Non-linear effects in LMS adaptive filters

Recent results demonstrate that adaptive filters implemented with the least mean square (LMS) algorithm can exhibit better mean square error (MSE) performance than the corresponding Wiener filter. We examine some conditions under which this can occur for implementations of an adaptive noise canceler and an adaptive equalizer. In particular, we demonstrate that because of the recursive LMS update equation, the LMS estimator is non-linear and uses much more information than that used by the corresponding Wiener filter. Under certain circumstances, this extra information can enhance the MSE performance of LMS over the Wiener filter. To quantify this effect, we use a transfer function approach to approximate the MSE of the LMS estimator. We also show that the LMS estimator is indeed bounded in MSE performance by a linear Wiener filter that explicitly uses the same information used in the LMS estimator