Adaptive Detection of a Signal Known Only to Lie on a Line in a Known Subspace, When Primary and Secondary Data are Partially Homogeneous

This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known line...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2006-12, Vol.54 (12), p.4698-4705
Main Authors: Besson, O., Scharf, L.L., Kraut, S.
Format: Article
Language:English
Subjects:
Adaptive signal detection
Applied sciences
Array processing
Covariance matrix
Derivation
detection
Detection, estimation, filtering, equalization, prediction
Detectors
Exact sciences and technology
Frequency
Information, signal and communications theory
Mathematical analysis
Mathematical models
maximal invariant statistic
Miscellaneous
Noise
Sensor arrays
Signal and communications theory
Signal detection
Signal processing
Signal to noise ratio
Signal, noise
Statistics
Steering
steering vector uncertainties
Studies
Subspaces
Telecommunications and information theory
Uncertainty
Vectors
Vectors (mathematics)
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Summary:This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2006.881262