Partial Relay Selection With Fixed-Gain Relays and Outdated CSI in Underlay Cognitive Networks

4696 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 9, NOVEMBER 2013

[10] K. C. Toh, M. J. Todd, and R. H. Tutuncu, “SDPT3: A Matlab softwarepackage for semidefinite programming,” Optim. Methods Softw., vol. 11,no. 1–4, pp. 545–581, Jan. 1999.

[11] A. F. Molisch and F. Tufvesson, “Multipath propagation models forbroadband wireless systems,” in CRC Handbook of Signal Processing forWireless Communications. Boca Raton, FL, USA: CRC, 2004.

[12] Technical Specification Group Radio Access Networks; DeploymentAspects, Third Generation Partnership Project TR 25.943 V10.0.0,2011.

Partial Relay Selection With Fixed-Gain Relays andOutdated CSI in Underlay Cognitive Networks

Bin Zhong, Zhongshan Zhang, Member, IEEE, Xu Zhang,Jun Wang, and Keping Long, Senior Member, IEEE

Abstract—The impact of an imperfect channel estimation on theamplify-and-forward (AF) mode cooperative communications systems isstudied, with some important factors, including the probability charac-teristic of the secondary user’s end-to-end signal-to-noise ratio (SNR), theoutage probability, the symbol error probability (SEP), and the channelcapacity, being analyzed. Different from the conventional relay selectionschemes, we assume that the primary users share their bandwidth with thesecondary users to enable a secondary relay-aided communication if theinterference added to the primary users is kept below a certain threshold inan underlay cognitive network. In particular, both the feedback delay andDoppler frequency shift are assumed to be within a tolerable range, and ascompared with the conventional methods, less channel state information(CSI) feedback is required in the proposed method due to partial relayselection being performed in the latter. The proposed scheme is validatedby carrying out both theoretical analysis and numerical simulation, andthe theoretical approximations of closed-form expressions for some figuresof merit, e.g., the outage probability, the SEP, and the channel capacity,are all consistent with the numerical results. The simulations also provethat the performance of the proposed scheme is considerably affected bysome other critical parameters, such as the number of relays, the channelcorrelation coefficient, and the interference threshold. In the presence ofmultiple candidate relays, an optimum solution in terms of either theoutage probability or the SEP performance can always be found withinthe SNR range of (0, 10 dB).

Index Terms—Amplify-and-forward (AF), cognitive radio, cooperativenetworks, outage probability, outdated channel state information (CSI),partial relaying.

Manuscript received September 17, 2012; revised April 27, 2013; acceptedMay 25, 2013. Date of publication May 31, 2013; date of current versionNovember 6, 2013. This work was supported in part by the National NaturalScience Foundation of China under Grant 61172050, by the National BasicResearch Program of China (973 Program) under Grant 2012CB315905, bythe Program for New Century Excellent Talents in University under GrantNECT-12-0774, by the Beijing Science and Technology Program under GrantZ111100054011078, by the Foundation of Beijing Engineering and TechnologyCenter for Convergence Networks and Ubiquitous Services, and by the NationalKey Projects under Grant 2012ZX03001029-005 and Grant 2012ZX03001032-003. This paper was presented in part at the IEEE Wireless Communicationsand Networking Conference, Shanghai, China, April 7–10, 2013. The reviewof this paper was coordinated by Prof. C. P. Oestges.

The authors are with the Institute of Advanced Network Technology andNew Services, and Beijing Engineering and Technology Research Center forConvergence Networks and Ubiquitous Services, University of Science andTechnology Beijing, Beijing 100083, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected];[email protected]).

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.2013.2265280

I. INTRODUCTION

Cooperative relays forward copies of the message of a source to adestination using relaying channels, in addition to the directly source-to-destination (S → D) link, and the diversity gain of the relayingsystem is consequently improved. By using multiple relays, both thediversity gain and radio coverage of a cooperative communicationssystem can be thus improved by combatting the severe multipathfading [1]–[3]. However, in the presence of multiple relays, a smartresource-allocation algorithm is required to guarantee an orthogonalchannel (in either the time or frequency domain) being allocated toeach relay to effectively mitigate the interrelay interference [4]. Asthe number of relays increases, the cost of an orthogonal resourceallocation in terms of spectral efficiency may deteriorate the overallperformance of the cooperative system [5], [6].

In consideration of the aforementioned challenge, relay selectioncan be regarded as one of the most attractive methods to solvethe complicated interference mitigation issue met in the multirelaynetwork systems [7]. In general, the existing relay selection methodscan be classified into two categories, i.e., the opportunistic relayselection and the partial relay selection [8]–[10], where in the former,the SNR of both the source-to-relay (S → R) and relay-to-destination(R → D) links is required by the central unit [8], but in the latter,the SNR of only the S → R or R → D link is necessarily considered[9]. Considering imperfect channel state information (CSI) with ahigh feedback rate and a sufficiently high maximum Doppler shift,the partial relay selection has advantages over the opportunistic relayselection in term of both outage and symbol error probabilities (SEPs)[10]. Moreover, in a cognitive network, the selected relays for thesecondary users should maintain a strict interference threshold in theirsignal transmission to avoid the primary users being interfered bysecondary users [11]–[13].

Currently, most of the studies about relay selection have beenfocused on the scenarios of a constant channel condition [14], [15].A partial relay selection method for the underlay cognitive networksis studied in [14], where the fixed-gain relays are assumed to op-erate in the amplify-and-forward (AF) mode. However, the practicalchannel condition is usually time variant, particularly in high-mobilityscenarios (a large Doppler shift is observed) with an accurate CSIfeedback being infeasible. In this case, performing relay selection byconsidering an outdated CSI feedback would be a suitable method tooptimize the performance of the cooperative systems at a reasonableCSI feedback cost [10]. To the best of the authors’ knowledge, partialrelay selection with an outdated CSI feedback in underlay cognitivenetworks has not been considerably studied in prior works.

In this paper, partial relay selection in underlay cognitive networksis studied, with fixed-gain AF relaying mode and an outdated CSIfeedback being considered. The CSI feedback burden can be greatlyreduced in a partial relay selection scheme due to an outdated CSIof the S → R link being required by the source node. Moreover,utilizing fixed-gain relays rather than adaptively variant gain relayscan further simplify the relaying operation and without sacrificing toomuch performance. As compared with the existing works, the maincontributions of this paper are exhibited as follows: 1) The impact ofthe interference on the primary user during the relay selection processof AF-based underlay cognitive radio networks is analyzed; 2) relayselection with imperfect CSI is studied; 3) partial relay selection withfixed-gain relays instead of full opportunistic relaying is studied; and4) approximated closed-form expressions of some figures of merit,including the outage probability, the SEP, and the channel capacity,have been considered for the proposed scheme.

0018-9545 © 2013 IEEE

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 9, NOVEMBER 2013 4697

Fig. 1. System model of a cognitive network, with cooperative relays beingclosed to a primary user.

The remainder of this paper is organized as follows. Section IIintroduces the system model of partial relay selection with fixed-gainrelays and outdated CSI feedback in underlay cognitive networks.The approximate closed-form expressions of some critical parameters,including the outage probability, the SEP, and the channel capacity,are derived in Section III. Section IV gives out the numerical results.Finally, Section V concludes this paper.

Notation: �{x} and �{x} are the real and imaginary parts of x,respectively. A circularly symmetric complex Gaussian variable withmean a and variance σ2 is denoted by z ∼ CN (a, σ2). γab representsthe SNR of link a → b by considering outdated CSI feedback. γab andγab stand for the mean and estimated SNR of link a → b, respectively.fX(·) and FX(·) represent the probability density function (pdf) andthe cumulative distribution function (cdf) of random variable (RV) X ,respectively. MX(s) denotes the moment-generating function (mgf)of RV X .

II. SYSTEM MODEL

Here, an underlay cognitive network, which consists of primary-userterminal P , secondary source terminal S, and N half-duplex AF fixed-gain relays (as denoted by the set of Ω = {Rn, n = 1, 2, . . . N}) witheach relay having a gain of g and destination terminal D, is considered,as shown in Fig. 1. Each link in the cognitive network system issubjected to zero-mean additive white Gaussian noise (AWGN) withvariance N0.

The fading in all S → Rn(n = 1, . . . , N) links is assumed to beindependent and identically distributed (i.i.d.) Rayleigh-distributedRVs with mean 0 and variance σ2

SR. Similarly, the fading in allRn → D and Rn → P links is assumed to be zero-mean i.i.d.Rayleigh-distributed RVs with variance σ2

RD and σ2RP , respectively.

The channel gain between terminals a and b is denoted by hab, wherea, b ∈ {S,P,D} ∪ Ω. Therefore, we have hab ∼ CN (0, σ2

ab), whereσ2SRi

= σ2SR, σ2

RiD= σ2

RD , and σ2RiP

= σ2RP ∀1 ≤ i ≤ N . More-

over, |hab|2 = (�{hab})2 + (�{hab})2, where �{hab} and �{hab}are i.i.d. zero-mean Gaussian RVs with common variance σ2

ab/2.|hab|2 can be thus formulated as an exponential RV with mean σ2

ab,

and its pdf is given by f|hab|2(x) = (1/σ2ab)e

−(x/σ2ab

).

In the following, without loss of generality, the transmission signalpower in each node is assumed to be Es. Considering cognitivenetwork systems (as shown in Fig. 1), S is communicating with Dthrough relay Rn. s(t) is assumed to be the signal transmitted by S.The received interference signal at node p through interference channelS → Rn → p can be written as

rp(t) = hRnP · g · hSRn · s(t). (1)

Furthermore, the interference signal power received at the primaryuser through the interference channel S → Rn → p can be derived as

InP = Esg2 |hSRn |

2 |hRnP |2 . (2)

The cdf of interference signal power received at the primary usercan be given by

FInP(λ) = 1 − 2

√λ

σ2SRn

σ2RnPEsg2

× K1

(2

√λ

σ2SRn

σ2RnPEsg2

)(3)

where K1(·) is the first-order modified Bessel functions of the secondkind, and λ represents a preset interference threshold signal powerreceived at the primary user.

In the proposed partial relay selection scheme, each candidate relaymay be activated with the probability of Pλ = FInP

(λ) or, otherwise,be dropped from the selection pool with a probability of Pλ = 1 −FInP

(λ). The set of relays (without loss of generality, the cardinalityof this set is assumed to be l, where l ≤ N ) out of N candidatessatisfying the aforementioned interference constraint can be thereforedenoted by Ω = {Rn|InP ≤ λ, n = 1, 2, . . . N}.

For each i.i.d. link S → Rn, n = 1, . . . , N , since the receivedSNR at Rn can be written as γSRn = Es(|h2

SRn|/N0) =

(Es/N0)(�{hSRn})2 + (�{hSRn})2, the pdf of γSRn isthus given by fγSRn

(x) = (1/γSRn)e−(x/γSRn ), where

γSRn = (Esσ2SRn

)/N0 denotes the mean of γSRn . Likewise,γSD and γRnD are exponentially distributed with parametersγSD = (Esσ

2SD)/N0 and γRnD = (Esσ

2RnD)/N0, respectively. For

the i.i.d. case, we can easily derive γSRi= γSR and γRiD = γRD ,

where ∀1 ≤ i ≤ N .

III. APPROXIMATED CLOSED-FORM ANALYSIS

A. PDF and CDF of the Relay-Selection Channel

Here, two scenarios, i.e., l ≥ 1 and l = 0, will be separately ana-lyzed as follows.

1) l ≥ 1: The secondary user selects the optimal relay according tothe following rule, i.e.,

k = arg maxi:Ri∈Ω

(γSRi) (4)

where γSRiis the estimated SNR at time t using the feedback CSI,

which is not the concurrent information due to the existence of thefeedback delay τ . For each a → b link, using the Jakes’ autocorrelationmodel, the correlation coefficient between hab and hab can be rep-resented as ρab = J0(2πτfab), where J0(·) denotes the zeroth-orderBessel function of the first kind, fab is the maximum Doppler Shifton the a → b links, and hab and hab represent the channel coefficientand its estimation, respectively. The relationship between hab and hab

is given by hab = ρabhab +√

1 − ρ2ab · wab, with wab representinga circularly symmetric complex Gaussian RV, whose distribution isidentical to hab.


The conditional pdf of γSRkfor a given l can be derived as [10]

fγSRk|l(γ|l) = l

l−1∑m=0

(−1)m(l−1m

)Ame−Amγ

(m+ 1)(5)

where

Am =(m+ 1)(

m(1 − ρ2SRk) + 1

)γSR

. (6)

Evidently, (5) leads to

FγSRk|l(γ|l) = l

l−1∑m=0

(−1)m(l−1m

)(1 − e−Amγ)

m+ 1. (7)

In the presence of cooperative relays, some combining method, e.g.,maximal-ratio combining, can be employed to optimize the effec-tive SNR as γtotal = γeq + γSD , where γeq = (γSRk

γRkD)/(G+γRkD) represents the SNR of the S → Rk → D link, and G =Es/(g

2N0), as defined by [16].From the Appendix, the joint pdf of γtotal and l is derived as

fγtotal, l �=0(γ, l �= 0) =N∑l=1

(N

l

)P lλP

N−lλ l

l−1∑m=0

(−1)m(l−1m

)m+ 1

× Am

AmγSD − 1

{e−γ/γSD − e−Amγ

}(8)

which leads to

Fγtotal,l �=0(γ, l �= 0) =N∑l=1

(N

l

)P lλP

N−lλ l

×l−1∑m=0

(−1)m(l−1m

)m+ 1

Am · Qm(γ) (9)

where

Qm(x)=1

Am

+1/γSDe−Amx

Am(Am−1/γSD)− e−x/γSD

Am−1/γSD

. (10)

2) l = 0: In this case, relays will be dropped from the selectionpool with probability Pr(l = 0) = PN

λ , if the selection threshold isnot met. The joint pdf and cdf can be derived as

fγtotal, l=0(γ, l = 0) = PNλ

1γSD

e− γ

γSD (11)

Fγtotal, l=0(γ, l = 0) = PNλ

(1 − e

− γγSD

)(12)

respectively. Hence, the unconditional cdf of the received SNR isderived as

Fγtotal(γ) =

N∑l=1

(N

l

)P lλP

N−lλ l

l−1∑m=0

(−1)m(l−1m

)m+ 1

Am

·Qm(γ) + PNλ

(1 − e

− γγSD

). (13)

B. Outage Probability Analysis

For a preset threshold γT , from (13), the outage probability of thepartial relay selection scheme with an outdated CSI feedback can be

derived as

Fγtotal(γT ) =

N∑l=1

(N

l

)P lλP

N−lλ l

l−1∑m=0

(−1)m(l−1m

)m+ 1

Am

× Qm(γT ) + PNλ

(1 − e

− γTγSD

). (14)

C. SEP Analysis

Using [17, Eq. (2.3–10)] and [18, Eq. (4)], the SEP of the proposedmethod is approximated as

Pe =β√2π

∞∫0

Fγtotal

(t2

η

)e−

t2

2 dγ

=β

2

N∑l=1

(N

l

)P lλP

N−lλ l

l−1∑m=0

(−1)m(l−1m

)m+ 1

Am · Gm

+β

2PNλ

(1 −

√ηγSD

2 + ηγSD

)(15)

where

Gm =1

Am

+1/γSD

Am(Am − 1/γSD)×√

η

η + 2Am

− 1(Am − 1/γSD)

√η

η + 2/γSD

(16)

and β and η are modulation-specified constants determined by modu-lation format.

D. Channel Capacity Analysis

In the presence of outdated CSI feedback, the approximate closed-form expression for the channel capacity of the proposed partial relayselection can be derived as

C= B

2

∞∫0

log2(1+γ)fγtotal,l=0(γ, l=0)dγ

+B

2

∞∫0

log2(1+γ)fγtotal,l�=0(γ, l �= 0)dγ

=B

2 ln 2

[PNλ e1/γSDE1

(1

γSD

)+D(N, l, γSR, γSD)

](17)

where

D(N, l, γSR, γSD) =

N∑l=1

(N

l

)P lλP

N−lλ l ·

l−1∑m=0

(−1)m(l−1m

)m+ 1

× θ(m, γSR, γSD) · Am

AmγSD − 1(18)

B stands for the signal bandwidth

θ(m, γSR, γSD)= γSDe1/γSDE1

(1

γSD

)− 1Am

· eAm ·E1(Am)

(19)

and E1(x) =∫∞x

(e−t/t)dt.


Fig. 2. Outage probability versus the average SNR of the S → D links withλ = 10 and ρSRk

= 0.707.

IV. NUMERICAL RESULTS

Here, without loss of generality, the relaying channels and theirinterference on the primary user are assumed to satisfy the followingconstraints, i.e., γSR = 1.5γSD , γRD = 1.8γSD , and γRP = 0.8γSD .Binary phase-shift keying modulation is considered in this paper, andthis implies that β = 1 and that η = 2. In particular, to simplify theanalysis, Es = 1, N0 = 1, and g = 1 are assumed.

The outage probability as a function of γSD for different N isshown in Fig. 2. Although using more relays implies obtaining ahigher probability of selecting the optimum relay at low SNR, furtherincreasing SNR may degrade the selectivity of the optimum relay dueto severer interference being added to the primary user. After the SNRapproaching a certain level (15 dB in this simulation), further increas-ing SNR may cause all the relays being dropped from the candidatepool. By keeping N = 3 and λ = 10 unchanged, for different ρSRk

,a smaller ρSRk

implies faster changes in channel state, and the outageprobability is therefore a monotonically decreasing function of ρSRk

,as shown in Fig. 3. Note that the selected relay may no longer beoptimum due to imperfect CSI feedback (i.e., with outdated CSI).Outage probability as a function of an SNR for different λ is alsoshown in Fig. 4, with N = 3 and ρSRk

= 0.707 being considered. Asλ → 0, all relays are dropped from the selection pool, and only theS → D link is used for data transmission. In this case, increasing λimplies more relays could become a candidate of the best relay, andthe outage probability is reduced accordingly.

SEP as a function of SNR is shown in Fig. 5, where an optimumSNR can always be found to obtain the lowest SEP for each N . For aspecific SNR level in the S → D link, more candidate relays impliesbetter SEP performance due to an improved spatial diversity gain.However, increasing SNR beyond a certain threshold may also degradethe SEP of the proposed relay selection. The effect of the channelcorrelation coefficient ρSRk

on SEP performance of the partial relayselection with outdated CSI feedback is also shown in Fig. 6. Similarto the outage probability performance, SEP is also a monotonicallydecreasing function of ρSRk

. Similarly, the SEP performance is also amonotonically decreasing function of λ.

The channel capacity as a function of SNR for the proposed relayselection scheme is described in Fig. 7. When SNR is smaller than10 dB, the channel capacity is a monotonically increasing functionof the number of available relays. However, the number of candidate

Fig. 3. Outage probability versus the average SNR of the S → D links withλ = 10 and N = 3.

Fig. 4. Outage probability versus the average SNR of the S → D links withN = 3 and ρSRk

= 0.707.

relays may decrease due to the interference from the secondary user,and this effect will consequently degrade the channel capacity. Basi-cally, using an accurate CSI feedback is beneficial to improving thechannel capacity as compared with that with outdated CSI, however,at the cost of a heavier CSI feedback burden. From this point of view,partial relay selection with outdated CSI feedback is a good choiceto optimize the tradeoff between the CSI feedback and the channelcapacity improvement.

The effect of ρSRkon the channel capacity is also analyzed in

Fig. 7, with N = 3 and λ = 10 being assumed in this simulation.The capacity with an imperfect CSI feedback is only slightly worsethan that with perfect channel estimates in a low-SNR regime, butthis performance gap diminishes as the SNR increases. Similarly, thecapacity is affected by λ, as shown in Fig. 7, where a larger λ implies ahigher capacity in the low-SNR regime but with the performance gaindiminishing as the SNR increases.


Fig. 5. SEP versus the average SNR of the S → D links with λ = 10 andρSRk

= 0.707.

Fig. 6. SEP versus the average SNR of the S → D links with λ = 10 andN = 3.

V. CONCLUSION

The impact of an imperfect channel estimation on the partial relayselection in AF relaying cooperative communications systems hasbeen studied, with the approximate closed-form expressions for somecritical figures of merit, including the probability characteristic of thesecondary user’s end-to-end SNR, the outage probability, the SEP,and the channel capacity, being derived. The validity of the proposedtheoretical approximation on the critical figures of merit, including theoutage probability, the SEP, and the channel capacity, was proven viasimulations, and the theoretical analysis matches the correspondingnumerical results well. It has been also shown in the numericalresults that some other parameters, including the number of relays,the channel correlation coefficient, and the interference threshold,significantly affect the system performance in the presence of multiplecandidate relays, and an optimum solution in terms of both outageprobability and SEP performance can always be found within the SNRrange of (0, 10 dB).

Fig. 7. Channel capacity versus the average SNR of the S → D links.

APPENDIX

APPROXIMATION OF fγtotal,l �=0(γ, l �= 0)

Using (7) and [19, Eq. (3.324.1)], the conditional cdf is derived as

Fγeq|l(γ|l) =Pr[γeq < γ|l]

= l

l−1∑m=0

(−1)m(l−1m

)m+ 1

×[1−2e−Amγ

√AmγG

γRD

K1

(2

√AmγG

γRD

)](20)

where Pr{·} stands for the probability distribution, and fγRkD(γ) =

(1/γRD)e−(γ/γRD). The joint pdf of γeq and l can be derived as

Fγeq,l �=0(γ, l �= 0)=N∑l=1

(N

l

)P lλP

N−lλ l

l−1∑m=0

(−1)m(l−1m

)m+1

Zm (21)

where

Zm = 1 − 2e−Amγ

√AmγG

γRD

K1

(2

√AmγG

γRD

)(22)

and K1(x) ≈ (1/x). Hence, (21) can be approximated as

Fγeq, l �=0(γ, l �= 0) ≈N∑l=1

(N

l

)P lλP

N−lλ l

l−1∑m=0

(−1)m(l−1m

)m+ 1

× [1 − e−Amγ ] (23)

which leads to

fγeq,l �=0(γ, l �= 0) =N∑l=1

(N

l

)P lλP

N−lλ l

l−1∑m=0

(−1)m(l−1m

)m+ 1

× Ame−Amγ . (24)

The mgf of γtotal is derived as

Mγtotal(s) = Mγeq(s)MγSD

(s) (25)


where

Mγeq(s)=

N∑l=1

(N

l

)P lλP

N−lλ l

l−1∑m=0

(−1)m(l−1m

)m+1

Am

s+Am

(26)

MγSD(s) =

∞∫0

e−sγfγSD(γ)dγ =

1/γSD

s+ 1/γSD

(27)

with fγSD(γ) = (1/γSD)e−(γ/γSD).

By performing inverse Laplace transform on Mγtotal(s), the joint

pdf of γtotal and l can be derived as

fγtotal,l �=0(γ, l �= 0) =N∑l=1

(N

l

)P lλP

N−lλ l

l−1∑m=0

(−1)m(l−1m

)m+ 1

× Am

AmγSD − 1{e−γ/γSD − e−Amγ}. (28)

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewers for theircritical comments, which greatly improved this paper.

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A Differential Feedback Scheme Exploiting theTemporal and Spectral Correlation

Mingxin Zhou, Leiming Zhang, Member, IEEE,Lingyang Song, Senior Member, IEEE, andMerouane Debbah, Senior Member, IEEE

Abstract—Channel state information (CSI) provided by a limited feed-back channel can be utilized to increase system throughput. However, inmultiple-input–multiple-output (MIMO) systems, the signaling overheadrealizing this CSI feedback can be quite large, whereas the capacity ofthe uplink feedback channel is typically limited. Hence, it is crucial toreduce the amount of feedback bits. Prior work on limited feedbackcompression commonly adopted the block-fading channel model, whereonly temporal or spectral correlation in a wireless channel is considered.In this paper, we propose a differential feedback scheme with full use ofthe temporal and spectral correlations to reduce the feedback load. Then,the minimal differential feedback rate over a MIMO time–frequency (ordoubly)-selective fading channel is investigated. Finally, the analysis isverified by simulation results.

Index Terms—Correlation, differential feedback, multiple-inputmultiple-output (MIMO).

I. INTRODUCTION

In multiple-input–multiple-output (MIMO) systems, channel adap-tive techniques (e.g., water-filling, interference alignment, beamform-ing, etc.) can enhance the spectral efficiency or the capacity of the

Manuscript received November 25, 2012; revised March 18, 2013; ac-cepted May 3, 2013. Date of publication June 5, 2013; date of currentversion November 6, 2013. This work was supported in part by the National973 project under Grant 2013CB336700, by the National Natural ScienceFoundation of China under Grant 61222104 and Grant 61061130561, by thePh.D. Programs Foundation of the Ministry of Education of China underGrant 20110001110102, and by the Opening Project of the Key Laboratory ofCognitive Radio and Information Processing (Guilin University of ElectronicTechnology). The review of this paper was coordinated by Prof. X. Wang.

M. Zhou and L. Song are with the State Key Laboratory of Advanced OpticalCommunication Systems and Networks, School of Electronics Engineeringand Computer Science, Peking University, Beijing 100871, China (e-mail:[email protected]; [email protected]).

L. Zhang is with Huawei Technologies Company Ltd., Beijing 100095,China (e-mail: [email protected]).

M. Debbah is with SUPELEC, Alcatel-Lucent Chair in Flexible Radio,91192 Gif-Sur-Yvette, France (e-mail: [email protected]).

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.2013.2266379

0018-9545 © 2013 IEEE

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Partial Relay Selection With Fixed-Gain Relays and Outdated CSI in Underlay Cognitive Networks