Local maximum likelihood multiuser detection for CDMA communications

The optimum multiuser detector achieves global maximum likelihood and has a complexity growing exponentially with the number of users. We propose the local maximum likelihood (LML) multiuser detectors with an arbitrary neighborhood size. As the neighborhood size is one, two, etc., up to the total number of users, the computational complexity of the LML detector is linear quadratic, etc., up to exponential in the total number of users. Every LML detector is associated with a local minimum error probability defined with the corresponding neighborhood size. A family of local-maximum-likelihood likelihood-ascent-search (LMLAS) detectors is proposed, each of which is shown to be an LML detector. An LMLAS detector monotonically increases likelihood step by step, and thus converges to an LML point in a finite number of search steps with probability one. Following any detector, an LMLAS detector can reduce the error probability of the initial detector to a local minimum or not change it when the initial detector is an LML detector with the same or larger neighborhood size with probability one