Exact bit-error probability for optimum combining with a Rayleigh fading Gaussian cochannel interferer

We derive expressions for the exact bit-error probability (BEP) for the detection of coherent binary phase-shift keying signals of the optimum combiner employing space diversity when both the desired signal and a Gaussian cochannel interferer are subject to flat Rayleigh fading. Two different methods are employed to reach two different, but numerically identical, expressions. With the direct method, the conditional BEP is averaged over the fading of both signal and interference. With the moment generating function based method, expressions are derived from an alternative representation of the Gaussian Q-function.