TY - GEN
T1 - Invariance of the distributions of normalized Gram matrices
AU - Howard, Stephen D.
AU - Sirianunpiboon, Songsri
AU - Cochran, Douglas
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Coherence
KW - Gram matrix
KW - Multiple-channel detection
KW - Stiefel manifold
UR - http://www.scopus.com/inward/record.url?scp=84907406334&partnerID=8YFLogxK
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U2 - 10.1109/SSP.2014.6884648
DO - 10.1109/SSP.2014.6884648
M3 - Conference contribution
AN - SCOPUS:84907406334
SN - 9781479949755
T3 - IEEE Workshop on Statistical Signal Processing Proceedings
SP - 352
EP - 355
BT - 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014
PB - IEEE Computer Society
T2 - 2014 IEEE Workshop on Statistical Signal Processing, SSP 2014
Y2 - 29 June 2014 through 2 July 2014
ER -