TY - GEN
T1 - Computing the largest eigenvalue distribution for complex Wishart matrices
AU - Jones, Scott R.
AU - Howard, Stephen D.
AU - Clarkson, I. Vaughan L.
AU - Bialkowski, Konstanty S.
AU - Cochran, Douglas
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/16
Y1 - 2017/6/16
N2 - 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.
AB - 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.
KW - CFAR thresholds
KW - Multi-channel detection
KW - Passive radar
KW - Wishart matrix
UR - http://www.scopus.com/inward/record.url?scp=85023764958&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85023764958&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2017.7952795
DO - 10.1109/ICASSP.2017.7952795
M3 - Conference contribution
AN - SCOPUS:85023764958
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3439
EP - 3443
BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Y2 - 5 March 2017 through 9 March 2017
ER -