A theoretical model for the deficient order pseudo-affine projection algorithm

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