Non-Wiener Mean Weight Behavior of LMS Transversal Equalizers With Sinusoidal Interference

The least mean-square (LMS) algorithm is generally expected to operate near the corresponding Wiener filter solution. An important exception occurs when the algorithm is used to adapt a transversal equalizer in the presence of additive narrowband interference. For this application, the steady-state LMS equalizer behavior does not correspond to that of the fixed Wiener equalizer: the mean of its weights is different from the Wiener weights, and its mean-square error performance may be significantly better than the Wiener performance. Assuming a large interference-to-signal ratio (ISR), we present the solution for the mean of the LMS weight vector in steady state, based on the Butterweck expansion of the weight update equation. The analytical results are valid for all (mean-square stable) step-sizes. Simulation results are included to support the analytical results and show that the analytical results predict the simulation results accurately, over a wide range of ISR.