Skip to Main content Skip to Navigation
Theses

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

Abstract : Large random matrix theory is a powerful mathematical tool used to study the performance of multi-user and multi-access communication systems. The objective of this thesis is to develop mathematical tools based on the theory of random matrices to apply them to the study of some performance indicators of multi-antenna systems. The first part of this thesis concerns the study of the fluctuations of the signal to interference plus noise ratio (SINR) at the output of the LMMSE estimator for multidimensional signals. As the SINR can be modeled as random quadratic forms, its fluctuations can be studied with the help of the random matrix theory. We show here that the distribution of these fluctuations is asymptotically Gaussian. The study of the SINR allows the comprehension of other performance indicators like the Bit Error Rate and the utage probability. The study of statistical properties of these two parameters is the aim of the second part of this thesis. The last part concerns the study of the so-called Shannon's Mutual Information. This statistique can be written as a spectral linear statistique of the eigenvalues of the Gram matrix based on the channel matrix which assumed to be random. We prove the asymptotic Gaussian behavior of the distribution of the fluctuations of this random variable and we give a closed-form expression for the variance. All our theoretical results are confirmed numerically.
Document type :
Theses
Complete list of metadatas

Cited literature [85 references]  Display  Hide  Download

https://pastel.archives-ouvertes.fr/pastel-00006336
Contributor : Ecole Télécom Paristech <>
Submitted on : Wednesday, October 20, 2010 - 8:00:00 AM
Last modification on : Friday, July 31, 2020 - 10:44:07 AM
Long-term archiving on: : Thursday, March 30, 2017 - 6:02:03 AM

Identifiers

  • HAL Id : pastel-00006336, version 1

Citation

Malika Kharouf. Fluctuations de fonctionnelles spectrales de grandes matrices aléatoires et applications aux communications numériques. Mathématiques [math]. Télécom ParisTech, 2010. Français. ⟨pastel-00006336⟩

Share

Metrics

Record views

392

Files downloads

221