On the optimality of classical coherent receivers of differentially encoded M-PSK

This paper demonstrates that the classical receiver used for coherent detection of differentially encoded M-ary phase-shift keying (M-PSK), namely, the one that makes optimum coherent decisions on two successive symbol phases and then differences these to arrive at a decision on the information phase is suboptimum when M>2. However, this receiver structure can be arrived at by a suitable approximation of the likelihood function used to derive the true optimum receiver whose structure is also given.