文档介绍：Supelec
Random Matrix Theory
for
munications
Merouane´ Debbah
merouane.******@
February, 2008
Presentation
Power allocation and Decoding order in receivers
1
Multiuser System Random Matrix Model
Multiuser system: K users, N dimensions
Received signal
1
y = HP2 s + n
1
p2 0 . . . 0
h11 h12 . . . h1K 1
1
h21 h22 . . . h2K 1 0 p2 . . . 0
H = . . . , P2 = 2
. . . . . . . . . .
. . . 0
1
hN1 . . . . . . hNK 2
0 0 · · · pK
k 2
hik are independent zero mean Gaussian variables with variance | g (i) | . In particular:
H = G ¯ W
where W is an N × K zero mean Gaussian matrix.
2
The G-model
The pattern mask G is a neat way of modelling all the systems (especially for
cross-system resource allocation problems) in order to have a unified framework based on
random matrices.
• OFDM systems: gk(i) = 0 if k =6 i.
• SIMO systems: g1(i) = g2(i) = ...gK(i) where gl(i) represents the lth eigenvalue of
the correlation matrix R (H = RW).
• MIMO with Kronecker model: gl(i) = λT (l).λR(i).
• CDMA systems in frequency selective channels: gl(i) represents the frequency
response of user l on carrier i
√√√
y = H1w1 P 1s1 + H2w2 P 2s2 + ... + HKwK P ksK + n
Toeplitz structure
H
Hi ∼ F DiF
√√√
y˜= D1w˜ 1 P 1s1 + D2w˜ 2 P 2s2 + ... + D˜ Kw˜ K P ksK + n˜
³ ´ 1
= G ¯ W˜ P2 s + n˜
• Ad-works....
3
Multiuser ressource allocation: problem statement
• Based on a given set of target rates, what should be the adequate power allocations?
• Can the required rates be always satisfied?
• What is the minimum required knowledge such as each user determines solely the
power to satisfy his rate (centralized versus non centralized system)?
• For the MMSE-SIC, what is the decoding order for a given set of rates?
4
Multiuser receiver: MMSE and MMSE-SIC
• MMSE (Mininum Mean-Square Error receiver)
H −1 H 2
Output: ˆs = H (A) y with A = HH + σ IN
Maximizes SINR ov