The recursive adaptive LMS filter--A line enhancer application and analytical model for the mean weight behavior

A mathematical model is presented for the recursive adaptive filter (RAF) configured as an adaptive line enhancer (ALE) in the frequency domain. The inputs for the model are Markovian and the number of recursive taps is selected to equal the order of the Markov process. Thus, the RAF structure is sufficient to realize the Wiener filter. Assuming that the expectations of all filter-data interactions factor, a system of four deterministic equations for the mean weights is derived. In steady state, the mean weights converge to the Wiener filter, and hence minimize the mean-square error. Excellent agreement between this analysis and stochastic simulations support the expectation-splitting assumptions.