Study On Adaptive Filtering LMS Algorithm

Adaptive filtering algorithm is a class of important algorithms in signal processing.The LMS algorithm proposed by Widrow and Hoff in 1960 is one of the most important algorithm,which is widely used in the field of linear signal processing.However,the performance of the nonlinear model is not good,and the appearance of the kernel method provides theoretical support for solving the problem.In practical application,the signal encountered may be complex value signal,and adaptive filtering algorithm in complex number field is also a hot research topic.Around these aspects,the paper is divided into four chapters.The main work of this paper is as follows:The first chapter introduces the research history and current situation of adaptive filtering LMS algorithm.The second chapter,firstly,the related theories of Wiener filtering and LMS algorithm are introduced.Secondly,the convergence of LMS algorithm is proved.Finally,an improved variable step size LMS algorithm(VSNLMS algorithm)is proposed for the slow convergence of LMS algorithm.The simulation results show that the algorithm is excellent performance.The third chapter,the traditional LMS algorithm can not solve the nonlinear filtering problem well.By introducing nuclear knowledge,in this paper,an improved KLMS algorithm(VSKNLMS algorithm)is proposed.And the feasibility of the improved algorithm is illustrated by simulation experiments.The fourth chapter based on the relevant theoretical knowledge of complex reproducing kernel Hilbert space and Wirtinger's calculus,CKLMS algorithm for dealing with nonlinear filtering problems in complex fields is obtained.And the convergence of CKLMS algorithm is detailed derivation.