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

In this paper, decision-feedback differential detection (DF-DD) of M-ary differential phase-shift keying (MDPSK) signals, which has been introduced previously for the additive white Gaussian noise (AWGN) channel by Leib et al. (1988) and Edbauer (1992), is extended to flat 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 filters of infinite order. It is shown that in this case, for ideally bandlimited fading processes the error floor of conventional differential detection (DD) can be remove entirely. Simulation results confirm that DF-DD with feedback filters of finite order can reduce the error floor of conventional DD significantly.