On Minimum-BER Linear Multiuser Detection for DS-CDMA Channels

The minimum bit-error rate (MBER) linear multiuser detection of direct-sequence code-division multiple-access (DS-CDMA) communications is considered. It is shown that the problem of MBER linear multiuser detection is equivalent to a constrained optimization problem where the constrained space is the surface and interior of a hyperellipsoid. It is further shown that any solution of the constrained optimization problem must be a solution of a set of nonlinear equations. Based on these the MBER linear multiuser detector of the two-user case is obtained. For general cases, we propose a convex subspace of the constrained space and show that the BER cost function is convex on the subspace and therefore has a unique solution. Some sufficient conditions that guarantee the convex subspace always contains the global minimizer are provided, which show that if the signal-to-noise ratio (SNR) is sufficiently large, the convex subspace always contains the global minimizer. A Newton method is developed for the set of nonlinear equations and computer simulation gives some illustrative examples