Convergence analysis of the sign algorithm for adaptive filtering

Abstract

We consider the convergence analysis of the sign algorithm for adaptive filtering when the input processes are uncorrelated and Gaussian and a fixed step size /spl mu/>0 is used. Exact recursive equations for the covariance matrix of the deviation error are established for any step size /spl mu/>0. Asymptotic time-averaged convergence for the mean-absolute deviation error, mean-square deviation error, and for the signal mean-square estimation error are established. These results are shown to hold for arbitrary step size /spl mu/>0.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>