The Research Of Subband Adaptive Filtering Algorithm Based On System Identification

Adaptive filters are one of the research hotspots in the field of signal processing,due to their great flexibility and self-learning capability,thus playing an important role in communication,control,biomedical and other fields.Among them,subband adaptive filter is an important research direction.Since the normalized subband adaptive filtering algorithm can maintain better performance when the input signal has higher correlation,and it requires lesser computation,its algorithm has attracted the attention and research of scholars in recent years.However,the normalized subband adaptive filtering algorithm still has some problems,and its convergence rate will be significantly slowed down when identifying different unknown systems,and its performance can be seriously degraded or even fail when encountering impulsive interference.In order to solve these problems,some research work has carried out in this study:（1）In order to improve the performance of the algorithm under the impulsive interference.The proposed algorithm is based on the maximum mixture correntropy criterion and fractional order calculus.On the one hand,the robustness of the maximum mixture correntropy criterion can effectively suppress the influence of abnormal noise values on the performance of the algorithm.On the other hand,the fractional order calculus is added to the weight update,because the fractional order calculus takes into account the overall information of the data in weighted form,which can more accurately describe the actual system and further improve the performance of the algorithm to identify the unknown system.Making the proposed algorithm has better the convergence rate.（2）To address the problem that the algorithm cannot balance convergence and stability,and has poor impulsive resistance.This thesis proposes a new normalized subband adaptive filtering algorithm based on the logarithmic hyperbolic cosine cost function.The mean square convergence performance of the proposed algorithm is also analyzed using reasonable assumptions and energy conservation methods.In addition,to solve the problem that the proposed algorithm will decrease when the unknown system is sparse.One scheme is developed by using the L₀-norm constraint of the estimated coefficient vector into the above cost function.Another scheme is used by curve tight frame as a sparsity-inducing norm into the cost function.The combination can not only solve the trade-off between the convergence rate and the steady-state error,but also ensure the robustness and the recognition tracking performance of the algorithm.Based on the above two schemes,two sparse algorithms based on different norm constraints are derived.（3）To solve the performance degradation problem of the algorithm in the recognition of sparse systems,the sign subband adaptive filtering algorithm derived from the low-order norm has stronger robustness.So the L₁-norm constraint of the weight vector is introduced in its cost function.Secondly,the improved coefficient proportionate matrix is integrated into the weight update equation.And the combination and improvement of the two have better attraction to non-zero values in sparse impulse responses,which enables the algorithm to obtain the optimal proportional step calculation method,thus improving the ability of the algorithm to identify sparse systems.