Investigations on Sparse System Identification with l0 -LMS, Zero-Attracting LMS and Linearized Bregman Iterations

Abstract

Identifying a sparse system impulse response is often performed with the l0 -least-mean-squares (LMS)-, or the zero-attracting LMS algorithm. Recently, a linearized Bregman (LB) iteration based sparse LMS algorithm has been proposed for this task. In this contribution, the mentioned algorithms are compared with respect to their parameter dependency, convergence speed, mean-square-error (MSE), and sparsity of the estimate. The performance of the LB iteration based sparse LMS algorithm only slightly depends on its parameters. In our opinion it is the favorable choice in terms of achieving sparse impulse response estimates and low MSE. Especially when using an extension called micro-kicking the LB based algorithms converge much faster than the l0 -LMS.