An Improved q-Least Mean Square Algorithm for Sparse System Identification

Abstract

Least mean square (LMS) algorithm is very familiar and used successfully in adaptive filters which are widely used in several areas such as wireless communication or image processing. However, it is inefficient for some situations such as the constant step-size in its update equation or eigenvalue spread of the input autocorrelation matrix. Besides, the performance of the LMS algorithm deteriorates for a system identification problem when we deal with a sparse system in which the most of the coefficients are zero or near zero. In this work a new sparsity based LMS-type algorithm has been proposed. It exploits the advantages of the recently proposed q-LMS algorithm which is based on q-calculus, a variable step-size LMS algorithm in which a function is used to adjust the step-size and the zeroattraction factor derived by an additional l 0 norm in its error function. The proposed algorithm has been compared with both q-LMS algorithm and zero-attracting function controlled variable step-size LMS algorithms according to the convergence speed and mean square deviation. Experiments showed that the new algorithm has a faster convergence without sacrificing from mean square deviation level for a sparse system identification with an uncorrelated or correlated input signals.