Research On Affine Projection Adaptive Filtering Algorithm Based On Minimum Error Entropy

As an important and basic content of signal processing technology,filter design has been widely concerned.The adaptive filter is widely used in applications such as channel equalization,system identification,echo cancellation,etc.because it does not require prior knowledge of the input signal,strong adaptability to unknown environments,and dynamic adjustment of filter parameters.However,with the expansion of adaptive algorithm applications,adaptive filtering algorithms are also facing some new problems: for example,the influence of non-Gaussian noise widely existed in nature,the sparsity of channels in some communication systems,strong correlation of input signals in multimedia transmission systems,etc.The Minimum Error Entropy(MEE)criterion is a criterion based on second-order Renyi entropy to constrain the change of error signal,so it can effectively suppress the mutation caused by error or noise,so the criterion is widely used to replace the second-order statistic in traditional filtering algorithms to reduce the effect of non-Gaussian noise on the algorithm.Affine Projection Algorithm(APA),derived from the Normalized Least Mean Square(NLMS)algorithm,is an adaptive filtering algorithm based on data reuse,thus APA class algorithms have faster convergence speeds,lower steady-state errors and better processing ability for strongly correlated signals than LMS class algorithms.Firstly,based on the in-depth study of entropy theory and adaptive filtering algorithm,this thesis combines the minimum error entropy criterion and affine projection algorithm to suppress non-Gaussian noise,and introduces the ?-law proportionate matrix to reduce the influence of sparse system,while considering strongly correlated input signal and Newton method are used as the solution to form a new algorithm: Minimum Error Entropy-Law Proportionate Affine Projection Algorithm based on Newton Method(MEE-MPAPA-Newton).Secondly,combined with Affine Projection Algorithm and Minimum Error Entropy Algorithm,and using the idea of convex combination to integrate the two,Convex Minimum Error Entropy Affine Projection Algorithm(CMEEAPA)is proposed.The CMEEAPA algorithm combines the advantages of Affine Projection Algorithm and Minimum Error Entropy Algorithm,which has strong suppression ability against non-Gaussian noise and fast convergence speed.Finally,the proposed two new algorithms,the Improved Proportionate Affine Projection Sign Algorithm(IPAPSA),the Proportionate Minimum Error Algorithm(PMEE)and other adaptive filtering algorithms are compared under different Gaussian noises and sparse systems in simulation.The results of theoretical analysis and simulation experiments verify the effectiveness and robustness of the two new algorithms.