Efficient evaluation of exact error probability for optimum combining of M-ary PSK signals

In this paper, we derive an exact expression for the symbol error probability (SEP) for coherent detection of M-ary PSK signals using array of antennas with optimum combining in a Rayleigh fading environment. The proposed analytical framework is based on the theory of orthogonal polynomials and we give an effective technique to derive the SEP involving only one integral with finite integration limits. The result is general and valid for an arbitrary number of receiving antennas or co-channel interferers.