A new variable step size method for the LMS adaptive filter

In this paper, a new cost function for improving the performance of the least mean square (LMS) method is proposed. The proposed cost function is convex. The first derivative of the proposed cost function is continue. The prove of the convexity of the function is presented. The theoretical study of the convergence characteristic shows that lower error and faster convergence can be obtained by using the proposed function. The proposed function provide large weighting factor when the error is small. On the hand, when the error is large, a small weighting factor is applied. By doing so, the effect of the noise can be reduced. The simulation results show that indeed we can lower final error and faster convergence when small a is applied than that of large a as in the conventional LMS.