1. Optimal CSD and Truncated SVD for Channel Estimation
Month Year
doc.: IEEE yy/xxxxr0
September 2008
Optimal CSD and Truncated SVD for Channel Estimation
Date:
Authors:
Wahyul Syafei, KIT JAPAN
John Doe, Some Company

2. Month Year
doc.: IEEE yy/xxxxr0
September 2008
Abstract
Adjusting the cyclic shift of long training field will minimize the condition number. Truncating the singular value decomposition of the estimated channel will minimize the noise effect. Combination of both technique will enhance the channel estimation quality
Wahyul Syafei, KIT JAPAN
John Doe, Some Company

3. Optimal CSD and Truncated SVD for Channel Estimation
September 2008
Optimal CSD and Truncated SVD for Channel Estimation
Singular-Value truncation: minimizing noise effect on estimated CIR.
Cyclic shift adjustment of Long preamble on the successive antenna: minimizing Condition-number between singular values of the estimated CIR.
Wahyul Syafei, KIT JAPAN

4. … … MIMO-OFDM Tx system September 2008 Channel Coding Mux CP
Time domain
Cyclic shift
Channel Coding
Mux CP
Long Preamble 1 d1
Mapper
IFFT
Mux CP
Long Preamble 2 d2
Mapper
IFFT … …
Mux CP
Long Preamble N dN
Mapper
IFFT
Wahyul Syafei, KIT JAPAN

5. Maximum Likelihood Decoder
September 2008
MIMO-OFDM Rx system
Error detection
Maximum Likelihood Decoder de
Mux CP
Channel estimation 1 d1
FFT de
Mux CP
Channel estimation 2 d2
FFT … … de
Mux CP
Channel estimation N dN
FFT
Wahyul Syafei, KIT JAPAN

6. Cyclic Shifting on LTF September 2008 Tx Antenna # LTF 1 STF C0 C1 C2
SIG
DATA 2
STF cs C0 C1 C2
SIG
DATA N
STF C2 cs C0 C1
SIG
DATA
Wahyul Syafei, KIT JAPAN

7. MISO case September 2008 L1 h1 Long preamble 1 rlp Channel estimator
Error of ML estimation
will be minimized if: or
with
L are the long preamble symbols and
already known by the receiver.
Wahyul Syafei, KIT JAPAN

8. September 2008
MISO case 32 32
145
Wahyul Syafei, KIT JAPAN

9. SV-Truncation September 2008
To minimize the noise effect, SV-truncation ( ) is proposed.
From the known LTF: 
The new term of known LTF becomes:
Estimated CIR is:
Exp.
the truncated SVD
for q =2, 32 32
145
Wahyul Syafei, KIT JAPAN

10. SV-Truncation V X+ L U rlp,j September 2008 (32 X 32) Proposed
Add zeros
FFT
S/P S D
(32 X 145)
(145 X 1)
(32 X 1)
(16 X 1) 64
(64 X 1)
Inner
product
(32 X 145)
(32 X 145)
(145 X 145)
Wahyul Syafei, KIT JAPAN

11. Condition Number September 2008
The ratio between the biggest singular value to the smallest one, written as:
If the CN =1, then is the constant X identity matrix and zeros matrix,
which is easier to be handled.
Regarding the SVD truncation, there is a Partial Condition Number:
Find the smallest value (PCN  1), by adjusting the cyclic shift,
as shown in Simulation 1.
Wahyul Syafei, KIT JAPAN

12. Simulation 1, find the optimal CS
September 2008
Simulation 1, find the optimal CS
CS=80
CS=18
CS=64
No truncation
Wahyul Syafei, KIT JAPAN

13. Find the optimal q September 2008  1. Consider the noise part.
2. Consider the channel error.
where
and…
Wahyul Syafei, KIT JAPAN

14. Find the optimal q September 2008 where Example for q = 0, 32 32
Considering the channel error and noise part, we have.
 min
as shown in Simulation 2.
Wahyul Syafei, KIT JAPAN

15. Simulation 2, find the optimal q
September 2008
Simulation 2, find the optimal q
CS=18 samples;
min J is found at q=4
CS=80 samples;
min J is found at q=5
CS=64 samples;
min J is found at q=5
Wahyul Syafei, KIT JAPAN

16. Simulation 3, Performance
September 2008
Simulation 3, Performance
LTF type
IEEE802.11a
FEC
Viterbi R=1/2, K=7
Configuration
2X2 MIMO OFDM
Channel
,Exponential attenuation
Antenna diversities
STBC and Rx diversity
Fading
Independent, slow fading
Modulation
BPSK
CS;q
18;4 , 64;5 , 80;5
Wahyul Syafei, KIT JAPAN

17. September 2008
Conclusion
The truncation of SVD of the estimated channel will minimize the noise effect.
The cyclic shift adjustment will minimize the partial condition number of SVD of the estimated channel.
The combination of both will increase the quality of channel estimation.
Wahyul Syafei, KIT JAPAN

18. References IEE802.11a IEE802.11n draft September 2008
Wahyul Syafei, KIT JAPAN