CDMA multiuser detection: a nonlinear programming approach

The optimum receiver to detect the bits of multiple code-division multiple access (CDMA) users has an exponential complexity in the number of active users in the system. Consequently, many suboptimum receivers have been developed to achieve good performance with less complexity. We take the approach of approximating the solution of the optimum multiuser detection problem (OMUD) using nonlinear programming relaxations. First, we observe that some popular suboptimum receivers indeed correspond to relaxations of the optimal detection problem. In particular, one proposed approximation method yields to iterative solutions which correspond to previously proposed heuristic nonlinear detectors. Using a nonlinear programming approach, we identify the convergence properties of these iterative detectors. Secondly, we propose a relaxation that yields a receiver which we call the generalized minimum mean squared error detector. We give a simple iterative implementation of the detector. Its performance is evaluated and comparisons to other suboptimum detection schemes are given.