A CFAR Adaptive Subspace Detector for First-Order or Second-Order Gaussian Signals Based on a Single Observation

In this paper, we consider the problem of detecting a signal in Gaussian noise with unknown covariance matrix, in partially homogeneous environments where the test and training data samples share the same noise covariance matrix up to an unknown scaling factor. One solution to this problem is the ad...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2011-11, Vol.59 (11), p.5126-5140
Main Authors: Liu, J., Zi-Jing Zhang, Yun Yang, Hongwei Liu
Format: Article
Language:English
Subjects:
Adaptive matched filter
adaptive subspace detector
Applied sciences
Computer simulation
Covariance matrix
Detection, estimation, filtering, equalization, prediction
Detectors
Exact sciences and technology
False alarms
first-order Gaussian model
Gaussian
generalized likelihood ratio test
Information, signal and communications theory
Likelihood ratio
Maximum likelihood estimation
Monte Carlo methods
Noise
performance analysis
Probability
second-order Gaussian model
Signal and communications theory
Signal, noise
Studies
Subspaces
Telecommunications and information theory
Training data
Variable speed drives
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Summary:In this paper, we consider the problem of detecting a signal in Gaussian noise with unknown covariance matrix, in partially homogeneous environments where the test and training data samples share the same noise covariance matrix up to an unknown scaling factor. One solution to this problem is the adaptive subspace detector (ASD) with a single or multiple observations. However, the probabilities of false alarm and detection of this ASD have not been obtained yet. In this paper, these expressions are derived on the basis of a single observation, which are confirmed with Monte Carlo simulations. It is shown that the ASD has a constant false alarm rate property with respect to both the shared noise covariance matrix structure and the independent scaling of the noise in the test data. In addition, we prove that for the First-Order model where the signal of interest is assumed to be a deterministic but unknown vector, the ASD derived with the generalized likelihood ratio test is consistent with that derived with an ad hoc two-step design procedure.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2011.2164073