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

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