Noncoherent Decision Feedback Multiuser Detection for Nonorthogonal Multipulse Modulation

| The problem of noncoherent multiuser detection for nonorthogonal multipulse modulation (NMM) over the Gaussian multiuser channel was studied in [1]. In that work, the idea of noncoherent decorrelation for NMM was introduced and post-decorrelative detectors were derived and analyzed. In this paper, we introduce the concept of noncoherent decision feedback that forms the basis for another set of solutions to the same problem. As in coherent decision feedback, the users are detected in a pre-determined order so that the decision for a particular user can take advantage of the decisions already made for previous users. In contrast to coherent decision feedback however, the feedforward and feedback transformations in the noncoherent case are themselves functions of the matched lter outputs so that they are randomly time-varying from symbol-to-symbol. An e cient implementation of the noncoherent decision feedback detector is suggested which, for M-ary modulation and a Kuser channel, requires O(MK) computational complexity. Upper and lower (genie-aided) bounds on symbol error probability of the proposed detectors are obtained. It is shown that signi cant improvements over the post-decorrelative noncoherent detectors of [1] are possible. Su cient conditions are obtained which guarantee, without ignoring errorpropagation e ects, that the asymptotic (high SNR) performance of the generalized likelihood ratio test (GLRT) based decision feedback strategy can be as good as its genie-aided version in which past users' decisions are perfect.