Combinations of Adaptive Filters with Coefficients Feedback

Parallel combinations of adaptive filters have been effectively used to improve the performance of adaptive algorithms and address typical trade-offs, such as the one between convergence rate and steady-state error. In these combinations, the component filters are usually run independently and then combined, which leads to a well known convergence stagnation effect. Conditional transfers of coefficients between filters were introduced in an attempt to handle this issue. This work introduces a more natural way of accelerating convergence to steady-state by cyclically feeding back the overall coefficients to all component filters. Besides coping with convergence stagnation, this new topology allows several adaptive algorithms—e.g., mixed norm, data reusing, and variable step size—to be posed as combinations of simple adaptive filters, bridging an important conceptual gap. Steady-state and tracking analysis accounting for a myriad of component filters are derived for combinations with and without feedback. Transient analyses of the typical convex and affine supervisors are extended to general activation functions and applied to combinations with cyclic coefficients feedback. Numerical examples are provided to illustrate how coefficients feedback can improve the performance of several existing parallel combinations at a small additional computational cost.