A systematic approach to the design and analysis of optimum DPSK receivers for generalized diversity communications over Rayleigh fading channels

A generalized diversity channel is introduced that models a variety of wireless communication systems that use time, frequency, multipath, and/or antenna diversity with various interbranch correlations between signaling waveforms and the fading and additive noise processes. In the context of this general model, a systematic approach to the design and analysis of optimum noncoherent differential phase-shift keying (DPSK) receivers is introduced. In particular, it is shown how the minimum error probability (MEP) and the generalized likelihood ratio tests (GLRT) can be applied to obtain optimal noncoherent combining rules. A comparative error-rate analysis of the GLRT and MEP detectors and an ad hoc equal-gain combiner is provided for binary signaling, and the suitability of the three schemes is determined as a function of fading characteristics. The asymptotic bit-error-rate analysis is undertaken for the MEP detector for slow and fast fading channels. An estimator-detector decomposition of the noncoherent MEP rule is obtained which allows an insightful comparative study of the fundamental limits of binary phase-shift keying and DPSK modulation-detection methods for both slow and fast fading. The results of this paper are also applicable to postdecorrelative receivers in multiuser channels.