Local Maximum Likelihood Multiuser Detection

It is well-known that the optimum multiuser detector achieves the global maximum likelihood (GML) detection in the entire set of hypotheses and several other iterative detectors such as the SAGE detector achieve the local maximum likelihood (LML) detection in the smallest neighborhood. In this paper, we generalize the local maximum likelihood detection into any size of neighborhood. The characteristics of LML points and LML regions are discussed. It is shown that as neighborhood size increases, the number of LML points decreases, the LML region shrinks and is closer to the optimum decision region, the error probability of an LML detector decreases and its computational complexity increases. Each LML detector achieves a local minimum error probability. We develop a family of local maximum likelihood likelihood ascent search (LMLAS) detectors. An LMLAS detector monotonically increases likelihood in each search step until arriving at an LML point. It monotonically reduces the error probability of an initial detector to a local minimum error probability unless the initial detector is an LML detector with probability one. Simulations demonstrated the tradeoff between error performance and computational complexity via choice of neighborhood size. As the number of users and processing gain increase with their ratio kept a constant, the error performance of LMLAS detectors improves. EDICS: 3-ACCS Multiuser and multiacess communication Submitted to IEEE Trans. on Signal Processing, October 12, 2002 1 This work is in part prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011, and by a grant #64453-00-33 from The City University of New York PSC-CUNY Research Award Program. The U. S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.