Computing the largest eigenvalue distribution for complex Wishart matrices
Scott R. Jones, Stephen D. Howard, I. Vaughan L. Clarkson, Konstanty S. Bialkowski, Douglas Cochran
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 λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> of G, which arises in passive radar detection of a rank-one signal. Although the distribution of λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> 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.
BibTeX
@inproceedings{icassp2017_computingthelarg,
title = {Computing the largest eigenvalue distribution for complex Wishart matrices},
author = {Scott R. Jones and Stephen D. Howard and I. Vaughan L. Clarkson and Konstanty S. Bialkowski and Douglas Cochran},
booktitle = {ICASSP 2017},
year = {2017}
}