An enhanced normalized step-size algorithm based on adjustable nonlinear transformation function for active control of impulsive noise

Abstract Impulsive noise is widely distributed in various scenarios and becomes an important challenge for the practical applications of active noise control (ANC) system. The conventional ANC algorithms based on the transformation function have a fixed compression level for error signal, leading to slow convergence and weak noise reduction under certain circumstances. To overcome this defect, this paper proposes an enhanced filtered-x arctangent error Least Mean Square (EFxatanLMS) algorithm by designing an adjustable nonlinear transformation function of error signal with arctangent form. Specifically, a compression factor is introduced in the transformation function to govern the compression shape of the function so as to realize ideal effect on impulsive noise with different intensities. For the purpose of further optimizing the capability of the proposed algorithm, an improved normalized step-size EFxatanLMS (NSS-EFxatanLMS) algorithm is proposed. It adopts a novel time-varying normalized function to adjust the step-size coefficient to the appropriate value adaptively. Numerical simulations verify the effectiveness of the proposed algorithms for Gaussian noise and non-Gaussian impulsive noise.