Coherent multiuser detection for linear modulation has been the subject of intense research in the past decade. Noncoherent detection for linear differentially phase shift keyed modulation has also received considerable attention in recent years. This paper considers for the first time the problem of noncoherent multiuser detection for M-ary nonlinear nonorthogonal modulation in the synchronous Gaussian channel. A key idea proposed here is that of a noncoherent decorrelative front end for nonlinear modulation. Like its counterpart in linear modulation, that front-end eliminates multiuser interference and reduces the multiuser detection problem into that of single-user detection over an equivalent (noise-enhanced) single-user channel. However, the M effective signals of the equivalent single-user channel are correlated and of unequal energy. Noncoherent detection even in this single-user channel has been an open problem until now. We derive the optimum detector for this channel. It is unfortunately too complicated to implement or analyze. Two suboptimal detectors are hence proposed depending on whether the energies of the M signals are known or unknown at the receiver. For unknown energies, the generalised likelihood ratio test leads to a detector which is easy to implement. Error probability bounds are obtained for this detector. It is shown to be near-far resistant (in contrast to the conventional detector). For known energies, an asymptotic series expansion of a special function involved in the optimum noncoherent decision rule leads to the other suboptimum detector. Its analysis is more difficult but we nevertheless obtain exact expressions for error probability for binary modulation and bounds on error probability in the M-ary case. This detector can outperform the GLRT detector by a significant margin. Both detectors far outperform the conventional single-user detector.
['Mahesh K. Varanasi', 'A. Russ']
Noncoherent decorrelative multiuser detection for nonlinear nonorthogonal modulation