An invariance in system identification

In simulations and analysis involving adaptive system identification with FIR filters, a white noise input spectrum is usually assumed. We consider in this correspondence the effect of an autoregressive (all-pole) input. In particular, we prove that all but P of the optimum tap weights are invariant to the pole locations, where P is the number of poles in the input process. This invariance result provides some justification for the common practice of considering only white noise inputs in the analysis and simulation of adaptive filters.