Improved approximate QR-LS algorithms for adaptive filtering

This paper studies a class of O(N) approximate QR-based least squares (A-QR-LS) algorithm recently proposed by Liu in 1995. It is shown that the A-QR-LS algorithm is equivalent to a normalized LMS algorithm with time-varying stepsizes and element-wise normalization of the input signal vector. It red...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. II, Express briefs Vol. 51; no. 1; pp. 29 - 39
Main Authors: Chan, S.C., Yang, X.X.
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2004
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive filters
Algorithms
Approximation
Arithmetic
Complexity
Computer simulation
Decorrelation
Echo cancellers
Filtering algorithms
Least squares approximation
Mathematical analysis
Performance evaluation
Studies
System identification
Tantalum
Time varying systems
Vectors (mathematics)
ISSN:1549-7747, 1558-3791
Online Access:Get full text
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Summary:This paper studies a class of O(N) approximate QR-based least squares (A-QR-LS) algorithm recently proposed by Liu in 1995. It is shown that the A-QR-LS algorithm is equivalent to a normalized LMS algorithm with time-varying stepsizes and element-wise normalization of the input signal vector. It reduces to the QR-LMS algorithm proposed by Liu et al. in 1998, when all the normalization constants are chosen as the Euclidean norm of the input signal vector. An improved transform-domain approximate QR-LS (TA-QR-LS) algorithm, where the input signal vector is first approximately decorrelated by some unitary transformations before the normalization, is proposed to improve its convergence for highly correlated signals. The mean weight vectors of the algorithms are shown to converge to the optimal Wiener solution if the weighting factor w of the algorithm is chosen between 0 and 1. New Givens rotations-based algorithms for the A-QR-LS, TA-QR-LS, and the QR-LMS algorithms are proposed to reduce their arithmetic complexities. This reduces the arithmetic complexity by a factor of 2, and allows square root-free versions of the algorithms be developed. The performances of the various algorithms are evaluated through computer simulation of a system identification problem and an acoustic echo canceller.
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ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2003.821514