A variable step long LMS algorithm based on Bessel function was put forward, which established the functional relationship between the step size factor and the error signal. And this algorithm would be applied to the adaptive noise canceller in order to improve the ability of the algorithm of uncorrelated noise suppression. This algorithm has a larger step-size during initial convergence stage or unknown system parameters change in order to get a faster convergence time and tracking speed. Moreover, and it adjusts small step-size to achieve a very small steady-state maladjustment noise after the convergence of the algorithm.
