Effect of imperfect phase synchronization on the error rate performance of MPSK in Rayleigh, Rician and Nakagami fading channels

This paper provides a framework for error rate performance analysis of M-ary phase-shift keying (MPSK) systems with improper phase estimation over some common fading channels obeying Rayleigh, Rician, or Nakagami-m distribution. In addition, the channel is also perturbed by additive white Gaussian noise (AWGN). The phase distortions considered in the paper are random, unbiased, i.e. having zero-mean, and follows Tikhonov distribution. Analytical average symbol error probability (SEP) is calculated through a new efficient method and plotted as a function of signal to noise ratio (SNR) for different values of the modulation order, M. Our approach relies upon knowledge of the moment generating function (MGF) of the received SNR. The resulting expression is an integral over a finite range of integrands containing only elementary functions. Extensive Monte Carlo simulations were performed to validate the theoretical results. Although the SEP can be computed via direct numerical integration, the MGF method performs far better because direct integration suffers from numerical instability and inaccuracy due to the presence of infinite integration limits or may contain complex mathematical functions.