Equivalent channel for capacity analysis of differential detection over time-varying communication channels

This paper introduces the concept of equivalent channel for mutual information performance analysis of multiplesymbol differential MPSK (M -phase shift keying) over timecorrelated, time-varying flat-fading communication channels. It is proven that differential detection scheme theoretically preserves the channel information capacity when the observation interval approaches infinity. A state space approach is used to model time correlation of time varying channel phase. It is shown that the differential decoding implicitly uses a sequence of innovations of the channel process time correlation and this sequence is essentially uncorrelated (i.i.d). It enables utilization of multiple-symbol differential detection, as a form of blockby-block maximum likelihood sequence detection for capacity achieving mutual information performance.