system. Two remarks follow fromthis figure as follows. First, OPA SG-NC provides significant

6For the sake of simplicity and since we have the analytical solution for theoptimum power allocation in two-unicast NC-CC [given in (19)], we examinethe NC-CC system with K = 2.

3622 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

Fig. 7. Ratio of the sum rate offered by the OPA SG-NC to that offered byAF-CC versus session number K for ideal NC-CC and NC-CC consideringNC noise schemes.

sum-rate improvement over the EPA SG-NC, e.g., at sourcepower of 0.4 W, a gain of approximately 1.43 Kbps (equivalentto 18.21%) is achieved via the proposed power allocation.Second, while multi-unicast NC-CC using the proposed powerallocation outperforms AF-CC for all source power values,EPA SG-NC has poorer performance than AF-CC for small-to-medium source power values. However, this result cannotbe seen in the two-unicast case. This observation raises aquestion about how good the NC-CC can perform comparedwith the AF-CC when the number of sessions in the networkis increased. To answer this question, we plot the ratio of thesum rate offered by OPA SG-NC to that offered by AF-CCas a function of session number, i.e., K, in Fig. 7. The resultfor ideal NC-CC with the proposed relay power allocation isalso shown for comparison. One can see that the ratio for theNC-CC system considering NC noise decreases as the numberof sessions is increased. For example, OPA SG-NC performsworse than AF-CC when there are more than nine sessions inthe network. This is mainly due to the accumulation of high NCnoise at the destination nodes (that is not present in ideal NC-CC scheme) for increasing the number of sessions according to(13). This result is in accordance with the third observation inthe previous section: The higher the number of sessions in theNC-CC system, the higher the NC noise, and thereby, the lowerthe achievable rates. This motivates us to investigate the NC-CCperformance in a multi-unicast scenario with group allocationand to analyze the gains that grouping can offer in conjunctionwith the proposed relay power allocation.

IV. GROUP ALLOCATION

Here, we introduce grouping into the multi-unicast NC-CCsystem with power allocation. There are two reasons that leadus to consider grouping, which are summarized as follows.

• Based on the previous results, we observed that even whenusing relay power allocation, it may be better to allocatesessions into different groups with a smaller number ofsessions (rather than into a single group with K sessions)to reduce the impact of NC noise. On the other hand,

Fig. 8. Transmission scheme of the sources and the relay. (a) Direct schemeand (b) multigroup NC-CC scheme.

referring to the spectral efficiency factor of 1/(K + 1)in (13) for the information rate of a single-group NC-CCsystem compared with 1/(2K) in (14) for the non-networkcoded AF-CC, we observe that NC-CC may offer higherrates compared with AF-CC for an increasing numberof sessions. Therefore, it is essential to find the NC-CCscenario with an optimal number of sessions in each group.

• The grouping concept has also been used in degradedbroadcast channels [37] to reduce the complexity dueto successive interference cancelation. The complexity isalso an issue in the considered NC-CC system where PNCis essentially a form of linear interference cancelation withthe use of a priori information, i.e., a priori informationthat each destination directly obtains from other sources.Thus, effective grouping of sessions may reduce the com-plexity of the NC-CC system.

Let us first denote G as the number of available groups,where it has the maximum value of K, and use Gi to indicate theith group (ith set of sessions), where i = 1, . . . , G. We definean assignment matrix AG×K , whose elements are denoted byaik ∈ {0, 1}, where i = 1, . . . , G and k = 1, . . . ,K. The valueof aik has the following interpretation: aik = 1 means thatsource Sk is assigned to the ith group, i.e., Gi, and aik = 0means that Sk is not assigned to Gi. Each session can only beinvolved in exactly one group. That is,

∑Gi=1 aik = 1. There-

fore, Gi is the set of source nodes as Gi = {Sk|aik = 1, k =1, . . . ,K}. Note that, in case of A = IK×K , every session isassigned to a distinct group, and the system is the same as amulti-unicast AF-CC.

A. Multigroup Transmission Model

Each group Gi is a |Gi|-unicast NC-CC system and has thesame transmission details as a single-group case in Section IIwith |Gi| source–destination pairs. A modification to the timeblock structure of the NC-CC system is needed to enable suchsession grouping. Fig. 8 shows an example of the consideredtime block structure for multiple groups. In this case, thetransmission can be performed in two phases as follows. Inphase 1, K time blocks are used for transmission by the sourcenodes in a predetermined time block. In phase 2, G time blocksare used by the relay for transmitting linear combination ofsources’ information in Gi, where i = 1, . . . , G. Indeed, the

MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3623

relay mixes |Gi| overheard signals that belong to the Gi withour proposed power-allocation coefficients and transmits thecombined signal in the (K + i)th time block. As shown inFig. 8, under this scheme, the size of the time block for anysource in Gi, as well as for relay (for Gi transmission), willbe (|Gi|/(|Gi|+ 1))N.Ts, where N.Ts is the size of each timeblock under direct transmission. Indeed, the total available timefor Gi is |Gi| time blocks, i.e., |Gi|.N.Ts. As one additionaltime block is needed for the relay transmission, the lengthof each time block in Gi will be (|Gi|/(|Gi|+ 1))N.Ts. Thistime structure for the multigroup scheme results in a fair timeallocation among sessions (see [26] for more details).

B. Achievable Rate in the Multigroup NC-CC System

We can generalize the obtained achievable rate expression ofsingle-group NC-CC in (13) to the multigroup NC-CC systemas follows. Let us assume Sk is in group Gi. Under this settingand using the method in Section II, the mutual informationbetween Sk and Dk assigned to Gi, denoted by Ii

sk,dk, can be

obtained with (20), shown at the bottom of the page, and whereAi is the relay amplification gain for the ith group as

Ai =

√Pr∑K

�=1 α2s�

(Ps� |hs�,r|2 + σ2

s�,r

)ai�

(21)

and where αs� is the relay power-allocation coefficient such that∑K�=1 α

2s�ai� = 1 and |Gi| =

∑K�=1 ai� . We will consider how

to assign a session to a group in the following.

V. JOINT GROUP ASSIGNMENT AND POWER ALLOCATION

As aforementioned, from the system optimization point ofview, the overall rate of all sessions can be maximized by allo-cating the proper coefficient of relay power for cooperation andNC. Moreover, it is essential to allocate the sessions to optimalgroups. Therefore, to further enhance the performance of theNC-CC system, it is imperative to devise algorithms for jointoptimal group assignment and relay power allocation acrosssessions. The joint optimization problem with the objectiveof maximizing the overall sum rate while satisfying all theconstraints can be formulated as

Maximizeα,A

∑Gi=1 R

isum(α,A)

s.t. aik∈{0, 1}, for i=1, . . . , G,and k=1, . . . ,K

s.t.∑G

i=1 aik=1, for k=1, . . . ,Ks.t.

∑Kk=1 α

2skaik=1, for i=1, . . . , G

s.t. 0 ≤ αsk ≤1, for k=1, . . . ,K

(22)

where Risum(α,A) is the sum rate of the ith group and is

defined as

Risum(α,A) =

∑Sk∈Gi

Iisk,dk

(23)

where Iisk,dk

was given in (20). From (20), Risum is a function

of the assignment matrix A and the relay power allocationcoefficient vector α. Note that the problem in (22) can beviewed as a generalized assignment problem, which is an NP-hard problem [24], [26]. However, some special cases of thisproblem can be efficiently solved. For example, if we restrict|Gi| to at most two, the problem can be reduced to the maximummatching problem according to the following lemma.

Lemma 1: For the case where the size of groups are re-stricted to at most two, problem (22) can be reduced to maximalmatching.

Proof: First, let us give a brief description of the maximalmatching problem. Maximal weighted matching, which is agraph-theoretical problem, selects a subset of edges such thateach vertex is incident with at most one edge (or with exactlyone edge in the case of the perfect matching problem), andsecond, the total weight of the selected edges is as large aspossible [38].

Consider a multi-unicast NC-CC system with K sessions, inwhich the group size is restricted to at most two. We constructa weighted graph G(V,E), where the set V consists of 2Kvertices representing K physical source nodes, i.e., S1, . . . , SK ,and K auxiliary nodes S1, . . . , SK . Each pair of distinct ver-tices S� and Sk from the set {S1, . . . , SK} is joined by an edgewith weight equal to Ii

s�,d�+ Ii

sk,dk. This weight is equal to

the mutual information between S� and D� plus the mutualinformation between Sk and Dk, when S� and Sk are allocatedto the group i (with no other nodes in that group), and therelay power-allocation coefficients are set using the proposedscheme in Section III. Furthermore, each pair of nodes Sk andSk is joined by an edge with weight equal to IAF

sk,dk, as given in

(14). The optimization problem is then equivalent to finding amaximal weight matching in G(V,E). �

Maximum matching in a graph can be solved in polynomialtime [38]; hence, this special case of problem has a polynomialtime solution. This is an interesting observation because, inthe following Theorem 1, for an NC-CC system with EPA, wecan achieve an approximation factor of at least fm = g2m(gm +2)/(gm + 1)3 by restricting the size of groups by some positiveinteger gm. Note that there are exponentially many ways to dogroupings even when we restrict the size of groups to at mosttwo (i.e., gm = 2).

Theorem 1: In a multigroup NC-CC system with EPA, anyoptimal solution to problem (22) when the size of groups is

Iisk,dk

=W

K

|Gi||Gi|+1

log

1+

Psk |hsk,dk|2

σ2sk,dk

+PskA

2iα

2sk|hsk,r|2|hr,dk

|2

A2i |hr,dk

|2(∑K

�=1 α2s�σ2s�,r

ai�+∑K

�=1,� �=K

|hs�,r|2

|hs�,dk|2α

2s�σ2s�,dk

ai�

)+σ2

r,dk

(20)

3624 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

restricted to a positive integer gm is at most a factor of

fm =g2m(gm + 2)(gm + 1)3

(24)

smaller than any optimal solution to problem (22) with norestriction on the size of groups.

Proof: See Appendix B. �We will verify the tightness of the lower bound (24) in

Section V-B.To tackle the general problem, we divide it into two sub-

problems. The first subproblem finds the relay power-allocationcoefficient for a given A. This can be solved using the solutionpresented in Section III, by applying it to each group Gi asfollows:{

Maximizeα

Risum(α,A)

s.t.∑

Sk∈Giα2sk

= 1 and 0 ≤ αsk ≤ 1.(25)

In the second subproblem, by utilizing the results of the firstsubproblem, we attempt to find A that results in the optimumgroup assignment. The resulting group-allocation subproblemis an NP-hard problem [24] since any element of A has a valueof either 0 or 1, and the search dimension of A is 2K×K .One approach to solving this subproblem is do an exhaustivesearch. First, for any given A, we calculate power-allocationcoefficients for each group and then the sum rate accordingto (25) and (20), respectively. Next, we select the groupingthat gives the maximum sum rate. Unfortunately, this approachquickly becomes impractical as the number of users in thenetwork increases. Therefore, in the following, we proposea suboptimal greedy algorithm. Note that greedy algorithmshave also been developed in [24] and [25] to form groups orsubsets of nodes for the purposes of cooperation. However,they are not readily applicable to our NC-CC system underconsideration. In [24], a greedy algorithm has been developedfor partner and subcarrier allocation in a cooperative multiuserOFDM network. Using a greedy algorithm, Nosratinia andHunter [25] have proposed a cooperative partner assignmentto minimize the average outage probability over all users in acooperative network. The underlying networks in [24] and [25]are conventional cooperative networks with no NC and are verydifferent from ours.

A. Suboptimal Algorithm for Joint Grouping and Relay PowerAllocation in the NC-CC System

Here, we propose a suboptimal greedy algorithm to findthe assignment matrix A. In the proposed joint grouping andpower assignment algorithm, only the destination nodes (notthe source nodes) have to be informed by the relay of the as-signment matrix A and the power-allocation coefficient vectorα. The proposed algorithm is performed at the relay node.The relay then conveys the group assignment and the power-allocation coefficients to the destinations through a low-ratecontrol channel.

In each iteration, the algorithm assigns a session to a group.Then, considering the proposed relay power allocation, it cal-culates the new sum rate according to (23). This causes anincrease in the total sum rate. The objective is to find the “best”

session–group pair that maximizes the increase in overall sumrate after each iteration. As a result, there are K iterationsto be performed, and the complexity for each iteration of theproposed algorithm is O(K2). After an iteration, the assignedsession (i.e., the source assigned to a group) is removed fromthe set of unassigned sessions, which is denoted by B.

Algorithm 1: Joint group assignment and power allocation

1 Set A = IK×K and calculate the AF-CC rate based on (14)for all sessions in the network.

2 Select source Sk with the maximal AF-CC informationrate.•Set G = 1 and update A as a1k = 1, a1� = 0 for � �= k,

i.e., assign Sk to G1.•B ←− {S1, . . . , SK}\{Sk}

3 while B �= ∅ do4 for all elements of B, S�, do5 GG+1 = ∅

⋃S�

6 Hypotheses among G+ 1 available groups:• If ith group Gi includes S�: set ai� = 1.•Solve (25) and then find the corresponding group

sum rate from (23) for the group under consideration.Among all hypotheses, find the maximal sum-rateimprovement. In other words, find the group for S� thatresults in the best group sum rate; denote this group byG∗S�

and the corresponding sum rate by R∗S�

.end

7 Find the source S in B that results in the maximum R∗S obtained

in Step 6; denote this source by S∗.8 Update A based on G∗

S∗ (assign S∗ to its “best” group).9 Update B ←− B\{S∗}.

10 If GG+1 was selected as the best group then increase Gby one.end

Initially, A is set to the identity matrix, i.e., the initialscheme is the AF-CC. The sources are sorted according tothe source–destination-pair individual achievable informationrate in (14). The source Sk with the maximal information rateis selected, and A is updated as a1k = 1, a1� = 0 for � �= kand set G = 1 (e.g., assign Sk to G1). Next, for each sourceS� in B, among the G available groups, the algorithm makesG hypotheses that Gi, where i = 1 · · · , G, contains S�. It alsomakes the (G+ 1)th hypothesis that contains S� belongs to anew group, i.e., GG+1. Then, among the (G+ 1) hypotheses,the algorithm selects one that maximally increases the sum rate.For each hypothesis, the relay power allocation is obtained bysolving (25), and then, the group sum rate is obtained by (23).

After repeating this process for all sources in B, from allselected hypotheses, the algorithm chooses one hypothesis thatmaximally increases the sum rate, removes the correspondingsource from B, and updates A and α accordingly. Then,it goes back to determine the best session–group pair againand continues the iteration. The algorithm stops when all thesessions are assigned to groups, i.e., B = ∅, and outputs A andα as the answers of the joint optimization problem. Note thatthe proposed algorithm is suboptimal because of the greedylocal search. It is known that greedy algorithms may produce

MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3625

suboptimal results because they may construct results basedonly on local maxima within the search space [29]. In addi-tion, the iteration always converges because the sum rate isnondecreasing in each iteration. Algorithm 1 summarizes theproposed joint group assignment and power allocation.

Instead of continually computing the power allocation andgroup assignment based on instantaneous CSI, herein referredto as the exact scheme, we propose a practical scheme thatdetermines relay power allocation and group assignment inadvance based on long-term channel statistics. This schememaintains relay power-allocation vector and group assignmentmatrix throughout multiple block transmissions as long aschannel statistics and the network topology are unchanged.Hence, the complexity of looking for power allocation andgroup assignment and the required overhead to update thisinformation in the network is reduced. In the following, wecompare the exact and practical schemes.

B. Simulation Results

Here, we consider the performance of the four methods (EPASG-NC, OPA SG-NC, EPA MG-NC, and OPA MG-NC) basedon the proposed solutions for the multi-unicast scenario. Wediscuss the impact of these methods on the NC-CC systems intwo network topologies. The EPA MG-NC and OPA MG-NCschemes are outlined as follows. In the EPA MG-NC method,sessions are assigned to different groups. However, the relayuses equal power allocation to mix the received signals. Theproblem formulation in this case is a simplified version ofthe formulation given in (22), i.e., every αsk coefficient is setto 1/

√|Gi| for Sk ∈ Gi. The solution for this problem only

consists of group assignment for each session. In the OPAMG-NC method, joint power allocation and group assignmentare employed. The proposed suboptimal algorithm is used toderive the power-allocation coefficient vector and the groupassignment matrix. Note that all the simulation settings arethe same as those in Section III. In Fig. 9, we compare thesum-rate performance of four methods versus source powerfor a six-unicast NC-CC case. We also present results fordirect transmission and AF-CC for performance comparison. Inparticular, simulation results lead to the following conclusions.

1) As expected, EPA SG-NC produces a minimal sum rate,compared with all other NC-CC schemes, which is relatedto the mentioned tradeoff between bandwidth efficiencyand NC noise, and equal relay power-allocation scheme,which is not optimal when the network topology is notsymmetric. We consider this case as a lower bound forperformance comparison. We note that EPA SG-NC hasbetter performance than AF-CC for high source powervalues.

2) Compared with the single-group case, EPA MG-NC al-lows considerable performance gain achieved throughgrouping. It is clear that EPA MG-NC outperforms EPASG-NC for low-to-moderate source power values. How-ever, as the source power is increased, the differencebetween two schemes becomes smaller. In other words, asthe source power increases, the grouping algorithm tendsto locate sessions in a group with larger size. This can

Fig. 9. Average sum rate of the six-unicast NC-CC system versus sourcepower.

be explained from (13), which shows that the effect ofNC noise on mutual information becomes less prominentunder high source power condition.

3) OPA MG-NC presents the best sum-rate performance. Itprovides up to 64.1%, 14.88%, and 10.2% enhancementsin the sum rate, as compared with the EPA SG-NC, OPASG-NC, and EPA MG-NC, respectively. Therefore, ourproposed greedy algorithm performs well, which can beused in practical cases. Considering the overhead andcomplexity of OPA MG-NC, however, one can resignto OPA SG-NC as the next best method for high sourcepower values.

4) In Fig. 9, we also compare the suboptimal group alloca-tion obtained by our proposed greedy algorithm and thoseobtained by exhaustive search considering all possiblegroup allocations. Specifically, we compare OPA MG-NC with “OPA MG-NC, exhaustive,” where the proposedpower allocation is being used at the relay. We also com-pare EPA MG-NC with the “EPA MG-NC, exhaustive”scheme. In both cases, we observe that the performanceof the proposed suboptimal group allocation is highlycompetitive.

In Table I, we investigate the effect of the number of sessionson the proposed methods. In particular, we study the sum-rate performance of three methods (defined as the percentageof sum-rate enhancement of each method over the EPA SG-NC method) versus session number K and two source powervalues of 0.2 and 0.6 W. The following conclusions are drawnfrom Table I.

1) The higher the session number is, the higher the sum-rateimprovements will be; however, EPA MG-NC and OPAMG-NC allow more performance enhancement for highsession numbers. The intuitive reason is that increasingthe number of sessions increases the NC noise of eachsession in (8). Accordingly, the methods utilizing group-ing are more likely to improve the system performance.

2) The performance improvements decrease as the sourcepower increases.

3626 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

TABLE IEFFECT OF SESSION NUMBER ON THE SUM-RATE PERFORMANCE

(PERCENTAGE OF SUM-RATE ENHANCEMENT

OVER THE EPA SG-NC SCHEME)

Fig. 10. Average sum rate of a typical four-unicast NC-CC system versussource power. Results are also compared for practical and exact schemes.

It is interesting to see how good the proposed methods canperform for a typical network topology. To this end, we select atypical instance of four source–destination pairs with locations(135 m, 225 m)–(405 m, 315 m), (105 m, 375 m)–(15 m,105 m), (45 m, 375 m)–(105 m, 375 m), and (195 m, 105 m)—(435 m, 405 m), respectively. Fig. 10 reveals the average sumrate versus source power for this individual setting. Significantimprovement can be obtained by the proposed methods. Forexample, for low source power values, the sum-rate improve-ment of OPA MG-NC is up to 107% compared with EPA SG-NC. In this figure, we have also compared the difference insum-rate performance between using the proposed practicalscheme (using average channel power values) and the exactscheme (using instantaneous CSI) for power allocation andgroup assignment. The comparison shows a difference of up to1.31 and 1 Kbps at high source power values for OPA SG-NCand EPA MG-NC, respectively. This difference is expected asthe proposed practical schemes only use average channel powervalues. However, the decrease in complexity and overhead canbe more appealing than the resulting performance degradation.

Finally, we investigate the effect of restricting the group sizeon the sum-rate performance. We use f , which is defined in(29), as a factor to determine the reduction of the sum ratedue to restricting the size of groups to a positive integer gm.We also study the tightness of the lower bound of f , i.e.,fm, which is derived in Theorem 1. In Fig. 11, we plot fversus gm for a nine-unicast NC-CC system with EPA usingMonte Carlo simulation. It is observed that restricting the group

Fig. 11. Sum-rate reduction factor f due to restricting the size of groups to apositive integer gm, which is defined in (29), for varying gm. The lower boundfm, which is derived in Theorem 1, is also presented.

size reduces the sum-rate performance of the NC-CC system;however, as expected, this reduction decreases as gm increases.We also notice that the tightness of the derived lower bound fmimproves as gm increases.

VI. CONCLUSION

We have addressed the problem of NC noise reduction ina multi-unicast NC-CC system. One of our contributions indealing with NC noise was developing an optimum power-allocation framework at the relay. We provided a mathematicalframework for the achievable information rates of the systemwith the notion of power assignment and then presented anovel power-allocation scheme to maximize the total data rateamong all the sessions. We also provided a simple closed-formpower allocation for a two-unicast case. Through simulations,we showed the efficiency of the proposed power-allocationtechniques in helping overcome the adverse effects of NC noise.We observed that power optimization offers more gain for anasymmetric network scenario. The rate analysis and simulationresults revealed the fact that, despite the proposed power alloca-tion, the performance of the multi-unicast NC-CC is fundamen-tally limited by increasing the number of source–destinationpairs that share the same relay node. In particular, single-group NC-CC with power allocation performs worse than non-network coded AF-CC when there are more than nine sessionsin the network. Another contribution of this paper to tacklethis issue was developing a group assignment scheme to assignsessions to different groups for performing PNC at the relay. Wealso combined power allocation and group allocation to furtherimprove performance. For this purpose, we used a suboptimalgreedy algorithm to solve the NP-hard joint power and groupassignment problem and verified the efficiency of our algorithmin improving the system information rate compared with amulti-unicast system with no power or group allocation. It wasshown that, although proposed algorithms only rely on long-term channel statistics, they can effectively alleviate the impactof NC noise and notably enhance data rates in the NC-CCnetwork, particularly for a high number of sessions.

MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3627

APPENDIX ADEFINITION OF THE CONSTANTS IN (17) AND (18)

Here, we define the constants that were used in Section III as

C1∆=Ps1Pr|hr,d1

|2|hs1,r|2

C2∆=

(σ2s1,r

−σ2s2,r

) (Pr|hr,d1

|2+σ2r,d1

)−Pr|hs2,r|2|hr,d1

|2|hs2,d1

|2

× σ2s2,d1

+ σ2r,d1

(Ps1 |hs1,r|2 − Ps2 |hs2,r|2

)C3

∆=Pr|hr,d1

|2σ2s2,r

+Pr|hs2,r|2|hr,d1

|2|hs2,d1

|2 σ2s2,d1

+ σ2r,d1

(Ps2 |hs2,r|2 + σ2

s2,r

)C4

∆=Ps2Pr|hr,d2

|2|hs2,r|2

C5∆=

(σ2s1,r

−σ2s2,r

) (Pr|hr,d2

|2+σ2r,d2

)+Pr|hs1,r|2|hr,d2

|2|hs1,d2

|2

× σ2s1,d2

+ σ2r,d2

(Ps1 |hs1,r|2 − Ps2 |hs2,r|2

)C6

∆=Pr|hr,d2

|2σ2s2,r

+ σ2r,d2

(Ps2 |hs2,r|2 + σ2

s2,r

)C7

∆= 1 +

|hs1,d1|2Ps1

σ2s1,d1

, C8∆= 1 +

|hs2,d2|2Ps2

σ2s2,d2

A∆=C1C3C5(C8C5 − C4)− C2C4(C6 + C5)(C7C2 + C1)

B∆=C1C3 [2C8C5C6 + C4(C5 − C6)]

− C3C4(C5 + C6)(2C7C2 + C1)

C∆=C3 [C1C6(C8C6 + C4)− C4C7C3(C5 + C6)] .

APPENDIX BPROOF OF THEOREM 1

Consider a multigroup NC-CC system with K sessions andequal relay power-allocation scheme. A solution to problem(22) is called a g-restricted solution if the size of the groupsin the solution is at most g. An optimum g-restricted solutionis a g-restricted solution that has the highest sum rate amongall g-restricted solutions. To prove the theorem, we show thatany K-restricted solution with sum rate R can be convertedto a gm-restricted solution with a sum rate of at least fm ·R.If the size of all the groups in the K-restricted solution isat most gm, then no conversion is needed as the solution isalready a gm-restricted solution. Otherwise, there is at leastone group of size at least gm + 1. To convert this solution toa gm-restricted solution, we partition every group G of sizen = q · gm + r, where q ≥ 1 and 1 ≤ r < gm, into q groups,i.e., G1, . . . Gq , of size gm, and one group, i.e., Gq+1, of size r.In group Gq+1, we put the i-smallest, where 1 ≤ i ≤ r, indi-vidual achievable information rate [given in (14)] in group G.We show that the sum of the sum rates of groups Gi, where1 ≤ i ≤ q + 1, referred to as R, is at least fm times the sumrate of group G, R.

Denote the achievable information rate of the kth sessionassigned to Gi, where i ∈ {1, . . . , q + 1}, by Ii

sk,dk, which can

be readily derived with appropriate changes in power-allocationcoefficients in (20) as

Iisk,dk

=|Gi|

|Gi|+ 1bisk

where

bisk∆=

1K

log

(1 +

Psk |hsk,dk|2

σ2sk,dk

+Psk |hsk,r|2|hr,dk

|2ηisk

)

ηisk∆= |hr,dk

|2 ∑

S�∈Gi

σ2s�,r

+

S� �=Sk∑S�∈Gi

|hs�,r|2|hs�,dk

|2σ2s�,dk

+σ2r,dk

Pr

∑S�∈Gi

(Ps� |hs�,r|2 + σ2

s�,r

). (26)

In addition, denote the information rate of the kth sessionassigned to the group G of size n by Isk,dk

. Similarly, Isk,dk

can be written as

Isk,dk=

n

n+ 1bsk (27)

where

bsk∆=

1K

log

(1 +

Psk |hsk,dk|2

σ2sk,dk

+Psk |hsk,r|2|hr,dk

|2ηsk

)

ηsk∆= |hr,dk

|2(∑

S�∈Gσ2s�,r

+

S� �=Sk∑S�∈G

|hs�,r|2|hs�,dk

|2σ2s�,dk

)

+σ2r,dk

Pr

∑S�∈G

(Ps� |hs�,r|2 + σ2

s�,r

). (28)

Now, let us define the ratio

f∆=

R

R=

∑q+1i=1

∑sk∈Gi

Iisk,dk∑

sk∈G Isk,dk

(29)

and denote the lower bound of f by fm. Substituting Iisk,dk

and

Isk,dkinto (29), we get

f =

gmgm+1

∑qi=1

∑sk∈Gi

bisk + rr+1

∑sk∈Gq+1

bq+1sk

nn+1

∑sk∈G bsk

. (30)

For each Sk ∈ {G1, . . . , Gq, Gq+1}, from (26) and (28), we haveηisk < ηsk ; hence, bisk > bsk . Therefore, replacing bisk with bskfor all Sk ∈ {G1, . . . , Gq, Gq+1}, we have

f ≥gm

gm+1

∑qi=1

∑sk∈Gi

bsk + rr+1

∑sk∈Gq+1

bskn

n+1

∑sk∈G bsk

. (31)

3628 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

By defining x∆= (

∑qi=1

∑sk∈Gi

bsk/∑

sk∈Gq+1bsk), (31) can

be written as

f ≥ h(x)∆=

gmgm+1x+ r

r+1n

n+1 (x+ 1).

Note that

x ≥ qgmr

minSk∈{G1,...,Gq}

bsk

maxSk∈Gq+1

bsk.

Since Gq+1 consists of r nodes with the smallest individualachievable information rate in G, we get

minSk∈{G1,...,Gq}

bsk ≥ maxSk∈Gq+1

bsk .

Therefore

x ≥ qgmr

. (32)

The function h(x) is a strictly increasing function of x because

dh(x)

dx=

gmgm+1 − r

r+1n

n+1 (x+ 1)2> 0

and (gm/(gm + 1)) > (r/(r + 1)). Therefore, h(x) gets itsminimum value at x = qgm/r. Consequently

f ≥ h(qgm

r

)=

gmgm+1qgm + r

r+1rn

n+1n. (33)

Let n′ = q · gm. Thus, n = n′ + r. By (33), we have

f ≥ h(qgm

r

)=

gmgm+1n

′ + rr+1r

nn+1n

=

(gm

gm + 1

)n′ +

(gm+1gm

· rr+1

)r

nn+1n

>

(gm

gm + 1

)(n′ + r − 1

nn+1n

)

=

(gm

gm + 1

)(n− 1n

n+1n

)

=

(gm

gm + 1

)(1 − 1

n2

)

≥(

gmgm + 1

)(1 − 1

(gm + 1)2

)

=g2m(gm + 2)(gm + 1)3

(34)

which concludes the proof.

REFERENCES

[1] R. Ahlswede, N. Cai, S. R. Li, and R. W. Yeung, “Network informationflow,” IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 1204–1216, Jul. 2000.

[2] S. Katti, H. Rahul, W. Hu, D. Katabi, M. Medard, and J. Crowcroft,“XORs in the air: Practical wireless network coding,” IEEE/ACM Trans.Netw., vol. 16, no. 3, pp. 497–510, Jun. 2008.

[3] S. Zhang, S. C. Liew, and P. P. Lam, “Hot topic: Physical-layer networkcoding,” in Proc. 12th Annu. Int. Conf. MOBICOM, Los Angeles, CA,Sep. 2006, pp. 358–365.

[4] S. Katti, S. Gollakota, and D. Katabi, “Embracing wireless interference:Analog network coding,” in Proc. ACM SIGCOMM, Kyoto, Japan, Aug.2007, pp. 397–408.

[5] R. H. Y. Louie, Y. Li, and B. Vucetic, “Practical physical layer net-work coding for two-way relay channels: Performance analysis and com-parison,” IEEE Trans. Wireless Commun., vol. 9, no. 2, pp. 764–777,Feb. 2010.

[6] P. Popovski and H. Yomo, “Wireless network coding by amplify-and-forward for bi-directional traffic flows,” IEEE Commun. Lett., vol. 11,no. 1, pp. 16–18, Jan. 2007.

[7] Z. Ding, T. Wang, M. Peng, W. Wang, and K. Leung, “On the designof network coding for multiple two-way relaying channels,” IEEE Trans.Wireless Commun., vol. 10, no. 6, pp. 1820–1832, Jun. 2011.

[8] T. J. Oechtering and H. Boche, “Bidirectional regenerative half-duplexrelaying using relay selection,” IEEE Trans. Wireless Commun., vol. 7,no. 5, pp. 1879–1888, May 2008.

[9] P. Larsson, N. Johansson, and K.-E. Sunell, “Coded bi-directional re-laying,” in Proc. IEEE Veh. Technol. Conf., VTC Spring, Melbourne,Australia, May 2006, pp. 851–855.

[10] Z. Ding, K. K. Leung, D. L. Goeckel, and D. Towsley, “On the study ofnetwork coding with diversity,” IEEE Trans. Wireless Commun., vol. 8,no. 3, pp. 1247–1259, Mar. 2009.

[11] Z. Ding, T. Ratnarajah, and K. K. Leung, “On the study of network codedAF transmission protocol for wireless multiple access channels,” IEEETrans. Wireless Commun., vol. 8, no. 1, pp. 118–123, Jan. 2009.

[12] Y. Chen, S. Kishore, and J. Li, “Wireless diversity through network cod-ing,” in Proc. IEEE WCNC, Las Vegas, NV, Apr. 2006, pp. 1681–1686.

[13] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity inwireless networks: Efficient protocols and outage behavior,” IEEE Trans.Inf. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004.

[14] S. Sharma, Y. Shi, J. Liu, Y. T. Hou, S. Kompella, and S. F. Midkiff,“Network coding in cooperative communications: Friend or foe?” IEEETrans. Mobil. Comput., vol. 11, no. 7, pp. 1073–1085, Jul. 2012.

[15] S. Sharma, Y. Shi, J. Liu, Y. T. Hou, and S. Kompella, “Is networkcoding always good for cooperative communications?” in Proc. IEEEINFOCOM, San Diego, CA, Mar. 2010, pp. 1990–1998.

[16] Z. Mobini, P. Sadeghi, and S. Zokaei, “Network coding noise reductionvia relay power allocation in a two-unicast wireless system,” in Proc.IEEE Int. Symp. PIMRC, Toronto, ON, Canada, Sep. 2011, pp. 1459–1464.

[17] Y. Zhao, R. Adve, and T. J. Lim, “Improving amplify-and-forward re-lay networks: Optimal power allocation versus selection,” IEEE Trans.Wireless Commun., vol. 6, no. 8, pp. 3114–3123, Aug. 2007.

[18] M. Hasna and M.-S. Alouini, “Optimal power allocation for re-layed transmissions over Rayleigh-fading channels,” IEEE Trans.Wireless Commun., vol. 3, no. 6, pp. 1999–2004, Nov. 2004.

[19] M. Chen and A. Yener, “Power allocation for F/TDMA multiuser two-wayrelay networks,” IEEE Trans. Wireless Commun., vol. 9, no. 2, pp. 546–551, Feb. 2010.

[20] Z. Yi, M. Ju, and I.-M. Kim, “Outage probability and optimum powerallocation for analog network coding,” IEEE Trans. Wireless Commun.,vol. 10, no. 2, pp. 407–412, Feb. 2011.

[21] A. A. Zaidi, M. N. Khormuji, S. Yao, and M. Skoglund, “Optimizedanalog network coding strategies for the white Gaussian multiple-accessrelay channel,” in Proc. IEEE ITW, Stockholm, Sweden, Oct. 2009,pp. 460–464.

[22] V. Havary-Nassab, S. Shahbazpanahi, and A. Grami, “Optimal distributedbeamforming for two-way relay networks,” IEEE Trans. Signal Process.,vol. 58, no. 3, pp. 1238–1250, Mar. 2010.

[23] A. D. Coso, U. Spagnolini, and C. Ibars, “Cooperative distributed MIMOchannels in wireless sensor networks,” IEEE J. Select. Areas Commun.,vol. 25, no. 2, pp. 402–414, Feb. 2007.

[24] Z. Han, T. Himsoon, W. P. Siriwongpairat, and K. J. R. Liu, “Resource al-location for multiuser cooperative OFDM networks: Who helps whom andhow to cooperate,” IEEE Trans. Veh. Technol., vol. 58, no. 5, pp. 2378–2391, Jun. 2009.

[25] A. Nosratinia and T. E. Hunter, “Grouping and partner selection in coop-erative wireless networks,” IEEE J. Sel. Areas Commun., vol. 25, no. 2,pp. 369–378, Feb. 2007.

MOBINI et al.: POWER ALLOCATION AND GROUP ASSIGNMENT FOR REDUCING NC NOISE 3629

[26] S. Sharma, Y. Shi, Y. T. Hou, H. D. Sherali, and S. Kompella, “Optimizingnetwork-coded cooperative communications via joint session groupingand relay node selection,” in Proc. IEEE INFOCOM, Blacksburg, VA,Apr. 2011, pp. 1898–1906.

[27] T. S. Rappaport, Wireless Communications, Principles and Practice,2nd ed. Upper Saddle River, NJ: Prentice-Hall, 2002.

[28] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.:Cambridge Univ. Press, 2004.

[29] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numer-ical Recipes: The Art of Scientific Computing, 3rd ed. Cambridge, U.K.:Cambridge Univ. Press, 2007.

[30] F. Chen, W. Su, S. Batalama, and J. Matyjas, “Joint power optimizationfor multi-source multi-destination relay networks,” IEEE Trans. SignalProcess., vol. 59, no. 5, pp. 2370–2381, May 2011.

[31] IEEE Standard for Local and Metropolitan Area Networks, Part 16: AirInterface for Fixed and Mobile Broadcast Wireless Access Systems, IEEEStd. 802.16e-2005, Feb. 2006.

[32] R. H. Clarke, “A statistical theory of mobile-radio reception,” Bell Syst.Tech. J., vol. 47, no. 6, pp. 957–1000, 1968.

[33] C. S. Patel, G. L. Stuber, and T. G. Pratt, “Simulation of Rayleigh-faded mobile-to-mobile communication channels,” IEEE Trans.Commun., vol. 53, no. 11, pp. 1876–1884, Nov. 2005.

[34] L. Fei, L. Qinghua, L. Tao, and Y. Guangxin, “Impact of relay locationaccording to SER for amplify-and-forward cooperative communications,”in Proc. IEEE IWASID, Beijing, China, Apr. 2007, pp. 324–327.

[35] Y. Li, “Distributed coding for cooperative wireless networks: An overviewand recent advances,” IEEE Commun. Mag., vol. 47, no. 8, pp. 71–77,Aug. 2009.

[36] P. Sadeghi, P. O. Vontobel, and R. Shams, “Optimization of informationrate upper and lower bounds for channels with memory,” IEEE Trans. Inf.Theory, vol. 55, no. 2, pp. 663–688, Feb. 2009.

[37] W. P. Tam and T. M. Lok, “Joint grouping and scheduling in complexity-constrained broadcasting ad-hoc networks,” in Proc. IEEE ICUFN,Hong Kong, Jun. 2010, pp. 165–170.

[38] R. Diestel, Graph Theory, 3rd ed. New York: Springer-Verlag, 2005.

Zahra Mobini (S’10) received the B.S. degree inelectrical engineering from Isfahan University ofTechnology, Isfahan, Iran, in 2006 and the M.S.degree in electrical engineering from M.A. Univer-sity of Technology, Tehran, in 2007. She is cur-rently working toward the Ph.D. degree with theDepartment of Electrical and Computer Engineering,K. N. Toosi University of Technology, Tehran.

From November 2010 to November 2011, shewas a Visiting Researcher with the Research Schoolof Engineering, Australian National University,

Canberra, Australia. Since September 2007, she has been a Research Assistantwith the Wireless Networks Research Laboratory, Department of Electrical andComputer Engineering, K.N. Toosi University of Technology. Her researchinterests include communication systems theory, wireless communications,cooperative networks, and network coding.

Parastoo Sadeghi (S’02–M’06–SM’07) receivedthe B.E. and M.E. degrees in electrical engineeringfrom Sharif University of Technology, Tehran, Iran,in 1995 and 1997, respectively, and the Ph.D. degreein electrical engineering from The University of NewSouth Wales, Sydney, Australia, in 2006.

From 1997 to 2002, she worked as a ResearchEngineer and then as a Senior Research Engineerwith Iran Communication Industries, Tehran, andwith Deqx (formerly known as Clarity Eq), Sydney,Australia. She has visited various research institutes,

including the Institute for Communications Engineering, Technical Universityof Munich, Munich, Germany, from April to June 2008; and the MassachusettsInstitute of Technology, Cambridge, from February to May 2009. She is cur-rently a Fellow with the Research School of Engineering, Australian NationalUniversity, Canberra, Australia. She is the author or coauthor of more than 80refereed journal or conference papers and is a Chief Investigator for a numberof Australian Research Council Discovery and Linkage Projects. Her researchinterests include wireless communications systems and signal processing.

Dr. Sadeghi received IEEE Region 10 Student Paper Awards in 2003and 2005 for her research on the information theory of time-varying fadingchannels.

Majid Khabbazian (M’11) received the under-graduate degree in computer engineering from theSharif University of Technology, Tehran, Iran; theMaster’s degree in electrical and computer engi-neering from the University of Victoria, Victoria,BC, Canada; and the Ph.D. degree from the Univer-sity of British Columbia, Vancouver, BC, Canada,respectively.

From 2009 to 2010, he was a Research Fellowwith the Computer Science and Artificial Intelli-gence Laboratory, Massachusetts Institute of Tech-

nology, Cambridge. He is currently an Assistant Professor with the Departmentof Electrical and Computer Engineering, University of Alberta, Edmonton,AB, Canada. His research interests include wireless networks, distributedalgorithms, applied cryptography, and network security.

Saadan Zokaei received the Master’s degree in elec-trical engineering from the University of Tehran,Tehran, Iran, and the Ph.D. degree in electrical en-gineering from the Department of Communicationand Information Technology, University of Tokyo,Tokyo, Japan, in 1994.

He is currently an Associate Professor with theDepartment of Electrical and Computer Engineering,K. N. Toosi University of Technology, Tehran. Hisresearch interests include information security, wire-less networks, and next-generation networks.