Blind stochastic gradient methods for optimal minimum variance CDMA receivers

Constrained optimization methods have received considerable attention as a means to derive blind multiuser receivers with low complexity. In this paper the receiver's output variance is minimized subject to appropriate constraints which depend on the multipath structure of the signal of interest. The constraint equations can be written in parametric form, and the constraint parameters jointly optimized with the linear receiver's parameters. We develop stochastic gradient based solutions for this joint, constrained optimization problem. Different variations of constrained LMS-type algorithms are presented and global convergence is established. The performance of the proposed methods is compared with other blind and trained methods. Moreover, the constraint parameters are observed to converge to the channel parameters of the user of interest at high SNR.