Computing the largest eigenvalue distribution for complex Wishart matrices

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

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

6 Scopus citations

Abstract

In multi-channel detection, sufficient statistics for Generalized Likelihood Ratio and Bayesian tests are often functions of the eigenvalues of the Gram matrix formed from data vectors collected at the sensors. When the null hypothesis is that the channels contain only independent complex white Gaussian noise, the distributions of these statistics arise from the joint distribution of the eigenvalues of a complex Wishart matrix G. This paper considers the particular case of the largest eigenvalue λ1 of G, which arises in passive radar detection of a rank-one signal. Although the distribution of λ1 is known analytically, calculating its values numerically has been observed to present formidable difficulties. This is particularly true when the dimension of the data vectors is large, as is common in passive radar applications, making computation of accurate detection thresholds intractable. This paper presents results that significantly advance the state of the art for this problem.

Original languageEnglish (US)
Title of host publication2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3439-3443
Number of pages5
ISBN (Electronic)9781509041176
DOIs
StatePublished - Jun 16 2017
Event2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States
Duration: Mar 5 2017Mar 9 2017

Other

Other2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
CountryUnited States
CityNew Orleans
Period3/5/173/9/17

Keywords

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

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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  • Cite this

    Jones, S. R., Howard, S. D., Clarkson, I. V. L., Bialkowski, K. S., & Cochran, D. (2017). Computing the largest eigenvalue distribution for complex Wishart matrices. In 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings (pp. 3439-3443). [7952795] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2017.7952795