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

• Published in: IEEE transactions on signal processing Vol. 55; no. 3; pp. 1093 - 1103
• Main Authors: Li, Jiangyuan, Wei, Gang, Chen, Fangjiong
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-03-2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Bit error rate; Channels; Code-division multiple-access (CDMA); Computer simulation; constrained optimization; Constraint optimization; Constraints; Cost function; Detection, estimation, filtering, equalization, prediction; Detectors; Equivalence; Exact sciences and technology; Information, signal and communications theory; linear detector; Mathematical models; minimum bit-error rate (MBER); Multiaccess communication; Multiuser detection; multiuser detection (MUD); Nonlinear equations; Optimization; Signal and communications theory; Signal to noise ratio; Signal, noise; Studies; Subspace constraints; Subspaces; Sufficient conditions; Telecommunications and information theory; Multiuser detection; Computer simulation; Bit error rate; Wireless telecommunication; Subspace method; multiuser detection (MUD); Constrained optimization; Non linear equation; linear detector; Direct detection; Sufficient condition; Code-division multiple-access (CDMA); Code division multiple access; minimum bit-error rate (MBER); Cost function; Convex function; Newton method; Direct sequence; Signal detection; Signal to noise ratio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2006.888059

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