A Variable Step Size LMS Adaptive Filtering Algorithm Based on L2 Norm

On the basis of the traditional LMS algorithm and several improved algorithms, a variable step size LMS algorithm is proposed in this paper, which is based on the L2 norm. In this algorithm, a new nonlinear relationship between the step size and the error signal is established by introducing the input signal into the step size iteration function, so that it can reflect the impact of input signal on performance. Meanwhile, the smoothing factor is added to make the step size determined by current error value and also previous error, bringing it a certain noise immunity. In this paper, theoretical analysis and simulation experiments are conducted to compare the new algorithm with other existing algorithms from convergence speed, tracking performance and steady state mean square error (MSE). According to the simulation results, the proposed algorithm has a higher speed of convergence and better performance on tracking than those algorithms, whereas the steady state MSE remains the same as others.