Decision-feedback differential detection of MDPSK for flat Rayleigh fading channels

In this paper, decision{feedback di erential detection (DF{DD) ofM{ary di erential phase{shift keying (MDPSK) signals, which has been introduced previously for the additive white Gaussian noise (AWGN) channel by Leib et al. [1] and Edbauer [2], is extended to at Rayleigh fading channels. The DF{DD metric is derived from the multiple{symbol detection (MSD) metric and for error{free feedback an exact expression for the bit error rate for the widely used QDPSK constellation (M = 4) is calculated. Furthermore, the dependence of the bit error rate on the power spectrum of the fading process is investigated for feedback lters of in nite order. It is shown that in this case, for ideally bandlimited fading processes the error oor of conventional di erential detection (DD) can be removed entirely. Simulation results con rm that DF{ DD with feedback lters of nite order can reduce the error oor of conventional DD signi cantly.