Exact expectation analysis of the LMS adaptive filter for correlated Gaussian input data

The author presents a method for deriving a set of linear update equations that can be used to predict the exact statistical behavior of a finite-impulse-response (FIR) least-mean-square (LMS) adaptive filter operating on finite-time-correlated input data. Using this method, one can derive exact bounds on the LMS step size to guarantee mean and mean-square convergence. The equation-deriving procedure is recursive and algorithmic, and a program written in the MAPLE symbolic-manipulation software package that automates the derivation for arbitrarily long adaptive filters operating on correlated data is described. Extensive computer simulations indicate that the exact analysis is much more accurate than previous analysis in predicting adaptation behavior under correlated data conditions. The results also indicate that analysis based on the commonly used independence assumption can be inaccurate in predicting the transient behavior of adaptive filters, even in slow adaptation situations.<>