文档介绍：Supelec
Random Matrix Theory
for
munications
Merouane´ Debbah
merouane.******@
February, 2008
Presentation
MIMO Channel Modelling and random matrices
1
Where do we stand on Channel Modelling
Google search: ”MIMO Wireless Channel Modelling”
• Over 15 000 publications on channel modelling
• At a rate of 10 papers per day, 1 500 days (nearly 4 years)!
• The models are different and many validated by measurements!
Three conflicting schools
• Geometry based channel models.
• Stochastic channel models based on channel statistics
• Do not model, use test measurements
Not even within each school, all experts agree on fundamental issues.
2
MIMO System Model
Rx Tx
The channel is linear, noise is additive
r Z
ρ
y(t) = Hnr×nt(τ)x(t −τ)dτ+ n(t)
ntr
ρ
Y(f, t) = Hnr×nt(f, t)X(f) + N(f)
nt
3
Why do we need a channel model?
Our Vision
Step 1: Collection of information
The user (or base station) download information on his environment (dense, number of
buildings,...) through a localization service process
Step 2: Model generation
A statistical channel model is automatically created (at the base station or the mobile unit)
integrating only that information and not more!
Step 3: High speed connection
The coding scheme is adapted to the (statistical not realization) model
Example
• Additive Gaussian: Euclidean distance coding
• Rayleigh : rank and determinant criteria
This scenario could be called ”User customized channel model coding service” and is a
viable scenario from a Soft Defined Radio perspective.
4
Why do we need a statistical channel model?
Ergodic Channel Capacity: (The receiver knows the channel and the transmitter knows
the statistics) ³ ´
ρ H
C = maxQE(C(Q)) with C(Q) = log det In + H QH
2 t nt
Q = E(XXH) = I only with zero mean Gaussian MIMO model!
The need to model: Statistical channel models stimulate creativity (patents!):
• to optimize the codes
• to estimate the chan