Performance analysis of L0-LMS with Gaussian input signal

Sparse signal processing has attracted much attention in recent years. io-LMS, which inserts a penalty of approximated la 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 l
0
-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 l
0
-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.