  Zero-attracting least-mean-square (ZA-LMS) algorithm has been widely used for
online sparse system identification. It combines the LMS framework and
$\ell_1$-norm regularization to promote sparsity, and relies on subgradient
iterations. Despite the significant interest in ZA-LMS, few works analyzed its
transient behavior. The main difficulty lies in the nonlinearity of the update
rule. In this work, a detailed analysis in the mean and mean-square sense is
carried out in order to examine the behavior of the algorithm. Simulation
results illustrate the accuracy of the model and highlight its performance
through comparisons with an existing model.
