Average symbol error probability for M-ary DDPSK

A unified and exact analysis of the symbol error probability (SEP) for M-ary doubly-differential phase-shift keying (M-DDPSK) is presented. The SEP is expressed in terms of Fourier coefficients of the probability density function of the composite phase at the receiver input which are available for several channel scenarios including the additive white Gaussian noise, the fading, the fading-shadowing and the cochannel interference type of channel. Useful numerical results, obtained through the analytical expressions derived, are presented to compare the performance of 8-DDPSK and 8-DPSK over a channel in which, in addition to additive noise, a constant carrier frequency shift and Nakagami fading affect the transmission.