Variable Step-size LMS Algorithm Based on Hyperbolic Tangent Function

To solve the problem that the least mean square (LMS) algorithm cannot balance the convergence rate and steady-state mean square error (MSE) well and require excessive manual adjustment of parameters, this paper proposes a parameter-free variable step-size LMS algorithm based on the hyperbolic tangent function. First, the algorithm uses the hyperbolic tangent function to establish a nonlinear relationship between the error and the step size. Based on this, the average value of the error signal is used to update the step size. Further, the accumulated error value is multiplied by its average value and added to the input signal energy. Then, the algorithm is normalized by using this value to prevent the algorithm divergence due to the sudden increase in the signal power. The convergence proof of the proposed algorithm is provided in this paper. The simulation results indicate that the proposed algorithm can automatically adjust the parameters. The convergence rate and the steady-state MSE are better than those of other algorithms for both high and low signal-to-noise ratios.