Minimum error probability and suboptimum noncoherent detection for nonlinear nonorthogonal synchronous signaling over a Rayleigh fading channel

Coherent multiuser detection for linear modulation has been the subject of much research in the past decade. Noncoherent detection for linear differentially phase shift keyed modulation has received considerable attention in the past few years, whereas research in the field of noncoherent detection for nonlinear modulation in correlated-waveform multiple access channels has been far more limited. This paper considers for the first time the problem of noncoherent multiuser detection for binary, nonlinear, nonorthogonal signaling over a synchronous, frequency-nonselective Rayleigh fading channel. A minimum error probability multiuser detector is derived and analyzed through asymptotically convergent upper and lower bounds on error probability. This detector has an exponential (in the number of users) time complexity. Consequently, a suboptimum Noncoherent Decorrelative Energy Detector (NDED) is proposed, whose complexity is linear in the number of users. The NDED is analyzed exactly in terms of error probability. An asymptotic performance analysis is undertaken for the NDED and, to serve as a comparison, for the conventional detector. It is shown that the former is near-far resistant, the latter, however, near-far limited.