An estimator for the eigenvalues of the system matrix of a periodic-reference LMS algorithm

Tuomas Haarnoja, Kari Tammi, Kai Zenger

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

Abstract

The convergence analysis of the Least Mean Square (LMS) algorithm has been conventionally based on stochastic signals and describes thus only the average behavior of the algorithm. It has been shown previously that a periodic-reference LMS system can be regarded as a linear time-periodic system whose stability can be determined from the monodromy matrix. Generally, the monodromy matrix can only be solved numerically and does not thus reveal the actual factors behind the dynamics of the system. This paper derives an estimator for the eigenvalues of the monodromy matrix. The estimator is easy to calculate, and it also reveals the underlying reason for the bad convergence of the LMS algorithm in some special cases. The estimator is confirmed by comparing it to the precise eigenvalues of the monodromy matrix. The estimator is found to be accurate for the eigenvalues close to unity
Original languageEnglish
Title of host publicationProceedings of 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
PublisherIEEE Institute of Electrical and Electronic Engineers
Pages3777-3780
ISBN (Electronic)978-1-4673-0046-9
ISBN (Print)978-1-4673-0045-2, 978-1-4673-0044-5
DOIs
Publication statusPublished - 2012
MoE publication typeNot Eligible
EventIEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Kyoto, Japan
Duration: 25 Mar 201230 Mar 2012

Conference

ConferenceIEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
Abbreviated titleICASSP 2012
CountryJapan
CityKyoto
Period25/03/1230/03/12

Keywords

  • LMS algorithm
  • monodromy matrix
  • estimator for the eigenvalues
  • convergence rate

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    Haarnoja, T., Tammi, K., & Zenger, K. (2012). An estimator for the eigenvalues of the system matrix of a periodic-reference LMS algorithm. In Proceedings of 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 (pp. 3777-3780). IEEE Institute of Electrical and Electronic Engineers. https://doi.org/10.1109/ICASSP.2012.6288739