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This article is part of the series Adaptive Partial-Update and Sparse System Identification.

Open Access Research Article

Set-Membership Proportionate Affine Projection Algorithms

Stefan Werner1*, José A Apolinário2 and Paulo SR Diniz3

Author Affiliations

1 Signal Processing Laboratory, Helsinki University of Technology, Otakaari 5A, Espoo 02150, Finland

2 Department of Electrical Engineering, Instituto Militar de Engenharia, Rio de Janeiro 2229-270, Brazil

3 Signal Processing Laboratory, COPPE/Poli/Universidade Federal do Rio de Janeiro, Rio de Janeiro 21945-970, Brazil

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EURASIP Journal on Audio, Speech, and Music Processing 2007, 2007:034242  doi:10.1155/2007/34242

The electronic version of this article is the complete one and can be found online at: http://asmp.eurasipjournals.com/content/2007/1/034242


Received:30 June 2006
Revisions received:15 November 2006
Accepted:15 November 2006
Published:18 January 2007

© 2007 Stefan Werner et al.

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.

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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