On the optimum gain parameter in LMS adaptation

In this correspondence, the optimum selection of the adaptation parameter μ in LMS adaptive estimation is discussed for a white data covarianee matrix. It is shown via analysis and numerical evaluation, that the optimum selection of μ is a complicated function of the number of filter taps, the initial weight setting, the Wiener weights, and the number of learning samples, μ is not chosen, in general, to yield the most rapid transient response. For most cases of interest, a smaller value of μ will be selected for slower adaptation and smaller misadjustment error at the end of the learning phase.