Analysis of the FXLMS algorithm with norm-constant time-varying primary path

We analyze the behaviors of active noise control with a time-varying primary path using a statistical-mechanical method. The principal assumption used in the analysis is that the impulse responses of the primary path and adaptive filter are sufficiently long. We analyze a novel model in which the reference signal is not necessarily white and the primary path is time-varying while its norm is kept constant in the mean sense. We show the existence of macroscopic steady states and the optimal step size.