Research On Adaptive Filtering Algorithms With Correlated Input Signals

Adaptive filter enables optimal filtering by adaptively adjusting the weight coefficients without knowing more a priori information about the input signals,which has been a research hotspot in the field of signal processing for a long time,and has been widely used in many fields,including wireless communications and geological exploration.As the input signals to be processed in practical applications tend to be strongly correlated,this paper focuses on the adaptive filtering algorithms that handle such input signals.Based on a detailed description of the design principles,classical algorithms,application areas and performance evaluation criteria of adaptive filtering algorithms,the paper addresses some problems with existing algorithms and the main contributions are summarized as follows:(1)To solve the contradictory problem between convergence speed and steady-state error in the traditional Affine Projection(AP)algorithm with a fixed regularization factor,two different combined regularization factor methods for AP algorithm are proposed by introducing a variable mixing factor.Using the mixing factor,two separate regularization factors can be adaptively combined,and the mixing factor is updated by using the stochastic gradient descent method and the minimization of posterior error energy method,respectively,to finally obtain two performance enhancement schemes.Furthermore,mathematical theoretical analysis including the stability performance and computational complexity,as well as MATLAB experimental simulations are carried out for the two schemes,which demonstrate the excellent performance of the two algorithms in system identification and echo cancellation applications.(2)For the robust identification problem of sparse systems,three sparse DRMCC algorithms are presented by introducing different sparse penalty terms into the Data Reusing Maximum Correlation Criterion(DRMCC)algorithm,and the DRMCC with Correntropy Induced Metric Penalty Term(DRMCCCIM)algorithm is verified to be more favorable through simulations.Meanwhile,in order to further balance the convergence speed and steady-state error of the DRMCCCIM algorithm,a variable matrix-type step-size DRMCCCIM algorithm is formulated by adopting a variable step-size scheme with an improved Gaussian function,and the better performance of the proposed algorithm is demonstrated in the simulation of sparse systems with impulsive noise.The research content and the proposed algorithms solve the contradiction problem between the convergence speed and steady-state error of the AP algorithm with correlated input signals,and give some performance improvement schemes for corresponding adaptive filtering algorithms under the condition of sparse system with impulsive noise.However,the proposed algorithms are still in the stage of theoretical analysis and simulation validation,and have yet to be verified and applied in practice.