Detection and classification of spectrally equivalent processes using higher order statistics

This paper addresses the problem of detecting two spectrally equivalent processes, which are modeled by a noisy AR process and an ARMA process. Higher order statistics (HOS) are shown to be efficient tools for detection. Two HOS-based detectors are derived for the binary hypothesis testing problem (...

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Bibliographic Details
Published in:IEEE transactions on signal processing 1999-12, Vol.47 (12), p.3326-3335
Main Authors: Coulon, M., Tourneret, J.-Y., Swami, A.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Asymptotic properties
Closed-form solution
Detection, estimation, filtering, equalization, prediction
Detectors
Equivalence
Exact sciences and technology
Exact solutions
Higher order statistics
Information, signal and communications theory
Mathematical analysis
Parametric statistics
Phase shift keying
Probability
Quadrature amplitude modulation
Signal and communications theory
Signal processing
Signal, noise
Spectra
Statistical analysis
Statistics
Telecommunications and information theory
Testing
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Summary:This paper addresses the problem of detecting two spectrally equivalent processes, which are modeled by a noisy AR process and an ARMA process. Higher order statistics (HOS) are shown to be efficient tools for detection. Two HOS-based detectors are derived for the binary hypothesis testing problem (i.e., known signal spectrum): The first detector exploits the asymptotic Gaussianity of the sample estimates of the cumulants. The second detector exploits the singularity of a certain matrix based on HOS. The more general composite hypothesis testing problem (i.e., with unknown signal spectrum) is then considered and a detector proposed. The performances of the different detectors are compared in terms of receiver operating characteristic (ROC) curves. Approximate closed-form expressions are derived for the threshold and the ROCs of the three detectors.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.806076