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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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