A stochastic model for the deficient order Affine Projection algorithm

This paper presents a statistical analysis of the Affine Projection (AP) adaptive algorithm for autoregressive (AR) input signals when the order of the AP algorithm is smaller than the order of the AR process. Deterministic recursive equations are derived for the mean weight and mean-square error behavior. Monte Carlo simulations show excellent agreement with the theoretical predictions in steady-state and, under certain conditions, during transient. These results are of special interest in practical applications where the computational complexity prevents implementation of the sufficient order AP algorithm for high order AR inputs.