Error smoothing in adaptive LMS algorithms

In this paper, an output error smoothing filter has been applied to the traditional gradient based adaptive filter. The rationale for this modification is to increase the convergence rate and decrease the minimum expected mean square error by ensuring a more stable region of operation. It was shown that smoothing the output error is equivalent to smoothing the desired response and the input. As a result, convergence to Wiener-Hopf solution is slightly modified to reflect the smoothing operation. However, convergence rate can be significantly improved and the minimum expected mean square error can be reduced with the proper choice of smoothing filter coefficients.