Non-Wiener Weight Behavior of LMS Transversal Equalizers

The least mean square (LMS) algorithm is widely assumed to operate around the corresponding Wiener filter solution. It has been observed that an exception to this popular perception occurs when the algorithm is used to adapt a transversal equalizer in the presence of additive narrowband interference. In the latter case, the steady-state LMS behavior does not correspond to the Wiener filter: its mean weights are different from the Wiener weights, and its mean squared error performance may be significantly better than the Wiener performance. Starting from the Butterweck expansion of the weight update equation, we derive a recursive approximation for the mean of the LMS weight vector in steady-state. The analytical approximation is good for all step-sizes where the expansion converges, as supported by the simulation results.