This paper enumerates the strengths and defects of the traditional least mean square (LMS) algorithm for adaptive filtering, and then designs a novel LMS algorithm with variable step size and verifies its performance through simulation. In our algorithm, the step size is no longer adjusted by the square of the error (e2(n)), but by the correlation between the current error and the error of a previous moment e(n-D). In this way, the algorithm becomes less sensitive to the noise with weak autocorrelation, and manages to achieve fast convergence, high time-varying tracking accuracy, and small steady-state error. The simulation results show that our algorithm outperformed the traditional LMS algorithm with fixed step size in convergence speed, tracking accuracy and noise suppression. The research findings provide a new tool for many other fields of adaptive filtering, such as adaptive system identification and adaptive signal separation.

This paper briefly analyses and discusses the advantages and disadvantages of the commonly used LMS adaptive filtering algorithm, proposes a new nonlinear functional relationship between step factor μ and error signal e ( n). And improve methods for variable step-size LMS algorithm appropriately. The algorithm utilizes the correlation value e (n) e (n -D) of output error signal to adjust the step factor μ, solves the inconsistency problem of error performance and convergence time.The algorithm is applied in the simulation of several typical signals processing system, and computer simulation results confirm the theoretical analysis.

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