Convergence of an Adaptive Filter with Signed Error Filtering

In recent years, the need for high speed adaptive filters has prompted the search for alternatives to the popular LMS algorithm. One modification is the replacement of the prediction error term in the LMS update kernel by its signum function. At the same time, in noise and echo cancellation problems, reduced residual noise variance often requires error filtering. In this paper we consider the situation where the signum function of such a filtered error appears in the update kernel. Without the signum function the error model of the filtered algorithms is similar to those in output error identifiers, and a Strictly Positive Real error filter suffices for convergence. We analyze this signed filtered error algorithm to show that the presence of the sign operator requires a stronger condition (labeled Strictly Dominant Passive) on the error filter and give a globally uniform convergence proof subject to their satisfaction.