Adaptive Parameters Adjustment for Group Reweighted Zero-Attracting LMS

Overview & Synopsis

Group zero-attracting LMS (GZA-LMS) and its reweighted variant (GRZA-LMS) have been proposed for system identification with structural group sparsity of the parameter vector. Similar to most adaptive filtering algorithms with regularized penalty, GZA-LMS/GRZA-LMS suffers from a trade-off between convergence rate and steady-state performance, meanwhile between the degree of sparsity and estimation bias. Therefore, it is pivotal to properly set the step-size and regularization parameter of the algorithms. Based on a transient behavior model of GZA-LMS/GRZA-LMS, a variable-parameter GRZA-LMS algorithm is proposed to address this issue. By minimizing the mean-square-deviation at each time instant, we obtain closed-form expressions of the optimal step-size and regularization parameter. Simulation results illustrate the effectiveness of the proposed algorithms in both white and colored input cases.