Error probability for optimum combining of M-ary PSK signals in the presence of interference and noise

An exact expression for the symbol-error probability (SEP) for coherent detection of M-ary phase-shift keying using an array of antennas with optimum combining in a Rayleigh fading environment is derived, based on the theory of orthogonal polynomials. In particular, performance analysis in the presence of multiple uncorrelated equal-power cochannel interferers and thermal noise is considered, starting from problems related to the eigenvalues distribution of complex Wishart matrices. 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 and/or cochannel interferers. Based on our efficient method, new results that are useful for the design of wireless systems are obtained.