文档介绍：Supelec
Random Matrix Theory
for
munications
Merouane´ Debbah
merouane.******@
February, 2008
Program
Course 1: Overview and Historical development.
Course 2: Probability and convergence measures review.
Course 3: Basic Results on Random Matrix Theory
Course 4: What about deterministic matrices?
Course 5: Stieltjes Transform Method.
Course 6: Results on Unitary Random Matrix Theory
Course 7: The role of the Cauchy-Stieltjes transform munications
Course 8: Free probability theory and random matrices
Course 9: Free deconvolution for signal processing applications
Course 10 MIMO Channel Modelling and random matrices
Course 11: Asymptotic analysis of (MC)-CDMA systems
Course 12: Asymptotic Analysis of MIMO systems
Course 13: Asymptotic design of receivers
Course 14: Decoding order in receivers
Course 15: Game theory and Random matrix theory
1
Presentation
Overview and Historical development
2
Random Matrix Theory
3
Random Matrix Theory
Cited as one of the ”modern tools” in mathematics and used in the proof of an
important result in prime number theory
4
Applications of Random Matrix Theory
• Wigner (55) , Dyson (67) : Random matrix theory and the statistical theory of energy
levels of nuclei.
• Potters (00), Bouchaud (00) : Random matrix theory and financial correlations.
• Voiculescu (91) , Biane (00), Hiai, Petz (00): Random matrix theory and Free probability
Theory.
• Silverstein (89), Pastur (72), Girko (90), Edelman (89): Random matrix theory and
Cauchy-Stieltjes transform.
• Speicher (92): Random matrix theory binatorics.
• Tanaka (01), Moustakas (03), Sengupta (03) : Random matrix Theory and statistical
mechanics approach.
5
Random Matrices: Some Dates in Wireless
Communications
• Tse & Hanly (99), Evans & Tse (00) : Asymptotic Performance of Linear Receivers for
certain CDMA systems
• Foschini & Gans (96), Telatar (99) : Shannon Capacity for MIMO systems.
• Verdu´ & Shamai (99, 00), Tu