1. 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
http://www.jaist.ac.jp/is/labs/matsumoto-lab
Tad Matsumoto, Fellow, IEEE
Visiting Fellow, Royal Academy of Engineering in UK
Japan Advanced Institute of Science and Technology (JAIST)
matumoto@jaist.ac.jp
Paradigm Shift in Turbo Processing:
From P2P to Networks
Centre for Wireless Communications, University of Oulu
tadashi.matsumoto@ee.oulu.fi
P.O.Box 4500, University of Oulu FIN-90014, FINLAND

2. School of Information Science
Symbol Duration T
･･･
･･･
τ
1G
･･･
･･･
τ
First path
Last Path
2G
τ
･･
･･
3G
τ<<T No inter-symbol interference (ISI)
τ≒T only minor ISI τ>>T Severe ISI
Single Carrier Signaling：Time Domain Behavior
Tx Rx
Delay Spread τ
“0” “1” “1” “0”
“0” “1” “1” “0”
“0” “1” “1” “0”
“0” “1” “1” “0”
Characterized by Multipath Propagation

3. School of Information Science
Single carrier signaling is Green!:
The number of the signal points increases exponentially!
What happens if there are a lot
more multipath components?
Single Carrier Signaling：Time Domain Behavior
2 x 2 MIMO setup QPSK signal
transmitted over 20 path
propagation channel!

4. Principle of MIMO SC-MMSE Turbo
equalization
Soft symbols constructed
from decoder feedback
sˆ
[ ])(2 kbλ
[ ])(1 kbλ

5. Block-wise Time Domain MIMO
SC-MMSE Equalizer: My 2002 Equation
where
diag denotes a diagonal matrix constructed
by its argument elements
Computational complexity is dominated
by the matrix inversion Σ−1.
Tx antenna
Soft symbols constructed
from decoder feedback
Covariance of the soft cancellation output
[ ] [ ]{ }22
ˆ)ˆ)(ˆ( ssEdiagssssE H
−=−−=Λ
Complexity: O[N3(L+K)3]
Problematic!!!
Soft Cancellation Output
Frame Length
Number of Receive Antennas
Path Length

6. Finally, the equalizer output vector is given by:
Diagonal Block
By Exploiting Beneficial Properties of
Frequency Domain Processing, it Ends up with
My 2005 Equation (Green!!!)
( )[ ]FΞIΔΞΞΞFΓ f
m
fHffH
m
H
m diag
12 −
+≈ σ
(2x2 MIMO)
Now, analysis, including EXIT analysis, is EASY!

7. Number of Users = U, Each user uses 2 Tx antennas and Rx uses 4 antenns.
(Multi-user MIMO) Frame length = 512
Complexity is at a logarithm order of the
frame length K and is Independent of the
Path Number L!
2002
2005