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Channel Analysis and Estimation for OFDM Systems with Doppler Effect
Advisor : Yung-An Kao
Student : Chien-Hsin Hsu
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Outline
Introduction Channel Analysis and Simulation Channel Estimation and Simulation Conclusion
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Introduction (1/2)
I propose the time-variant channel analysis which focuses on the same subcarrier in the different OFDM symbols.
Time-variant channel analysis. a pilot-based estimation scheme (2-D linear interpolation).
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Introduction (2/2)
Mathematics model of Jakes’ Fading Channel and Line-of-Sight (LOS) component of the received signal.
7-path channel model, which includes the LOS.
Specification of the 7-path channel model according to COST 207.
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Channel Analysis (1/2)
Fig. 1. The block diagram of an OFDM system.
Do not consider “CFO”, “SFO” and “noise”.
k : k-th subcarrierl : l-th OFDM symbol
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Channel Analysis (2/2)
HFk(ejω) is obtained by an ensemble average of 100 ind
ependent simulation runs. HF6(ejω).
[ ] [ ] [ ]mm
y n x m h n
( )jkHF e [ ]kH l 2
DFTl : time index
1
0
[ ] [ ] [ ]N
l lm
y n x m h n m
,, , , ,
,
k lk l k l k l k l
k l
YY X H H
X
(N : N points FFT)
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Simulation Environment
For DVB-T : Transmission mode : 2K Mode V=120km/hr. Modulation level chooses QPSK. fc=862MHz. Number of input OFDM symbol is 2 frame and there
are 68 OFDM symbols in one frame. Ts=7/64μs and 7/48μs are selected. GI=1/32 and 1/4.
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Simulation Results
Fig. 2. HF6(ejω) versus normalized frequency
for DVB-T (GI=1/32, Ts=7/64μs).Fig. 3. HF6(e
jω) versus normalized frequency for DVB-T (GI=1/4, Ts=7/48μs).
HF6(ejω) HF6(e
jω)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5000
10000
15000
Normalized frequency
V=120 km/hr
1/17
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Normalized frequency
V = 120 km/hr
3/34
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Channel Estimation (1/4)
Channel estimation can be achieved by inserting pilots.
1-D linear interpolation is widely used in the industry (Channel frequency response and pilot). 2-D linear interpolation is proposed to solve the problem.
Down-sampling and aliasing. Fig. 4.
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Channel Estimation (2/4)
Fig. 4. The pilot arrangement for DVB-T.
symbol 66
symbol 1symbol 2
symbol 0
symbol 3
symbol 67
k = 0
k = 1704 if 2K Modek = 6816 if 8K Mode
pilotdata
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Channel Estimation (3/4)
1,2 1,1 1,5
1,3 1,1 1,5
1,4 1,1 1,5
3 1
4 41
( )2
1 3
4 4
H H H
H H H
H H H
Fig. 5. The diagram of 2-D linear interpolation.
H1,4
symbol 1
symbol 2
symbol 3
symbol 4
symbol 5
symbol 6
symbol 7
k = 1k = 2
k = 3k = 4
H1,1
H1,5
H4,6
H4,2
H4,4
H2,4
2,4 1,4 4,4
3,4 1,4 4,4
2 1
3 31 2
3 3
H H H
H H H
Step 1. The interpolation at the same subcarrier in the different OFDM symbols.
Step 2. The interpolation at the different subcarriers in the same OFDM symbol.
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Channel Estimation (4/4)
The error (interpolated channel and Hk[l]) is considered as noise. noise average power, or say, mean square error (MSE).
Noise average power is obtained by an ensemble average of 100 independent simulation runs. “total” noise average power.
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Simulation Environment
For DVB-T : Transmission mode : 2K Mode V=20km/hr, 40km/hr, 60km/hr~120km/hr Modulation level chooses QPSK. fc=862MHz. Number of input OFDM symbol is 2 frame and there
are 68 OFDM symbols in one frame. Ts=7/64μs, 8/64μs and 7/48μs. GI=1/32 and 1/4.
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Simulation Results
Fig. 6. Total noise average power versus V for DVB-T (GI=1/4, Ts=7/64μs, 8/64μs, 7/48μs).
Fig. 7. Total noise average power versus V for DVB-T (GI=1/32, Ts=7/64μs, 8/64μs, 7/48μs).
20 30 40 50 60 70 80 90 100 110 1200
0.002
0.004
0.006
0.008
0.01
0.012
0.014
V (km/hr)
Tota
l noi
se a
vera
ge p
ower
Ts=7/64 us
Ts=8/64 usTs=7/48 us
20 30 40 50 60 70 80 90 100 110 1200
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
V (km/hr)
Tota
l noi
se a
vera
ge p
ower
Ts=7/64 us
Ts=8/64 usTs=7/48 us
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Conclusion
It is clear the bandwidth of HFk(ejω) increase with incr
easing the velocity.
The performance of 2-D linear interpolation can be evaluated from the bandwidth of HFk(e
jω).
We can decide the largest interval of pilot at the same subcarrier in the different OFDM symbols from the bandwidth of HFk(e
jω).
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References
[1] Chengshan Xiao, Yahong R. Zheng, and Norman C. Beaulieu, Fellow, IEEE “Second-order Statistical Properties of WSS Jakes’ Fading Channel Simulator,” IEEE Transactions on Communications, vol. 50, No. 6, June 2002.
[2] Matthias Patzold, Mobile Fading Channels, John Wiley & Sons Ltd, 2002.
[6] ETSI, “Digital video broad-casting (DVB); Framing structure, channel- coding and modulation for digital terrestrial television,” EN 300 744, v1.4.1,Jan. 2001.
[3] Alan V. Oppenheim, Ronald W. Schafer with John R. Buck, Discrete-Time Signal Processing, Prentice Hall International, Inc., 2nded, 1999.
[4] Alan V. Oppenheim, Alan S. Willsky, with S. Hamid Nawab, Signals & Systems, Prentice Hall, 2nded, 1996.
[5] Theodore S, Rappaport, Wireless Communications-Principles and Practice, Prentice Hall PTR, 2nded, 1996.
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~~~~ thanks for your attention ~~~~