A Novel Variable Step Size LMS Adaptive  Filtering Algorithm and Its Simulation

The common variable step size LMS algorithms have many drawbacks, such as the poor performance of the step function, the fixed parameters and the sensitivity to noise. The paper presents the HTLMS algorithm based on modified hyperbolic tangent by setting a nonlinear function between estimation error e(n) and step size factor μ(n). In the algorithm, the step size factor is adjusted by the absolute value of the product of the current and former errors. The algorithm also introduces the disturbance of the absolute estimation error to update the tapping vector of the adaptive filter, thus the algorithm has faster convergence speed, better performance of noise suppression and lower steady state error. The simulation shows that compared with several LMS algorithms, the novel algorithm has faster convergence speed and better steady state error under different SNR conditions.