Optimally near-far resistant multiuser detection in differentially coherent synchronous channels

The noncoherent demodulation of differentially phase-shift keyed signals transmitted simultaneously via a synchronous CDMA channel is studied under the assumption of white Gaussian background noise. A class of noncoherent linear detectors is defined with the objective of obtaining the optimal one. The performance criterion considered is near-far resistance, which denotes worst-case multiuser asymptotic efficiency over near-far environments. It is shown that the optima1 linear detector is a noncoherent decorrelating detector. This detector is analogous to the coherent decorrelating detector that was obtained from similar considerations for the coherent CDMA channel by Lupas and Verdu. The commonality between the properties of the decorrelating detectors for coherent and noncoherent channels is established. In particular, it is shown that no other DPSK multiuser detector achieves a higher near-far resistance than does the noncoherent decorrelator, i.e., the optimally near-far resistant linear detector is optimally near-far resistant.