A Simple Sparsity-aware Feature LMS Algorithm.

Many real systems have inherently some type of sparsity. Recently, the feature least-mean square (F-LMS) has been proposed to exploit hidden sparsity. Unlike the existing algorithms, the F-LMS algorithm performs a linear combination of the adaptive coefficients to reveal and then exploit the hidden sparsity. However, many systems have also plain besides hidden sparsity, and the F-LMS algorithm is not able to exploit the former. In this paper, we propose a new algorithm, named simple sparsity-aware F-LMS (SSF-LMS) algorithm, that is capable of exploiting both kinds of sparsity simultaneously. The hidden sparsity is exploited just like in the F-LMS algorithm, whereas the plain sparsity is exploited by means of the discard function applied to the filter coefficients. By doing so, the proposed SSFLMS algorithm not only outperforms the F-LMS algorithm when plain sparsity is also observed, but also requires fewer arithmetic operations. Numerical results show that the proposed algorithm has faster speed of convergence and reaches lower steady-state mean-squared error (MSE) than the F-LMS and classical algorithms, when the system has plain and hidden sparsity.