Performance analysis of L0-LMS with Gaussian input signal

Sparse signal processing has attracted much attention in recent years. l₀-LMS, which inserts a penalty of approximated l₀ norm in the cost function of standard LMS algorithm, is one of the recently proposed sparse system identification algorithms. Numerical simulation results and intuitive explanations demonstrate that l₀-LMS has rather small steady-state misalignment and fast convergence rate, especially with selected parameters, compared to its various precursors. In this paper, the mean square performance of l₀-LMS is theoretically analyzed based on uncorrelated Gaussian input, independence assumption, and some other reasonable assumptions. We deduce the convergence condition on step-size, the steady-state mean square deviation, as well as the criterion on parameters selection. Finally, computer simulations verified the above theoretical results and confirmed the adopted assumptions hold well.