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On false alarm rate of matched filter under distribution mismatch

Besson, Olivier On false alarm rate of matched filter under distribution mismatch. (2015) IEEE Signal Processing Letters, 22 (2). 167-171. ISSN 1070-9908

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Official URL: http://dx.doi.org/10.1109/LSP.2014.2352362


The generalized likelihood ratio test (GLRT) is a very widely used technique for detecting signals of interest amongst noise, when some of the parameters describing the signal (and possibly the noise) are unknown. The threshold of such a test is set from a desired probability of false alarm $\Pfa$ and hence this threshold depends on the statistical assumptions made about noise. In practice however, the noise statistics are seldom known and it becomes crucial to characterize $\Pfa$ under a mismatched distribution. In this letter, we address this problem in the case of a simple binary composite hypothesis testing problem (matched filter) when the threshold is designed under a Gaussian assumption while the noise actually follows an elliptically contoured distribution. We also consider the inverse situation. Generic expressions for the assumed and actual $\Pfa$ are derived and illustrated on the particular case of Student distributions for which simple, closed-form expressions are obtained. The latter show that the GLRT based on Gaussian assumption is not robust while that based on Student assumption is.

Item Type:Article
Additional Information:Thanks to IEEE editor. (c) 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. The definitive version is available at http://ieeexplore.ieee.org
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Laboratory name:
Département d'Electronique, Optronique et Signal - DEOS (Toulouse, France) - Signal, Communication, Antenne et Navigation - SCAN
Deposited On:12 Dec 2014 14:16

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