The optimum noncoherent multiuser detector is obtained for generalized diversity symbol-synchronous communication systems that employ nonorthogonal multipulse modulation. A unified approach is adopted to simultaneously address various forms of diversity such as time, frequency, multipath, and/or receiver-amenna diversity. Upper and lower bounds on the average bit-error probability of the optimum noncoherent detector are derived. While these bounds are numerically computable, they are too complicated to give insights about the relative influence of system parameters on the essential behavior of the bit-error rate. To address this issue, an asymptotic (low noise) analysis of the bit-error probability is undertaken. It is shown that the upper and lower bounds are indeed asymptotically convergent. A formula for the asymptotic efficiency of the optimum noncoherent detector is thereby derived. Interestingly, the asymptotic efficiency is found to be positive, and independent of the signal strengths of the interfering users.

The jointly optimum noncoherent multiuser detector is obtained for nonlinear nonorthogonal modulation over the frequency nonselective Rayleigh-fading multiple-access channel. Upper and lower bounds on the average bit-error probability are derived. While these bounds are numerically computable, they are too complicated to give insight into the relative influence of the system parameters on the essential behavior of the bit-error rate. Hence this paper develops an asymptotic analysis of the average bit-error probability. In particular, it is shown that the upper and lower bounds are asymptotically convergent. An exact formula for the asymptotic efficiency of the optimum noncoherent detector is derived. Interestingly, the asymptotic efficiency is found to be positive and independent of the signal strengths of the interfering users. In contrast, the noncoherent detector which would be optimal in a single-user channel (the "conventional detector"), when used over the multiuser channel, has an asymptotic efficiency that is identically equal to zero no matter what the powers of the interferers may be. While the performance analysis of the optimum detector provides the fundamental limit on achievable error rate, the implementational complexity of the optimum detector is exponential in the number of users. As a low-complexity alternative, a decorrelative energy detector is also proposed and analyzed in terms of error probability and asymptotic efficiency.

This paper introduces the problem of noncoherent detection for nonorthogonal multipulse modulation in the context of the synchronous multiuser Gaussian channel. Each user sends an M-ary information symbol by transmitting one of M possibly nonorthogonal waveforms. Furthermore, the M signals of one user are allowed to be correlated with the signals of all other users. A key idea proposed here is that of a noncoherent decorrelative receiver front end. Like its counterpart in single-pulse modulation, this front end eliminates multiuser interference. It therefore reduces the multiuser detection problem into decoupled single-user problems over equivalent noise-enhanced single-user channels. Each equivalent single-user channel is rather general and can be described as one where the waveforms employed are not only correlated, but are also of unequal energies. Several new results pertaining to the design and analysis of optimum and suboptimum noncoherent detectors for this single-user channel are obtained. In the multiuser channel, these detectors constitute the post-decorrelative processing units for each user.

Coherent multiuser detection for linear modulation has been the subject of much research. Noncoherent detection for linear differentially phase shift keyed modulation has also received considerable attention, 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.