Performance analysis of adaptive filters equipped with the dual sign algorithm

A convergence analysis for stochastic gradient adaptive filters equipped with the dual sign algorithm (DSA) is presented. Expressions for the mean and mean-squared values of the coefficient misalignment vector are derived under the assumption that the input signal is Gaussian. The main differences between the current analysis and previous analyses are: (1) the present analysis is valid for arbitrary autocorrelation matrices, and (2) the analysis does not approximate the behavior for the DSA as switching between two sign algorithms a certain amount of time after the DSA is initialized. A simulation example comparing the analytical results with empirical ones is presented and the two curves show excellent agreement with each other