Steady-state mean-square deviation analysis of improved ℓ0-norm-constraint LMS algorithm for sparse system identification

Abstract

The ℓ0-norm-constraint LMS (ℓ0-LMS) algorithm is one of the widely used sparse LMS algorithms for the identification of sparse system, and its performance is quite attractive compared to other precursors. However, ℓ0-LMS is still confronted with some limitations on the optimal parameter selection and the estimated coefficient accuracy of sparse system identification. In this paper, we proposed an improved ℓ0-LMS (ℓ0-ILMS) algorithm to address these limitations. The convergence condition and the parameter selection rules for optimal steady-state mean-square deviation (MSD) of ℓ0-ILMS are discussed. Compared with ℓ0-LMS, the steady-state MSD of ℓ0-ILMS is lower and less sensitive to the tuning parameters and measurement noise power. Numerical simulations comparing the performance of standard LMS, ℓ0-LMS and ℓ0-ILMS demonstrate the effectiveness of ℓ0-ILMS.