Research On Adaptive Algorithms Against Impulsive Noise

Adaptive filtering algorithms play an important role in the field of signal processing.Common application scenarios include denoising,echo cancellation,channel equalization,and system identification.The most popular adaptive algorithms are the least mean square(LMS)and normalized least mean square(NLMS)algorithms because of their advantages of low computational complexity and good stability.In order to introduce the basic structure of the adaptive algorithm,we conduct the derivation of the classic adaptive algorithms against impulsive noise,which can provide ideas for the improvement of adaptive algorithms against impulsive noise.Impulsive noise is a common type of noise.However,the traditional non-negative algorithms will fail to converge due to the existence of impulsive noise.Through the study of the characteristics of the sigmoid framework,the proposed sigmoid nonnegative least mean square(S-NNLMS)algorithm embeds the conventional nonnegative cost function into the sigmoid framework,which can suppress the impact of impulsive noise.To solve the step size selection and unbalanced convergence problems,the inversely-proportional sigmoid nonnegative least mean square(IP-SNNLMS)algorithm based on inverse proportional function is proposed.A robust nonnegative least mean square(R-NNLMS)algorithm based on step-size scaler is proposed to improve the robustness performance of the nonnegative least mean square(NNLMS)algorithm in the impulsive noise occurring.Meanwhile,the inversely-proportional robust nonnegative least mean square(IP-RNNLMS)algorithm is proposed to improve the convergence rate of the algorithm for sparse systems identification.The proposed algorithms have good convergence performance under impulsive and non-impulsive noise conditions.Affine Projection(AP)algorithms can suppress the impact of impulsive noise and the influence of colored inputs.The affine projection Weibull M-transform least mean square(APWMLMS)algorithm based on the Weibull M-transform cost function is proposed to improve the convergence performance of the existing AP algorithms.The simulation results show that the proposed algorithm has significant improvement in convergence performance compared with other algorithms,which simultaneously preserves performance in terms of against impulsive interference and colored input.In practical applications,some constraints need to be added to the estimated parameters due to the inherent characteristics of the system.The boxed-constraint least mean fourth(BXCLMF)algorithm adds Boxed constraint based on the least mean fourth(LMF)algorithm model.We combine the Karush-Kuhn-Tucker(KKT)conditions and the fixed-point iteration algorithm to derive the BXCLMF algorithm.The simulation results demonstrate that the BXCLMF algorithm has a great improvement in convergence performance compared with the boxed-constraint least mean square(BXCLMS)algorithm under various noise conditions.