On the convergence of subgradient based blind equalization algorithm

SubGradient based Blind Algorithm (SGBA) has recently been introduced [A.T. Erdogan, C. Kizilkale, Fast and low complexity blind equalization via subgradient projections, IEEE Trans. Signal Process. 53 (2005) 2513–2524; C. Kizilkale, A.T. Erdogan, A fast blind equalization method based on subgradient projections, Proceedings of IEEE ICASSP 2004, Montreal, Canada, vol. 4, pp. 873–876.] as a convex and low complexity approach for the equalization of communications channels. In this article, we analyze the convergence behavior of the SGBA algorithm for the case where the relaxation rule is used for the step size. Our analysis shows that the monotonic convergence curve for the mean square distance to the optimal point is bounded between two geometric-series curves, and the convergence rate is dependent on the eigenvalues of the correlation matrix of channel outputs. We also provide some simulation examples for the verification of our analytical results related to the convergence behavior.