Optimum noncoherent multiuser detection for DPSK modulation in generalized diversity Rayleigh fading channels: an asymptotic minimum error probability analysis

The jointly optimum noncoherent multiuser detector for DPSK modulation in generalized diversity Rayleigh fading channels (GDRF) was presented in [1] and bounds on the error probability were obtained. In the numerical examples of [1] these bounds were seen to converge. This paper examines analytically the behavior of the bounds for high signal-to-noise ratio (SNR) scenarios. Slowly fading channels, where the fading coefficients are essentially constant over two successive symbol intervals, and fast fading channels, where the fading coefficients can vary from one symbol interval to the next, are considered. For slow fading, the asymptotic convergence of the upper bound to the lower bound is proved. The asymptote that is reached for high values of the SNR does not depend on the interfering users’ energies, establishing thereby the near-far resistance of the optimum multiuser DPSK detector. For fast fading the error floor reached for high SNRs is bounded from below and above.