Combined regularization parameter for normalized LMS algorithm and its performance analysis

Abstract

This paper presents a combined regularization parameter for normalized least-mean-square (CRP-NLMS) algorithm. The proposed algorithm adaptively combines two different regularization parameters by employing a time-varying mixing parameter that is derived by minimizing the energy of noise-free a posteriori error. To avoid large fluctuations, the mixing parameter is updated in a moving-average method. A novel reset method is designed to improve the tracking capability when the unknown system encounters a sudden change. We illustrate that the proposed mixing parameter is also available for the nonstationary system modeled by a random walk process. In particular, the theoretical analyses including the transient and steady-state mean-square error (MSE) are performed. Simulations for system identification scenarios demonstrate the merits of Kour finding and support the theoretical analysis.