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DOI 10.1007/s11277-012-0518-5

Performance Analysis of Partial Relay Selection

in Cooperative Spectrum Sharing Systems

Daniel Benevides da Costa · Sonia Aïssa · Charles Casimiro Cavalcante

Published online: 1 February 2012

© Springer Science+Business Media, LLC. 2012

Abstract In recent years, cooperative diversity and cognitive radio have received consid-erable attention from the wireless communications community due to its performance gains and spectrum utilization improvements, respectively, when compared to the traditional com-munications techniques. In one hand, cooperative diversity combats the signal fading caused by the multipath propagation. On the other hand, cognitive radio offers an efficient way to enhance spectrum utilization. However, these two promising technologies have been usually studied apart. In this paper, motivated by the important benefits of cooperative commu-nications, we introduce decode-and-forward relays in primary/secondary spectrum sharing systems with the aim to provide a higher performance for the secondary user. Our analysis considers a partial relay selection in the first-hop transmission, with the relay nodes pertaining to the selected cluster positioned relatively close together (location-based clustering). The end-to-end performance of the secondary communication is investigated for several number of fading channels, such as Generalized Gamma (orα−µ), Nakagami-m, and Rayleigh. In particular, considering Rayleigh fading channels, closed-form expressions for the average bit error rate and outage probability are derived. Illustrative numerical examples are provided and the influence of the number of relays, fading parameters, and noise power imbalance between the hops on system performance is discussed.

Keywords Cooperative diversity·End-to-end performance·Relay selection·

Spectrum sharing systems

D. B. da Costa

Federal University of Ceara (UFC), Sobral, CE, Brazil e-mail: danielbcosta@ieee.org

S. Aïssa

INRS-EMT, University of Quebec, Montreal, QC, Canada e-mail: aissa@emt.inrs.ca

C. C. Cavalcante (

B

)

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1 Introduction

Among the promising wireless communication techniques that have emerged recently are cooperative diversity [1–3] and cognitive radio [4–6]. Both techniques have shown great potential for improving the performance of wireless networks and meeting the demands of future wireless applications. Cooperative communications combat signal fading due to mul-tipath propagation by enabling a set of cooperative relays to forward the received information to destination. This regime exploits spatial diversity through cooperation among distributed antennas belonging to multiple terminals in wireless systems. Cognitive radio, on the other hand, offers an efficient way to improve spectrum utilization. In this case, spectrum shar-ing concepts allow secondary users (SUs) to access the licensed spectrum provided that the primary users (PUs) communication is not compromised. For such an operation, a maximum allowable interference level at the PU receivers (called interference temperature) is defined, and SUs should take into account this threshold during the transmission in order to adjust their transmit powers not to damage the quality reception of the PUs.

Despite the importance of studying the performance of spectrum sharing systems in a cooperative diversity scenario, the number of works in this research area is still exiguous (see for instance [7–11] and references therein). In addition, all previous works have assumed a Rayleigh fading scenario and, therefore, the impact of fading parameters of other general fading scenarios in the end-to-end performance still remains to be examined.

Regarding relay selection schemes, partial relay selection was lately proposed in [12] and finds applicability in practical ad-hoc and sensor networks. In such selection strategy, the relays are assumed to be positioned relatively close together and are selected by a long-term routing process. Insightful discussions about this selection strategy can be found in [13] for dual-hop fixed-gain relaying scenarios. For instance, it is shown in [13] that, depending on the channel quality of the hops, the use of only two relays is enough to achieve high perfor-mance and overcome the relaying cost. In practice, this means that the required instantaneous feedback from a large number of relays is not necessary (a feedback from only two relays is sufficient) and thus the system complexity can be reduced significantly. Interestingly, a similar behavior can also be observed when decode-and-forward (DF) relays are employed in spectrum-sharing systems, as will be seen here from the numerical results.

Although the use of dual-hop cooperative networks with partial relay selection in spec-trum-sharing systems seems to be very promising from a practical point of view, to the best of the authors’ knowledge, up to now there are no works in the literature that investigate the performance and benefits of such system model in generalized fading scenarios. In this paper, assuming Generalized Gamma (orα−µ[14]), Nakagami-m[15], and Rayleigh fading sce-narios, we investigate the end-to-end performance of dual-hop cooperative spectrum-sharing systems, with partial relay selection in the first-hop transmission. The average bit error rate (BER) and the outage probability of the SU communication are studied. For the Generalized Gamma and Nakagami-mfading scenarios, the analytical formulations are given in terms of multifold integrals. On the other hand, for Rayleigh fading scenarios (a special case of the two previous ones), closed-form expressions are obtained for these performance metrics. In our analysis, DF relays are employed to help in the communication process. These kinds of relays demodulate and decode the transmitted signal from the source before re-encoding it prior to transmission toward the destination. Illustrative numerical examples are provided and the influence of the number of relays, fading parameters, and noise power imbalance between the hops on system performance is discussed.

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system model’s functionality are performed for a better understanding by the readers. Also, the channel models considered in this paper are briefly presented. Section3begins by pro-viding a unified analytical framework for the BER and outage probability analysis of the system under study. Unfortunately, closed-form expressions for these performance metrics are not attained for the Generalized Gamma and Nakagami-mfading scenarios. However, for Rayleigh fading environments, closed-form expressions are achieved. Section4shows some numerical results, sustained by insightful discussions. Finally, in Sect.5, the main conclu-sion of this paper is drawn. It is also shown that the outage probability (OP) can readily be achieved from our formulations, and the guidelines for such are presented. Hereafter,FY(·) and fY(·)are used to denote the cumulative distribution function (CDF) and the probability density function (PDF) of an arbitrary random variableY, respectively.

2 System and Channel Models

2.1 System Model

We consider a dual-hop cooperative spectrum-sharing system where PUs and SUs share the same frequency band in a given geographical area, as shown in Fig.1. PU transmitters are not taken into account since the focus of this paper is on the SU communication. To help in this latter, the SU source has the availability of an arbitrary number of relay clusters from which one cluster is chosen based on the average signal-to-noise ratio (SNR)1and instan-taneous channel state information which is limited to the SU source’s neighborhood. This is illustrated in Fig.1a. Once the cluster of relays is selected, the SU source will have an arbitrary number of DF relays inside this cluster for helping in the SU communication. In this case, the source decides by itself how many relays pertaining to the selected cluster will participate in the selection. After defining the number of relays participating in the selection (represented by the dotted square in Fig.1b), the SU source continuously monitors the qual-ity of its connectivqual-ity with these relays via transmission of a local feedback. Based on this information, the SU source selects the best link (source-relay) for data transmission, which means the one with highest instantaneous SNR (represented by R3in Fig.1b). The readers are referred to [12] for more details about this selection strategy, called partial relay selection, in cooperative communications. In this paper, we go beyond the pioneering purpose of [12] by applying this promising selection scheme in a spectrum-sharing system. Note that the SU transmission is constrained by power limitation not to harm the PU quality reception. This will be explained later.

As relays in the selected cluster are close together, this guarantees the same average effec-tive noise power (AENP) for all the links pertaining to the first hop and to the second hop. The AENP in the first hop is defined byρ1=ES Rk

2

1] =E[α1/σ12], withE[·]denoting expectation,βS Rk (k = 1, . . . ,L) are the channel gains of links originating from the SU transmitter,α1 is the interference-channel gain represented by a dotted arrow in Fig.1b, andσ12is the noise variance. For the second-hop, we have only two links to be considered and the AENP is defined byρ2 = E[β2/σ22] =E[α2/σ22], where, analogously to the first-hop case,β2, α2, andσ22 represent the channel gain pertaining to the SU communication, the interference-channel gain, and the noise variance, respectively. All channel gains are assumed to be mutually independent with unit mean. The relays operate in a half-duplex

1In a given cluster, the relays are assumed to be close together so that the link source-relay undergoes the

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source Selected Cluster destination R4 R1 R5 R6 RM

...

R2 R3 L relays participating in the

selection receiver receiver source Cluster 1 destination SU Cluster 2

...

Cluster n (a) receiver receiver (b) 1, W1

2, W2

SR3

P1TX P 2 TX

2

1 2

( ) ( ) PU PU PU PU SU SU SU

Fig. 1 Dual-hop cooperative spectrum-sharing system:(a)The SU source selects a cluster of relays with the highest average SNR;(b)The SU communication is performed through the best relay chosen from a given subset of the selected cluster

mode, and the additive noise terms are zero-mean mutually independent Gaussian processes with variancesσ12andσ22as aforementioned. Although different mean values can reflect the effects of path-loss, the unit mean assumption simplifies analysis and efficiently delivers key observations.

In a spectrum sharing system, the SU is allowed to operate in the licensee’s spectrum as long as the total interference power it causes to the PU receiver remains below a certain threshold. For such, in the first-hop, the SU source listens to the interference channelα1. Then, the SU source adjusts its transmit powerP1TX(α1)so that the allowable interference levelW1is satisfied, i.e.,

P1TX(α1)=

P1, α1 WP11 W1

α1, α1>

W1

P1

. (1)

From (1), note that whenα1is less thanW1/P1, the SU source can transmit at maximum powerP1. After this power adjustment, a partial relay selection is performed. In other words, from a set ofLout ofMrelays, the SU source selects the best source-relay link for the trans-mission, i.e., the link which provides the maximumβS Rk

2

1. Denoting the instantaneous SNR of each link as

γS Rk =

P1TX(α1)βS Rk σ12 =

⎧ ⎨

PS Rk σ2

1

, α1 WP11 WS Rk

α1σ12

, α1> WP11

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it follows that the instantaneous SNR of the first-hop can be written as

γ1= max k=1,...,L

γS Rk

. (3)

In the SU second-hop transmission, the selected relay listens to the interference channel

α2 and adjusts its transmit power P2TX to satisfy the interference power levelW2. This is done similar to (1) but replacing:P1 → P2,W1 →W2, andα1 →α2. Consequently, the instantaneous SNRγ2of the second-hop can be expressed as (2) making the aforementioned substitutions and also replacingβS Rkbyβ2andσ12byσ22.

It is assumed that both, the SU source and the selected relay, have perfect knowledge of their respective interference channel gains. This can be obtained by direct feedback from the PU receivers or by indirect feedback from a third-party such as a band manager which mediates between the PUs and SUs.2 As an alternative to the feedback schemes, the SU transmitters (source and selected relay) can obtain the information through periodic sensing of pilot signals from the PU receivers assuming the channel reciprocity [19]. In addition, it is noteworthy that, for the relay selection, the PU source continuously monitors the quality of its connectivity with the relays via the transmission of a local feedback [12].

2.2 Channel Models

The Generalized Gamma fading model (orα-µfading model [14]) considers that the sig-nal is composed by multipath clusters propagating in a non-homogeneous environment. It includes as special cases important other fading models, such as Nakagami-mand Weibull. (Therefore, the Negative Exponential, One-Sided Gaussian, and Rayleigh are also special cases of it). It can be written in terms of two physical parameters, namelyχandµ. Roughly speaking, the parameterχ is related to the non-linearity of the environment, whereas the parameterµis associated to the number of multipath clusters. Employing this fading model to characterize the channels pertaining to the dual-hop cooperative spectrum sharing system under study, the PDF and CDF of the channel gains3can be written as

fξ(ξ )=

χ µµξχ µ2 −1

2Γ (µ) exp

−µξχ2 , (4)

Fξ(ξ )=1−

Γµ, µ ξχ2

Γ (µ) , (5)

where: (a) whenξ =βS Rk orξ =α1, thenµ µ1andχ χ1, and (b) whenξ =β2 or ξ =α2, thenµµ2andχ χ2. Also, in (4) and (5),Γ (·)denotes the Gamma function [20, Eq. 8.310.1] andΓ (·,·)represents the incomplete Gamma function [20, Eq. 8.350.2].

It is noteworthy that by settingχ =2 andµ=1, the Generalized Gamma fading sce-nario reduces to the Rayleigh one, whereas by settingχ =2 andµ=m, the Generalized Gamma fading scenario reduces to the Nakagami one with fading parameterm. Therefore, the respective PDFs and CDFs for these two other fading models can be easily attained from (4) and (5) by making the appropriate substitutions.

2Although CSI feedback between primary and secondary users still seems impractical, the band manager,

which can exchange control information between primary and secondary users, was introduced as a virtual network component [16]. CSI estimation without feedback is also available through the methodology pre-sented in [17]. In practice, interference channel management between the primary and secondary systems is considered in [18].

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3 Performance Analysis

In this Section, based on the system model described above, a unified analytical framework for the average BER and outage probability of the SU communication is presented. Firstly, given that DF relays are considered, the average BER can be obtained as [21]

Pe=Pe1+Pe2−2Pe1Pe2, (6)

wherePe1 andPe2 denote the average BER of the first-hop and second-hop, which can be

derived according to [22] as

Pei = 1 √ 2π ∞ 0 Fγi t2 c exp −t 2 2

dt, i=1,2, (7)

wherecis a constant related to the modulation format. As partial relay selection is employed in the first-hop, from the order statistics theory,1(γ )can be expressed as

1(γ )= [FγS Rk(γ )]

L. (8)

In order to getS Rk(γ ), let Z =WS Rk/σ 2

1 andX = α1. Then, based on the statistical theory [23], the PDF ofγS Rk can be written as

fγS Rk(γ )= σ12 P1 FX W 1 P1

fβS Rk

γ σ12 P1 + ∞ W1 P1

x fZx)fX(x)d x

= σ 2 1 P1 FX W1 P1

S Rk

γ σ12 P1 + ∞ W1 P1 σ12 W1

x fβS Rk

γ xσ12 W1

fX(x)d x. (9)

Unfortunately, assuming a Generalized Gamma fading scenario or a Nakagami-mfading scenario, a closed-form expression to (9) is not possible to be attained. Because of this, we will not proceed further in the analytical derivation for these two fading models so that, in Sect.4, the performance analysis for these two cases will be investigated numerically in terms of multifold integrals. However, for Rayleigh fading channels, it is possible to arrive at a closed-form expression and it is presented next. Knowing thatβS Rkandα1are exponentially distributed with unit mean, (9) can be rewritten after transformation of variates as

S Rk(γ )= σ

2 1

P1

e

γ σ12

P1

1−eW1

P1

+W

2 1

P1

W1+P1+γ σ12

(W1+γ σ12)2

eW1+γ σ12

P1 . (10)

By integrating (10) with respect toγ, it follows that

S Rk(γ )=1−e

γ σ12

P1 + γ σ 2 1

W1+γ σ12

eW1+γ σ12

P1 . (11)

Finally, substituting (11) into (8) and making use of the binomial theorem [24, Eq. 3.1.1], we obtain

1(γ )=

L

ϕ=0 L−ϕ

l=0 L ϕ L −ϕ l

(−1)l

γ σ12

W1+γ σ12 ϕ

elγ σ12

P1 e−ϕ

W1+γ σ12

P1

(7)

Subsequently, plugging (12) into (7) and performing the required integral, the average BER of the first-hop assuming Rayleigh fading can be attained in closed form as

Pe1=

L

ϕ=0 L−ϕ

l=0 L ϕ L −ϕ l

(−1)l

c

2 e −ϕW1

P1

P1

c P1+2(ϕ+1)σ12

×1F1

ϕ;1

2;

(ϕ+1)W1

P1 +

c W1 2σ12

2W1

σ12

Γ (ϕ+12)

Γ (ϕ)

×1F1

1 2+ϕ;

3 2;

(ϕ+1)W1

P1 +

cW1 2σ12

, (13)

where1F1(·; ·; ·)is the Kummer confluent hypergeometric function [24, Eq. 13.1.2]. Turning our attention to the second-hop transmission at the SU side, for Rayleigh fading channels it can be easily seen that the CDF ofγ2 has the same form as (11). Then, making the appropriate substitutions in (11), such CDF can be written as

2(γ )=1−e

−γ σ

2 2

P2 + γ σ 2 2

W2+γ σ22

eW2+γ σ22

P2 . (14)

Now, substituting (14) into (7) and solving the required integral, the average BER of the second-hop is obtained as

Pe2 =

1 2

1+(e− W2

P2 1)

c P2

c P2+2σ22 −

e cW2

22

πc W2 2σ22 ×erfc

W2(c P2+2σ22) 2P22

,

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where erfc(·)is the complementary error function [24, Eq. 7.1.2].

Finally, substituting (13) and (15) into (6), an exact easy-to-evaluate expression for the average BER of cooperative spectrum-sharing systems using DF relays, with partial relay selection, and undergoing Rayleigh fading is attained. As far as the authors are aware, this expression has never been presented in the literature before. In addition, for the Generalized Gamma and Nakagami-mfading scenarios, the average BER can be numerically evaluated by following the steps described in this Section. Unfortunately, closed-form expressions are not possible to be achieved, but the authors will put efforts to further investigate this in future works.

Another important performance measure is the outage probability (OP). In dual-hop DF relaying systems, an outage event occurs if either one of the two hops is in outage [21]. Denoting the outage threshold value, below which the signal undergoes outage, asγth, and using statistical probability theorem, the OP can be mathematically expressed as

Pout=Pr[min{γ1, γ2}< γth] =1−Pr[γ1> γth]Pr[γ2> γth]

=1−(1−Pr[γ1≤γth])(1−Pr[γ2≤γth])=Fγ1(γth)+Fγ2(γth)−Fγ1(γth)Fγ2(γth).

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By substituting (12) and (14) into (16), a closed-form expression for the outage proba-bility of cooperative spectrum-sharing systems using DF relays, with partial relay selection, and undergoing Rayleigh fading is attained. for the Generalized Gamma and Nakagami-m

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4 Numerical Plots and Simulations

We now show illustrative numerical examples for the performance metrics derived in the previous section. For the Rayleigh fading scenario, our analytical formulations have been validated by means of Monte Carlo simulations but, due to the proximity of the curves and in order to avoid entanglement, simulation data have been omitted in some graphics. In addition, for the Nakagami-mand Generalized Gamma fading scenarios, the curves have been plotted numerically by following the steps described in Sect.3. Results were generated considering a binary phase shift keying (BPSK) scheme, which corresponds to settingc=2 in the derived expressions.

Figures2and3plot the average BER in terms of the AENP of each hop for Rayleigh and Nakagami-mfading scenarios, respectively. The Nakagami-mfading parameters have been set tom1 =m2 =2. As the channel gains have unit mean, it follows thatρ1 =1/σ12and

ρ2=1/σ22. For illustration purposes, it is assumed thatρ1=ρ2. We keepP1=P2=20 dB and vary the interference powersW1 = W2. As expected, when these latter increase, the performance improves. Analyzing the influence of the number of relays on the average BER performance, it can be noticed that the curves are very close whenL>1, being practically identical for high values ofρ1=ρ2. This allows us to say that choosing no more than two out ofM relays to participate in the selection is sufficient to achieve a good performance.

Fig. 2 Average BER of dual-hop cooperative spectrum-sharing systems with partial relay selection for different values ofL

and assuming Rayleigh fading

Fig. 3 Average BER of dual-hop cooperative spectrum-sharing systems with partial relay selection for different values ofL

and assuming Nakagami-m

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Fig. 4 Average BER of dual-hop cooperative spectrum-sharing systems with partial relay selection for different values of the Nakagami-mfading parametersm2and, by setting

L=2 andm1=2

Fig. 5 Average BER of dual-hop cooperative spectrum-sharing systems with partial relay selection for different fading scenarios and assumingL=2

In practice, this means that the required instantaneous feedback from a large number of relays is not necessary (a feedback from only two relays is sufficient) and thus the system complexity can be reduced significantly. This fact was previously observed in [13] for fixed-gain relays (but without spectrum-sharing concepts), and now it is also attested in spectrum-sharing sys-tems employing DF relays. In addition, the same conclusions also hold when the Generalized Gamma fading scenario is investigated but, in order to avoid repetition of the plots, we opt to not include graphics showing the variation ofLfor this fading scenario.

Figure4plots the average BER in terms of the AENP of each hop for Nakagami-m assum-ingP1 = P2 =20 dB,W1 = W2 =0 dB, andL =2. By settingm1 =2, the variation of the fading parameterm2is investigated. As the Nakagami-mfading model has one degree of freedom (given by the parameterm) more than the Rayleigh one, this contributes for the increasing of the diversity gain. Note that the diversity gain for the Rayleigh fading scenario is always the same (please check Fig.2). On the other hand, for the Nakagami-mfading, the diversity gain depends on the value of the fading parameters, which is attested by checking the slopes of the curves in Fig.4. Then„ whenm2increases, the diversity gain also increases. This was expected since the fading parametermdescribes the severity of the fading.

Figure5performs a comparison of the average BER, considering BPSK signaling, w.r.t.

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Fig. 6 Average BER of dual-hop cooperative spectrum-sharing systems with partial relay selection assumingL=2

Fig. 7 Outage probability versus

W1=W2of cooperative

spectrum-sharing systems with partial relay selection for Rayleigh fading scenarios

Gamma has one more DoF than the Nakagami-mand two more than the Rayleigh, the curves are showing the impact of such higher number of DoF for them. It worths to mention that, besides the higher number of DoF, the Generalized Gammma distribution is also important being considered due to the fact it is more general and includes the other ones as special cases, what makes the analysis more relevant.

Figure6sketches the average BER versusρ1for the Rayleigh fading scenario by con-sidering the following parameters:P1 = P2 = 10 dB,W1 = W2 = −5 dB, and L = 2. The influence of the noise power imbalance on the BER performance is investigated. Note that whenρ2increases, i.e., whenσ22decreases, the performance improves. This leads to the conclusion that such power imbalance can be either advantageous or harmful for the overall system performance. Whenρ2< ρ1, it is detrimental; otherwise, it is beneficial.

Figures7and8depict the outage probability performance in different situations. One can note that when the threshold increases the outage probability also increases. Further, in Fig.7

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Fig. 8 Outage probability versus

γthof cooperative

spectrum-sharing systems with partial relay selection for Rayleigh fading scenarios

5 Concluding Remarks

The end-to-end performance of dual-hop cooperative spectrum-sharing systems with DF relaying and partial relay selection was investigated. More specifically, a closed-form expres-sion for the average BER was derived. Illustrative numerical results were provided and it was observed that the selection based on only two relays is sufficient from a practical point of view. This fact plays a crucial role in the design of future cognitive radio systems. In addition, we would like to emphasize that although our analytical derivations departed from a clustered setting, they can be readily extended to general non-clustered frameworks.

Acknowledgments D. B. da Costa would like to thank the Ceará Council of Scientific and Technological Development (Grant no. BP1-0031-00090.01.00/10) by the financial support and C. C. Cavalcante thanks the partial financial support from National Council of Scientific and Technological Development (CNPq) under the grant no. 307681/2008-4.

References

1. Laneman, J. N., Tse, D. N. C., & Wornell, G. W. (2004). Cooperative diversity in wireless networks: Efficient protocols and outage behavior.IEEE Transactions on Information Theory, 50(12), 3062–3080. 2. Sendonaris, A., Erkip, E., & Aazhang, B. (2003). User cooperation diversity—part I: System

descrip-tion.IEEE Transactions on Communications, 51(11), 1927–1938.

3. da Costa, D. B., & Aíssa, S. (2010). Performance analysis of relay selection techniques with clustered fixed-gain relays.IEEE Signal Processing Letters, 17(2), 201–204.

4. Mitola, J., et al. (1999). Cognitive radio: Making software radio more personal. IEEE Personal Communications,6(4), 13–18.

5. Gastpar, M. (2007). On capacity under receive and spatial spectrum-sharing constraints.IEEE Trans-actions on Information Theory, 53(2), 471–487.

6. Musavian, L., & Aïssa, S. (2009). Fundamental capacity limits of cognitive radios in fading environments with imperfect channel information.IEEE Transactions on Wireless Communications, 57(11), 3472– 3480.

7. Musavian, L., & Aïssa, S. (2009). Cross-layer analysis of cognitive radio relay networks under quality of service constraints. InProceedings of IEEE Vehicular Technology Conference (VTC-S’09), Barcelona, Spain(pp. 1–5).

8. Zhang, Q., Jia, J., & Zhang, J. (2009). Cooperative relay to improve diversity in cognitive radio networks.IEEE Communication Magazine, 47(2), 111–117.

(12)

10. Asghari, V., & Aïssa, S. (2010). Cooperative relay communication performance under spectrum-sharing rsource requirements. In Proceedings of IEEE International Conference on Communications (ICC), Cape Town, Africa.

11. Luo, L., Zhang, P., Zhang, G., & Qin, J. (2011). Outage performance for cognitive relay networks with underlay spectrum sharing.IEEE Communication Letters, 15(7), 710–712.

12. Krikidis, I., Thompson, J., McLaughlin, S., & Goertz, N. (2008). Amplify-and-forward with partial relay selection.IEEE Communication Letters, 12(4), 235–237.

13. da Costa, D. B., & Aïssa, S. (2009). End-to-end performance of dual-hop semi-blind relaying systems with partial relay selection.IEEE Transactions on Wireless Communications, 8(8), 4306–4315. 14. Yacoub, M. D. (2007). Theα−µdistribution: A physical fading model for the Stacy distribution.IEEE

Transactions on Vehicular Technology, 56(1), 27–34.

15. Nakagami, M. (1960).The m-distribution—A general formula of intensity distribution of rapid fading, statistical methods in radio wave propagation. Elmsford: Pergamon.

16. Peha, J. M. (2005). Approaches to spectrum sharing.IEEE Communications Magazine, 43(2), 10–12. 17. Zhang, R., & Liang, Y. C. (2008). Exploiting hidden power-feedback loops for cognitive radio. In

Proceedings of 3rd IEEE DySPAN(pp. 1–5).

18. Buljore, S., Harada, H., Filin, S., Houze, P., Tsagkaris, K., Holland, O., Nolte, K., Farnham, T., & Iva-nov, V. (2009). Architecture and enablers for optimized radio resource usage in heterogeneous wireless access networks: The IEEE 1900.4 working group.IEEE Communications Magazine, 47(1), 122–129. 19. Zhao, Q., Geirhofer, S., Tong, L., & Sadler, B. M. (2008). Opportunistic spectrum access via periodic

channel sensing.IEEE Transactions on Signal Processing, 56(2), 785–796.

20. Gradshteyn, I. S., & Ryzhik, I. M. (2007). Table of integrals, series, and products(7th ed.). San Diego, CA: Academic.

21. Hasna, M. O., & Alouini, M.-S. (2003). End-to-end performance of transmission systems with relays over Rayleigh-fading channels.IEEE Transactions on Wireless Commmunications, 2(6), 1126–1131. 22. Zhao, Y., Adve, R., & Lim, T. J. (2006). Symbol error rate of selection amplify-and-forward relay

systems.IEEE Communications Letters, 10(11), 757–759.

23. Papoulis, A. (2002).Probability, random variables, and stochastic processes(4th ed.). New York, NY: McGraw-Hill.

24. Abramowitz, M., & Stegun, I. A. (1972).Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York, NY: Dover.

Author Biographies

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coordinating a project with partnership of researchers from Brazil and China. He is also recipient of three conference Paper Awards: one at the IEEE International Symposium on Computers and Communications (ISCC) 2009, one at the 13th International Symposium on Wireless Personal Multimedia Communications (WPMC) 2010, and another at the XXIX Brazilian Telecommunications Symposium (SBrT 2011). He has been a Member of the IEEE and Communications Society since 2006.

Sonia Aïssa received her Ph.D. degree in Electrical and Computer Engineering from McGill University, Montreal, QC, Canada, in 1998. Since then, she has been with the National Institute of Scientific Research-Energy, Materials, and Telecommunications (INRS-EMT), University of Quebec, Montreal, QC, Canada, where she is a Profes-sor. From 1996 to 1997, she was a Researcher with the Department of Electronics and Communications of Kyoto University, Kyoto, Japan, and with the Wireless Systems Laboratories of NTT, Kanagawa, Japan. From 1998 to 2000, she was a Research Associate at INRS-EMT, Mon-treal. From 2000 to 2002, while she was an Assistant Professor, she was a Principal Investigator in the major program of personal and mobile communications of the Canadian Institute for Telecommunica-tions Research (CITR), leading research in radio resource management for code division multiple access systems. From 2004 to 2007, she was an Adjunct Professor with Concordia University, Montreal. In 2006, she was Visiting Invited Professor with the Graduate School of Infor-matics, Kyoto University, Japan. Her research interests lie in the area of wireless and mobile communications, and include radio resource management, cross-layer design and opti-mization, design and analysis of multiple antenna (MIMO) systems, cognitive and cooperative transmission techniques, and performance evaluation, with a focus on Cellular, Ad Hoc, and Cognitive Radio networks. Dr. Aïssa was the Founding Chair of the Montreal Chapter IEEE Women in Engineering Society in 2004– 2007, acted or is currently acting as Technical Program Leading Chair or Cochair for the Wireless Com-munications Symposium of the IEEE International Conference on ComCom-munications (ICC) in 2006, 2009, 2011 and 2012, as PHY/MAC Program Chair for the 2007 IEEE Wireless Communications and Networking Conference (WCNC), and as Technical Program Committee Cochair of the 2013 IEEE Vehicular Technol-ogy Conference – spring (VTC). She has served as a Guest Editor of the EURASIP Journal on Wireless Communications and Networking in 2006, and as Associate Editor of the IEEE Wireless Communications Magazine in 2006-2010. She is currently an Editor of the IEEE Transactions on Wireless Communications, the IEEE Transactions on Communications and the IEEE Communications Magazine, and Associate Editor of the Wiley Security and Communication Networks Journal. Awards and distinctions to her credit include the Quebec Government FQRNT Strategic Fellowship for Professors-Researchers in 2001–2006; the INRS-EMT Performance Award for outstanding achievements in research, teaching and service, in 2004 and 2011; the IEEE Communications Society Certificate of Appreciation in 2006–2011; and the Technical Community Service Award from the FQRNT Center for Advanced Systems and Technologies in Communications (SY-TACom) in 2007. She is also co-recipient of Best Paper Awards from IEEE ISCC 2009, WPMC 2010, IEEE WCNC 2010 and IEEE ICCIT 2011; and recipient of NSERC (Natural Sciences and Engineering Research Council of Canada) Discovery Accelerator Supplement Award.

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Imagem

Fig. 1 Dual-hop cooperative spectrum-sharing system: (a) The SU source selects a cluster of relays with the highest average SNR; (b) The SU communication is performed through the best relay chosen from a given subset of the selected cluster
Fig. 2 Average BER of dual-hop cooperative spectrum-sharing systems with partial relay selection for different values of L and assuming Rayleigh fading
Fig. 4 Average BER of dual-hop cooperative spectrum-sharing systems with partial relay selection for different values of the Nakagami-m fading parameters m 2 and, by setting L = 2 and m 1 = 2
Fig. 6 Average BER of dual-hop cooperative spectrum-sharing systems with partial relay selection assuming L = 2
+2

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