Large random matrices and performance evaluation of large digital communication systems

Organizers: Merouane Debbah (Institut Eurecom) and Philippe Loubaton (University of Marne La Vallee)

Until the late nineties, exhaustive simulations were thought to be the only way to get some hints on how communications systems with many users/antennas behave even for basic performance measures such as bit error probability or channel capacity. 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: for systems depending on many parameters, the random matrix theory approach was shown to be able to capture the key meaningful parameters of interest and as a consequence simplify the framework optimization problem.

The results led to very active research in many fields such as (MC)-CDMA systems (with large spreading factors and large number of users) or MIMO systems (with large number of transmit and received antennas) just to name a few. The tools rely on the asymptotic behaviour of the eigenvalues of large random matrices. The first related result in this field 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, the tools, although undoubtly important, are still not currently very popular in the signal processing community. The purpose of this special session is to contribute to the diffusion of these tools in the community in order to make large system analysis a standard tool in the Signal Processing for Communication community. The first paper is an overview of existing related works, and other papers present recent new results concerning the performance of multi-user and MIMO systems.

Regular lectures:

• Title: An Overview of Large System Analysis for Multi-Input Multi-Output Channels
  Authors: Michael Honig (Northwestern University), Matthew Peacock (The University of Sydney), Iain Collings (The University of Sydney)
• Title: Asymptotic Outage Capacity of Multi-Antenna Channels
  Authors: Antonia Tulino (Universita' degli Studi di Napoli), Sergio Verdu (Princeton University)
• Title: Linear receivers for multiuser MIMO channels
  Authors: Giorgio Taricco (Politecnico di Torino), Ezio Biglieri (Politecnico di Torino), Alessandro Nordio (Politecnico di Torino)
• Title: On the Asymptotic Performance of MIMO Correlated Ricean Channels
  Authors: Julien Dumont (University of Marne La Vallee), Philippe Loubaton (University of Marne La Vallee), Samson Lasaulce (CNRS-LSS), Merouane Debbah (Institut Eurecom)
• Title: Asymptotic Performance of Code-reference Spatial Filters for Multicode DS/CDMA
  Authors: Francisco Rubio (CTTC) Xavier Mestre (CTTC)
• Title: Spectral efficiency of CDMA Uplink Cellular Networks
  Authors: Nicolas Bonneau (INRIA), Merouane Debbah (Eurecom), Eitan Altman (INRIA), Giuseppe Caire (Eurecom)