Mean-Square Deviation Analysis of Affine Projection Algorithm

• Published in: IEEE transactions on signal processing Vol. 59; no. 12; pp. 5789 - 5799
• Main Authors: Park, PooGyeon, Lee, Chang Hee, Ko, Jeong Wan
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive filters; affine projection algorithm (APA); Algorithms; Applied sciences; Covariance matrix; Detection, estimation, filtering, equalization, prediction; Deviation; Error analysis; Errors; Exact sciences and technology; Information, signal and communications theory; Iterative methods; Mathematical analysis; Mean square error methods; mean-square deviation (MSD); Noise measurement; Projection; Projection algorithms; Signal and communications theory; Signal, noise; Steady-state; Telecommunications and information theory; Vectors (mathematics); Covariance; Simulation; affine projection algorithm (APA); Adaptive filters; Cross correlation; Theoretical study; Signal processing; mean-square deviation (MSD); Iterative method; Adaptive filter; Affine transformation; Algorithm
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2165709

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 n most recent accumulated iterations, rather than a typical analysis based on a current single iteration, is suggested to reveal a previously unseen phenomenon, where n 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.