The Research Of Variable Step Size Adaptive LMS Filtering Algorithms

It is difficult to keep the balance between convergence speed and steady-state error for the existed variable step size adaptive LMS algorithm,taking into account the shortcoming that if get one and will lose the other.Some new non-linear functions that conform to the step size adjustment mechanism are designed and built mainly by studying the variable step size adaptive filtering algorithms and the change based on the cost functions and its applications in this thesis,and at the same time,some corresponding new methods that can improve algorithm tracking and filtering performance are provided,and some new variable step size adaptive LMS(Variable Step Size Adaptive LMS,VSSALMS)and normalized variable step size LMS(Normalized Variable Step Size Adaptive LMS,NVSSALMS)filtering algorithms are proposed.It mainly includes the following two aspects: 1.Because the traditional adaptive algorithm uses a fixed step to adjust the step variable value,the result of this processing is: the algorithm sacrifices the steady-state Performance to obtain a high rate of convergence speed;the cost of the steady-state performance is obtained for algorithm is the convergence rate.Therefore,the focus of this thesis is to build a new type of nonlinear function relationship and related derivative functions that conform to the principle of VSSALMS filter algorithm step size adjustment mechanism,and analyze and organize the theoretical part and use the computer to take the experimental platform conducts simulations that are highly realistic;2.Designing a new cost function that conforms for the algorithm,conducting the theoretical analysis and research on the corresponding adaptive weight update equation through derivation and verification;At the end,some kinds of new VSSALMS or NVSSALMS filtering algorithms are designed by combined with nonlinear variable step size functions,and the theoretical performance analysis and the computer simulation of the designed algorithms is confirmed.The specific work is as follows:(1)Through the research and analysis of many VSSALMS filtering algorithms that have been proposed,a non-linear function relationship of the Sigmoid function enhanced with logarithmic function characteristics is established between the step size and the error signal,and a new logarithmic Sigmoid function VSSALMS filtering algorithm is proposed.(2)The step size adjustment function starts from the most basic Versoria function(standardized Versoria function),it uses the auto-correlation estimation of the error to adjust the control step size,and a kind of Versoria function with variable step length is built.The adaptive filtering algorithm can eliminate the influence of irrelevant noise and improve the anti-noise ability of the system.(3)Through the theoretical analysis of the Cauchy-Lorentz function,the step size is controlled by the variation of the error,and the nonlinear relationship of the Cauchy-Lorentz function with the error as the variation is built,and it is proposed that it has a faster convergence speed and a more rapid convergence rate.A NVSSALMS filtering algorithm based on Cauchy density function is proposed that with small steady-state error,super mean square error and lower misadjustment.