Pole optimisation in adaptive Laguerre filtering

In Laguerre-based adaptive filtering, the pole can be used as an extra degree of freedom. An optimal pole is difficult to determine on the basis of a squared error criterion. A compaction criterion, on the other hand, does yield a simple explicit expression for the pole in terms of characteristics derived from the impulse response of the system. In this paper. it is shown how these characteristics can be calculated directly from a Laguerre expansion of the impulse response. For truncated Laguerre series, this implies a much faster algorithm than the one based on characteristics derived from the impulse response. Such an algorithm can be used to construct an adaptive Laguerre-based adaptive system, where the current estimated Laguerre expansion can be used to determine the pole in a next step. Simulation results on the behaviour of such a system for a synthetic signal are given in terms of signal cancellation and convergence speed.