HAL : hal-00421980, version 2

arXiv : 0910.0827

DOI : 10.1109/TIT.2011.2111710

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

IEEE Transactions on Information Theory 57, 4 (2011) 2400-2419

Versions disponibles :

v1 (05-10-2009)

v2 (31-05-2010)

Performance of Statistical Tests for Single Source Detection using Random Matrix Theory

Pascal Bianchi 1, Merouane Debbah 2, Mylène Maïda 3, Jamal Najim 1

(04/2011)

This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum Likelihood Test is studied and yields the analysis of the ratio between the maximum eigenvalue of the sampled covariance matrix and its normalized trace. Using recent results of random matrix theory, a practical way to evaluate the threshold and the $p$-value of the test is provided in the asymptotic regime where the number $K$ of sensors and the number $N$ of observations per sensor are large but have the same order of magnitude. The theoretical performance of the test is then analyzed in terms of Receiver Operating Characteristic (ROC) curve. It is in particular proved that both Type~I and Type~II error probabilities converge to zero exponentially as the dimensions increase at the same rate, and closed-form expressions are provided for the error exponents. These theoretical results rely on a precise description of the large deviations of the largest eigenvalue of spiked random matrix models, and establish that the presented test asymptotically outperforms the popular test based on the condition number of the sampled covariance matrix.

1 :	Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
	Télécom ParisTech – CNRS : UMR5141
2 :	Chaire Radio Flexible Alcatel-Lucent/Supélec (Chaire Radio Flexible)
	SUPELEC – ALCATEL-LUCENT
3 :	Laboratoire de Mathématiques d'Orsay (LM-Orsay)
	CNRS : UMR8628 – Université Paris XI - Paris Sud

Domaine

:

Mathématiques/Probabilités Mathématiques/Statistiques Statistiques/Théorie Mathématiques/Théorie de l'information et codage Informatique/Théorie de l'information et codage

Mots Clés : cognitive radio – statistical test – large random matrices – large deviations

hal-00421980, version 2

http://hal.archives-ouvertes.fr/hal-00421980

oai:hal.archives-ouvertes.fr:hal-00421980

Contributeur : Jamal Najim <>

Soumis le : Lundi 19 Avril 2010, 11:49:19

Dernière modification le : Jeudi 21 Février 2013, 22:06:27