A Numerical Method for Estimating Error Rate Performance of MPSK System influenced by Fisher-Snedecor Fading

The aim of this paper is to estimate the error probability in coherent detection of multilevel phase-shift keying (MPSK) signals transmitted through a channel in which the multipath fading and shadowing are present simultaneously together with thermal noise. To describe this type of fading, we use a Fisher-Snedecor model that was proposed relatively recently. For this fading model, using the Fourier series, we first represent the probability density function (PDF) of the composite signal phase. We present expressions for the coefficients in the Fourier series, that were previously derived by ourselves. We examine the convergence of this series for different numerical values of the channel parameters. Next, we present the expression for estimating the error probability in MPSK signal detection. Based on this, we examine the influence of multipath fading severity and the shadowing spread on the numerical values of the error probability for different number of phase levels. The obtained results enable a further evaluation of the performance of differentially coded signals, as well as an evaluation of the influence of the phase noise both on the error probability and the mutual information in the channel with this type of fading.