Cognitive full-duplex relay networks under the peak interference power constraint of multiple primary users

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1 Cognitive full-duplex relay networs under the pea interference power constraint of ultiple priary users Doan, X-T., Nguyen, N-P., Yin, C., da Costa, D. B., & Duong, T. Q Cognitive full-duplex relay networs under the pea interference power constraint of ultiple priary users. EURASIP Journal On Wireless Counications and Networing, DOI: /s y Published in: EURASIP Journal On Wireless Counications and Networing Docuent Version: Publisher's PDF, also nown as Version of record Queen's University Belfast - Research Portal: Lin to publication record in Queen's University Belfast Research Portal Publisher rights Doan et al. 217 This article is distributed under the ters of the Creative Coons Attribution 4. International Licensehttp://creativecoons.org/licenses/by/4./, which perits unrestricted use, distribution, and reproduction in any ediu, provided you give appropriate credit to the original authors and the source, provide a lin to the Creative Coons license, and indicate if changes were ade. General rights Copyright for the publications ade accessible via the Queen's University Belfast Research Portal is retained by the authors and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requireents associated with these rights. Tae down policy The Research Portal is Queen's institutional repository that provides access to Queen's research output. Every effort has been ade to ensure that content in the Research Portal does not infringe any person's rights, or applicable UK laws. If you discover content in the Research Portal that you believe breaches copyright or violates any law, please contact openaccess@qub.ac.u. Download date:2. Nov. 218

2 Doan et al. EURASIP Journal on Wireless Counications and Networing :8 DOI /s y RESEARCH Open Access Cognitive full-duplex relay networs under the pea interference power constraint of ultiple priary users Xuan-Toan Doan 1, Na-Phong Nguyen 1, Cheng Yin 1,DanielB.daCosta 2 and Trung Q. Duong 1* Abstract This paper investigates the outage perforance of cognitive spectru-sharing ulti-relay networs in which the relays operate in a full-duplex FD ode and eploy the decode-and-forward DF protocol. Two relay selection schees, i.e., partial relay selection PRS and optial relay selection ORS, are considered to enhance the syste perforance. New exact expressions for the outage probability OP in both schees are derived based on which an asyptotic analysis is carried out. The results show that the ORS strategy outperfors PRS in ters of OP, and increasing the nuber of FD relays can significantly iprove the syste perforance. Moreover, novel analytical results provide additional insights for syste design. In particular, fro the viewpoint of FD concept, the priary networ paraeters i.e., pea interference at the priary receivers, nuber of priary receivers, and their locations should be carefully considered since they significantly affect the secondary networ perforance. Keywords: Cognitive radio networs, Full-duplex, Decode-and-forward, Perforance analysis 1 Introduction The explosion of data traffic over wireless counication has brought a huge deand for spectru resources. Cognitive radio has arisen as a proising technology for efficiently utilizing the liited spectru [1, 2]. The ey principle behind the functionality of a spectru sharing approach also nown as underlay strategy in cognitive radio networs CRNs is that unlicensed secondary users are allowed to access the licensed spectru as long as the interference fro the secondary transitters is harless to the priary receivers [3]. In order words, the secondary transitters need to set their transit powers in order to not cause any interference to the priary networ that is above a predefined level. This power adjustent iplies a reduction in the coverage area of the secondary networ. Fortunately, cooperative relay schees, which can enhance the coverage of wireless networs by deploying helping nodes to transfer inforation fro the source *Correspondence: trung.q.duong@qub.ac.u This paper has been presented in part at International Conference on Recent Advances on Signal Processing, Telecounications & Coputing SigTelCo, Da Nang, Vietna, January Queen s University Belfast, Belfast, UK Full list of author inforation is available at the end of the article to the destination, have been introduced in CRNs with spectru-sharing environent see, for instance, [4 8]. Specifically, different relay selection schees assuing aplify-and-forward AF and decode-and-forward DF relaying protocols, were studied in [6 8], and the results showed that by applying appropriate cooperative schees, cognitive relay networs can significantly attain iproved perforance. However, the aforeentioned studies eployed halfduplex HD relays, which are inefficient fro the spectru usage point of view. Note that a conventional relay uses two tie-slots for two operating phases, i.e., listening to essages fro the inforation source node and relaying essage to the destination. To tacle this spectral inefficiency, full-duplex FD techniques have been proposed for relay networs [9, 1], which enable relay nodes to transit and receive signals siultaneously at the price of self-interference. Although self-interference is an undesirable effect in practice, the developents in signal processing and antenna technologies have proven that FD techniques are a proising solution for efficient spectru usage in the next generation of wireless counication [11 13]. Moreover, the effect of FD techniques on relay networs has attracted wide attention Doan et al. 217Open Access This article is distributed under the ters of the Creative Coons Attribution 4. International License which perits unrestricted use, distribution, and reproduction in any ediu, provided you give appropriate credit to the original authors and the source, provide a lin to the Creative Coons license, and indicate if changes were ade.

3 Doan et al. EURASIP Journal on Wireless Counications and Networing :8 Page 2 of 1 recently [14 16]. The authors in [17 19] investigated a FD, dual-hop, AF syste, in which the self-interference variance was odeled as a function of transit power. In [2], the authors studied different relay selection policies based on the availability of syste s channel state inforation CSI at the source node of a ultiple AF FD relay syste. In [21], otivated by increental-df protocol, the authors proposed a new cooperative protocol for FD relays naed as increental-selective-df and copared its perforance with selective-df protocol in Naagai fading environent. In [9], the authors exained the outage probability OP of a DF relay networ to find the optial duplex ode of the considered syste. However, in all these aforeentioned studies, the influence of spectru-sharing environent on FD relay networs is not well understood. Motivated by this observation, in this paper, we study the perforance of cognitive FD relay networs in the presence of ultiple FD relays and ultiple priary receivers. The contributions of the paper can be suarized as follows: Two relay selection schees, naely, optial relay selection ORS and partial relay selection PRS, based on the availability of the syste CSI at the secondary inforation source are proposed. Due to the existence of the coon rando variables RVs, i.e., the channels fro the source and/or selected relay to ultiple priary receivers, the signal-to-noise-ratios SNRs of all lins becoe correlated which aes the analysis troublesoe. To get around this challenge, we first apply the conditional probability on these RVs and then derive the analytical expressions for the OP of the considered syste. Specifically, the exact and asyptotic expressions of OP in PRS and ORS schees are also obtained. The derived results reveal several insights. For instance, it is shown that the priary networ s paraeters, i.e., the pea interference constraint, the distance fro the priary receivers to the secondary transitters, and the nuber of priary receivers, have a high ipact on the perforance of the secondary networ and should be carefully designed. In addition, ORS strategy outperfors PRS 1 in ters of OP, and increasing the nuber of FD relays can significantly iprove the syste perforance. The rest of this paper is organized as follows. The syste and channel odels are introduced in Section 2. Exact and asyptotic expressions for the OP assuing ORS and PRS policies are derived in Sections 3 and 4, respectively. Nuerical results are presented in Section 5, which are corroborated through Monte Carlo siulations. Finally, the ain conclusions are outlined in Section 6. Appendices A, B, C, and D present the proofs of four Leas. 2 Syste and channel odels We consider a cognitive relay networ consisting of one secondary transitter S, K secondary FD DF relays R, {1,..., K}, one secondary receiver D, andm priary receivers P, {1,..., M}, as shown in Fig. 1. We assue that the priary transitters are located sufficiently far away fro the secondary nodes so as not to ipinge any interference upon the received signals at the relays and destination and not to cause perturbation on the relay selection process. The node S is equipped with a single antenna and eploys a transit power P S. Meanwhile, R is equipped with two antennas one receive antenna and one transit antenna for operating in FD ode 1. All the channels are assued to experience Rayleigh fading, in which the respective channel power gains are exponentially distributed. Since a spectru sharing approach is adopted and R is in full-duplex ode, the transit power fro S and R is constrained by the priary networ s pea interference paraeter I p as follows: I p P S ax SP 2 + P R ax R P 2 =1,...,M =1,...,M 1 Fro 1, non-optial condition for P S and P R can be selected as follows: I p P S = 2 ax SP =1,...,M 2 I p P R = 2 ax R P =1,...,M 3 where P S and P R are the transit powers of S and R, respectively, h SP and h R P denote the channel coefficients pertaining to the S P and R P lins, P 1 P S h S h P M h S R 1 h R R R K Fig. 1 Cognitive spectru sharing networ h D D

4 Doan et al. EURASIP Journal on Wireless Counications and Networing :8 Page 3 of 1 respectively. The CSI of the channel gains fro the source and relays to priary users can be obtained fro direct feedbac fro PU-Rx or indirect feedbac fro band anager [22]. The transission is perfored in two hops. In the first hop, S transits inforation to R,wherethesubscript indicates the aiding relay that is chosen in the relay selection process, which will be detailed next. Because R siultaneously receives and forwards inforation, self-interference occurs at the receive antenna of R. Furtherore, although R applies self-interference cancellation techniques, the self-interference channel at R, i.e., h R, cannot be fully itigated and is odeled as an independent Rayleigh distributed channel [23]. In addition, we assue that the ipact of interference fro the priary transitter on secondary networ is neglected when the priary transitter is located far away fro secondary receiver [24, 25]. Thus, the received signal at R is given by y R = P S h SR x S + P R h R x R + n R, 4 where x S and x R represent the transitted signals fro S and R,respectively,h SR is the channel coefficient fro S to R,andn R N, N is the additive white Gaussian noise AWGN at R. After decoding the received inforation fro S, R forwards the decoded essage to D in the second hop. The received inforation at D can be expressed as y D = P R h R Dx R + n D, 5 where h R D denotes the channel coefficient fro R to D and n D N, N stands for the AWGN ter at D. The signal-to-interference-plus-noise-ratio SINR at R and SNR at D can be written, respectively, as = P S h SR 2 P R h R 6 + N γ 2 = P R h R D 2. 7 N In the considered syste, we assue that R eploys a DF protocol thans to its better perforance in the presence of self-interference copared to that of AF protocol [26]. Thus, the end-to-end SNR can be coputed as [5] γ = in, γ 2. 8 Fro 8, the capacity of the overall transission S R D can be expressed as C = log 2 [1 + γ ]. 9 Knowing that the OP is defined as the probability that the channel capacity of the considered syste falls below a given threshold, such a etric can be forulated as P {C < R th } = P { γ < 2 R th 1 } = F γ β, 1 where P{ } denotes probability, F γ represents the cuulative distribution function CDF of γ, β = 2 R th 1, and R th isthetargetrateofthesecondarynetwor. 3 analysis 3.1 Partial relay selection PRS In soe networs, such as wireless sensor networs, the energy and coputational resources are liited. Therefore, utilizing aiding relay based on full global CSI is infeasible. Motivated by this fact, in PRS schee, the node S uses the CSI solely of the channels pertaining to firsthop transission to select the aiding relay R p that has the best lin fro S, i.e., PRS = arg ax hsr =1,...,K Fro 2, 3, 6, and 7, the SINR of the first hop and the SNR of the second hop are forulated, respectively, as 1 = = 2 = = I p 2 ax h SP =1,...,M 2 ax h SR 2 =1,...,K I p 2 ax =1,...,M h RpP 2 h Rp 2 + N ax h ax h SP =1,...,M 2 SR 2 =1,...,K ax h h RpP =1,...,M 2 Rp 2 + 1, 12 I p h Rp D 2 2 ax =1,...,M h R p P 2 N h Rp D 2 ax h R p P 13 =1,...,M where = I p 2N. Fro 8, 12, and 13, the end-to-end SNR of the considered PRS policy is given by γ PRS = in γ1 PRS, γ 2 PRS. 14 Fro 12 14, we have the following lea. Lea 1 The OP of the considered PRS schee is given as follows: P PRS out = 1 + M 1 =1 2 =1 =1 M M 1 2 K P λ SP 2βλ SR βd + 2 P F 1 1, 2; 3; 1 + 1λ SP βλ λ SR RD β + P 2 15

5 Doan et al. EURASIP Journal on Wireless Counications and Networing :8 Page 4 of 1 where 2 F 1, ; ; sybolizes the Gaussian hypergeoetric function [27], Eq and λ 1 X is the ean value of exponential rando variable h X X {SR, R D, SP, R P, R }. Proof The proof is given in Appendix A. 3.2 Optial relay selection ORS In ORS schee, the node S is assued to be a stationary base station that has rich energy and powerful coputational resources. Therefore, S is able to collect and process all the syste CSI to choose the aiding relay that can axiize the capacity of the considered syste. In this case, the aiding relay R o is selected according to the following rule: ORS = arg ax =1,...,K in, γ 2 16 The end-to-end SNR is given by γ ORS = ax =1,...,K in, γ 2, 17 where and γ 2 denote the SINR of the first hop and the SNR of the second hop, respectively, and are expressed as = γ 2 = ax h h SP =1,...,M 2 SR 2 ax h h RpP =1,...,M 2 Rp 2 + 1, 18 h R D 2 ax =1,...,M h R P 19 Fro 17 19, we have the following lea. Lea 2 The OP of the considered ORS schee is given as follows: P ORS out where M =1 nλ n SP 1 n+1 K 1 exp nλ SPy dy, n=1 2 M 1 = λ RP exp βλ SR y γ =1 1 βλ SR y exp βλ βλrd SR + P y Ei βλ } SR βλrd + P y + βd + P 21 Proof The proof is given in Appendix B. 4 Asyptotic outage analysis In this section, an asyptotic outage analysis is carried out in order to gain further insights into the syste perforance. As will be shown, the considered syste has null diversity order because of the self-interference effect inherent to the FD technique 2. In addition, fro the asyptotic expressions, we can observe that in the high SNR regie, the perforance of the considered syste does not depend on the channel of the second hop. In other words, to enhance the perforance of the considered syste, the perforance of the first hop ust be strengthen. 4.1 Partial relay selection Lea 3 In the high SNR regie, the OP of the considered syste with PRS schee can be expressed as P PRS high SNR out =1 2 =1 =1 M M 1 2 K P λ SP 2βλ SR 2 P 2 2 F 1 1, 2; 3; 1 1λ SP βλ SR P Proof The proof is given in Appendix C. 4.2 Optial relay selection Lea 4 In the high SNR regie, the OP of the considered syste with ORS schee can be expressed as P ORS out where 2 = high SNR 1 =1 Ei n=1 M nλ n SP 1 n+1 K 2 exp nλ SPy dy, 23 M 1 +1 βλ SRP y βλ SRP y βλsr P exp y. 24 Proof The proof is given in Appendix D. 5 Nuerical results and discussions In this section, nuerical exaples are presented to show the ipact of the networ s paraeters on the overall syste perforance. The accuracy of our analysis is attested by Monte Carlo siulations, in which a perfect agreeent between the analytical and siulated curves

6 Doan et al. EURASIP Journal on Wireless Counications and Networing :8 Page 5 of 1 is observed. Without loss of generality, we adopt a twodiensional topology in which the coordinates x, y of S, R, andd are,, 2,, and3,, respectively.thus, the Euclidian distance between the nodes can be calculated as d AB = x A x B 2 + y A y B 2,whereA is placed at x A, y A and B has the coordinate x B, y B. In order to tae the path-loss into account, we assue λ X = dx α, where α denotes the path-loss exponent and λ X {λ SP, λ SR, P, D, }. Without loss of generality, in the plots, we set α = 4andthetargetrate of the secondary networ R th =.4 bits/s/hz, and = 22. Figures 2 and 3 show the effect of the priary users locations on the syste OP for the PRS and ORS schees, respectively. Fro these figures, one can observe that as the priary receivers ove farther fro the secondary transitters, the perforance of the secondary networ iproves. The reason is that the longer the distance between the priary receiver and the secondary transitter results in the higher the transit power of the secondary transitter, which iplies a better secondary transission. In addition, the effects of the priary networ s pea interference constraint on the secondary networ are also revealed. Note that, if the pea interference constraint is too sall, the secondary transitters will not have sufficient transit power to ensure good transissions. On the other hand, if the pea interference constraint is too high, the transit power at the FD relays will be large, resulting in high levels of self-interference. Besides, these two figures also show that the ORS schee outperfors PRS one. In Fig. 4, the effect of the nuber of priary receivers on syste OP is investigated. As can be seen, when the SNR is low, increasing the nuber of priary P1, 3 P1, 4 P1, 2 Optial Relay Selection Analysis Asyptotic Siulation Fig. 3 Effect of priary users positions on the syste OP for ORS schee receivers decreases the perforance of the considered syste. However, at high SNR regions, increasing the nuber of priary receivers will force the secondary transitters to reduce their transit powers, reducing the self-interference at the relay and consequently the OP. Figures 5 and 6 illustrate the influence of selfinterference on the secondary networ s perforance by varying the ean power of self-interference channel, i.e., 1. As expected, the worse the quality of the self-interference channel is, the better the syste perforance is. Particularly, as the SNR of the considered syste is high, the saller the ean power of self-interference channel is, the higher the syste diversity gain is. In addition, the results show that applying ORS schee can 1 Partial Relay Selection P1,3 P1,4 P1,2 Analysis Siulation Asyptotic db Fig. 2 Effect of priary users positions on syste OP for PRS schee Analysis M=3 Analysis M=6 Analysis M=9 Siulation Asyptotic ORS PRS M=3,6,9 M=3,6, db Fig. 4 OP for different nubers of priary receivers

7 Doan et al. EURASIP Journal on Wireless Counications and Networing :8 Page 6 of 1 1 Partial Relay Selection =5 = K=7,8,9 PRS K=7,8,9 ORS Analysis Asyptotic Siulation = db Fig. 5 Effect of self-interference on the syste OP with PRS schee 1-4 Siulation Analysis Asyptotic db Fig. 7 OP for different nubers of FD relays restraint the effect of self-interference better than PRS schee. Figure 7 deonstrates the influence of the nuber of relays on the syste OP. When the nuber of relays increases, the perforance of the considered syste is enhanced. Particularly, a ore significant iproveent can be witnessed in ORS schee than in PRS schee. Figure 8 shows the coparison in syste s capacity between FD and HD relays. We can observe that applying FD relays can help the syste achieve a higher capacity. The reason is that FD relays can listen and transit inforation siultaneously while HD relays have two phases of operation, i.e., listening to the inforation source and relaying signal to the destination. 6 Conclusions In this paper, the syste perforance in ters of outage probability of a cognitive FD relay networ in the presence of ultiple priary receivers has been evaluated. In particular, two relay selection strategies, naely ORS and PRS, have been proposed to enhance the perforance of the syste. New exact and asyptotic expressions for the OP of the PRS and ORS schees were derived. The results showed that the ORS schee has a better perforance than PRS schee. In addition, increasing the nuber of FD relays can enhance the syste perforance. Priary networ designing paraeters, i.e., the pea interference constraint, the nuber of priary receivers, and their locations, have great influences on the perforance of the secondary networ and should be indfully considered Optial Relay Selection 2.5 Full Duplex Half Duplex ORS Analysis Asyptotic Siulation =5 =1 =15 Capacity Bits/s/Hz PRS db Fig. 6 Effect of self-interference on the syste OP with ORS schee I P db Fig. 8 Coparison between FD and HD relays

8 Doan et al. EURASIP Journal on Wireless Counications and Networing :8 Page 7 of 1 Endnotes 1 Dual-antenna FD ipleentation is one of any ways to deploy FD ode, including single-antenna FD ipleentation. 2 In the considered syste, the transit power at the full-duplex relay is non-optial. A transit power optiization schee at full-duplex relay can be considered to restrain the self-interference effect. Appendix A: Proof of Lea 1 Let X 1 = = ax h SR =1,...,K ax h SP =1,...,M X 3 = h Rp X 4 = ax h R p P =1,...,M X 5 = h Rp D The CDF and the probability density function PDF of X 1 can be expressed as F X1 x = 1 f X1 x = =1 =1 K K 1 +1 exp λ SR x, λ SR exp λ SR x. 27 In the sae way, the CDF and PDF of are given by M F X2 x = exp λ SP x, =1 28 M f X2 x = 1 +1 λ SR exp λ SP x, =1 29 and the CDF and PDF of X 4 can be written as M F X4 x = exp λ RP x, =1 3 M f X4 x = 1 +1 λ RP exp P x. =1 31 Finally, the CDF and PDF of X 3 are given by F X3 x = 1 exp x, 32 f X3 x = exp x, 33 and the CDF and PDF of X 5 are given by F X5 x = 1 exp D x, 34 f X5 x = D exp D x. 35 Fro 12 and 13, γ1 PRS follows: 1 = γ X 1 1 X 3 and 2 can be rewritten as X 4 + 1, 36 X 5 2 =. 37 X 4 Since γ1 PRS and γ2 PRS be expressed as F β = depend on X 4,theCDFof can [ 1 1 F β ] 1 F β f X4 xdx. 38 In order to derive F β, we need to deterine F β and F β. Inthiscase,F β can be written as { γ1 X 5 F β = P <β X 4 = 1 exp } X4 β = F X5 DX 4 β Siilarly, F β can be calculated as { X γ1 1 } X F β = P 2 X γ 3 1 X <β = = 1 + K Ei F X1 [β + y ] x f X2 x f X3 y dxdy, X 4 1 =1 = λ SP X 4 [ βλ SR 1 + 1λ SP βλ SR M 1 [ 1 exp ] D + 1λ SP βλ SR ] X 4, 4 where Ei denotes the exponential integral function and 4 is obtained with the help of [27], Eq By substituting 39 and 4 into 38, 15 is attained.

9 Doan et al. EURASIP Journal on Wireless Counications and Networing :8 Page 8 of 1 Appendix B: Proof of Lea 2 Let Y 1 = h SR Y 3 = h R Y 4 = ax h R P =1,...,M Y 5 = h R D = in, γ 2. The CDF and PDF of Y 4 are given by M F Y4 x = exp λ RP x, =1 41 M f Y4 x = 1 +1 λ RP exp P x. =1 42 Fro 18 and 19, and γ 2 can be rewritten as = Y 1 Y 3 Y 4 + 1, 43 γ 2 = Y 5 Y Since,for {1,..., K}, depends on,thecdfof can be expressed as γ ORS F γ ORS β = [ F β ] K fx2 y dy, 45 Fro 43 and 44, note that and γ 2 depend on Y 4. Therefore, the CDF of conditioned on can be calculated by [ F β = 1 1 Fγ1,Y 4 β 1 Fγ2 Y 4 β ] f Y4 x dx. 46 On the other hand, the CDF of γ 2 conditioned on Y 4 can be calculated as { } γ1 Y 5 F γ2 Y 4 β = P <β Y 4 { = P Y 5 < βy } 4 βy4 = F Y5 = 1 exp βdy 4, 47 Finally, the CDF of conditioned on and Y 4 can be calculated as { Y1 Y 3 F γ1,y 4 β = P Y + 1 <β 4 γ { 1 Y3 = P Y 1 <β + 1 } Y 4 y = F Y1 Y Y 4 = 1 + βλ SR Y 2 Y 4 } exp β f Y3 y dy βλ SRY 2, 48 where F Y1 x = 1 exp λ SR x and f Y3 x = exp x. Thus, fro 48, 47, and 42, the CDF of conditioned on can be calculated as F β = 1 M 1 +1 P X + βλ 2 SR x exp βλ RDx P x dx =1 exp βλ SR M = 1 =1 βλ SR exp βλ SR Ei βλ SR βλrd 1 +1 P exp βλ SR βλrd + P + P γ 1 + βd + P, 49 where 49 is obtained with the help of [27], Eq Now, by substituting 49 and f X2 x = =1 into 45, 2 is attained. M 1 +1 λ SR exp λ SP x Appendix C: Proof of Lea 3 At high SNR regions, i.e., assuing high, 18 can be rewritten as 1 = γ X 1 1 X 3 X large X 1X 4 X 3. 5

10 Doan et al. EURASIP Journal on Wireless Counications and Networing :8 Page 9 of 1 Thus, the CDF of 1 F β = =1 =1 conditioned on X 4 is given by 1 λ SP X 4 exp βλ SR M K 1 1 λ SP X 4 Ei βλ SR λ SP X 4 βλ SR Now, analyzing F β at high,wehavethat F β = 1 exp DX 4 β, a DX 4 β, where step a is obtained by using the McLaurin expansion of expx and neglecting the high order ites for sall x. Maing use of the above results, it can be shown that the CDF of γ PRS is given by [ ][ ] b F X 4 x=1 1 F x F x F x, 53 where step b is perfored by neglecting the high order ters. By substituting 51 into 53, and after soe atheatical anipulations, 22 is obtained. Appendix D: Proof of Lea 4 For high, F γ2 Y 4 and F γ1 Y 4 can be rewritten as follows: F γ2 Y 4 β = 1 exp βλ RDY 4 c βdy 4, 54 F γ1,y 4 β = 1 exp βλ SRY 2 Y + βλ 2 SR γ Y 1 4 d 1 + βλ SR Y 2 Y 4, 55 where steps c and d are perfored by using the McLaurin expansion of expx and neglecting the high order ters for sall x. In addition, the CDF of conditioned on and Y 4 can be forulated as F,Y 4 β = 1 [ 1 F γ1,y 4 β ][ 1 F γ2 Y 4 β ] e F γ1,y 4 β, 56 where step e is perfored by neglecting the high order ters. Fro 55 and 56, the CDF of conditioned on can be found as F β = M =1 exp 1 +1 βλ SRP βλsr P Ei βλ SRP Finally, by replacing 57 and f X2 y = 1 n+1 M nλ n SP exp nλ SP y n=1 into 45, 23 is obtained. Acnowledgeents This wor was supported by the Newton Institutional Lin under Grant ID Copeting interests The authors declare that they have no copeting interests. Author details 1 Queen s University Belfast, Belfast, UK. 2 Departent of Coputer Engineering, Federal University of Ceará, Sobral, Brazil. Received: 12 June 216 Accepted: 12 Deceber References 1. J Mitola, GQ Maguire, Cognitive radio: aing software radios ore personal. IEEE Pers. Coun. 64, KJ Ki, TQ Duong, HV Poor, Perforance analysis of cyclic prefixed single-carrier cognitive aplify-and-forward relay systes. IEEE Trans. Wireless Coun. 121, A Goldsith, S Jafar, I Maric, S Srinivasa, Breaing spectru gridloc with cognitive radios: an inforation theoretic perspective. Proc. IEEE. 975, VNQ Bao, TQ Duong, DB da Costa, GC Alexandropoulos, A Nallanathan, Cognitive aplify-and-forward relaying with best relay selection in non-identical Rayleigh fading. IEEE Coun. Lett. 173, KJ Ki, TQ Duong, X-N Tran, Perforance analysis of cyclic prefixed single-carrier spectru sharing systes with best relay selection. IEEE Trans. Signal Process. 612, Y Yang Yan, J Jianwei Huang, J Jing Wang, Dynaic bargaining for relay-based cooperative spectru sharing. IEEE J. Sel. Areas Coun. 318, TQ Duong, DB da Costa, TA Tsiftsis, C Zhong, A Nallanathan, Outage and diversity of cognitive relaying systes under spectru sharing environents in Naagai- fading. IEEE Coun. Lett. 1612, T Duong, V Bao, H-J Zepernic, Exact outage probability of cognitive AF relaying with underlay spectru sharing. IET Electronics Lett. 4717, T Kwon, S Li, S Choi, D Hong, Optial duplex ode for df relay in ters of the outage probability. IEEE Trans. Veh. Technol. 597, I Kriidis, HA Suraweera, S Yang, K Berberidis, Full-duplex relaying over bloc fading channel: a diversity perspective. IEEE Trans. Wireless Coun. 1112, T Riihonen, S Werner, R Wichan, Mitigation of loopbac self-interference in full-duplex MIMO relays. IEEE Trans. Signal Process. 5912, D Ki, H Lee, D Hong, A survey of in-band full-duplex transission: fro the perspective of PHY and MAC layers. IEEE Coun. Surv. Tuts. 174, J Zhou, T-H Chuang, T Dinc, H Krishnasway, Integrated wideband self-interference cancellation in the RF doain for FDD and full-duplex wireless. IEEE J. Solid-State Circ. 512,

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