Noncoherent decorrelative detection for nonorthogonal multipulse modulation over the multiuser Gaussian channel

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.