Random Matrix Theory for Wireless Communications

15 hours Course by Dr. Merouane Debbah

April 13-15, Limassol, Cyprus



Presentation of the Course

The asymptotic behaviour of the eigenvalues of large random matrices has been extensively studied since the fifties. One of the first related result was the work of Eugène Wigner in 1955 who remarked that the eigenvalue distribution of a standard Gaussian hermitian matrix converges to a deterministic probability distribution called the semi-circular law when the dimensions of the matrix converge to infinity. Since that time, the study of the eigenvalue distribution of random matrices has triggered numerous works, in the theoretical physics as well as probability theory communities. However, as far as communications systems are concerned, until the mid 90's, intensive simulations were thought to be the only technique to get some insight on how communications behave with many parameters. All this changed in 1997 when large system analysis based on random matrix theory was discovered as an appropriate tool to gain intuitive insight into communication systems. In particular, the self-averaging effect of random matrice was shown to be able to capture the parameters of interest of communication schemes. The results led to very active research in many fields such as, just to name a few:

(MC)-CDMA systems with large spreading factors and large number of users

MIMO systems with large number of transmit and received antennas

Design of multi-stage detectors

Modelling of communication cystems

Ad-hoc networks with a great number of nodes


The course is held in conjunction with WiOpt 2007, the 5th Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks April 16-20, Limassol, Cyprus

Objective

The course is intended to give a comprehensive overview of random matrices and their application to the analysis and design of communication systems. As communication systems become more and more complex, the course should provide the students/researchers with appropriate mathematical tools to cope with the analysis and design of suited schemes.

Program


Overview and Historical development
Probability and convergence measures review
Some Results on deterministic matrices
Stieltjes Transform Method
Results on Unitary Random Matrix Theory
The role of the Cauchy-Stieltjes transform in communications
Asymptotic analysis of (MC)-CDMA systems
Asymptotic Analysis of MIMO systems
Asymptotic design of receivers
Random matrices and open topics

The course will be based on the following books and monographs:
"The semi-circle Law, Free Random Variables and Entropy", F. Hiai and D. Petz, American Mathematical Society, 2000.
"Random Matrices and Wireless Communications", A. Tulino and S. Verdu, Foundations and Trends in Communications and Information Theory, NOW, The Essence of Knowledge, 2004.

General Information


Number of hours: 15 hours
Location: Mediterranean Beach Hotel, a four star hotel situated in the heart of Limmassol, Cyprus.
Time: Friday 13/04/07 (9h-12h and 14h-17h), Saturday 14/04/07 (9h-12h and 14h-17h) and Sunday 15/04/07 (9h-12h)
Language: English
Responsible teacher: Prof. Merouane Debbah (Institut Eurecom 2229 Route des Cretes B.P. 193 06904 Sophia Antipolis Cedex, France, email: debbah@eurecom.fr).
Hotels: a limited number of places have been reserved at the Mediterranean Beach Hotel, a four star hotel situated in the heart of Limmassol, Cyprus. Rooms can be shared to split costs. Contact Ephie Deriche (INRIA) for information on prices, email: Ephie.Deriche@sophia.inria.fr.


Registration

The course will be limitted to 50 persons. Priority in registration will be given to members of IFANY. Thanks to the sponsorship of IFANY and INRIA, there will be no registration fees.

Those interested should send their intention to participiate to Ephie Deriche till January 31, 2007, with their name, address, phone and fax number.

Contact person for registration: Ephie Deriche (INRIA), email: Ephie.Deriche@sophia.inria.fr.

Sponsorship and organization

The course is organized and sponsored by IFANY (InFormAtioN theorY: New challenges and new interdisciplinary tools), which is a collaborative project financed by INRIA.