Robustness of the filtered-x LMS algorithm: part 1: necessary conditions for convergence and the asymptotic pseudospectrum of Toeplitz matrices


Fraanje, R., Verhaegen, M. and Elliott, S.J. (2007) Robustness of the filtered-x LMS algorithm: part 1: necessary conditions for convergence and the asymptotic pseudospectrum of Toeplitz matrices. IEEE Transactions on Signal Processing, 55, (8), 4029-4037. (doi:10.1109/TSP.2007.896083).

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Original Publication URL: http://dx.doi.org/10.1109/TSP.2007.896083

Description/Abstract

Errors in the secondary path model of the filtered-x LMS (FXLMS) algorithm will lead to its divergence when the eigenvalues of the cross-correlation matrix between the estimated filtered reference and the true filtered reference signals are not all located in the right half plane. This cross-correlation matrix has a (block) Toeplitz structure whose dimension is determined by the number of adaptive filter coefficients. Using results on the asymptotic pseudospectrum of Toeplitz matrices, a frequency-domain condition on the model is derived to ensure stability. The condition is sufficient and necessary for a large number of filter coefficients. A transient analysis shows that the sufficient condition given by Wang and Ren [1999] is only necessary to prevent an initial increase of the error in the adaptive filter coefficients (critical behavior).

Item Type: Article
Additional Information:
ISSNs: 1053-587X (print)
Related URLs:
Keywords: toeplitz matrices, adaptive filter coefficients, asymptotic, pseudospectrum, block Toeplitz structure, cross-correlation matrix eigenvalues, filtered-x LMS algorithm robustness, frequency-domain condition, secondary path model, transient analysis, true filtered, reference signals
Subjects: Q Science > Q Science (General)
T Technology > TA Engineering (General). Civil engineering (General)
Divisions: University Structure - Pre August 2011 > Institute of Sound and Vibration Research > Signal Processing and Control
ePrint ID: 49555
Date Deposited: 15 Nov 2007
Last Modified: 27 Mar 2014 18:33
URI: http://eprints.soton.ac.uk/id/eprint/49555

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