New variable step size LMS adaptive spectral-line enhancement algorithm

Seeing that the ideal error of adaptive line enhancers (ALE) is not equal to zero, a novel variable step size LMS (least mean square) algorithm is presented. This algorithm builds a nonlinear relationship between the step size and the weighting coefficient, which makes the step size decrease with the change of weighting coefficients until the step size reduces to zero. In order to accelerate the convergence rate further, a step-vector is also introduced to adjust each weight vector value in real time. The step size of this algorithm increases at the beginning or before following up the signal automatically, and it will reduce to zero during the steady state. The LFM signal is taken as an example to verify the validity of the proposed algorithm in filtering the noise of non-stationary signals. The result shows this algorithm is better compared to the former.