Differential BPSK modulation for cooperative communication systems in time-selective rayleigh fading channels

In this paper, we consider the amplify-and-forward (AF) relaying cooperative communication system employing differential binary phase-shift-keying (DBPSK) modulation in time-selective (fast) Rayleigh fading channels. When channel gains are fast-varying, it is well known that differential modulation can ease the channel estimation process and reduce the power and bandwidth overhead occurred in coherent modulation schemes. Unlike the previous work on this topic which always assumed the channel gains are the same over two adjacent symbol periods, we model the channel time-selectivity exactly in our formulation and derive the optimal diversity combining weights for the AF relaying system based on the maximum likelihood criterion. Since the optimum combining rule depends on the channel gains of the relay-to-destination links which are usually unavailable in the context of differential modulation, we propose a suboptimal diversity combining rule which replaces the instantaneous channel gains by their second order statistics. Compared with the performance of the diversity combining rule without taking the time-selectivity into account, computer simulation results show that the proposed diversity combining rule has superior performance for the AF relaying system in time-selective Rayleigh fading channels, especially when the relay and destination nodes have different Doppler spreads.