Invariance of the distributions of normalized Gram matrices

Stephen D. Howard, Songsri Sirianunpiboon, Douglas Cochran

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

4 Scopus citations

Abstract

Normalized Gram matrices formed from multiple vectors of sensor data, and functions of the eigenvalues of such matrices in particular, have a long history in connection with multiple-channel detection. The determinant and various other functions of the eigenvalues of these matrices arise as detection statistics in a variety of multichannel problems, and knowledge of their distributions under the H0 assumption that the sensor channels are independent and contain only white gaussian noise is consequently important for determining false-alarm probabilities for multi-channel detectors. Invariance of the H0 distribution of the eigenvalues to one data channel is significant in some applications. This paper derives the H0 distribution of a normalized Gram matrix and, as corollaries, obtains the distribution of the determinant as well as invariance results for the matrix that carry over to its spectrum. The essential symmetry property of white gaussian noise on which these results depend is also noted.

Original languageEnglish (US)
Title of host publication2014 IEEE Workshop on Statistical Signal Processing, SSP 2014
PublisherIEEE Computer Society
Pages352-355
Number of pages4
ISBN (Print)9781479949755
DOIs
StatePublished - Jan 1 2014
Event2014 IEEE Workshop on Statistical Signal Processing, SSP 2014 - Gold Coast, QLD, Australia
Duration: Jun 29 2014Jul 2 2014

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings

Other

Other2014 IEEE Workshop on Statistical Signal Processing, SSP 2014
CountryAustralia
CityGold Coast, QLD
Period6/29/147/2/14

Keywords

  • Coherence
  • Gram matrix
  • Multiple-channel detection
  • Stiefel manifold

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications

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  • Cite this

    Howard, S. D., Sirianunpiboon, S., & Cochran, D. (2014). Invariance of the distributions of normalized Gram matrices. In 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014 (pp. 352-355). [6884648] (IEEE Workshop on Statistical Signal Processing Proceedings). IEEE Computer Society. https://doi.org/10.1109/SSP.2014.6884648