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Theses

Fluctuations de fonctionnelles spectrales de grandes matrices aléatoires et applications aux communications numériques.

Abstract : The random matrix theory presents a powerful tool to study of the performance indices of wireless communication systems. the Objective of this thesis is to develop some theoretical results based on the random matrix theory to study fluctuations of some performance indicators of multi-antennas systems. The first contribution of this thesis consists to establish a central limit theorem type results to the study of the random quadratic forms fluctuations. Our approach consists to writting the random quadratic forms as a martingale differences and to use the CLT for martingales. In the multi-antenna systems technologies, the signal-to-noise ratio can be written as a quadratic form based on the channel matrix. Knowing the asymptotic behavior of the SNR allows us to describ the behavior of auther performance indices like the bit-error-rate and the outage probability. Secondly, we are interested by the study of the fluctuations of a given spectral function (logdet) of Gram random matrices. We prove that, when centered and properly rescaled, this statistic satisfy a CLT. The variance expression is given and can be easily implemented. In the field of wireless communications, this statistic (logdet) can model the capacity of the transmission channel.
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Submitted on : Sunday, January 30, 2011 - 8:32:35 PM
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Malika Kharouf. Fluctuations de fonctionnelles spectrales de grandes matrices aléatoires et applications aux communications numériques.. Mathématiques [math]. Ecole nationale supérieure des telecommunications - ENST, 2010. Français. ⟨tel-00560837⟩

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