Cauchy Distribution Function-Penalized LMS for Sparse System Identification

It is well known that the zero-attracting least mean square (ZA-LMS) algorithm and reweighted zero-attracting LMS (RZA-LMS) algorithm outperform the standard LMS algorithm in sparse systems. However, because the ZA-LMS algorithm does not distinguish the size of the tap coefficients, its performance in low-sparse or non-sparse systems declines rapidly. Although RZA-LMS selectively attracts taps with small magnitudes, there is extra attraction to large tap coefficients, which can increase the steady-state mean square error (MSE). In this paper, a Cauchy distribution function-penalized LMS (C-LMS) algorithm is proposed. The proposed algorithm changed the penalty term of the cost function into Cauchy distribution function, which can decrease the attraction to large tap coefficients and enhances the force to the small tap coefficients. The simulation results indicate that the C-LMS can achieve lower steady-state MSE than other algorithms in sparse systems and demonstrates similar performance to the conventional LMS algorithm in non-sparse system.