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Random Matrix Theory applied to the Estimation of Collision Multiplicities

Escrig, Benoît Random Matrix Theory applied to the Estimation of Collision Multiplicities. (2012) International Journal On Advances in Networks and Services, vol. 5 (n° 3 & 4). pp. 269-278. ISSN 1942-2644

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Official URL: http://www.iariajournals.org/networks_and_services/index.html

Abstract

This paper presents two techniques in order to estimate the collision multiplicity, i.e., the number of users involved in a collision [1]. This estimation step is a key task in multi-packet reception approaches and in collision resolution techniques. The two techniques are proposed for IEEE 802.11 networks but they can be used in any OFDM-based system. The techniques are based on recent advances in random matrix theory and rely on eigenvalue statistics. Provided that the eigenvalues of the covariance matrix of the observations are above a given threshold, signal eigenvalues can be separated from noise eigenvalues since their respective probability density functions are converging toward two different laws: a Gaussian law for the signal eigenvalues and a Tracy-Widom law for the noise eigenvalues. The first technique has been designed for the white noise case, and the second technique has been designed for the colored noise case. The proposed techniques outperform current estimation techniques in terms of mean square error. Moreover, this paper reveals that, contrary to what is generally assumed in current multi-packet reception techniques, a single observation of the colliding signals is far from being sufficient to perform a reliable estimation of the collision multiplicities.

Item Type:Article
Additional Information:Thanks to IARIA Journals editor. The definitive version is available at http://www.iariajournals.org/ The original PDF of the article can be found at International Journal On Advances in Networks and Services : http://www.iariajournals.org/networks_and_services/netser_v5_n34_2012_paged.pdf
HAL Id:hal-00793345
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Paul Sabatier-Toulouse III - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université de Toulouse I-Sciences Sociales - UT1 (FRANCE)
Laboratory name:
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Deposited By: Benoit Escrig
Deposited On:22 Feb 2013 09:30

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