A new symbol error rate calculation for Rayleigh fading multichannel reception of MPSK signals

A new closed form expression is provided for calculating the probability that an M-ary phase shift keying (MPSK) signal will lie in a particular decision region when received over N independent and identically distributed Rayleigh fading channels corrupted by additive white Gaussian noise. This expression is applied to provide a unified method to derive the exact symbol error rate of an MPSK signal, considering N channel diversity reception such as maximal ratio combining, equal gain combining, and selection combining.