Performance Analysis of a Gauss-Optimal Receiver for a Receive Diversity PLC System in Nakagami-$m$ Noise Environment

This paper proposes a novel optimal receiver for an $N$ -branch receive diversity power line communication (PLC) system subject to Rayleigh fading and perturbed by Nakagami-m background noise. A Gauss-optimal receiver is obtained from the optimal receiver which is further utilized to derive a closed form expression for the symbol error probability (SEP) for binary phase-shift keying (BPSK) modulation using a characteristic function approach under the condition that mN is an integer. An asymptotic expression for the SEP at high signal-to-noise ratio (SNR) shows the diversity order of the PLC system to be independent of the noise shape parameter $m$. Numerical studies demonstrate that the diversity order of the optimal receiver is preserved with the suboptimal receiver as well. Furthermore, the advantage of using multiple receive branches in terms of achieving better error performance and the effect of the shape parameter $m$ on the SEP of the suboptimal receiver are also presented.