Symbol error rate of wireless multiuser relay networks in Nakagami-m fading channels

This paper analyzes the performance of wireless multiuser relay networks (MRN) in unbalanced Nakagami-m fading channels. For such networks, we consider a single channel state information (CSI)-based amplify-and-forward (AaF) relay. We derive a new exact expression for the symbol error rate (SER), which is in closed-form and applies to a wide variety of modulations. Subsequently we present a simplified asymptotic expression for the SER in the high signal-to-noise ratio (SNR) regime to identify key performance metrics such as the diversity order and array gain. Our asymptotic result explicitly reveals the direct relationship between the diversity order and both the number of destinations and the per-hop fading parameters. Moreover, we highlight the effect of the number of destinations on the optimal relay location aiming at minimizing the SER. The validity of our analysis is substantiated by numerical results.