Approximate closed-form expression for the average BER of M-ary PSK with Gaussian-distributed phase error

Abstract

In this paper, we derive an approximate closed-form expression for the average bit error rate (BER) of M-ary phase shift keying (PSK) with Gaussian-distributed phase error over an additive white Gaussian noise channel. The derived closed-form expression is provided as a linear combination of error functions, which is a function of signal to noise ratio, modulation order, and the variance of phase error. Thus, it offers a convenient way to compute the average BER of M-ary PSK with Gaussian-distributed phase error. To validate the theoretical results, we compare the results obtained from the proposed expression with those from computer simulations.