Combination of LMS Adaptive Filters with Coefficients Feedback

TL;DR

This paper introduces a novel adaptive filter combination method that cyclically feeds back the combined coefficients to all filters, enhancing convergence, tracking, and stability without complex coefficient transfers.

Contribution

Proposes a new topology for adaptive filter combinations using cyclic coefficient feedback, improving performance and stability over traditional methods.

Findings

Improved convergence and tracking performance.

Enhanced stability of adaptive filter combinations.

Low computational overhead for the proposed method.

Abstract

Parallel combinations of adaptive filters have been effectively used to improve the performance of adaptive algorithms and address well-known trade-offs, such as convergence rate vs. steady-state error. Nevertheless, typical combinations suffer from a convergence stagnation issue due to the fact that the component filters run independently. Solutions to this issue usually involve conditional transfers of coefficients between filters, which although effective, are hard to generalize to combinations with more filters or when there is no clearly faster adaptive filter. In this work, a more natural solution is proposed by cyclically feeding back the combined coefficient vector to all component filters. Besides coping with convergence stagnation, this new topology improves tracking and supervisor stability, and bridges an important conceptual gap between combinations of adaptive filters and variable step size schemes. We analyze the steady-state, tracking, and transient performance of this topology for LMS component filters and supervisors with generic activation functions. Numerical examples are used to illustrate how coefficients feedback can improve the performance of parallel combinations at a small computational overhead.