Variable Step Size Normalized sign Algorithm for fast convergent adaptive filters with robustness against impulse noise

In this paper, a new algorithm for adaptive filters, named Variable Step Size Normalized Sign Algorithm (VSS-NSA), is proposed and studied. The normalizing factor introduced in the Sign Algorithm (SA) makes the filter insensitive to variations in filter input power as in the Normalized LMS Algorithm (NLMSA). Although the proposed variable step size control algorithm is very simple, it was found to be effective in significantly improving the convergence rate and the tracking performance of the Normalized Sign Algorithm (NSA), while still preserving the robustness of the SA or NSA against impulse noise. Simulations with various examples verify the above performance of the VSS-NSA. Analysis of the VSS-NSA is developed for theoretical calculation of the filter convergence. Theoretical convergence curves for the VSS-NSA are compared with the simulation results, where good agreement is observed, showing the validity of the theory.