Analysis of error-gradient adaptive linear estimators for a class of stationary dependent processes

In many applications, the training data to be processed by an adaptive linear estimator can be assumed to have a finite correlation length. An exact analysis for this class of problems that yields the coefficient bias, coefficient correlation matrix, and mean square estimation error is obtained via a stochastic imbedding procedure. A power series expansion in the gain parameter is used to obtain simplified expressions of order one for the above statistical moments. These new expressions are shown to contain the terms that would result from an analysis based upon the assumption of independent training data plus additional terms arising from data correlation. Algorithm convergence properties are studied by identifying the appropriate matrix eigenvalues from the first-order theory.