BackgroundThe 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 Eugene Wigner in 1955 who remarked that the eigenvalue distribution of a standard Gaussian hermitian matrix converges to a deterministic robability 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 matrices 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:
- MIMO Broadcast systems with a large large number of users
- MIMO (and Network MIMO) systems with a large number of users
- Design of multi-stage detectors
- Channel modelling of communication systems
- Flexible networks
Objective of the Lecture Series
The lecture series is intended to give a comprehensive overview of random matrices and their application to the analysis and design of communication systems (LTE, Cognitive networks). As communication systems become more and more complex, the lecture series should provide the students/researchers with appropriate mathematical tools to cope with the analysis and design of suited schemes.
General Information on the instructor
Prof. Mérouane Debbah
Mérouane Debbah was born in Madrid, Spain. He entered the Ecole Normale Suprieure de Cachan (France) in 1996 where he received his M.Sc and Ph.D. degrees respectively in 1999 and 2002. From 1999 to 2002, he worked for Motorola Labs on Wireless Local Area Networks and prospective fourth generation systems. From 2002 until 2003, he was appointed Senior Researcher at the Vienna Research Center for Telecommunications (FTW) (Vienna, Austria) working on MIMO wireless channel modeling issues. From 2003 until 2007, he joined the Mobile Communications de-partment of the Institut Eurecom (Sophia Antipolis, France) as an Assistant Professor. He is presently a Professor at Supelec (Gif-sur-Yvette, France), holder of the Alcatel-Lucent Chair on Flexible Radio. His research interests are in information theory, signal process-ing and wireless communications. Mérouane Debbah is the recipient of the "Mario Boella" prize award in 2005, the 2007 General Symposium IEEE GLOBECOM best paper award, the Wi-Opt 2009 best paper award, the Newcom++ best paper award as well as the Valuetools 2007,Valuetools 2008 and CrownCom2009 best student paper awards. He is a WWRF fellow.