Phase distributions of Rayleigh faded signal with selection diversity reception

Closed form, but simple to use expressions for the phase difference distribution of a Rayleigh faded signal perturbed by AWGN are derived for L-branch ideal selection diversity reception. The distribution of the coherently detected signal phase under Rayleigh fading is also derived from the phase difference distribution. How the distributions are affected by the receive filter induced signal distortion and by the noise correlation is discussed. As an application, the derived distributions are applied to calculate the symbol error rates of 8DPSK and 8CPSK, and the results are graphically presented to demonstrate that diversity reception significantly reduces the error rates. The effect of phase errors arising from carrier frequency offset for 8DPSK and imperfect carrier recovery for 8CPSK is also discussed.<>