Open Access

Set-Membership Proportionate Affine Projection Algorithms

  • Stefan Werner1Email author,
  • José A ApolinárioJr.2 and
  • Paulo S R Diniz3
EURASIP Journal on Audio, Speech, and Music Processing20072007:034242

DOI: 10.1155/2007/34242

Received: 30 June 2006

Accepted: 15 November 2006

Published: 18 January 2007

Abstract

Proportionate adaptive filters can improve the convergence speed for the identification of sparse systems as compared to their conventional counterparts. In this paper, the idea of proportionate adaptation is combined with the framework of set-membership filtering (SMF) in an attempt to derive novel computationally efficient algorithms. The resulting algorithms attain an attractive faster converge for both situations of sparse and dispersive channels while decreasing the average computational complexity due to the data discerning feature of the SMF approach. In addition, we propose a rule that allows us to automatically adjust the number of past data pairs employed in the update. This leads to a set-membership proportionate affine projection algorithm (SM-PAPA) having a variable data-reuse factor allowing a significant reduction in the overall complexity when compared with a fixed data-reuse factor. Reduced-complexity implementations of the proposed algorithms are also considered that reduce the dimensions of the matrix inversions involved in the update. Simulations show good results in terms of reduced number of updates, speed of convergence, and final mean-squared error.

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Authors’ Affiliations

(1)
Signal Processing Laboratory, Helsinki University of Technology
(2)
Department of Electrical Engineering, Instituto Militar de Engenharia
(3)
Signal Processing Laboratory, COPPE/Poli/Universidade Federal do Rio de Janeiro

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Copyright

© Stefan Werner et al. 2007

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.

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