Proportionate Adaptive Filters From a Basis Pursuit Perspective

In this letter, we show that the normalized least-mean-square (NLMS) algorithm and the affine projection algorithm (APA) can be decomposed as the sum of two orthogonal vectors. One of these vectors is derived from an ℓ 2 -norm optimization problem while the other one is simply a good initialization...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 17; no. 12; pp. 985 - 988
Main Authors: Benesty, Jacob, Paleologu, Constantin, Ciochină, Silviu
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2010
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive filters
Algorithms
APA
basis pursuit
Convergence
Decomposition
echo cancellation
Echo cancellers
Least mean square algorithms
Mathematical analysis
NLMS
Optimization
PAPA
PNLMS
Projection
Signal processing
Signal processing algorithms
Vectors (mathematics)
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary:In this letter, we show that the normalized least-mean-square (NLMS) algorithm and the affine projection algorithm (APA) can be decomposed as the sum of two orthogonal vectors. One of these vectors is derived from an ℓ 2 -norm optimization problem while the other one is simply a good initialization vector. By replacing this optimization with the basis pursuit, which is based on the ℓ 1 -norm optimization, we derive the proportionate NLMS (PNLMS) algorithm and the proportionate APA (PAPA). Many other adaptive filters can be derived following this approach, including new ones.
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2010.2082529