Computing the Largest Eigenvalue Distribution for Non-central Wishart Matrices

Scott R. Jones, Douglas Cochran, Stephen D. Howard, I. Vaughan L. Clarkson, Konstanty S. Bialkowski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue λ1 of the Gram matrix formed from data, which has a Wishart distribution. Although exact expressions for the distribution of λ1 are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. Following on recent work addressing this issue under the null hypothesis, this paper presents a method to calculate values of this distribution under the alternative hypothesis, allowing tractable computation of receiver operating characteristic curves.

Original languageEnglish (US)
Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4290-4294
Number of pages5
ISBN (Electronic)9781479981311
DOIs
StatePublished - May 1 2019
Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: May 12 2019May 17 2019

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2019-May
ISSN (Print)1520-6149

Conference

Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
CountryUnited Kingdom
CityBrighton
Period5/12/195/17/19

Fingerprint

Statistics
Distribution functions
Radar

Keywords

  • CFAR thresholds
  • Multi-channel detection
  • Passive radar
  • Wishart matrix

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Jones, S. R., Cochran, D., Howard, S. D., Clarkson, I. V. L., & Bialkowski, K. S. (2019). Computing the Largest Eigenvalue Distribution for Non-central Wishart Matrices. In 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings (pp. 4290-4294). [8682417] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2019-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2019.8682417

Computing the Largest Eigenvalue Distribution for Non-central Wishart Matrices. / Jones, Scott R.; Cochran, Douglas; Howard, Stephen D.; Clarkson, I. Vaughan L.; Bialkowski, Konstanty S.

2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 4290-4294 8682417 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2019-May).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Jones, SR, Cochran, D, Howard, SD, Clarkson, IVL & Bialkowski, KS 2019, Computing the Largest Eigenvalue Distribution for Non-central Wishart Matrices. in 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings., 8682417, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2019-May, Institute of Electrical and Electronics Engineers Inc., pp. 4290-4294, 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019, Brighton, United Kingdom, 5/12/19. https://doi.org/10.1109/ICASSP.2019.8682417
Jones SR, Cochran D, Howard SD, Clarkson IVL, Bialkowski KS. Computing the Largest Eigenvalue Distribution for Non-central Wishart Matrices. In 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 4290-4294. 8682417. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2019.8682417
Jones, Scott R. ; Cochran, Douglas ; Howard, Stephen D. ; Clarkson, I. Vaughan L. ; Bialkowski, Konstanty S. / Computing the Largest Eigenvalue Distribution for Non-central Wishart Matrices. 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 4290-4294 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).
@inproceedings{6b716bf24df0432489d6134c07158bfe,
title = "Computing the Largest Eigenvalue Distribution for Non-central Wishart Matrices",
abstract = "Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue λ1 of the Gram matrix formed from data, which has a Wishart distribution. Although exact expressions for the distribution of λ1 are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. Following on recent work addressing this issue under the null hypothesis, this paper presents a method to calculate values of this distribution under the alternative hypothesis, allowing tractable computation of receiver operating characteristic curves.",
keywords = "CFAR thresholds, Multi-channel detection, Passive radar, Wishart matrix",
author = "Jones, {Scott R.} and Douglas Cochran and Howard, {Stephen D.} and Clarkson, {I. Vaughan L.} and Bialkowski, {Konstanty S.}",
year = "2019",
month = "5",
day = "1",
doi = "10.1109/ICASSP.2019.8682417",
language = "English (US)",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "4290--4294",
booktitle = "2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings",

}

TY - GEN

T1 - Computing the Largest Eigenvalue Distribution for Non-central Wishart Matrices

AU - Jones, Scott R.

AU - Cochran, Douglas

AU - Howard, Stephen D.

AU - Clarkson, I. Vaughan L.

AU - Bialkowski, Konstanty S.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue λ1 of the Gram matrix formed from data, which has a Wishart distribution. Although exact expressions for the distribution of λ1 are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. Following on recent work addressing this issue under the null hypothesis, this paper presents a method to calculate values of this distribution under the alternative hypothesis, allowing tractable computation of receiver operating characteristic curves.

AB - Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue λ1 of the Gram matrix formed from data, which has a Wishart distribution. Although exact expressions for the distribution of λ1 are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. Following on recent work addressing this issue under the null hypothesis, this paper presents a method to calculate values of this distribution under the alternative hypothesis, allowing tractable computation of receiver operating characteristic curves.

KW - CFAR thresholds

KW - Multi-channel detection

KW - Passive radar

KW - Wishart matrix

UR - http://www.scopus.com/inward/record.url?scp=85068969932&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068969932&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2019.8682417

DO - 10.1109/ICASSP.2019.8682417

M3 - Conference contribution

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 4290

EP - 4294

BT - 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

ER -