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.
N1 - Publisher Copyright: © 2019 IEEE.
PY - 2019/5
Y1 - 2019/5
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
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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.
T2 - 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
Y2 - 12 May 2019 through 17 May 2019
ER -