Swish Function Based LMS Algorithm with Variable Step Size

In order to improve the convergence speed of the existing LMS algorithms, a new LMS algorithm with variable step size based on the Swish function is proposed, and the effects of the parameters in the new algorithm on the performance are analyzed, and the convergence speeds of the new algorithm are compared with those of the fixed-step-length LMS algorithm, the SVSLMS algorithm, the LMS algorithm based on the inverse hyperbolic tangent function, and the LMS algorithm based on the Sa function in different signal-to-noise environments. The results show that the new algorithm requires the least number of iterations to reach convergence and has the fastest convergence speed. Finally, the real vehicle noise is analyzed for active control, and the range of error values is analyzed to obtain the noise reduction of 80%, 90%, 92.5% and 95% for the fixed-step LMS algorithm, the SVSLMS algorithm, the LMS algorithm based on the inverse hyperbolic tangent function, and the LMS algorithm based on the Sa function, respectively, and the reduction of the new algorithm is 96%, which indicates that the new algorithm has the smallest convergence error and the best convergence performance.