  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.
