IN WIRELESS networks, cooperative communications offer

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 62, NO 3, MARCH AF Cooperative CDMA Outage Proaility Analysis in Naagami-m Fading Channels Ali Mehemed, Student Memer, IEEE, and Walaa Hamouda, Senior Memer, IEEE Astract The performance of amplify-and-forward (AF) cooperative code-division multiple-access (CDMA) systems is analyzed over independent nonidentical (ini) Naagami-m fading channels In the underlying AF relaying scheme, each relay applies interference suppression to the received signal to mitigate the effect of multiple-access interference (MAI) where a soft estimate is otained efore signal amplification taes place The outage proaility of the system is analyzed using the cumulative distriution function (cdf) of the total signal-to-noise ratio (SNR) at the ase station In that, we derive a simplified yet tight lower ound for the AF relaying system We also define an approximation for the proaility density function (pdf) of the total SNR, which enales us to derive an asymptotic outage proaility of the system The derived asymptotic outage proaility is used to evaluate the achievale diversity order for various system parameters Simulations are presented to verify the accuracy of our analytical results Index Terms Code-division multiple-access (CDMA), cooperative communications, Naagami fading, outage proaility I INTRODUCTION IN WIRELESS networs, cooperative communications offer the aility to implement spatial diversity, which improves the performance over fading channels without the need for multiple antennas at the transmitter and/or receiver sides It has een shown that user cooperation diversity with multirelays, a new form of space diversity, has the potential to enhance the channel capacity and the reliaility of wireless communication systems [1], [2] Within the research on user cooperation diversity, amplify-and-forward (AF) is a simple cooperative scheme in which the relay (ie, cooperative user) transmits an amplified version of the received partner s signal to the ase station [3] Recently, multiuser cooperative systems, such as the multicarrier code-division multiple access (MC-CDMA) and the optical CDMA, have een implemented ased on the directsequence CDMA (DS-CDMA) approach Cooperative DS- CDMA, as one common networ of user cooperation diversity, has een investigated using nonorthogonal spreading codes for synchronous networs over Rayleigh fading channels in [4] Manuscript received Novemer 21, 211; revised March 28, 212 and June 22, 212; accepted Septemer 28, 212 Date of pulication January 4, 213; date of current version March 13, 213 This wor was supported y the Natural Sciences and Engineering Research Council of Canada under Grant N8861 The review of this paper was coordinated y Dr W Zhuang The authors are with the Department of Electrical and Computer Engineering, Concordia University, Montreal QC H3G 1M8, Canada ( a_alifar@ececoncordiaca; hamouda@ececoncordiaca) Digital Oject Identifier 1119/TVT In [4], the authors employed a modified minimum-meansquare-error detector as a multiuser detector (MUD) for DS-CDMA cooperative networs to mitigate the effect of multiple-access interference (MAI) The performance of multiuser AF relay networs has also een studied in [5] where Liu et al derived an approximation for the outage proaility over Rayleigh fading channels The joint iterative power allocation and the interference cancelation for DS-CDMA systems using AF relaying were analyzed in [6] In their wor, the authors determined the required power level for a multirelay system In [7], performance analysis of incremental-relaying cooperative diversity networs over Rayleigh fading channels is presented where a complete analytical method is introduced to otain closed-form expressions for the error rate, outage proaility, and the average achievale rate using decode-andforward (DF) and AF over independent nonidentical (ini) Rayleigh fading channels Given field measurements, it is nown that the Rayleigh fading model cannot represent the statistical characteristics of many wireless environments In that context, the Naagami fading model is well-nown as a generalized distriution, where many fading environments can e modeled [8] In [9], a performance analysis of time-division multiple-access relay protocols over independent and identically distriuted (iid) Naagami-m fading channels is presented Atapattu et al [9] considered an Alamouti-coded system with two-stage protocols and fixed-gain AF On the other hand, Fang et al [1] evaluated the it error rate (BER) of a cooperative downlin transmission scheme for DS-CDMA systems over Naagami-m fading channels to achieve cooperative diversity In their wor, they also proposed transmitter zero forcing at the ase station for suppressing the downlin multiuser interference In [11], Suraweera et al analyzed the outage proaility of cooperative relay networs over iid Naagami-m fading channels Along the same lines, Yang et al [12] studied the performance of downlin multiuser relay networs using single-relay AF where the outage proaility was evaluated at a high SNR In a single-user system, performance analysis for opportunistic DF with a selection comining receiver at the destination has een evaluated in terms of the outage proaility over nonidentical Naagami-m fading channels in [13] In [14], the performance of cooperative CDMA systems using adaptive DF relaying over Naagami-m fading channels was investigated In [14], a closed-form expression for the outage proaility using the moment-generating function (MGF) for the total SNR at the ase station was otained In the literature, there have een many wors on the analysis of DF and AF relaying, particularly in the case of Rayleigh /$ IEEE

2 117 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 62, NO 3, MARCH 213 fading Here, different from previous wors, we derive a new lower ound and asymptotic expression for the outage proaility of cooperative diversity in DS-CDMA using AF relaying over Naagami-m fading with maximal-ratio-comining receiver at the ase station In that, an approximate proaility density function (pdf) for the total SNR at the ase station is determined at high SNR This approximation is then used to evaluate the asymptotic outage proaility of the system We consider asynchronous transmission where we study the effect of MAI and intersymol interference at oth the relay and the ase station for AF cooperative CDMA systems To overcome the effect of MAI, a MUD at oth the relay and the ase station is employed to convert the inter-user channels into parallel interference-free fading channels Here, different from previous wors, our AF scheme employs MAI cancelation to otain a soft estimate of the transmitted data for the source The rest of this paper is organized as follows In Section II, we introduce the system model The outage proaility for AF relaying is analyzed in Section III Section IV provides some simulation and numerical results Finally, conclusions are drawn in Section V II SYSTEM MODEL An uplin K-user asynchronous nonorthogonal DS-CDMA system over ini Naagami-m fading channel is considered A half-duplex system is assumed, and each user is equipped with a single antenna A single-relay cooperation system is studied where the group of users {1, 2,,K} is arranged into groups, each of two cooperating partners The cooperation taes place in two time slots In the first time slot, each user s roadcasts its signal to its partner r and to station In the second time slot, the partner amplifies the received signal and retransmits a soft estimate of the output of the MUD in an attempt to cancel the effect of MAI The independent fading channel coefficients etween partners and the ase station are defined as follows: source relay h sr, source ase station h s, and relay ase station h r All are modeled as ini Naagami-m random variales (RVs) The instantaneous SNRs of different lins are denoted y γ sr = h sr 2 (E s /N o ), γ s = h s 2 (E s /N o ), and γ r = h r 2 (E s /N o ), where E s is the transmitted signal energy, N o is the noise spectral energy, and h sr 2, h 2 s, and h r 2 are gamma distriuted RVs with a pdf given y p γij (x) = Bm ij ij Γ(m ij ) xm ij 1 exp( xb ij ) (1) where m ij > 5 is the fading parameter, Γ( ) is the gamma function [15, eq (831, 1)], B ij = m ij / γ ij with average SNR, and γ ij = E h ij 2 E s /N o and E denote expectation The cdf of γ ij is then given y F γij (x) = γ(m ij,xb ij ) Γ(m ij ) where γ(, ) is the lower incomplete gamma function [15, eq (835, 1)] (2) III OUTAGE PROBABILITY ANALYSIS A repetition-ased cooperative diversity scenario is applied where the relay amplifies the received signal and transmits a soft estimate of the desired user signal to the ase station [3] The allowale degrees of freedom of the cooperative system, ie, K/2N, depend on the total numer of users K, length of the availale spreading code N, and the factor 1/2, which refers to the andwidth expansion required for relaying due to the half-duplex constraint [16] In the following, the performance of the cooperative diversity protocol under diversity comining is investigated Let us first consider the direct lin etween the source s and the ase station, where the mutual information is defined y [16] ( ) I s = K 2N log 2Nγ s K [ 2 R 1 ], s {1,,K} s, s (3) where R is the (Kf Kf) cross-correlation matrix at the ase station receiver, which is defined as [17] R = ρ 1, 1 ρ 1, 2 ρ 1,K ρ 2, 1 ρ 2, 2 ρ 2,K ρ K, 1 ρ K, 2 ρ K, K (4) with ρ ij eing the cross correlation etween any two spreading codes C i and C j [R 1 ] ij represents the ith row and the jth column elements of the inverse of the cross-correlation matrix R 1, and f is the frame length In (3), 2N/K 2 is the normalized discrete-power constraint [16] Given that outage will occur when the spectral efficiency R exceeds the mutual information I s, one can define the outage proaility of the noncooperative system as From (3) and (5), we have [ ( K P out = P r 2N log P out = P r [I s < R] (5) 2Nγ s K [ ] 2 R 1 s, s ) ] < R = P r [γ s <γ th s ] (6) where γ th s =(2 2NR/K 1)/(2N/K 2 [R 1 ] s, s) From(6), one can notice that P [γ s <γ th s ] is the cdf of γ s, which is given y (2) as P noncoop = P r [γ s <γ th s ]= γ (m s,b s γ th s ) (7) Γ(m s ) A Outage Proaility Lower Bound In AF, the relay (ie, cooperative user) transmits an amplified version of the received partner s signal after linear filtering using a decorrelator detector (DD) as a MUD Here, the average mutual information on AF relaying in DS-CDMA for the single-relay cooperative system is derived

3 MEHEMED AND HAMOUDA: AF COOPERATIVE CDMA OUTAGE PROBABILITY ANALYSIS 1171 The received signal during an ith data symol duration at the ase station in the first transmission phase is given y [17] r 1 (t) = f 1 i= s=1 K x s (i)c s (t τ s it )h s (i)+n 1 (t) it t<(i + 1)T (8) where x s (i) {1, 1} is the ith data symol of user s, C s (t) is the spreading code of user s with spreading gain N = T /T c, T is the it period, T c is the chip period, and τ s is the random transmit delay of the sth user, which is assumed to e uniformly distriuted along the symol period n 1 (t) is the additive white Gaussian noise (AWGN) with zero mean and variance σ 2 n = N o The received signal at relay r can e written as r r (t) = f 1 K i= s=1,s r x s (i)c s (t τ s it )h sr (i)+n r (t) (9) where n r (t) is an AWGN with zero mean and variance σ 2 n = N o In the second phase, each cooperating user transmits the amplified version of the received signal to the ase station, which is expressed as r 2 (t) = f 1 i= s=1 K r r (t D s τ r ) h r (i) β + n 2 (t) (1) where r is the relay cooperating with user s, n 2 (t) is the AWGN with zero mean and variance σn 2 = N o, and D s is the transmission delay during the second transmission period β is the amplification factor for the AF scheme at the relay node, which is expressed as [3] β = E s E s h sr 2 + N o (11) where E s is the transmitted signal energy The output of the an of matched filters at the ase-station receiver and the relay, and y dropping the time index from modules (8) (1), can e defined in vector form for the first phase as y 1 = R H s, x + n 1 (12) where x is the (Kf 1) user data vector of the K total users defined as x =[x 1 (1),,x 1 (f),,x K (1),,x K (f)] T, and H s, is the (Kf Kf) channel coefficient matrix etween the source and the ase station defined as h 1, (1) H s, = h 1, (f) (13) h K, (f) Under the assumption of frequency-flat fading, we use a locfading channel model, assuming that different channels experience roughly the same fading conditions (or equivalently the same channel coefficients) over the whole duration of each frame f n 1 is the (Kf 1) AWGN vector with iid elements each of zero mean and variance σ 2 n = N o Similarly, the output of the an of matched filters at the relay can e defined as y r = R r H s, r x + n r, r {1,,K} (14) where R r is the (Kf Kf) relay cross-correlation matrix; H s, r is the (Kf Kf) channel coefficient matrix etween the sources and the relay, with ρ K, K = and h K, K = s = r in R r and H s, r, respectively, ie, ρ 1, 1 ρ 1, 2 ρ 1,K ρ 2, 1 ρ 2, 2 ρ 2,K R r = (15) ρ K, 1 ρ K, 2 ρ K, K h 1,r h 2,r H s, r = (16) h K, r and n r is the AWGN vector with zero mean and variance σ 2 n = N o The output of the an of matched filters at the ase station in the second transmission phase is given y y 2 = R H r, (y r )β + n 2 (17) with H r, eing the channel coefficient matrix etween the relays and the ase station, and n 2 eing the AWGN vector with zero mean and variance σn 2 = N o Employing a DD at the ase station, we have z 1 = ( R 1 ) y1 = H s, x + R 1 n 1 (18) In addition, considering the MUD at the relay side (ie, no decoding is done), the soft data estimate at the decorrelator output is given y z r = ( R 1 ) r yr = H s, r x + R 1 r n r (19) In the cooperative phase, the decorrelator output at the ase station is given y z 2 = ( R 1 ) y2 = H r, H s, r βx + H r, βr 1 r n r + R 1 n 2 (2) Considering the ith data it of the sth user, s {1,,K}, the decorrelator output at the ase station for the first and second transmission phases of (18) and (2) can e rewritten, respectively, as [z s (i)] 1 = h s, x s (i)+n 1 (21) [z s (i)] 2 = h r, h s, r βx s (i)+h r, βn r + N 2 (22) where [z s (i)] 1 and [z s (i)] 2 are the decision statistics corresponding to the ith it for user s, and N 1 =[R 1 ] s, sn r, N r = [R 1 n r, and N 2 =[R 1 ] s, sn 2 are the sth element in the corresponding vector

4 1172 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 62, NO 3, MARCH 213 Now, the average mutual information for AF CDMA transmission can e derived using a vector representation of (21) and (22) as [ ] [ ] [ ] [zs (i)] 1 h = s 1 x s (i)+ N r (23) [z s (i)] }{{ 2 } z h r βh sr }{{} h h r β 1 }{{} G N 1 N 2 }{{} N Since the channel is assumed to e memoryless, the average mutual information I AF can e defined as [3] I AF I(x, z) log 2 det (I +(E s hh H ) ( GE NN H G H) ) 1 (24) where the covariance of the noise E NN H =diag(, ] s, s, ) Then [ ] hh H h = s 2 h s h H r βhh sr h H s h rβh sr h r 2 β 2 h sr 2 ( GE NN H G H) 1 1 N = o[r 1 ] s, s 1 h r 2 β 2 N o[r 1 r ] +N r, r o[r 1 and det of (24) is calculated as ( det I +(E s hh H ) ( GE NN H G H) ) 1 = 1 + E s h s 2 E [ ] s h r 2 β 2 h sr 2 N o R 1 h s, s r 2 β 2 + (25) Sustituting (11) into (25), and after many algeraic manipulations, we have det (I +(E s hh H ) ( GE NN H G H) ) 1 = 1 + E s h s [ ] 2 N o R 1 s, s + E s h r 2 E s h r 2 Es + E s h sr 2 h sr (26) It is shown that (26) is increasing in β; therefore, the amplification factor for the AF in (11) should e active [3] After sustitution and algeraic manipulations, using γ ij = h ij 2 (E s /N o ) and the normalized discrete-power constraint as in [16], I AF can e finally written as I AF = K 2N log Nγ s K [ ] 2 R 1 s, s + 2Nγ sr K 2 [R 1 2Nγ sr K 2 [R 1 2Nγ r K 2 [R 1 + 2Nγ r +1 r ] K 2 r, r [R 1 (27) For simplicity, we define X s =(2Nγ s )/(K 2 [R 1 ] s, s), X sr = (2Nγ sr )/(K 2 [R 1 ), and X r =(2Nγ r )/(K 2 [R 1 ), where the total SNR at the ase station is X total = X s + X sr X r X sr + X r + 1 (28) Using the lower ound defined in [18], we have X total X up = X s +min(x sr,x r ) (29) Note that the SNR value X up in (29) is analytically more tractale than the exact value in (28) This will simplify the derivation of the outage proaility, and as shown in [18], it represents an accurate measure in medium and high SNRs Given the cdf of X r defined in (2), the cdf of min(x sr,x r ) can e defined as F min(xsr,x r )(γ th )=1 P [X sr >γ th and X r >γ th ] = 1 Γ(m sr,b sr γ th ) Γ(m sr ) Γ(m r,b r γ th ) Γ(m r ) (3) After some manipulation, the cdf of the sum of gamma RVs is derived, as shown in the Appendix, and expressed as F Xtotal (y) = γ(m s,γb s ) Bm s s Γ(m s ) Γ(m s ) exp ( y(b sr + B r )) ( x (ms 1) exp ( x(b s B sr B r )) (B sr) n i= ( ) n ( 1) y n x n= = r 1 (B r ) i i ( 1) f y i f x f dx (31) f f= Finally, the P out for the AF scheme can e determined numerically y solving the integral in (31) using mathematical software such as Maple and Mathematica In the case of Naagami-m fading channels, the closed-form expression for the pdf of the total SNR is intractale to derive In what follows, we provide a closed-form expression for the asymptotic outage proaility B Approximate Distriutions of the Total SNR The asymptotic outage proaility is traditionally otained using the pdf of the indirect lin etween s r and r Due to the intractaility of the pdf of X total given in (28), it ecomes difficult to otain a closed-form expression for the outage proaility in the AF case Instead, we employ an approximation of this distriution at high SNR This approximation, as will e shown, will enale us to derive a closed-form expression for the outage proaility of the underlying system At high SNR, (1) can e approximated as p γij (γ) Bm ij ij Γ(m ij ) γm ij 1 + HO (32) where HO stands for high-order terms Applying Laplace transform to (32), and with the help of [19], the MGF is given y M γij (s) = Bm ij ij s m ij (33)

5 MEHEMED AND HAMOUDA: AF COOPERATIVE CDMA OUTAGE PROBABILITY ANALYSIS 1173 Using the method in [18], the pdf of the approximate distriution for lin s r can e written as f γs, r, (γ) f γs, r (γ)+f γr, (γ) (34) where f γs, r (γ) and f γr, (γ) can e approximated at high SNR as in (32), ie, f γs, r (γ) Bm sr sr Γ(m sr ) γm sr 1 + HO (35) f γr, (γ) Bm r r Γ(m r ) γm r 1 + HO (36) Examining (34) when E s /N o, a simplified expression for the f γs, r, (γ) is given y f γs, r, (γ) Ψγ m r 1 + HO (37) Fig 1 Outage proaility for cooperative AF DS-CDMA over the iid Naagami-m fading channel where m r =min(m sr,m r ), and Bsr msr Γ(m sr ), m sr <m r B Ψ= m r r Γ(m r ), m sr >m r 1 Γ(m r ) (Bm r sr + B m r r ), m sr = m r = m r (38) Hence, the pdf of the SNR is given y f γaf (γ) f γs, (γ)+f γs, r, (γ) (39) and the corresponding MGF is given y Using(33),wehave M AF (s) =M s (s) M s, r, (s) (4) M AF (s) =B m ΨΓ(m s r ) s s m (41) s+m r Finally, P out is defined as L 1 {(M AF (s))/s; t} t=γth, ie, γ (m s+m r ) th P out (s) =B m s s ΨΓ(m r) Γ(m s + m r + 1) (42) From (42), one can see that the achieved diversity order is (m s + m r ) with m r =min(m sr,m r ) defined efore, whereas the achieved diversity order for the DF case presented in [14] is given y (m s + m r ) IV NUMERICAL RESULTS AND DISCUSSIONS In what follows, we present our analytical and simulation results for the outage proaility In all results, we set the spreading gain to N = 31 for a system with numer of users K = 16 Without loss of generality, we assume that the spectral efficiency R = 1 it/sec/hz A DD is used to mitigate the effect of MAI Fig 1 shows P out for oth noncooperative and cooperative AF relaying over iid Naagami-m fading channel It is clear that the outage proaility derived is tight at medium and high SNRs As shown in Fig 1, the AF cooperative CDMA system offers a considerale outage proaility gain compared Fig 2 Outage proaility for cooperative AF DS-CDMA with different fading figures m and considering ini Naagami fading channels with the noncooperative system In Fig 2, we present the outage proaility of the AF scheme over the ini Naagami-m fading channel As noted, when m ij increases, the system performance is improved In Figs 1 and 2, one can see the improved accuracy of the derived lower ound given y (28) for the outage proaility as the SNR increases In Fig 3, the asymptotic outage proaility given y (42) for the AF scheme is investigated Fig 3 confirms the accuracy of the approximation at medium and high SNRs, where the system performance is improved when the fading parameter m ij ecomes large Fig 3 also demonstrates the variation in the diversity order otained from (42) To examine the effect of MAI on the AF scheme, we consider the three following scenarios In the first system scenario, namely multiuser detection at the ase station (MUD-BS), the MUD is only applied at the ase station In the second scenario, ie, MUD-R-BS, the MUD is applied at oth the relay and the ase station In the third scenario, conventional detection, referred to as conventional R-BS, only matched filter detection is employed at the relay and the ase station Fig 4 depicts the average BER performance of cooperative CDMA over Naagami-m fading channels for the AF scheme when considering the three aforementioned systems As noted from these results, the optimum performance will e achieved when employing interference cancelation at oth the relay and the

6 1174 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 62, NO 3, MARCH 213 APPENDIX PROOF OF EQUATIONS (31) In this Appendix, we derive F Xtotal (y) of (31) We have I AF = K ) (1 2N log X sr X r + X s + (43) X sr + X r + 1 We can rewrite (43) as I AF = log (1 +(X s + X min )) (44) Fig 3 Asymptomatic outage proaility for cooperative AF DS-CDMA with different fading figures m and considering ini Naagami fading channels where = K/2N and X min =min(x sr,x r ) The outage proaility then is written as P out = P r [I AF < R] =P r [ log (1 +(X s + X min )) < R] (45) which yields P out = P r [X s + X min <y] (46) where y = 2 R/ 1 Having X s G(m s, γ s ) and X min G(m min, γ min ) as two gamma RVs, we derived the cdf of the sum of two gamma RVs to get the outage proaility as P out = F Xtotal (y) =P r [X s + X min <y] Fig 4 BER comparison etween cooperative AF and DF DS-CDMA with fading figures m ij = 15 ase station, whereas the case of MUD-BS only suffers from SNR loss due to the amplification of unwanted interfering signals In oth systems, full diversity is achieved for the AF scheme On the other hand, the BER of the conventional matched filter (conventional R-BS) exhiits an error floor at a certain SNR level due to the aggregate effect of multiuser interference at the relay and the ase station These results demonstrate that the mitigation of multiuser interference is essential to reach the diversity advantage of the cooperative system V C ONCLUSION The performance of AF cooperative diversity in a DS-CDMA system under the diversity comining of the relayed information at the ase station over Naagami-m fading channels is investigated The cooperative system studied employs multiuser detection to mitigate the effect of multiuser interference at oth the ase station and the relay sides A lower ound on the outage proaility of the AF cooperative system is derived In addition, an asymptotic outage proaility expression is derived where we evaluated the overall system diversity under different system settings Moreover, the impact of MAI on AF is studied, where the AF relaying is shown to achieve a satisfactory diversity gain without multiuser detection at the relay terminal = = = Then, we can get F Xtotal (y) = P r [X s + X min <y X s = x] f Xs (x)dx P r [X min <y x X s = x] f Xs (x)dx F Xr (y x)f Xs (x)dx (47) As in (1), the pdf of X s is f Xs (x) = and as in (2), the cdf of X min is F Xmin (y x)f Xs (x)dx, for y (48) Bm s s Γ(m s ) xm s 1 exp( xb s ) (49) F Xmin (y) =1 P [X sr >yandx r >y] = 1 Γ(m sr,b sr y) Γ(m sr ) F Xmin (y x) =1 Γ(m sr,b sr (y x)) Γ(m sr ) Γ(m r,b r y) (5) Γ(m r ) Γ(m r,b r (y x)) (51) Γ(m r )

7 MEHEMED AND HAMOUDA: AF COOPERATIVE CDMA OUTAGE PROBABILITY ANALYSIS 1175 From [15, eq (8352, 6)], we have Γ(n, x) =(n 1)! exp( x) Then, using (52), we can rewrite (51) as F Xmin (y x) n 1 m= x m m! (52) 1 = 1 Γ(m sr ) (m 1 sr 1)! Γ(m r ) (m r 1)! exp ( (y x)b sr )exp( (y x)b r ) n= (B sr (y x)) n r 1 i= (B r (y x)) i (53) From [15, eq (8339, 1)], we have Γ(m sr )=(m sr 1)! and Γ(m r )=(m r 1)! Therefore, we can rewrite (53) as F Xmin (y x) =1 exp ( y(b sr + B r )) exp (x(b sr +B r )) (y x) n r 1 i= n= (B r ) i (y x) i (54) Using the inomial expansion as in [15, eq (1111)], where (a + x) n = n = ( n ) x a n, (54) can e written as F Xmin (y x) = 1 exp ( y(b sr + B r )) exp (x(b sr + B r )) r 1 ( 1) x y n i= n= (B r ) i i f= = ( ) n ( 1) f x f y i f f By sustituting (55) into (48) and using (49), we get F Xtotal (y) = 1 exp ( y(b sr + B r )) exp (x(b sr + B r )) = n= ( m n r 1 )( 1) x y n (B r ) i i= i ( 1) f x f y i f f Xs (x)dx f f= (55) = f Xs (x)dx exp (x(b sr + B r )) r 1 x y n i= f Xs (x)exp( y(b sr + B r )) (B r ) i n= i f= = ( ) n ( 1) ( 1) f x f y i f dx f (56) Finally, the total cdf can e written after some manipulation as F Xtotal (y) = γ(m s,γb s ) Γ(m s ) Bm s s Γ(m s ) exp ( y(b sr + B r )) x (ms 1) exp ( x(b s B sr B r )) n= r 1 i= (B r ) i = ( ) n ( 1) y n x i f= REFERENCES ( 1) f y i f x f f dx (57) [1] A Sendonaris, E Erip, and B Aazhang, User cooperation diversity Part I System description, IEEE Trans Commun, vol 51, no 11, pp , Nov 23 [2] A Sendonaris, E Erip, and B Aazhang, User cooperation diversity Part II Implementation aspects and performance analysis, IEEE Trans Commun, vol 51, no 11, pp , Nov 23 [3] J Laneman, D Tse, and G Wornell, Cooperative diversity in wireless networs: Efficient protocols and outage ehavior, IEEE Trans Inf Theory, vol 5, no 12, pp , Dec 24 [4] L Venturino, X Wang, and M Lops, Multiuser detection for cooperative networs and performance analysis, IEEE Trans Signal Process, vol 54, no 9, pp , Sep 26 [5] X Liu, X Zhang, and D Yang, Outage proaility analysis of multiuser amplify-and-forward relay networ with the source-to-destination lins, IEEE Commun Lett, vol 15, no 2, pp 22 24, Fe 211 [6] R de Lamare and S Li, Joint iterative power allocation and interference suppression algorithms for cooperative DS-CDMA networs, in Proc IEEE VTC, 21, pp 1 5 [7] S Ii and M Ahmed, Performance analysis of incremental-relaying cooperative-diversity networs over Rayleigh fading channels, IET Commun, vol 5, no 3, pp , Fe 211 [8] N Beaulieu and C Cheng, Efficient Naagami-m fading channel simulation, IEEE Trans Veh Technol,vol54,no2,pp ,Apr25 [9] S Atapattu, N Rajatheva, and C Tellamura, Performance analysis of TDMA relay protocols over Naagami-m fading, IEEE Trans Veh Technol, vol 59, no 1, pp 93 14, Jan 21 [1] W Fang, L-L Yang, and L Hanzo, Performance of DS-CDMA downlin using transmitter preprocessing and relay diversity over Naagami-m fading channels, IEEE Trans Wireless Commun, vol 8, no 2, pp , Fe 29

8 1176 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 62, NO 3, MARCH 213 [11] H A Suraweera, P J Smith, and J Armstrong, Outage proaility of cooperative relay networs in Naagami-m fading channels, IEEE Commun Lett, vol 1, no 12, pp , Dec 26 [12] N Yang, M Elashlan, and J Yuan, Outage proaility of multiuser relay networs in Naagami-m fading channels, IEEE Trans Veh Technol, vol 59, no 5, pp , Jun 21 [13] F Xu, F Lau, Q Zhou, and D-W Yue, Outage performance of cooperative communication systems using opportunistic relaying and selection comining receiver, IEEE Signal Process Lett, vol 16, no 4, pp , Jan 29 [14] A Mehemed and W Hamouda, Outage analysis of cooperative CDMA systems in Naagami-m fading channels, IEEE Trans Veh Technol, vol 61, no 2, pp , Fe 212 [15] I S Gradshteyn and I M Ryzhi, Tale of Integrals, Series, and Products San Diego, CA: Academic, 1994 [16] K Vardhe, D Reynolds, and M Valenti, The performance of multi-user cooperative diversity in an asynchronous CDMA uplin, IEEE Trans Wireless Commun, vol 7, no 5, pp , May 28 [17] A Eid, W Hamouda, and I Dayou, Performance of multi-relay coded cooperative diversity in asynchronous code-division multiple-access over fading channels, IET Commun, vol 5, no 5, pp , Mar 211 [18] S Ii and M Ahmed, Performance analysis of cooperative diversity wireless networs over Naagami-m fading channel, IEEE Commun Lett, vol 11, no 4, pp , Apr 27 [19] GE Roerts and H Kaufman, Tale of Laplace Transformers Philadelphia, PA: Sannders, 1966 Walaa Hamouda (SM 6) received the MASc and PhD degrees in electrical and computer engineering from Queen s University, Kingston, ON, Canada, in 1998 and 22, respectively Since July 22, he has een with the Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada, where he is currently an Associate Professor Since June 26, he has een the Concordia University Research Chair in Communications and Networing His current research interests include multiple-input multipleoutput space time processing, cooperative communications, wireless networs, multiuser communications, cross-layer design, and source and channel coding Dr Hamouda served or is serving as the Technical Cochair of the Wireless Networs Symposium, the 212 Gloal Communications Conference, the Ad hoc, Sensor, and Mesh Networing Symposium of the 21 International Communications Conference (ICC), and the 25th Queen s Biennial Symposium on Communications He also served as the Trac Cochair of the Radio Access Techniques of the 26 IEEE Vehicular Technology Conference (IEEE VTC- Fall 26) and of the Transmission Techniques of the IEEE VTC-Fall 212 From Septemer 25 to Novemer 28, he was the Chair of the IEEE Montreal Chapter in Communications and Information Theory He has received numerous awards, including the Best Paper Award of the ICC 29 and the IEEE Canada Certificate of Appreciation in 27 and 28 He serves as an Associate Editor for the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, the IEEE COMMUNICATIONS LETTERS,andIET Wireless Sensor Systems Ali Mehemed (S 11) was orn in Liya He received the MASc degree (with honors) in electrical engineering from the Technical University of Budapest, Budapest, Hungary, in 25 He is currently woring toward the PhD degree with the Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada His PhD research is focused on the performance of cooperative direct-sequence code-division multipleaccess systems in Naagami-m fading channels Since 28, he has een a Research Assistant with the Department of Electrical and Computer Engineering, Concordia University