Mean-Square Deviation Analysis of Affine Projection Algorithm

This paper presents an improved mean-square deviation (MSD) analysis of the standard affine projection algorithm (APA) based on two distinctive features. First, the propagation model of the error covariance includes the cross-correlation between the current weight error vector and the prior measurement noises associated with the reused inputs; such a cross-correlation has merely been considered previously. Second, the analysis based on most recent accumulated iterations, rather than a typical analysis based on a current single iteration, is suggested to reveal a previously unseen phenomenon, where denotes the tap-length of the filter. Simulation results are in better agreement with the proposed theoretical results, than the previous theoretical ones, over a wide range of parameters such as tap-length, projection order, and step-size.