A Novel Variable step length LMS Algorithm based on Arctangent Compound Function

Compared with the traditional least mean square error (LMS) algorithm, the variable step length LMS adaptive filtering algorithm can achieve better filtering results. However, a compromise must be made between the convergence rate and the steady-state error in the convergence process. To further improve the performance of the algorithm and solve the contradiction between the convergence speed and the steady-state error, a novel variable step length LMS adaptive filtering algorithm is proposed in this paper. The proposed method establishes a non-linear function between the error and the convergence factor, and uses the correlation value of the error to adjust the step size to improve the anti-interference ability of the algorithm. Simulation results indicate that the proposed method has approximately the same steady-state error performance compared with the improved LMS algorithm based on the Sigmoid function. However, the computational complexity of the novel algorithm is small and a faster convergence rate is guaranteed. Finally, the algorithm is applied to the application of direct-path wave cancellation of passive bistatic radar. Simulation experiments show that the algorithm has achieved a better cancellation effect, which further proves the effectiveness of the proposed method.