Improved Zero-Attracting LMS Algorithm for the Adaptive Identification of Sparse System

Abstract

The ZA-LMS (Zero-Attraction Least Mean Square) algorithm is an efficient sparse system identification algorithm. The core of it is to exert attraction on the weight coefficients in the process of iteration to make the error close to zero as far as possible. However, if the weight coefficients are applied with the same attraction, it leads to the slow convergence of the algorithm due to the insufficient attraction when the weight coefficient is close to zero. And when the weight coefficient is large, the steady-state error of the algorithm will increase due to the immoderate pressure applied. At the same time, the fixed step size and regularization parameter make it difficult for the algorithm to maintain a suitable trade-off between the steady state error and the fixed step size. Therefore, considering the aspects of the attraction operator, step size, and regularization parameter, an improved algorithm named VP-LZA-LMS (Variable Parameters and Logarithmic function based ZA-LMS) is suggested in this essay. Firstly, the original penalty term in ZA-LMS is changed using the logarithmic function, and then a new weight updating equation is derived, which enables the algorithm to exert different attractive force according to the value of the coefficient during updating. Secondly, on the basis of the reduced mean square deviation, new formulas are created that allow the step size and regularization parameter to be changed in real time in line with the error. The imbalance between the steady state error and the convergence rate is alleviated by the step size and regularization parameter's variability. Finally, simulation findings demonstrate that the suggested VP-LZA-LMS algorithm outperforms some existing similar algorithms in terms of convergence and tracking performance under the condition of white and colored input