Convergence analysis of RLS-DCD algorithm

The Recursive least squares (RLS)-dichotomous coordinate descent (DCD) algorithm recently introduced for adaptive filtering is characterized by low complexity, while possessing fast convergence. However, predicting the convergence performance of the RLS-DCD algorithm is still an open issue. Known approaches are found not applicable, as in the RLS-DCD algorithm, the normal equations are not exactly solved at every time instant and the sign function is involved at every update of the filter weights. In this work, we propose an approach for convergence analysis of the RLS-DCD algorithm based on computations with only deterministic correlation quantities. This new approach can be also used for other adaptive filtering algorithms based on iterative solving the normal equations.