Performance analysis of adaptive filters equipped with the dual sign algorithm

Adaptive filters equipped with the sign algorithm are attractive in many applications because of their computational simplicity. Unfortunately, their slow speed of convergence is a major limitation. The dual sign algorithm (DSA) is a means by which the convergence speed can be increased without overly degrading the steady-state performance and with a minimal amount of additional computational complexity. This paper presents a convergence analysis for adaptive filters equipped with the dual sign algorithm. Previous analyses of the dual sign algorithm were based on two assumptions: 1) the input sequence to the adaptive filter is white; 2) the behavior for the DSA is such that it switches from an adaptive filter equipped with the sign algorithm with a relatively large convergence constant to another one with a smaller convergence constant a certain amount of the after the filter is initialized. Both these restrictions are removed for Gaussian input signals in our analysis. A simulation example that shows good match between theoretical and empirical results is also presented in this paper.