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Adaptive detection in elliptically distributed noise and under-sampled scenario

Besson, Olivier and Abramovich, Yuri Adaptive detection in elliptically distributed noise and under-sampled scenario. (2014) IEEE Signal Processing Letters, 21 (12). 1531-1535. ISSN 1070-9908

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Official URL: http://dx.doi.org/10.1109/LSP.2014.2344695


The problem of adaptive detection of a signal of interest embedded in elliptically distributed noise with unknown scatter matrix $\R$ is addressed, in the specific case where the number of training samples $T$ is less than the dimension $M$ of the observations. In this under-sampled scenario, whenever $\R$ is treated as an arbitrary positive definite Hermitian matrix, one cannot resort directly to the generalized likelihood ratio test (GLRT) since the maximum likelihood estimate (MLE) of $\R$ is not well-defined, the likelihood function being unbounded. Indeed, inference of $\R$ can only be made in the subspace spanned by the observations. In this letter, we present a modification of the GLRT which takes into account the specific features of under-sampled scenarios. We come up with a test statistic that, surprisingly enough, coincides with a subspace detector of Scharf and Friedlander: the detector proceeds in the subspace orthogonal to the training samples and then compares the energy along the signal of interest to the total energy. Moreover, this detector does not depend on the density generator of the noise elliptical distribution. Numerical simulations illustrate the performance of the test and compare it with schemes based on regularized estimates of $\R$.

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
HAL Id:hal-01070911
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > WR Systems (USA)
Laboratory name:
Département d'Electronique, Optronique et Signal - DEOS (Toulouse, France) - Signal, Communication, Antenne et Navigation - SCAN
Deposited By: Olivier Besson
Deposited On:02 Oct 2014 14:53

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