A normalized frequency domain LMS adaptive algorithm

A scheme is presented for obtaining an input power estimate for setting the algorithm gain parameter μ separately in each frequency bin in the frequency domain LMS adaptive algorithm. This is particularly important if the input has large spectral variations, and a single feedback parameter, set on the broad-band power, could result in instability in the adaptive filters in some frequency bins. The estimate is incorporated directly into the algorithm as a data dependent time-varying stochastic μ(n). Using a Gaussian data model and sample-to-sample data independence, first-order linear difference equations are derived and solved for the mean and misadjustment errors. The performance of the scheme is compared to the case for which the input power level is known a priori. For the same transient response, only about ten samples need be averaged to yield the same misadjustment error.