Study Of Variable Step Size LMS Adaptive Filtering Algorithm

In 1967 Window and Hoff proposed adaptive filter theory, which makes the filter parameters can be automatically adjusted to the optimum value, to achieve optimal filtering. The performance of adaptive filter is a good and easy hardware implementation. Filtering algorithm decides the performance of the filter, the design of algorithm occupies the position play a decisive role in the whole process of design of the filter. The pursuit of fast convergence speed, smaller steady-state error, the calculation complexity of the algorithm is low, easy hardware implementation in the field of signal processing has become the objective of the study. The least mean square(LMS) algorithm has better convergence performance and steady-state error performance characteristics results which is developed based on the wiener filtering theory, plus LMS simple algorithm, less calculation, easy implementation of hardware, has been widely used in channel equalization, noise processing, system identification, linear prediction and other fields.This paper bases on discussing the adaptive filter theory, through introduces some of the current most important adaptive filtering algorithm and its application, analysis and study of traditional LMS algorithm, and summarizes the characteristics of the existing variable step size LMS algorithm. In order to overcome the shortcomings of traditional fixed step size LMS algorithm in convergence speed and steady-state error performance, this paper puts forward a new variable step size LMS adaptive filter algorithm based on hyperbolic sine function, and analysis the parameters of a, b, c effects on the performance of the new algorithm. Through the simulation of authentication of this algorithm in convergence speed and steady-state error performance significantly better than the fixed step size LMS algorithm and the SVS-LMS algorithm proposed in the literature [57].Because of the different noise environments, the adaptive filtering algorithm in convergence speed and steady-state misadjustment can be affected by different signal to noise ratio. Through mathematical variation on the hyperbolic tangent function, this paper proposes a new modified variable step size LMS algorithm. Comparing the new improved algorithm with former algorithm, the new algorithm has faster convergence speed, the steady state time-varying tracking speed and smaller misadjustment obviously.