Approximate error probability of MPSK for optimum combining with multiple interferers in a Rayleigh fading

This work presents the approximate symbol error rate (SER) of M-ary phase shift keying (MPSK) for optimum combining (OC) with multiple co-channel interferers in a flat Rayleigh fading channel. The closed-form expression for the ordered mean eigenvalues of interference-plus-noise covariance matrix is derived for the first-order approximation to avoid Monte Carlo simulation and multiple numerical integrals in the cases of arbitrary numbers of interferers and antenna elements. We also derive the closed-form expression for approximate SER of MPSK for OC in terms of the average SER of MPSK for maximal ratio combining (MRC). From the simple evaluation of ordered mean eigenvalues, the first-order approximation gives a simple and accurate way to analyze the performance of OC in the presence of the arbitrary number of interferers.