Journal of Communications Vol. 8, No. 6, June 2013 Performance Analysis of Two-Way AF Cooperative Relay Networks over Weibull Fading Channels Xinjie Wang1,2, Hao Zhang1,3, T. Aaron Gulliver3, Wei Shi1 and Hongjiao Zhang1 1 Department of Electrical Engineering, Ocean University of China, Qingdao, China 2 College of Communication and Electronics, Qingdao Technological University, China 3 Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada Email: [email protected]; [email protected]; [email protected]; [email protected] [email protected] Abstract—The performance of two-way amplify-and-forward and symbol error probability (SEP) for two-way AF (AF) cooperative relay networks over independent but not relaying were analyzed with perfect channel state necessarily identically distributed Weibull fading channels is information (CSI) over Rayleigh fading channels in [11], studied. Tight closed form approximations for the overall [12]. In [13], two-way relaying in mixed Rayleigh and outage probability (OOP) and the average symbol error Rician fading channels was considered. The exact probability (ASEP) are derived. The analysis is verified by expressions for OP, SEP and average sum-rate were simulation, and the accuracy is shown to be excellent, especially derived over Nakagami-m fading channels in [14]. at high signal noise ratio (SNR). According to the analysis, increasing the fading parameter, the power scaling parameter, or However, the above results only consider the performance in terms of single user outage and SER. the number of relays, can improve the system performance when the best relay is selected. Since the quality of service (QoS) requirements for bidirectional links are the same as for two-way relaying, Index Terms—Two-way relay network; Weibull fading channel; the overall outage probability (OOP) and average SEP Outage probability; Symbol error probability; Amplify and performance can be used to evaluate the performance of forward both links. In [15], the OOP and average symbol error probability (ASEP) performance of two-way AF based I. INTRODUCTION relaying protocols over Rayleigh fading channels was investigated. The corresponding performance over Cooperative relaying techniques have recently gained attention as an efficient way to mitigate fading in wireless Nakagami-m fading channels was considered in [16], [17]. The performance with a cascaded fading networks. Most conventional cooperative relay networks are half-duplex and employ a relaying mode such as distribution such as the cascaded generalized-K amplify-and-forward (AF), decode-and-forward (DF), or distribution [18] has also been investigated. The Weibull incremental relaying [1]. The performance of cooperative distribution has been recommended for mobile radio diversity networks was investigated in [2]. To enhance systems as well as the Nakagami-m distribution [19]. The performance, selective DF and opportunistic relaying performance of a conventional cooperative relay network networks have been proposed, and the outage over a Weibull fading channel was analyzed in [20]-[23]. performance and symbol error rate (SER) analyzed in [3]. However, the overall performance of two-way relaying Further, the average symbol error probability of a multi- has not been investigated over these channels. branch dual-hop cooperative network in Rayleigh and In this paper, two-way AF relaying with multiple Nakagami-m fading channels was analyzed in [4], [5]. relays over independent but not necessarily identically The strategy of selecting the best relay and Nth best relay distributed Weibull fading channels is examined. Tight from amongst several relays has been proposed to closed-form approximations for the OOP and ASEP are enhance the spectral efficiency [6]-[9]. The performance derived. These results are validated by simulation, and of conventional one-way cooperative systems has been the effect of the channel parameters on performance is investigated extensively. examined. To further improve the spectral efficiency, two-way The remainder of this paper is organized as follows. AF and DF cooperative relaying protocols have been Section II presents the system model, and the overall introduced [10]. In this case, only two time steps are outage probability is derived in Section III. The overall required to transmit a symbol. The outage probability (OP) error probability is derived in Section IV. Performance results are given in Section V based on the analysis in the previous sections. Finally, some conclusions are given in Manuscript received April 20, 2013; revised June 15, 2013, accepted Section VI. June 18, 2013 This work was supported by the International S&T Cooperation Program of Qingdao, China under Grant No. 12-1-4-137-hz. II. SYSTEM MODEL Corresponding author email: [email protected] doi:10.12720/jcm.8.6.372-377 ©2013 Engineering and Technology Publishing 372 Journal of Communications Vol. 8, No. 6, June 2013 The two-way relay model is shown in Fig. 1. Two respectively. The signal-to-noise ratios (SNRs) of the source nodes S1 and S2 exchange information via the links S1 R j S2 and S2 R j S1 are given by best relay R . Thus, there is no direct connection k 12jj (6) between S1 and S2 . Rk is selected from the set of relay 12j 12jj21 nodes R j , j=1, 2, ..., N. All nodes operate in half-duplex 12jj fashion and are equipped with a single antenna. hij is the 21j (7) 2112jj channel coefficient between source node Si (i=1, 2) and 2 R j . The channel coefficients hij are independent but not respectively, where ij P S| h ij | / N0 , i=1, 2. When PN , (6) and (7) can be expressed as necessarily identically distributed (i.n.d.) random S 0 variables that follow the Weibull distribution. 12jj 12j (8) 12jj 2 and 12jj (9) 21j 212jj In the second time slot, the best relay Rk is selected to relay the signal, and is selected as follows [15] k arg max min1jj 2 , 2 1 (10) jN{1.. } Figure. 1 The two-way AF relay cooperative network. The channel coefficient hij is a Weibull random variable, so the probability density function (PDF) of h According to the protocol of two-way relay networks ij [10], in the first time slot the signal received at the jth can be written as [23] relay is given by 2ij 2ij 21 x ij f||h x x exp (11) y P h x P h x n (1) ij ij ij j s1 j 1 s 2 j 2 j ij ij where Ps is the transmitted signal energy from Si , xi is where Eh(2 )/ 1 1/ , ()x is the Gamma the normalized signal with unit energy, and n is additive ij ij ij j function, is the power scaling parameter for the white Gaussian noise (AWGN) at relay R j with zero ij channel between S and R , and is the fading mean and variance N0 . i j ij In the second time slot, if relay R is selected to relay severity parameter for the channel between S and R j . j i The PDF of the instantaneous SNR ij can be expressed the signal, it scales the received signal by G j , and as broadcasts the resulting signal to S1 and S2 . Then the ij ij 1 x signal received at Si from relay R j is given by ij f x x exp (12) ij ij ij ij ij ySi G j h ij y j n i (2) where PN/ . With perfect channel state information at R , we have ij ij S 0 j P III. OVERALL OUTAGE PROBABILITY G R (3) j P| h |22 P | h | N For a two-way AF relaying system employing the best s1 j s 2 j 0 relay Rk , an overall outage event occurs when at least where PR is the transmitted signal energy from R j . For one of 12k and 21k fall below the threshold th . Thus convenience, let P = P . s R the overall outage probability can be defined as After the self-interference is removed, the received signals at S1 and S2 are given by Pout = Pr min(1k 2 , 2 k 1 ) th y G h() P h x n n (4) = Pr arg max min(1j 2 , 2 j 1 ) th S1 j 1 j s 2 j 2 j 1 jN{1.. } and N = Pr min(1j 2 , 2 j 1 ) th (13) yS2 G j h 2 j() P s h 1 j x 1 n j n 2 (5) j1 ©2013 Engineering and Technology Publishing 373 Journal of Communications Vol. 8, No. 6, June 2013 We have 1 where Q x exp t2 2 dt , and u and v 2 x Pr min(1j 2 , 2 j 1 ) th depend on the modulation employed, e.g. for BPSK u =1 =1 Pr min( , ) 1j 2 2 j 1 th and v =2 [24]. We then have 1j 2 j 1 j 2 j Pe = P( e | ) f ( ) d =1 Pr , (14) e e k 22 th th 0 1j 2 j 1 j 2 j 2 2 t ut = F() e2 dt Defining X 1 and X 1 , from (12) the 0 k 11jj 22jj 2 v corresponding PDF and CDF are N 2212jj u 22tt 1 exp 0 2 j1 vv12jj ij 1 1 fxX 1 exp (15) ij ij ij ij x x 2 ij ij t expdt (22) and 2 1 Fxexp (16) Asymptotically, 1 exp(x ) x as x 0 , so at high Xij x ij ij SNRs ( ij large), (21) can be expressed as respectively. Then 12jj2 N 22t u 22tt Pr min( , ) Pe e 2 dt 1j 2 2 j 1 th e 0 2 j1 vv12jj C 1 x =1 FXX f x dx ijj 21jj 2 2 2 N 22 th u 2 0 L D 2 i121 i 1 iN 1 j1 ijv 1 j FXX 2 x f x dx (17) 21jj 1 N th - N C 2 ijj 1 2 j1 (23) ij 2 j1 j where C 1/3 th and D 1/ 2 th .