Improved variable step-size least mean square algorithm based on Sigmoid function

Abstract

One of the research focuses on the least mean square (LMS) algorithm is how to design the variable step-size rule to make the LMS algorithm converge ratio and steady-state error. The step-size is relatively large in its early stages; that is, the algorithm at this stage converges quickly; when the algorithm tends to a steady-state, the step-size is relatively small, that is. It is at this stage that the steady-state estimation error is relatively tiny. Therefore, looking at it as a whole, the algorithm can converge quickly with lower steady-state errors. Therefore, this paper designs a new step-size rule based on the Sigmoid function and theoretically analyzes the convergence characteristics and steady-state performance. Experiments and simulation comparisons are carried out under the conditions of comparison. The theoretical analysis combined with experimental simulation verification: even if the linear system has a sudden change, this algorithm still has a faster convergence ratio and tracking speed and can obtain minor steady-state errors and steady-state offsets.