Optimum noncoherent multiuser decision feedback detection

A theory of noncoherent decision feedback multiuser detection for nonorthogonal binary modulation is developed that parallels that of coherent decision feedback multiuser detection for single-pulse modulation. In particular, an optimum noncoherent decision feedback detector is obtained that maximizes symmetric energy over a newly defined class of decision feedback detectors. Unlike the usual per-user performance metrics such as asymptotic efficiency or near-far resistance, the symmetric energy measure captures, with a single number, the asymptotic (high signal-to-noise ratio (SNR)) bit-error performance of all users at once. Several properties of the optimum decision feedback detector are established, one of which is that it outperforms the decision feedback generalized-likelihood ratio (GLR) detector in symmetric energy. It is also shown that, regardless of the order in which users are detected, the optimum noncoherent decision feedback detector outperforms its non-decision feedback counterpart in symmetric energy. Furthermore, two simple rules are obtained for determining the order in which users must be detected to guarantee that the optimum decision feedback detector outperforms its non-decision feedback counterpart (which in turn, is superior to the decorrelative GLR detector presented earlier) in terms of asymptotic effective energy for every user. In fact, one of the two (greedy) ordering rules also maximizes symmetric energy among all possible orderings. Such ordering rules are not available for the noncoherent decision feedback GLR detector in earlier work of the authors. Feasible sets of received energies are characterized in which it is possible, with power control, to achieve quality-of-service objectives for each user. None of the results in this paper make simplifying assumptions about the effects of error propagation. The term "noncoherent" in this work is used to denote that the receiver has no knowledge of the carrier phases and received signal energies of any of the users.