A Systematic Approach to Noncoherent Detection for DPSK Modulation in Multiuser Correlated Diversity Rayleigh Fading Channels

A correlated diversity Rayleigh fading (CDRF) channel models inter-diversity fading and signal correlations. This paper considers the multiuser CDRF channel wherein several users transmit information simultaneously using signals with inter-diversity as well as inter-user correlations. Each user employs DPSK modulation. Besides allowing simple noncoherent detection without channel estimation algorithms, DPSK is a modulation method of choice when the coherence time of the channel is too short to estimate the fading coefficients accurately. Until recently, the multiuser detectors suggested for the multiuser CDRF channel have been of the post-decorrelative type with ad-hoc equal-gain combining. A systematic approach to optimum DPSK detection for the single-user CDRF channel was introduced in [Var97]. This paper generalizes that work to the multiuser CDRF channel. As in [Var97], two different noncoherent detectors are obtained. For the slowly fading channel, where the fading coefficients are essentially constant over two successive symbol intervals, the generalized likelihood ratio test (GLRT) is derived. This rule can be implemented without knowledge of the fading statistics or the users’ energies. For both slow and fast fading channels, where in the latter, the fading coefficients can vary from one symbolinterval to the next, a multiuser minimum error probability (MEP) detector is also obtained. The MEP requires a limited knowledge of the statistics of the fading coefficients for its implementation. Upper and lower bounds on the bit error rate (BER) of the MEP and GLRT detectors are derived. In our numerical examples, these bounds converge for high signal-to-noise ratios for each detector. While these detectors are exponentially complex, their performances provide benchmarks for sub-optimal detectors. In particular, it is seen that the post-decorrelative detectors can be far from satisfactory.