Convergence analysis of gradient adaptive algorithms for arbitrary inputs without independence assumption

The authors propose a novel analytical model for the convergence of a gradient adaptive filter. This model describes the iterative behaviors of all components of the parameter vector estimate by a single scalar difference equation, i.e. with respect to the coordinate system consisting of the right eigenvectors of the input (or input-output for IIR ADF) correlation matrix; only one component in the direction of the input or input-output vector is changed while the other components remain intact. Based on this model, the conditions which guarantee the first and the second moment convergence, respectively, for arbitrary input signals (colored or white) are presented