Improved Variable Step Size LMS Algorithm Based on Arctangent Function

The stability and convergence speed of the traditional Least Mean Square (LMS) are always in a state of contradiction due to the fixed step size. According to the relevant researchers, replacing the fixed step size with a time-varying step size, we use the arctangent function to return the transformation of the step-change factor and the error in the Sigmoid Variable step-size LMS (SVSLMS) algorithm. Furthermore, we analyze the influence of the parameters in the step-change factor on the proposed algorithm. The proposed algorithm accelerates convergence speed and solves the problem because the step size changes too quickly of the Normal distribution Sigmoid Variable step-size LMS (N-SVSLMS) algorithm. The simulation conclusion presents the convergence speed of the algorithm is significantly improved.