Noncoherent decision feedback multiuser detection: optimality, performance bounds, and rules for ordering users

Abstract

An analytical framework for noncoherent decision feedback detection is introduced while considering nonorthogonal binary modulation (NBM) over the synchronous Gaussian K-user channel. Following the key idea of noncoherent decorrelating decision feedback detection (NC-DDFD) proposed previously, a K-parameter class of NC-DDFDs is defined. The symmetric energy measure is defined as the worst-case (over users) asymptotic effective energy for noncoherent detection. Without making any simplifying assumption about error propagation, the NC-DDFD that optimizes symmetric energy among the K parameter class of detectors is derived. Since the NC-DDFD based on the generalized likelihood ratio test (GLRT) belongs to the K-parameter class of NC-DDFDs, the optimum NC-DDFD outperforms the GLRT based NC-DDFD in symmetric energy. Like the latter detector, the optimum NC-DDFD does not require the knowledge of the energies or phases of any of the users' transmissions. Exact expressions for symmetric energy and upper and lower bounds for symbol error rate (SER) and asymptotic effective energies are obtained for the optimum NC-DDFD. Rules for ordering users are obtained that guarantee that the optimum NC-DDFD can user-wise outperform a parallel bank of post-decorrelative GLRT detectors.