Symbol Error Probability of DF Relay Selection over Arbitrary Nakagami- Fading Channels

We present a new analytical expression for the moment generating function (MGF) of the end-to-end signal-to-noise ratio of dual-hop decode-and-forward (DF) relaying systems with relay selection when operating over Nakagami- fading channels. The derived MGF expression, which is valid for arbitrary values of the fading parameters of both hops, is subsequently utilized to evaluate the average symbol error probability (ASEP) of -ary phase shift keying modulation for the considered DF relaying scheme under various asymmetric fading conditions. It is shown that the MGF-based ASEP performance evaluation results are in excellent agreement with equivalent ones obtained by means of computer simulations, thus validating the correctness of the presented MGF expression. 1. Introduction Cooperative communication through relay nodes has been shown to be capable of extending the radio coverage and improving the reliability of emerging wireless systems [1–3]. One of the bandwidth efficient dual-hop cooperative techniques combines the decode-and-forward (DF) relaying protocol with relay selection (RS) [4]. The performance of this technique has been studied in [4] over Rayleigh fading channels and in [5–7] for the more general Nakagami- fading channel model. However, in the latter works analytical expressions for the moment generating function (MGF) of the end-to-end signal-to-noise ratio (SNR) have been presented, which are valid only for the special case where the Nakagami -parameter of both hops takes integer values. In [5], the authors based their analysis on the tight approximation for the end-to-end SNR presented in [8], whereas [6, 7] utilized the end-to-end SNR characterization of [9]. Nevertheless, in realistic wireless communication scenarios, estimators for from field measurement data typically result in arbitrary values [10]. Moreover, restricting to only integer values severely limits the advantageous property of the Nakagami- fading distribution to adequately approximate the Rice and Hoyt ones [11]. Very recently, based on [9], the authors in [12] investigated the error probability of opportunistic DF relaying over Nakagami- fading channels with arbitrary . In this paper, capitalizing on the approach of [8], we present a new closed-form representation for the MGF of the end-to-end SNR of dual-hop DF RS-based systems which is valid for arbitrary-valued parameters for both Nakagami- faded hops. In addition, the derived expression is utilized to evaluate the average symbol error probability (ASEP) of -ary phase shift keying (PSK) modulation for the considered