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  • Research Article
  • Open Access

A Variable Step-Size Proportionate Affine Projection Algorithm for Identification of Sparse Impulse Response

EURASIP Journal on Advances in Signal Processing20092009:150914

  • Received: 13 January 2009
  • Accepted: 5 August 2009
  • Published:


Proportionate adaptive algorithms have been proposed recently to accelerate convergence for the identification of sparse impulse response. When the excitation signal is colored, especially the speech, the convergence performance of proportionate NLMS algorithms demonstrate slow convergence speed. The proportionate affine projection algorithm (PAPA) is expected to solve this problem by using more information in the input signals. However, its steady-state performance is limited by the constant step-size parameter. In this article we propose a variable step-size PAPA by canceling the a posteriori estimation error. This can result in high convergence speed using a large step size when the identification error is large, and can then considerably decrease the steady-state misalignment using a small step size after the adaptive filter has converged. Simulation results show that the proposed approach can greatly improve the steady-state misalignment without sacrificing the fast convergence of PAPA.


  • Convergence Speed
  • Adaptive Algorithm
  • Adaptive Filter
  • Slow Convergence
  • Posteriori Estimation Error

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Authors’ Affiliations

Department of Information Systems Engineering, Kochi University of Technology, 185 Miyanokuchi, Kochi 782-8502, Japan
School of Computer Science, Fudan University, 220 Handan Road, Shanghai, 200433, China


© Ligang Liu et al. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.