Convergence analysis of sparse LMS algorithms with l1-norm penalty based on white input signal

The zero-attracting LMS (ZA-LMS) algorithm is one of the recently published sparse LMS algorithms. It usesan l1-norm penalty in the standard LMS cost function. In this paper, we perform convergence analysis of the ZA-LMS algorithm based on white input signals. The stability condition is examined and the steady-state mean square deviation (MSD) is derived in terms of the system sparsity, system response length, and filter parameters (step size and zero-attractor controller). In addition, we propose a criterion for parameter selection such that the ZA-LMS algorithm outperforms the standard LMS algorithm. The results are demonstrated through computer simulations.