Tutorial SympoTIC’04
An Information Theoretic Point of View to MIMO Channel
Modelling
Merouane Debbah
Institut Eurecom, Mobile Communications Group
2229 Route des Cretes, B.P. 193, 06904 SOPHIA ANTIPOLIS CEDEX
France http://www.eurecom.fr/~debbah
The tutorial presents an in-depth introduction to recent results on MIMO channel modelling. A
unifying approach, based on the principle of Maximum Entropy, is provided to construct consistent
models: the consistency argument is at the heart of scientific inference and gives an explicit answer
to the problem posed by the striking number of papers dedicated to MIMO channel models1. Indeed,
nearly all the models proposed are different and moreover validated by measurement campaigns! Who
should we trust?
This tutorial aims at providing some partial answers to this question by combining the influence
of two fields namely Communication theory and Bayesian probability theory. Moreover, for each
channel model, an asymptotic analysis (in the number of antennas) of the achievable transmission
rate is conducted using tools of random matrix theory and central limit theorems are provided on the
asymptotic behavior of the mutual information. The results give means to design services based on
criteria such as quality of service or to derive useful metrics for channel measurements. At the final
stage of the tutorial, discussions on measurements performed in Oslo at 2.1 GHz and 5.2 GHz and
their interactions with the models proposed are given.
1A web search on ”Wireless channel Modelling” dated in November 2002 showed more than 5000 publications on
channel modelling. At a reading rate of 10 papers per day, it would take 500 days to have a small overview of the field!
Note that for the non-British community, the number of publications is even higher, as modelling takes only one l.