Bit error probability of coherent M-ary PSK over flat Rayleigh fading channels

Systems using coherent multilevel PSK to communicate over flat Rayleigh fading channels are considered. Presented is a closed-form expression for the exact bit error probability when the binary reflected Gray code is used to map bits to symbols. The result is a general, simple, and correct expression, which has not been previously available in the literature. A comparison between this new expression and previous approximate expressions shows that the difference is more significant for fading channels than for Gaussian channels.