Moments method for random matrices with applications to wireless communication.
type: Dataset
description: In this thesis, we focus on the analysis of the moments method, showing its importance in the application of random matrices to wireless communication. This study is conducted in the free probability framework. The concept of free convolution/deconvolution can be used to predict the spectrum of sums or products of random matrices which are asymptotically free. In this framework, we show that the moments method is very appealing and powerful in order to derive the moments/asymptotic moments for cases when the property of asymptotic freeness does not hold. In particular, we focus on Gaussian random matrices with finite dimensions and structured matrices as Vandermonde matrices. We derive the explicit series expansion of the eigenvalue distribution of various models, as noncentral Wishart distributions, as well as correlated zero mean Wishart distributions. We describe an inference framework so flexible that it is possible to apply it for repeated combinations of random ma- trices. The results that we present are implemented generating subsets, permutations, and equivalence relations. We developped a Matlab routine code in order to perform convolution or deconvolution numerically in terms of a set of input moments. We apply this inference framework to the study of cognitive networks, as well as to the study of wireless networks with high mobility. We analyze the asymptotic moments of random Vandermonde matrices with entries on the unit circle. We use them and polynomial expansion detectors in order to design a low complexity linear MMSE decoder to recover the signal transmitted by mobile users to a base station or two base stations, represented by uniform linear arrays.
identifier: NNT: 2011SUPL0011
issued: 2026-05-12T00:14:41.124050
language: en
modified: 2026-05-12T00:14:41.124055
contact point: Organization
  fn: CCSD
keyword: cognitive-networks
keyword: convolutiondeconvolution
keyword: detecteur-a-expansion-polynomial
keyword: free-probability
keyword: infoeu-reposemanticsdoctoralthesis
keyword: matrices-aleatoires
keyword: methode-des-moments
keyword: mimo-systems
keyword: moments-method
keyword: polynomial-expansion-detector
keyword: probabilites-libres
keyword: random-matrices
keyword: reseaux-cognitifs
keyword: reseaux-lineaires-uniformes
keyword: spiotherengineering-sciences-physicsother
keyword: systemes-mimo
keyword: theses
keyword: uniform-linear-arrays
landing page: https://theses.hal.science/tel-00805578

Moments method for random matrices with applications to wireless communication.
type: Distribution
format: HTML
issued: 2026-05-12T00:14:41.141684
modified: 2026-05-12T00:14:41.068718
access URL: https://theses.hal.science/tel-00805578

test_moissonnage_selune
type: Agent