A modified adaptive sign algorithm used on the hybrid norm error criterion

In this paper a modified adaptive sign (MSA) algorithm based on the hybrid norm error criterion is described. The hybrid norm error criterion to be minimized is built as a combined convex function of the mean-absolute error and the mean-absolute error to the third power. Under a set of mild assumptions, the nonlinear evolution equations that characterize the statistical mean and mean-squared behavior of the algorithm are derived. Computer simulations are carried out to verify the validity of our derivations.