IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS … TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO...

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, NO. XXX, VOL. YYY, MONTH YEAR 1

Relay-assisted Multi-user Video Streaming inCognitive Radio Networks

Yi Xu, Donglin Hu, and Shiwen Mao,Senior Member, IEEE

Abstract—Due to the drastic increase in wireless video traffic,the capacity of existing and future wireless networks will begreatly stressed, while interference will become the dominantcapacity limiting factor. In this paper, we investigate relay-assisted downlink multi-user video streaming in a cognitive radio(CR) cellular network. We incorporate zero-forcing precoding toallow transmitters collaboratively send encoded (mixed) signalsto all CR users, such that undesired signals will be canceled andthe desired signal can be decoded at each CR user. We presenta stochastic programming formulation of the problem, as wellas a problem reformulation that greatly reduces computationalcomplexity. In the cases of a single licensed channel and multiplelicensed channels with channel bonding, we develop an optimaldistributed algorithm with proven convergence and convergencespeed. In the case of multiple channels without channel bonding,we develop a greedy algorithm with a proven performance bound.The algorithms are evaluated with simulations and are shown toachieve considerable gains over two heuristic schemes.

Index Terms—Relay-enhanced cellular network; cognitive ra-dio; zero-forcing; optimization; video streaming.

I. I NTRODUCTION

Due to significant advances in wireless access technologiesand the proliferation of wireless devices and applications,there is a fundamental change in wireless network traffic.According to a Cisco study, the growth of wireless data ispredicted to be 11-fold between 2013 and 2018, and 66% ofthe increase in future wireless data will be video related [2].The capacity of existing and future wireless networks willbe greatly stressed. Coupled with the depleting spectrum anddense, chaotic deployment of base stations (BS), interferencewill become the major capacity limiting factor.

Cognitive radios (CR) provide an effective solution tomeet this critical demand, by exploiting co-deployed networksand sharing underutilized spectrum [3]. On the other hand,cooperative communicationsrepresents another effective so-lution to the capacity problem, where wireless nodes help

Manuscript received Dec. 30, 2013; revised Mar. 6, 2014; accepted Mar. 18,2014. This work was supported in part by the US National Science Foundation(NSF) under Grants CNS-0953513 and CNS-1247955, and through the NSFBroadband Wireless Access and Applications Center (BWAC) Site at AuburnUniversity. Part of this work was conducted when D. Hu was pursuing adoctoral degree at Auburn University. This work was presented in part atIEEE INFOCOM 2012, Orlando, FL, Mar. 2012 [1].

Y. Xu and S. Mao are with the Department of Electrical andComputer Engineering, Auburn University, Auburn, AL 36839-5201USA. D. Hu is with AT&T Labs, Inc., San Ramon, CA, USA.Email: [email protected], [email protected],[email protected].

Copyrightc©2014 IEEE. Personal use of this material is permitted. However,permission to use this material for any other purposes must be obtained fromthe IEEE by sending an email to [email protected].

Digital Object Identifier XXXX/YYYYYY

each other in information delivery to achieve the so-calledcooperative diversity[4]. Recently, researchers have beenexploring the idea of combining these two techniques [5]–[8], and the potential of cooperative CR networks has beendemonstrated with a testbed implementation [5]. Furthermore,Guan et al. in [9] addressed the challenging problem of jointvideo encoding rate control, power control, relay selection andchannel in cognitive ad hoc networks with cooperative relays.A solution algorithm based on a combination of the branchand bound framework and convex relaxation techniques wasproposed, and the performance evaluation results demonstratedthe efficacy of cooperation and CR for video streaming.

In this paper, we investigate relay-assisted multi-user videostreaming in a CR cellular networks, where videos are sup-ported to make the best use of the enhanced network capacity.We consider a base station (BS) and multiple relay nodes (RN)that collaboratively stream multiple videos to CR users withinthe network. It has been shown that the performance of acooperative relay link is mainly limited by two factors: (i)the half-duplex operation, since the BS–RN and the RN–usertransmissions cannot be scheduled simultaneously on the samechannel; and (ii) thebottleneck channel, which is usually theBS–user and/or the RN–user channel, which usually has poorquality due to obstacles, attenuation, multipath propagationand mobility [4]. To support high quality video service insuch a challenging environment, we assume a well plannedrelay network where the RNs are connected to the BS withhigh-speed wireline links. Therefore the video packets will beavailable at both the BS and the RNs before their scheduledtransmission time, thus allowing advanced cooperative trans-mission techniques to be adopted for streaming videos.

In particular, we consider zero-forcing precoding, a mul-tiuser interference suppression technique, where the BS andRNs simultaneously transmit encoded mixed signals to all CRusers, such that undesired signals will be canceled and thedesired signal can be decoded at each CR user [10], [11].We first present a stochastic programming formulation of theproblem of zero-forcing for video streaming in cooperativeCRnetworks. The cross-layer optimization formulation takesintoaccount important design factors including spectrum sensing,opportunistic spectrum access, cooperative relay, zero-forcingprecoding, and video QoS requirements. We then present areformulation of the problem based on Linear Algebra the-ory [12], such that the number of variables and computationalcomplexity can be greatly reduced.

We develop effective solution algorithms to the formulatedproblem. In particular, we consider three scenarios. In thecase of a single licensed channel, we develop a distributed

This is the author’s version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available athttp://dx.doi.org/10.1109/TCSVT.2014.2313898

Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].


algorithm based on dual decomposition [13], and prove itsguaranteed convergence and bounded convergence rate. Inthe case of multiple licensed channels with channel bonding(where a transmitter can aggregate all the available channels totransmit the encoded signal [14]), we show that the distributedalgorithm can still be used to achieve optimal solutions. Fi-nally, in the case of multiple licensed channels without channelbonding, we develop a greedy algorithm that leverages thesingle-channel algorithm for near-optimal solutions, andprovea lower bound for its performance. The proposed algorithmsare evaluated with simulations, and are shown to outperformtwo heuristic schemes that do not incorporate interferencesuppression techniques with considerable gains.

The remainder of this paper is organized as follows. Wepresent the system model and preliminaries in Section II andthe problem statement in Section III. The proposed solutionalgorithms are developed and analyzed in Section IV. Wepresent simulation results in Section V and discuss relatedwork in Section VI. Section VII concludes this paper.

II. SYSTEM MODEL AND PRELIMINARIES

We next present the system model, assumptions, and pre-liminaries that provide the basis for the problem formulationin Section III. Some of the preliminaries are derived/used inour prior work [15], [16]. We do not claim contribution herebut include the preliminaries for the sake of completeness.

A. Spectrum and Network Model

We consider a spectrum consisting of one common controlchannel (indexed 0) andM licensed channels (indexed from1 to M ). TheM licensed channels are allocated to a primarynetwork, and the common control channel is exclusively usedby a cooperative CR network co-located with the primarynetwork. As in prior work, we assume a synchronized timeslot structure for the licensed channels [3]. The states of theM licensed channels evolve over time independently, while theoccupancy of each channel follows a two-state discrete timeMarkov process [3]. Let~S(t) = [S1(t), S2(t), · · · , SM (t)]denote the network state in time slott, where elementSm(t)represents the status of channelm as:Sm(t) = 0 for an idlechannel andSm(t) = 1 for a busy channel. The utilizationof channelm can be derived asηm = PrSm = 1 =limt0→∞

1t0

∑t0t=1 Sm(t), for m = 1, · · · ,M .

In the relay-assisted CR cellular network, there is a CRBS (indexed1) and (K − 1) CR RNs (indexed from2 toK) deployed in the area to serveN active CR users. LetU = 1, 2, · · · , N denote the set of active CR users. Weassume that the BS and all the RNs are equipped with multipletransceivers: one is tuned to the common control channel andthe others are used to sense multiple licensed channels at thebeginning of each time slot, and to transmit encoded signalsto CR users. We consider the case where each CR user hasone software defined radio (SDR) based transceiver, whichcan be tuned to operate on any of the(M + 1) channels.If the channel bonding/aggregation techniques are used [14]),a transmitter can collectively use all the available channelsand a CR user can receive from all the available channels

simultaneously. Otherwise, only one licensed channel willbeused by a transmitter and a CR user can only receive from asingle chosen channel at a time.

To support high quality video service, we assume a wellplanned relay network, where the RNs are connected to theBS via broadband wireline connections. Although the relaysin LTE-Advanced networks are based on radio interfaces,there are also many solutions based on wireline connections.For example, in small cell networks, the small cell BS’s areconnected with the X2 interface through wireline connections.In [17], passive optical networks are deployed for the smallcell backhaul. In femtocell networks, the femtocell BS’s areconnected with the broadband wireline connections [16]. Inthe future Cloud Radio Access Network (C-RAN) architec-ture [18], light loaded BS’s are connected to a virtualizedbaseband unit (BBU) pool through optical connections, wherebaseband processing is shared among all the sites. As a result,the video packets will always be available for transmissionatthe RNs at their scheduled transmission time. To cope with themuch poorer BS–user and RN–user channels, the BS and RNsadopt zero-forcing to cooperatively transmit multiple videos toCR users, while exploiting the spectrum opportunities in thelicensed channels (see Section III).

B. Spectrum Sensing

Each time slot consists of a spectrum sensing phase anda data transmission phase. The BS and the RNs sense thelicensed channels and exchange their sensing results over thecommon control channel during the sensing phase. We adopta hypothesis test to detect channel availability. For channel m,the null hypothesis and the alternative hypothesis are

Hm0 : channelm is idle and H

m1 : channelm is busy.

We model both types of detection errors: (i) false alarm, whenan idle channel is considered busy and a spectrum opportunitywill be wasted; (ii) miss detection, when a busy channel isconsidered idle, which may cause collision with primary users.

Let Θml be thelth sensing result obtained on channelm,

with binary (0 or 1) values. The false alarm and miss detectionprobabilities associated withΘm

l , denoted byǫml andδml , are:

ǫml = Pr(Θml = 1|Hm

0 ) and δml = Pr(Θml = 0|Hm

1 ). (1)

Given L sensing results obtained for channelm for timeslot t, the corresponding sensing result vector is~Θm

L =[Θm

1 ,Θm2 , · · · ,Θm

L ]. Let PAm(~Θm

L ) := PAm(Θm

1 ,Θm2 , · · · ,Θm

L )be the conditional probability that channelm is available,which can be computed iteratively as

PAm(Θm

1 ) =

[

1 +ηm

1− ηm× (δm1 )1−Θm

1 (1− δm1 )Θm

1

(ǫm1 )Θm

1 (1− ǫm1 )1−Θm

1

]−1

PAm(~Θm

l ) := PAm(Θm

1 ,Θm2 , · · · ,Θm

l )

=

1 +

[

1

PAm(Θm

1 ,Θm2 , · · · ,Θm

l−1)− 1

]

×

(δml )1−Θm

l (1− δml )Θm

l

(ǫml )Θm

l (1− ǫml )1−Θm

l

−1

, l = 2, · · · , L.




In our prior work, we show that the more sensing results, themore accurate the channel state estimation [19]. Note that theproposed scheme does not distinguish where the sensing resultwas obtained. So it is also possible to have the CR users toparticipate in the sensing phase to collect more sensing resultsfor better prediction of the channel states.

C. Opportunistic Spectrum Access

With sensing resultPAm(~Θm

L ), each channelm will be op-portunistically accessed with probabilityPD

m (~ΘmL ) in time slot

t. When channelm is busy (i.e, with probability1−PAm(~Θm

L )),accessing the channel will cause collision to primary users.For primary user protection, such collision probability shouldbe bounded by a prescribed threshold, denoted asγm. Theprimary user protection constraint can be written as

[

1− PAm(~Θm

L )]

PDm (~Θm

L ) ≤ γm. (2)

Solving (2), the optimal channel access probability is

PDm (~Θm

L ) = min

γm/[

1− PAm(~Θm

L )]

, 1

. (3)

Define index variablesDm(t)’s to indicate the availablechannels that the BS or RNs access in time slott. That is,

Dm(t) =

0, channelm is accessed in time slott1, otherwise,

m = 1, 2, · · · ,M. (4)

Let A(t) be the set of available channels in time slott. Itfollows thatA(t) := m | Dm(t) = 0.

D. Zero-Forcing Precoding

We next briefly describe the main idea of zero-forcingconsidered in this paper [10]. Interested readers are referredto [20], [21] for insightful examples, a classification of variousinterference alignment scenarios, and practical considerations.

Consider two transmitters (denoted ass1 ands2 ) and tworeceivers (denoted asd1 and d2). Let X1 and X2 be thesignals corresponding to the packets to be sent tod1 andd2, respectively. The transmitterss1 and s2 send compoundsignalsa1,1X1 + a1,2X2 and a2,1X1 + a2,2X2, respectively,to the two receiversd1 and d2 simultaneously. LetGi,j bethe channel gain from transmittersi to receiverdj . If noise isignored, the received signalsY1 andY2 can be written as

[

Y1

Y2

]

=

[

G1,1 G1,2

G2,1 G2,2

]T [

a1,1 a1,2a2,1 a2,2

] [

X1

X2

]

:= GT ×A× ~X. (5)

From (5), it can be seen that both receivers can perfectlydecode their signals if the transformation matrixA is chosento be

GT−1

, i.e., the inverse of the channel gain ma-trix. With this technique, the transmitters are able to sendpackets simultaneously and the interference between the twoconcurrent transmissions can be effectively canceled at bothreceivers [21].

For the downlink video streaming application consideredin this paper, only the CSI of the downlink channel between

a BS or RN to the user is required. Therefore the operationis similar to the traditional cellular networks, where CSI isalso measured for, e.g., power control. The proposed schemecollects CSI in the same fashion as in existing cellular net-works, the only difference may be that the RNs also collectCSI for the channels from themselves to the users. Since relayshave been incorporated in modern cellular network standards(e.g., LTE-advanced), it is reasonable to assume that suchCSI measurement/feedback is available in practical systems.We assume accurate user channel gains in this paper. Theimpact of inaccurate measurements is a general problem foradopting interference suppression techniques. Several imple-mentations/testbed experiments have demonstrated the feasi-bility and robustness of applying interference managementtechniques in practical settings [20]–[22].

E. Video Performance Measure

We assume the BS streams multiple real-time videos,one to each active CR user, with help from the RNs. Themedium-grain quality scalability (MGS) option of H.264/SVCis adopted in our model because the scalability is very usefulto achieve a graceful quality degradation under the highlydynamic CR network environment [15], [23].

Due to the real-time constraint, we assume that each Groupof Pictures (GOP) must be delivered in the nextT timeslots. Video packets are transmitted in the decreasing orderof their significance to the quality of reconstructed video.To deal with the nonideal channels between BS (RNs) andusers, some error control mechanism must be adopted. Due toscalable coding, a lower significance packet will be uselessifa higher significance packet is not delivered. As a result, itisnecessary to ensure that a higher priority packet is receivedbefore sending the next packet. The video will be cut off whenthe deadlineT is reached, and the quality of the reconstructedvideo is proportional to how many packets can be successfullytransmitted within the deadline (with retransmissions andtheextra delay incurred). The effect of nonideal channels iscaptured in the problem formulation.

In [24], a simple linear R-D model is proposed for fine-granular quality scalability (FGS) videos and used in theoptimization of FGS video streaming over a WLAN. In [25],the authors provide a representative comparison of FGS andMGS and demonstrate the comparable performance of the twoapproaches, and the SVC Quality Scalability videos all exhibitsimilar linear rate-distortion characteristics for the rate rangeof interest. Therefore, the quality of reconstructed MGS videocan be modeled with a linear equation

W (R) = α+ β ×R, (6)

whereW (R) is the average peak signal-to-noise ratio (PSNR)of the reconstructed MGS video,R is the effective receivedrate of the enhancement layer at the receiver after the channellosses, andα and β are constants depending on the specificvideo sequence and codec.

III. PROBLEM FORMULATION

We present the problem formulation in this section. As dis-cussed in Section II, the video packets are available at boththe




BS and all the RNs before their scheduled transmission time;the BS and RNs adopt zero-forcing precoding to overcome thepoor BS–CR user and RN–CR user channels.

Let Xmj denote the signal to be transmitted to user

j on channel m, which has unit power. As illustratedin Section II-D, transmitterk sends a compound signal∑

j∈U amk,jXmj to all active CR users, whereamk,j ’s are the

weights to be determined. Ignoring channel noise, we cancompute the received signalY m

n at a usern as

Y mn =

K∑

k=1

Gmk,n

N∑

j=1

amk,jXmj =

K∑

k=1

N∑

j=1

amk,jGmk,nX

mj

=

N∑

j=1

Xmj

K∑

k=1

amk,jGmk,n, n = 1, 2, · · · , N, (7)

whereGmk,n is the channel gain from the BS (i.e.,k = 1) or an

RN k to usern on channelm. Note that to simplify notation,we useak,j , Gk,n andXj instead ofamk,j , G

mk,n andXm

j whenconsidering only one specific channel. For usern, only signalXn should be decoded and the coefficients of all other signalsshould be forced to zero. Thezero-forcing constraintscan bewritten as

K∑

k=1

ak,jGk,n = 0, for all j 6= n. (8)

Usually the total transmit power of the BS and every RN islimited by a peak powerPmax. SinceXj has unit power, forall j, the power of each transmitted signal is the square sumof all the coefficientsa2k,j . The peak power constraintcan bewritten as

N∑

j=1

|ak,j |2 ≤ Pmax, k = 1, · · · ,K. (9)

Recall that each CR user has one SDR transceiver that canbe tuned to receive from any of the(M+1) channels (withoutchannel bonding). Letbmj be a binary variable indicating thatuserj selects licensed channelm, defined as

bmj =

1, if user j receives from channelm0, otherwise,

j = 1, · · · , N, m = 1, · · · ,M. (10)

Then, we have the followingtransceiver constraint.∑

m∈A(t)

bmj ≤ 1, j = 1, · · · , N. (11)

Let wtj be the PSNR of userj’s reconstructed video at

the beginning of time slott and W tj the PSNR of userj’s

reconstructed video at the end of time slott. In time slott, wtj

is already known, whileW tj is a random variable depending

on the resource allocation and primary user activity duringthetime slot. That is,wt+1

j is a realization ofW tj .

We formulate a multistage stochastic programming problemto maximize the expected logarithm-sum of the PSNR’s atthe end of the GOP, i.e.,

∑Nj=1 E

[

log(WTj )]

, for proportionalfairness among the video sessions. The multistage stochastic

programming problem can be decomposed intoT serial sub-problems, one for each time slott, as [15]

maximize:N∑

j=1

E[

log(W tj )|wt

j

]

(12)

subject to:W tj = wt

j +Ψtj (13)

bmj ∈ 0, 1, for all m, j (14)

Constraints (8), (9) and (11),

whereΨtj is a random variable depending on spectrum sensing,

power allocation, and channel selection in time slott. This is amixed integer nonlinear programming problem (MINLP), withbinary variablesbmj ’s and continuous variablesak,j ’s.

In particular,Ψtj can have two possible values: (i) zero, if

the packet is not successfully received due to collision withprimary users; (ii) the objective value increment achievedintime slott if the packet is successfully received. For the lattercase, we have

Ψtj = Wj(R(t))−Wj(R(t− 1))

=βjB

T

∑

m∈A(t)

log2

1 +1

N0

(

K∑

k=1

amk,jGmk,j

)2

,

(15)

whereN0 is the noise power,βj is userj’s constant in thevideo quality model (6),B is the channel bandwidth, andTis the number of time slots per GoP. To make the problemmanageable, we assume the high SINR region, so thatΨt

j

in (15) can be approximated as

Ψtj ≈

βjB

T

∑

m∈A(t)

2 log2

(

1√N0

(

K∑

k=1

amk,jGmk,j

))

, (16)

subject toK∑

k=1

amk,jGmk,j > 0. (17)

Note that (17) corresponds to the data transmitted to userj,which has to be greater than 0 if userj is active. On theother hand, the zero-forcing constraint (8) ensures that theinterference

∑

k ak,jGk,n must be 0, whenj 6= n.Userj can successfully receive a video packet from channel

m if it tunes to channelm (i.e., bmj = 1) and the BS and RNstransmit on channelm (i.e., with probabilityPD

m (~ΘmL )). The

probability that userj successfully receives a video packet,denoted asP t

j , is

P tj = min

∑

m∈A(t)

bmj PDm (~Θm

L ), 1

. (18)

Therefore, we can expand the expectation in (12) to obtain areformulated problem as follows.

maximize:N∑

j=1

E[

P tj log(w

tj +Ψt

j) + (1− P tj ) log(w

tj)]

(19)

subject to: Constraints (8), (9), (11),(14) and (17).




IV. SOLUTION ALGORITHMS

In this section, we develop effective solution algorithms tothe stochastic programming problem (12). In Section IV-A, wefirst consider the case of a single licensed channel, and derivea distributed, optimal algorithm with guaranteed convergenceand bounded convergence speed. We then address the caseof multiple licensed channels. If channel bonding/aggregationtechniques are used [14], the distributed algorithm in Sec-tion IV-A can still be used to achieve optimal solutions. In thecase of multiple licensed channels without channel bonding,we develop a greedy algorithm with a performance lowerbound in Section IV-C.

A. Case of a Single Channel

1) Property : Consider the case when there is only onelicensed channel, i.e., whenM = 1. The K transmitters,including the BS and(K − 1) RNs, send video packets toactive users using the licensed channel when it is sensed idle.

For userj, the weight and channel gain vectors are:~aj =

[a1,j , a2,j , · · · , aK,j ]T and ~Gj = [G1,j , G2,j , · · · , GK,j ]

T,whereT denotesmatrix transpose. Due to spatial diversity,we assume that the~Gj vectors are linearly independent.

From (8), it can be seen that~aj is orthogonal to the(N−1)

vectors ~Gn’s, for n 6= j. Since~aj is a K by 1 vector, thereare at most(K− 1) normalized vectors that are orthogonal to~aj . Since the~Gj vectors are linearly independent, it followsthat (N − 1) ≤ (K − 1) and thereforeN ≤ K. Therefore,to successfully decode each signalXj , j = 1, 2, · · · , N , thenumber of active usersN should be smaller than or equal tothe number of transmittersK.

Note that the above reasoning provides a necessary condi-tion. The following additional constraints should be enforcedfor the channel selection variables.

N∑

j=1

bmj ≤ K, for all m ∈ A(t). (20)

That is, the number of active users receiving from any channelm cannot be more than the number of transmitters on thatchannel, which isK in the single channel case and less thanor equal toK in the multiple channel case. We first assumethatN is not greater thanK, and will remove this assumptionin the following subsection.

2) Reformulation and Complexity Reduction :With a singlechannel, all active users receive from channel 1. Thereforeb1j = 1, and bmj = 0, for m > 1, j = 1, 2, · · · , N . The for-mulated problem is now reduced to a nonlinear programmingproblem with constraints (8), (9), and (14). If the number ofactive users isN = 1, the solution is straightforward: all thetransmitters send the same signalX1 to the single user usingtheir maximum transmit powerPmax.

In general, the reduced problem can be solved with the dualdecomposition technique [13]. This problem hasK×N primalvariables (i.e., theak,j ’s), and we need to defineN(N − 1)dual variables (or, Lagrangian Multipliers) for constraints (8),and K dual variables for constraints (9). Before presentingthe solution algorithm, we first derive a reformulation of theoriginal problem (19) that can greatly reduce the number

Algorithm 1: Basis Computation Algorithm

1 if K > N then2 Solve homogeneous linear systemGT~x = 0 and get basis

[~v1, · · · , ~vK−N ] ;3 for i = 1 to K −N do4 ~ej,i = ~vi, for all j ;5 end6 end7 for j = 1 to N do8 OrthogonalizeG−j and get(N − 1) orthogonal vectors

~wj,i’s ;9 Calculate~ej,r as in (21) ;

10 end

of primal and dual variables, such that the computationalcomplexity can be reduced.

Lemma 1. Each vector~aj = [a1,j , a2,j , · · · , aK,j ]T can be

represented by the linear combination ofr nonzero, linearlyindependent vectors, wherer = K −N + 1.

Proof: From (8), each vector~aj is orthogonal to~Gi wherej 6= i. Define a reduced matrixG−j obtained by deleting~Gj

from G, i.e., G−j = [ ~G1, · · · , ~Gj−1, ~Gj+1, · · · , ~GN ]. Then~aj is a solution to the homogeneous linear systemG

T

−j~x = 0.Since we assume that the~Gi’s are all linearly independent, thecolumns ofG−j are also linearly independent [12]. Thus therank ofG−j is (N−1). The solution belongs to the null spaceof G−j . The dimension of the null space isr = K− (N − 1)according to the Rank-nullity Theorem [12]. Therefore, each~aj can be presented by the linear combination ofr linearlyindependent vectors.

Let Ej = ~ej,1, ~ej,2, · · · , ~ej,r be a basis for the nullspace ofG−j . There are many methods to obtain the basis,such as Gaussian Elimination. In the following, we present analternative scheme to compute the basis, which, however, hasthe same asymptotic complexity as Gaussian Elimination.

The algorithm for computing a basis is shown in Algo-rithm 1. In Steps 1–6, we first solve the homogeneous linearsystemG

T~x = 0 to get a basis[~v1, ~v2, · · · , ~vK−N ]. Notethat if K is equal toN , the basis is the empty set∅. Wethen set theK − N basis vectors to be the firstK − Nvectors in all the basesEj , j = 1, 2, · · · , N . In Step 8, weorthogonalize eachG−j and obtain(N−1) orthogonal vectors~ωj,i, i = 1, 2, · · · , N − 1. Finally in Step 9, we let therthvector ~ej,r be orthogonal to all the~ωj,i’s by subtracting allthe projections on each~ωj,i from ~Gj , as

~ej,r = ~ej,K−N+1 = ~Gj −N−1∑

i=1

~GT

j ~ωj,i

~ωT

j,i~ωj,i

~ωj,i. (21)

Lemma 2. The solution space constructed by the basis[~v1, ~v2, · · · , ~vK−N ] is a sub-space of the solution space ofG

T

−j~x = 0 for all j.

Proof: It can be shown that each vector~vi is a solutionof GT

−j~x = 0, for i = 1, 2, · · · ,K −N .

Lemma 3. The vectors[~v1, ~v2, · · · , ~vK−N , ~ej,r] computed inAlgorithm 1 is a basis of the null space ofG−j .




TABLE ICOMPARISON OFCOMPUTATIONAL COMPLEXITY FOR THE CASE OF A

SINGLE CHANNEL

Original Problem Reformulated Problem

Primal Variables KN (K −N + 1)NDual Variables N2 +K N +K

Proof: Obviously, the~vi’s are linearly independent. From(21), it is easy to verify that~ej,r is orthogonal to all the~ωj,i’s.Therefore,~ej,r is also a solution to systemGT

−j~x = 0. Since~Gj and~ωj,i are orthogonal to all the~vi’s, and~ej,r is a linearcombination of~Gj and~ωj,i, ~ej,r is also orthogonal and linearlyindependent to all the~vi’s. The conclusion follows.

Let Ej = [~v1, ~v2, · · · , ~vK−N , ~ej,r] and define coefficients~cj = [cj,1, cj,2, · · · , cj,r]T. Then we can represent~aj as a lin-ear combination of the basis vectors, i.e.,~aj =

∑rl=1 cj,l~ej,l =

Ej~cj . Eq. (16) can be rewritten as

Ψtj =

βjB

T

∑

m∈A(t)

2 log2

(

1√N0

(

~cTj ET

j~Gj

)

)

=βjB

T

∑

m∈A(t)

2 log2

(

1√N0

(

cj,r~eT

j,r~Gj

)

)

. (22)

Note that in the above equation, we omit the channel indexmfor simple notation. The second equality is because the firstK−N column vectors inEj are orthogonal to~Gj . The randomvariableW t

j in the objective function now only depends oncj,r. The peak power constraint can be revised as

N∑

j=1

[Ej(k)~cj ]2 ≤ Pmax, k = 1, · · · ,K, (23)

whereEj(k) is thekth row of matrixEj . And the constraintin (17) can be rewritten as

(Ej~cj)T ~Gj > 0 (24)

With such a reformulation, the number of primal and dualvariables can be greatly reduced. In Table I, we show thenumbers of variables in the original problem and in thereformulated problem. The number of primary variables isreduced fromKN to (K−N +1)N , and the number of dualvariables is reduced fromN2+K to N +K. Such reductionsresult in greatly reduced computational complexity.

3) Distributed Algorithm :The formulated problem can besolved by the BS in a centralized manner. Alternatively, wedevelop a distributed algorithm for (i) reducing the compu-tation load at the BS, (ii) reducing the burden of the BS oncollecting channel states for all users to all the relays, and (iii)making the system more robust.

For the distributed algorithm, we define non-negative dualvariables~µ = [µ1, · · · , µK , λ1, · · · , λN ]T for the inequality

constraints. The Lagrangian function is

L(C, ~µ) =N∑

j=1

E[

log(W tj (cj,r))|wt

j

]

+

K∑

k=1

µk(Pmax −N∑

j=1

[Ej(k)~cj ]2) +

N∑

j=1

λj(Ej~cj)T ~Gj

=

N∑

j=1

Lj(~cj , ~µ) + Pmax

K∑

k=1

µk, (25)

whereC is a matrix consisting of all column vector~cj ’s and

Lj(~cj , ~µ) = E[

log(W tj (cj,r))|wt

j

]

−K∑

k=1

µk[Ej(k)~cj ]2+

λj(Ej~cj)T ~Gj . (26)

The corresponding problem can be decomposed intoN sub-problems and solved iteratively [13]. In Stepτ ≥ 1, for givenvector ~µ(τ), each CR user solves the following sub-problemusing local information

~cj(τ) = argmaxLj(~cj , ~µ(τ)). (27)

Obviously, the objective function in (27) is concave. Therefore,there is a unique optimal solution. The CR users then exchangetheir solutions over the common control channel. To solve theprimal problem, we adopt the gradient method [13].

~cj(τ + 1) = ~cj(τ) + φ∇Lj(~cj(τ), ~µ(τ)), (28)

where∇Lj(~cj(τ), ~µ(τ)) is the gradient of the primal problemandφ is a small positive step size.

The master dual problem for a givenC(τ) is

min~µ

q(~µ) =

N∑

j=1

Lj(~cj(τ), ~µ) + Pmax

K∑

k=1

µk. (29)

Since the Lagrangian function is differentiable, the subgradientiteration method can be adopted.

~µ(τ + 1) = [~µ(τ)− ρ(τ)~g(τ)]+, (30)

whereρ(τ) = q(~µ(τ))−q(~µ∗)||~g(τ)||2 is a positive step size,~µ∗ is the

optimal solution,~g(τ) = ∇q(~µ(τ)) is the gradient of the dualproblem, and[·]+ denotes the projection onto the nonnegativeaxis. Since the optimal solution~µ∗ is unknown a priori, wechoose the mean of the objective values of the primal anddual problems as an estimate for~µ∗ in the algorithm. Theupdatedµk(τ+1) will again be used to solve the sub-problems(27). The distributed algorithm is shown in Algorithm 2, where0 ≤ κ ≪ 1 is a threshold for convergence.

4) Performance Analysis :We analyze the performance ofthe distributed algorithm in this section. In particular, we provethat it converges to the optimal solution at a speed faster than√

1/τ asτ goes to infinity.




Algorithm 2: Algorithm for the Case of a Single Channel

1 if N = 1 then2 Setak,j to Pmax for all k ;3 else4 Setτ = 0; ~µ(0) to positive values;C(0) to random values ;5 Compute basesEj ’s as in Algorithm 1 ;6 repeat7 τ = τ + 1 ;8 Compute~cj(τ) as in (28) ;9 Broadcast~cj(τ) on the common control channel ;

10 Update~µ(τ) as in (30) ;11 until ||~µ(τ)− ~µ(τ − 1)|| < κ;12 Computeak,j ’s ;13 end

Theorem 1. The seriesq(~µ(τ)) converges toq(~µ∗) as τ goesto infinity and the square error sum

∑∞τ=1(q(~µ(τ))− q(~µ∗))2

is bounded.

Proof: For the optimality gap, we have:

||~µ(τ + 1)− ~µ∗||2 = ||[~µ(τ)− ρ(τ)~g(τ)]+ − ~µ∗||2

≤ ||~µ(τ)− ρ(τ)~g(τ)− ~µ∗||2

= ||~µ(τ)− ~µ∗||2 − 2ρ(τ)(q(~µ(τ))− q(~µ∗))+

(ρ(τ))2||~g(τ)||2.

Since the step size isρ(τ) = q(~µ(τ))−q(~µ∗)||~g(τ)||2 , it follows that

||~µ(τ + 1)− ~µ∗||2 ≤ ||~µ(τ)− ~µ∗||2 − (q(~µ(τ))− q(~µ∗))2

||~g(τ)||2

≤ ||~µ(τ)− ~µ∗||2 − (q(~µ(τ))− q(~µ∗))2

g2, (31)

whereg2 is an upper bound of||~g(τ)||2. Since the second termon the right-hand-side of (31) is non-negative, it follows thatlimτ→∞ q(~µ(τ)) = q(~µ∗).

Summing Inequality (31) overτ , we have∞∑

τ=1

(q(~µ(τ))− q(~µ∗))2 ≤ g2||~µ(1)− ~µ∗||2.

That is, the square error sum is upper bounded.

Theorem 2. The sequenceq(~µ(τ)) converges faster than1/√τ as τ goes to infinity.

Proof: Assumelimτ→∞√τ(q(~µ(τ))−q(~µ∗)) > 0. Then

there is a sufficiently largeτ ′ and a positive numberξ suchthat

√τ(q(~µ(τ)) − q(~µ∗)) ≥ ξ, for all τ ≥ τ ′. Taking the

square sum fromτ ′ to ∞, we have:∞∑

τ=τ ′

(q(~µ(τ))− q(~µ∗))2 ≥ ξ2∞∑

τ=τ ′

1

τ= ∞. (32)

Eq. (32) contradicts with Theorem 1, which states that∑∞

τ=1(q(~µ(τ))− q(~µ∗))2 is bounded. Therefore, we have

limτ→∞

q(~µ(τ))− q(~µ∗)

1/√τ

= 0,

indicating that the convergence speed ofq(~µ(τ)) is faster thanthat of 1/

√τ .

TABLE IICOMPARISON OFCOMPUTATIONAL COMPLEXITY FOR THE CASE OF

MULTIPLE CHANNELS WITH CHANNEL BONDING

Original Problem Reformulated Problem

Primal Variables KNM (K −N + 1)NM

Dual Variables N2M +KM NM +KM

B. Case of Multiple Channels with Channel Bonding

When there are multiple licensed channels, we first considerthe case where the channel bonding/aggregation techniquesare used by the transmitters and CR users [14]). With channelbonding, a transmitter can utilize all the available channels inA(t) collectively to transmit the mixed signal. We assume thatat the end of the sensing phase in each time slot, CR userstune their SDR transceiver to the common control channel toreceive the set of available channelsA(t) from the BS. Theneach CR user can receive from all the channels inA(t) anddecode its desired signal from the compound signal it receives.

This case is similar to the case of a single licensed channel.Now all the active CR users receive from the set of availablechannelsA(t). We thus havebmj = 1, for m ∈ A(t), andbmj = 0, for m /∈ A(t), j = 1, 2, · · · , N . When all thebmj ’sare determined this way, problem (12) is reduced to a nonlinearprogramming problem with constraints (8) and (9). The dis-tributed algorithm described in Section IV-A can be appliedto solve this reduced problem to get optimal solutions. Thecomplexity reduction achieved by the reformulated problemispresented in Table II for this case.

C. Case of Multiple Channels without Channel Bonding

We finally consider the case of multiple channels withoutchannel bonding, where each CR user has a narrow band SDRtransceiver and can only receive from one of the channels.We first present a greedy algorithm that leverages the optimalalgorithm in Algorithm 2 for near-optimal solutions, and thenderive a lower bound for its performance.

1) Greedy Algorithm :WhenM > 1, the optimal solutionto problem (12) depends also on the binary variablesbmj ’s,which determines whether userj receives from channelm.Recall that there are two constraints for thebmj ’s: (i) eachuser can receive from at most one channel (see (11)); (ii)the number of users on the same channel cannot exceed thenumber of transmittersK (see (20)). Let~b be the channel allo-cation vector with elementsbmj ’s, andΦ(~b) the correspondingobjective value for a given user channel allocation~b.

We take a two-step approach to solve problem (12). First,we apply the greedy algorithm in Algorithm 3 to choose oneavailable channel inA(t) for each CR user (i.e., to determine~b). Second, we apply the algorithm in Algorithm 2 to obtaina near-optimal solution for the given channel allocation~b.

In Algorithm 3, ~υmj is a unit vector with 1 for the[(j −

1) × M + m]-th element and0 for all other elements, and~b = ~b + ~υm′

j′ indicates choosing channelm′ for user j′. Ineach iteration, the user-channel pair(j′,m′) that can achievethe largest increase in the objective value is chosen, as in Step3. The worst case complexity of Algorithm 3 isO(K2M2).




Algorithm 3: Channel Selection Algorithm for the Caseof Multiple Channels without Channel Bonding

1 Initialize ~b to a zero vector, user setU = 1, · · · , N anduser-channel setC = U ×A(t) ;

2 while C 6= ∅ do3 Find the user-channel pairj′,m′, such that

j′,m′ = argmaxj,m∈CΦ(~b+ ~υmj )− Φ(~b) ;

4 Set~b = ~b+ ~υm′

j′ and removej′ from U ;5 if

∑N

j=1bm

′

j = K then6 Removem′ from A(t) ;7 end8 Update user-channel setC = U ×A(t) ;9 end

2) Performance Bound :We next analyze the greedy al-gorithm and derive a lower bound for its performance. Letνl be the sequence from the first to thelth user-channel pairselected by the greedy algorithm. The increase in objectivevalue is denoted as:

Fl := F (νl, νl−1) = Φ(νl)− Φ(νl−1). (33)

Sum up (33) from 1 toS. We have∑S

l=1 Fl = Φ(νS) sinceΦ(ν0) = 0. Let Ω be the global optimal solution for user-channel allocation. Defineπl as a subset ofΩ. For givenνl,πl is the subset of user-channel pairs that cannot be allocateddue to the conflict with thel-th user channel allocationνl (butnot conflict with the user-channel allocations inνl−1).

Lemma 4. Assume the greedy algorithm stops inS steps, wehave

Φ(Ω) ≤ Φ(νS) +S∑

l=1

∑

σ∈πl

F (σ ∪ νl−1, νl−1).

Proof: The proof is similar to the proof of Lemma 7in [16] and is omitted for brevity.

Theorem 3. The greedy algorithm for channel selection inAlgorithm 3 can achieve an objective value that is at least1/|A(t)| of the global optimum in each time slot.

Proof: According to Lemma 4, it follows that:

Φ(Ω) ≤ Φ(νS)+

S∑

l=1

|πl|Fl ≤ Φ(νS)+(|A(t)|−1)

S∑

l=1

Fl

= |A(t)|Φ(νS). (34)

The second inequality is due to the fact that each user canchoose at most one channel and there are at mostmin|A(t)|−1, N pairs inπl according to the definition. Without loss ofgenerality, we assume there are more secondary users thanthe number of available channels. Then the number of pairsin πl is at most(|A(t)| − 1). The equality in (34) is because∑S

l=1 Fl = Φ(νS). Then we have:

1

|A(t)|Φ(Ω) ≤ Φ(νS) ≤ Φ(Ω). (35)

The greedy heuristic solution is lower bounded by1/|A(t)|of the global optimum.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Channel Utilization (η)

Rat

io (χ

)

M=6M=8M=10M=12

Fig. 1. Competitive ratioE[χ] defined in (36) versus channel utilizationη.

Define competitive ratioχ = Φ(νS)/Φ(Ω) = 1/|A(t)|.Assume all the licensed channels have identical utilization η.DefineD as the number of available channels. Note that allthe licensed channels have identical utilization and they areidentical distributed with Bernoulli distribution. Therefore, Dhas a Binomial distribution as

Pr(D = d) =

(

Md

)

ηM−d(1− η)d.

We defineχ = 1 when there is no available channels. Thenwe derive the expectation ofχ as

E[χ] = ηM +

M∑

d=1

(

1

d

)(

Md

)

ηM−d(1− η)d. (36)

In Fig. 1, we evaluate the impact of channel utilizationηand the number of licensed channelsM on the competitiveratio. We increaseη from 0.05 to 0.95 in steps of0.05 andincreaseM from 6 to 12 in steps of2. The lower bound (35)becomes tighter whenη is larger or whenM is smaller. Forexample, whenη = 0.6 and M = 6, the greedy algorithmsolution is guaranteed to be no less than 52.7% of the globaloptimal. Whenη is increased to 0.95, the greedy algorithmsolution is guaranteed to be no less than 98.3% of the globaloptimal. When|A(t)| = 1, the proposed scheme is optimal,which validates the earlier analysis in Section IV-A.

V. PERFORMANCEEVALUATION

We evaluate the performance of the proposed algorithmswith a MATLAB implementation and the JSVM 9.13 VideoCodec. For comparison, we develop two simpler heuristicschemes that do not incorporate interference alignment.

• Heuristic 1: each CR user selects the best channel inA(t) based on channel condition. The time slot is equallydivided among the users receiving from the same channel,to send their signals separately in each time slot.

• Heuristic 2: in each time slot, the active user with thebest channel is selected for each available channel. Theentire time slot is used to transmit this user’s signal.




Once channel assignment is determined, the PSNR incrementin time slot t achieved by Heuristic1 can be derived as

Ψtj =

βjB

T

∑

m∈A(t)

bmj∑

j bmj

log2

(

1 +1

N0

K∑

k=1

(Gmk,j)

2

)

. (37)

Similarly, Ψtj achieved by Heuristic2 can be derived as

Ψtj =

βjB

T

∑

m∈A(t)

bmj log2

(

1 +1

N0

K∑

k=1

(Gmk,j)

2

)

. (38)

As discussed in Section II-A, the dynamic of the licensedchannels are modeled by two-state discrete-time Markov pro-cesses. For the user channels, the channel fading-gain processis piecewise constant on blocks of one time slot, and fadingin different time slots are independent. The Rayleigh fadingmodel is used for all the simulation results reported in thispa-per. The proposed algorithm uses the video quality model (6)when solving the formulated problem. Then the solution isused in the simulations driven by the video data generated bythe JSVM 9.13 video codec using different test sequences.

A. Case of a Single Licensed Channel

In the first scenario, there areK = 4 transmitters, i.e., oneBS and three RNs. The channel utilizationη is set to 0.6and the maximum allowable collision probabilityγ is set to0.2. There are three active CR users, each receives an MGSvideo stream from the BS:Bus to CR user 1,Mobile to CRuser 2, andHarbor to CR user 3. The video sequences are inthe Common Intermediate Format (CIF, 252×288). The GOPsize of the videos is 16 and the delivery deadlineT is 10. Thefalse alarm probability isǫml = 0.3 and the miss detectionprobability isδml = 0.3 for all spectrum sensors. The channelbandwidthB is 1 MHz. The peak power limit is 10 W for allthe transmitters, unless otherwise specified.

We first examine the convergence rate of the distributedalgorithm. According to Theorem 2, the distributed algorithmconverges at a speed faster than1/

√τ asymptotically. We

compare the optimality gap of the proposed algorithm, i.e.,|q(τ)−q∗|, with series10/

√τ in Fig. 2. Both curves converge

to 0 asτ goes to infinity. It can be seen that the convergencespeed, i.e., the slope of the curve, of the proposed schemeis larger than that of10/

√τ after about10 iterations. The

convergence of the optimality gap is much faster than10/√τ ,

which exhibits a heavy tail.We next present the average Y-PSNRs of the three re-

constructed MGS videos in Fig. 3. Among three schemes,the proposed algorithm achieves the highest PSNR value. Toillustrate the visual quality of the reconstructed video, weplotted selected frames for each user in Fig. 4. The firstheuristic algorithm has an inferior performance since thereis no collaboration among the transmitters and time divisionmultiple access has to be adopted to avoid interference amongthe users choosing the same channel. The second heuristicalgorithm has the poorest performance, since for each timeslot only one cognitive user is active. Note that the proposedalgorithm is optimal in the single channel case. It achievessignificant improvements ranging from 3.64 dB to 5.02 dBover the two heuristic algorithms.

0 20 40 60 80 100 1200

2

4

6

8

10

Interation Index (τ)

Opt

imal

ity G

ap

q(τ)−q∗

10/sqrt(τ)

Fig. 2. Convergence rate of the distributed algorithm with asingle channel.

1 2 30

5

10

15

20

25

30

35

40

User Index

Y−P

SN

R (d

B)

Proposed SchemeHeuristic 1Heuristic 2

Fig. 3. Received video quality for each CR user with a single channel.

B. Case of Multiple Channels with Channel Bonding

In the second scenario, we investigate the case with twolicensed channels with channel bonding. The parameters arethe same as in the previous subsection, except thatM = 2.We also assume that CR users 1, 2, and 3 are streamingtest sequenceBus, Mobile, and Harbour, respectively. Thesimulation results are plotted in Figs. 5 and 6. Similar trendcan be observed as in Fig. 3, where the superior performanceof the proposed scheme is demonstrated.

For the two heuristic algorithms, we find that∑

j Ψtj in

Heuristic 1 is upper bounded by that of Heuristic 2. However,due to the effect of the initial values ofwt

j , which is essentiallyαi, and the bound of success probability in (18), the averageY-PSNR of Heuristic 1 is not necessarily lower than thatof Heuristic 2. For instance, in the single channel case, theaverage Y-PSNR of Heuristic 1 is higher than that of Heuristic2, since in Heuristic 2 only one CR user is selected. As thenumber of channels is increased to two, two CR users willbe selected with Heuristic 2. Hence the Y-PSNR performanceof Heuristic 2 catches up. We can expect that if the numberof available channels is greater than or equal to the numberof CR users, Heuristic 2 will achieve much higher Y-PSNRvalues than Heuristic 1.

Comparing to the proposed scheme, the two heuristic al-




(a) User1, Bus, Heuristic1.

(b) User1, Bus, Heuristic2.

(c) User1, Bus, Proposed.

(d) User2, Mobile, Heuristic1.

(e) User2, Mobile, Heuristic2.

(f) User2, Mobile, Proposed.

(g) User3, Harbor, Heuristic1.

(h) User3, Harbor, Heuristic2.

(i) User3, Harbor, Proposed.

Fig. 4. Comparison of the visual quality of the reconstructedframes for the three users.

gorithms have the advantage of low complexity. These twoschemes also exploit the diversity gain in multi-user commu-nications. These can be adopted when complexity or scalabilitybecomes the main objective than video quality.

C. Case of Multiple Channels without Channel Bonding

We next investigate the third scenario with six licensedchannels and four transmitters. There are 12 CR users, eachstreaming one of the three different videosBus, Mobile, andHarbor. The rest of the parameters are the same as those inthe single channel case, unless otherwise specified. Eq. (34)can also be interpreted as an upper bound on the globaloptimal, i.e., Φ(Ω) ≤ |A(t)|Φ(νL), which is also plottedin the figures. Each point in the following figures is theaverage of 10 simulation runs with different random seeds.The 95% confidence intervals are plotted as error bars, whichare generally negligible.

The impact of channel utilizationη on received videoquality is presented in Fig. 7. We increaseη from 0.3 to0.9 in steps of0.15, and plot the Y-PSNRs of reconstructedvideos averaged over all the 12 CR users. Intuitively, a smaller

η allows more transmission opportunities for CR users, thusallowing the CR users to achieve higher video rates and bettervideo quality. This is shown in the figure, in which all fourcurves decrease asη is increased. We also observe that thegap between the upper bound and proposed schemes becomessmaller asη gets larger, from 32.65 dB whenη = 0.3 to 0.63dB whenη = 0.9. This trend is also demonstrated in Fig. 1.The proposed scheme outperforms the two heuristic schemeswith considerable gains, ranging from 0.8 dB to 3.65 dB.

Finally, we investigate the impact of the number of trans-mittersK on the video quality. In this simulation we increaseK from 2 to 6 with step size 1. The average Y-PSNRs of allthe 12 CR users are plotted in Fig. 8. As expected, the moretransmitters, the more effective the interference alignmenttechnique, and thus the better the video quality. The proposedalgorithm achieves gains ranging from 1.78 dB (whenK = 2)to 4.55 dB (whenK = 6) over the two heuristic schemes.

VI. RELATED WORK

Video over wireless networks have been an active researcharea for years [26]–[30]. This work is closely related to the




1 2 30

5

10

15

20

25

30

35

40

45

User Index

Y−P

SN

R (d

B)


Fig. 5. Received video quality for each CR user for multiple channels withchannel bonding.

3 4 5 635

36

37

38

39

40

41

42

43

Number of transmitters (K)

Ave

rage

Y−P

SN

R (

dB)


Fig. 6. Reconstructed video quality vs. the number of transmittersK formultiple channels with channel bonding.

0.3 0.4 0.5 0.6 0.7 0.8 0.930

35

40

45

50

55

60

65

70

75

Channel Utilization (η)

Ave

rage

Y−P

SN

R (d

B)

Proposed schemeHeuristic 1Heuristic 2Upper bound

Fig. 7. Reconstructed video quality vs. channel utilization η in the multi-channel without channel bonding case.

prior work on cooperative communications [4] and that onCR networking [3]. There have been significant advancesin these areas, which laid out the foundation for this work.Researchers have been exploring the idea of combining thesetwo techniques [5], [6], [8]. In [5], an overview of cooperative

2 3 4 5 630

35

40

45

50

55

60

Number of Transmitters (K)

Ave

rage

Y−P

SN

R (d

B)

Proposed schemeHeuristic 1Heuristic 2Upper bound

Fig. 8. Reconstructed video quality vs. number of transmitters K in themulti-channel without channel bonding case.

relay scenarios and related issues was presented, along witha GNU Radio implementation of a MAC protocol. In [6],a centralized heuristic was presented to address the relayselection and spectrum allocation problem in CR networks.

Cooperative diversity has been exploited for wireless videostreaming in several recent papers [9], [31]–[34]. In [31],theauthors proposed a network-coding-based cooperative repairframework for peers in an ad-hoc wireless local area network(WLAN) to improve broadcast video quality during channellosses, where repair is optimized for broadcast video in arate-distortion manner. In [32], the authors proposed a scal-able video broadcast/multicast solution that integrates scalablevideo coding, 3G broadcast, and ad-hoc relays to balancethe system-wide and worst-case video quality of all viewersin a 3G cell. In [33], two-hop cooperative transmission wasintegrated with layered video coding and packet level forwarderror correction (FEC) to enable efficient and robust videomulticast in a cellular network, where multiple relays forwardthe data simultaneously using randomized distributed spacetime codes (RDSTC). In a recent paper [34], a problem ofjoint rate control, relay selection, and power allocation forvideo streaming over cooperative networks was formulatedand solved, aiming to maximize the sum PSNR of a set ofconcurrent video sessions.

The problem of video over CR networks has only beenstudied in a few recent papers [15], [16], [23], [35]–[38].In [35], a dynamic channel selection scheme was proposed forCR users to transmit videos over multiple channels. In [36],a distributed joint routing and spectrum sharing algorithmforvideo streaming over CR ad hoc networks was described andevaluated with simulations. In our prior work, we consideredvideo multicast in an infrastructure-based CR network [15],unicast video streaming over multihop CR networks [23] andCR femtocell networks [16]. In [37], the impact of systemparameters residing in different network layers are jointly con-sidered to achieve the best possible video quality for CR users.Unlike the heuristic approaches in [35], [36], the analytical andoptimization approach taken in this paper yields algorithmswith optimal or bounded performance. In [38], Ding andXiao investigated the problem of enabling multi-source video




on-demand applications in multi-interface cognitive wirelessmesh networks. Both centralized and distributed algorithms aredeveloped for joint multipath routing and spectrum allocationfor video sessions to minimize the total bandwidth cost.

As point-to-point link capacity approaches the Shannonlimit, there has been considerable interest on exploiting in-terference to improve wireless network capacity [10], [11],[20], [21], [39]. In addition to information theoretic workon asymptotic capacity [10], [11], practical issues have beenaddressed in [20]–[22], [39], [40] In [39], the authors pre-sented a practical design of analog network coding to exploitinterference and allow concurrent transmissions, which doesnot make any synchronization assumptions. In [20], interfer-ence alignment and cancellation is incorporated in MIMOLANs, and the network capacity is shown, analytically andexperimentally, to be almost doubled. In [21], the authorspresented a general algorithm for identifying interferencealignment and cancellation opportunities in practical multi-hopmesh networks. The impact of synchronization and channelestimation was evaluated through a GNU Radio implemen-tation. In [40], the authors present a relay-assisted ARQscheme, where a distributed beamforming-based interferencecancellation scheme is used for cognitive relays to exploitspectrum opportunities for retransmission of lost packets.In [22], the authors presented the design and experimentalevaluation of Simultaneous TRansmission with OrthogonallyBlinded Eavesdroppers (STROBE), where multi-antenna APscan construct simultaneous data streams using Zero- ForcingBeamforming (ZFBF). This work certainly justified the via-bility of the proposed scheme in this paper.

VII. C ONCLUSION

In this paper, we investigated the problem of relay-assistedmulti-user scalable video streaming in a relay enhanced CRcellular network. We presented a stochastic programming for-mation, and derived a reformulation that leads to considerablereduction in computational complexity. A distributed optimalalgorithm was developed for the case of a single channeland the case of multi-channel with channel bonding, withproven convergence and convergence speed. We also presenteda greedy algorithm for the multi-channel without channelbonding case, with a proven performance bound. The proposedalgorithms were evaluated with simulations and were shownto outperform two heuristic schemes without interferencealignment with considerable gains.

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Yi Xu received the M.S. degrees in Electronic Engi-neering from Tsinghua University, Beijing, China in2010 and the B.S. degree in Electronic InformationEngineering from University of Electronic Scienceand Technology of China, Chengdu, China in 2007.Since 2011, he has been pursuing the Ph.D. degreein the Department of Electrical and Computer En-gineering, Auburn University, Auburn, AL, USA.His research interests include Optimization, GameTheory, MIMO, OFDM, IDMA and Cognitive RadioNetworks.

Donglin Hu received the Ph.D. degree in Electricaland Computer Engineering in 2012, and the M.S.in Probability and Statistics in 2011, from AuburnUniversity, Auburn, AL, USA. He received the M.S.degree from Tsinghua University, Beijing, China, in2007 and the B.S. degree from Nanjing Universityof Posts and Telecommunications, Nanjing, Chinain 2004, respectively, both in electrical engineering.He was a postdoctoral fellow at Auburn Universityfrom 2012 to 2013 and is currently a Senior Memberof Technical Staff with AT&T Labs. His research

interests include cognitive radio networks, cross-layer optimization, algorithmdesign for wireless network and multimedia communications.

Shiwen Mao (S’99-M’04-SM’09) received Ph.D.in electrical and computer engineering from Poly-technic University, Brooklyn, NY in 2004. He isthe McWane Associate Professor in the Departmentof Electrical and Computer Engineering, AuburnUniversity, Auburn, AL, USA.

His research interests include wireless networksand multimedia communications, with current focuson cognitive radio, small cells, 60 GHz mmWavenetworks, free space optical networks, and smartgrid. He is on the Editorial Board of IEEE Transac-

tions on Wireless Communications, IEEE Internet of Things Journal, IEEECommunications Surveys and Tutorials, Elsevier Ad Hoc Networks Journal,and Wiley International Journal on Communication Systems. He serves asthe Director of E-Letter of Multimedia Communications Technical Committee(MMTC), IEEE Communications Society for 2012–2014. He servesas Techni-cal Program Vice Chair for Information Systems (EDAS) of IEEE INFOCOM2015, symposium co-chairs for many conferences, including IEEE ICC, IEEEGLOBECOM, ICCCN, IEEE ICIT-SSST, among others, Steering CommitteeMember for IEEE ICME (2014-2016) and AdhocNets, and in various rolesin the organizing committees of many conferences.

Dr. Mao received the 2013 IEEE ComSoc MMTC Outstanding LeadershipAward and the NSF CAREER Award in 2010. He is a co-recipient ofTheIEEE ICC 2013 Best Paper Award and The 2004 IEEE CommunicationsSociety Leonard G. Abraham Prize in the Field of Communications Systems.



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