Modified variable step size transform domain LMS algorithm

Transform domain is an effective method to accelerate the convergence of adaptive algorithm with the highly correlated input, but there is still a contradiction between the requirement of convergence speed and steady-state misadjustment. A modified variable step size scheme based on the transform domain LMS is proposed in this paper. The variable step size factor is controlled by the error autocorrelation, and the influence of irrelevant observation noise is eliminated. In this paper, the convergence and steady-state performance of the proposed algorithm are theoretically analyzed under the stationary and non-stationary state, respectively, and the optimal algorithm parameters are given. The same steady-state error is set in the simulation, and the results show that the algorithm proposed in this paper converges 1300 points earlier than the algorithm with fixed step size under the stationary state, and 1400 points earlier under the non-stationary state, besides, the convergence speed is improved compared with other algorithms with variable step size.