Noncoherent Decode-and-Forward Cooperative Systems with Maximum Energy Selection Ha X. Nguyen 1 , Cuu V. Ho 2 , Chan Dai Truyen Thai 3 , Danh T. Nguyen 4 1 ha.nguyen@ttu.edu.vn, School of Engineering, Tan Tao University Tan Duc Ecity, Duc Hoa, Long An Province, Vietnam 2 cuu.hv@cb.sgu.edu.vn, Department of Electronics and Telecommunications, Saigon University 273 An Duong Vuong, District 5, Ho Chi Minh City, Vietnam 3 chan.thai@ifsttar.fr, Univ Lille Nord de France F-59000, Lille, IFSTTAR, LEOST, F-59650, Villeneuve d’Ascq, France 4 nthanhdanh0410@gmail.com, Faculty of Electronics and Telecommunications, University of Science Vietnam National University, Ho Chi Minh City, Vietnam Abstract—This paper investigates the performance of a max- imum energy selection receiver of an adaptive decode-and- forward (DF) relaying scheme for a cooperative wireless system. In particular, a close-form expression for the bit-error-rate (BER) is analytically derived when the system is deployed with binary frequency-shift keying (BFSK) modulation. The thresholds used at the relays to address the issue of error propagation are opti- mized to minimize the BER. While finding the optimal thresholds requires information on the average signal-to-noise ratios (SNRs) of all the transmission links in the system, the approximate threshold at each relay that requires only information on the average SNR of the source-corresponding relay is investigated. It is also shown that the system achieves a full diversity order with the approximate thresholds . Both analytical and simulation results are provided to validate our theoretical analysis. I. I NTRODUCTION Frequency shift keying (FSK) is a popular modulation scheme in noncoherent communications in which the receiver does not require any channel state information (CSI) to decode the transmitted signals [1]. Consequently, using FSK signals in cooperative systems has been focused recently since there is a complexity advantage in decoding [2]–[7]. It is due to the fact that there are many wireless fading channels involved in the systems [8], [9], which makes the task of channel estimation more difficult. With the decode-and-forward (DF) protocol employing FSK in cooperative systems, reference [3] proposed maximum likelihood (ML) and suboptimal piecewise linear (PL) schemes to decode the signals at the destination. However, it was shown that the system could not achieve a full diversity order due to the error forwarding at the relays. References [6], [7] proposed to use a threshold at the relays to address the issue of error propagation for binary frequency- shift keying (BFSK) modulation. While the destination in [6] combines all the signals from the retransmitting relays, the destination in [7] selects only one signal with the largest magnitude of the energy difference to decode. Unfortunately, designing the optimal thresholds to minimize the average bit- error-rate (BER) of the system relies on the MATLAB Op- timization Toolbox and a theoretical analysis of the diversity order is not available. This paper studies the maximum energy selection (MES) receiver, i.e., selecting the maximum output from the square- law detectors of all branches to perform a detection, for a threshold-based (i.e., adaptive) DF cooperative system. While the destination in [7] relies on the maximum magnitude of the energy difference, the destination in this paper employs the maximum energy from the square-law detectors to detect the transmitted signal. The approximate thresholds that achieve full diversity are provided in this paper. Note that the direct link between the source and destination is considered in this work while the work in [7] assumes that there is no such a link. II. SYSTEM MODEL 0D[LPXP (QHUJ\ 6HOHFWLRQ 6RXUFH 'HFRGH DQG )RUZDUG WK  U . θ θ > 5HPDLQ 6LOHQW < 1 5HOD\  5HOD\ . 'HVWLQDWLRQ 'HFRGH DQG )RUZDUG WK  U θ θ > 5HPDLQ 6LOHQW < 1 Fig. 1. System description of the proposed scheme. Fig. 1 illustrates the signal transmission from the source (node 0) to destination (node K +1) with the assistance of K half-duplex relays (node i, i =1,...,K). The relays retransmit signals to the destination in orthogonal channels. In this paper, we assume that the fading channel coefficient between transmit node i and receive node j , denoted by h i,j , and the noise component at receive node j , denoted by n i,j , are modeled as zero-mean complex Gaussian random variables with variances σ 2 i,j and N 0 , respectively. The instantaneous signal-to-noise ratio (SNR) of the channel between node i and node j , which is denoted by γ i,j , is given as γ i,j = The 2013 International Conference on Advanced Technologies for Communications (ATC'13) 978-1-4799-1089-2/13/$31.00 ©2013 IEEE 136