1. 應用於OFDM 系統之強健化 內部接收機架構設計
指導老師:高永安
學 生:蘇家弘
A Robust Inner Receiver Structure Design
for OFDM Systems

2. Outline OFDM system block diagram OFDM baseband signal model
Inner receiver structure
Channel estimation
LMS algorithm
Selection of 
Pilot-based phase estimator
Dynamic simulation by Simulink 5.0
Conclusion and future work

3. OFDM system block diagram
Up convert
CFO
SFO
強調兩顆震盪器 Eq .
n: n-th sample point
k: k-th subcarrier
l: l-th subcarrier
Down convert

4. Carrier Frequency Offsets
CFO simulation
CFO is due to the oscillator mismatch from up convert and down convert f

5. CFO calculation for IEEE 802.11a
Maximum quantity of CFO = 20ppm for 5GHz
k: k-th subcarrier, l: l-th OFDM symbol , N=64, n=80

6. Sampling Frequency Offsets
SFO is caused by the oscillator mismatch between A/D & D/A converter
SFO simulation
TTX
TRX
When TRX > TTX

7. SFO calculation for IEEE 802.11a
TTX=1/(20MHz 400Hz),
TRX=1/(20MHz 400Hz)
k: k-th subcarrier, l: l-th OFDM symbol , N=64, n=80

8. OFDM baseband signal model
OFDM baseband signal after IFFT at the transmitter side
The received OFDM baseband signal before FFT
(2)
(1)
要述說The CFO has been compensated in time domain, 所以after FFT 之後只有residual CFO
n: n-th sample point
k: k-th subcarrier
l: l-th subcarrier

9. OFDM baseband signal model
The received OFDM signal is influenced by channel effect, residual CFO, SFO, initial symbol timing offset and before FFT we can describe (2) as follows:
(3)
Td : initial symbol timing offset
Hk : frequency response of channel
: residual CFO
: initial phase offset
Ts : sampling clock period at the transmitter
Ts’: sampling clock period at the receiver
CFO
SFO
要述說The CFO has been compensated in time domain, 所以after FFT 之後只有residual CFO

10. OFDM baseband signal model
The ICI produced by residual CFO is much smaller compared to Gaussian noise.
N’k,l combine Ik,l and Nk,l
and (3) can be modified as:
(4)
與AWGN相比,由殘餘CFO所造成的ICI非常小,所以…

11. OFDM baseband signal model
The effect of CFO and SFO can be represented as :
(5)
and

12. The difference between inner and outer receiver
M. Speth, S. A. Fechtel, G. Fock and H. Meyr, “Optimum Receiver Design for Wireless Broad-band Systems Using OFDM-Part II,” IEEE Trans. Commun., vol. 49, pp , Apr
Decoding &
demodulation

13. Inner receiver structure
Input
signal
Frame detection:利用training sequence來作,找出frame
Symbol timing:利用training sequence找出OFDM symbol的起始位置
Buffer:收到的訊號在此補償由訊框同步粗調和符元同步細調估計出的偏差量
FFT

14. Inner receiver structure
Training sequence
Initial coefficient
FFT D a t
Update coefficient
of equalizer
Phase
compensation
Frequency
Domain
Equalizer
Pilot
1.訊號通過FFT之後,先將training sequence利用LSE(Least Square Error)的方法求出等化器初始值
2.然後將等化器初始值與接在training sequence後面的data部分相乘,補償通道效應和相角旋轉
3.雖然CFO已經在time domain預先補償過,但是仍舊會有殘餘的相角偏差,所以在此是以每個OFDM symbol中的pilot來估測
4.而經過等化過後的訊號, 補償由pilot估測出來的殘餘相角偏差
5.最後在送至outer receiver作解碼解調變的工作
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1.在這個架構中,等化器的部分是採用LMS演算法,其初始值是由training sequence利用LSE所求得
2.等化過後且補償過殘餘相角的訊號作為LMS的output signal,也就是Yk,l,其中k代表子載波,l代表OFDM symbol
3.Yk,l經過hard decision之後作為LMS等化器的desired signal, dk,l
4.因為每個子載波上的LMS等化器,可能會因為殘餘相角偏移量隨著OFDM symbol累積過大而追不上相角變化,所以input signal必須預先補償由前一個OFDM symbol估測出來的殘餘相角偏差,這也市此內部街收機架構的一大重點,使用pilot-based phase estimator來輔助LMS等化器追蹤相角
Pilot-based
phase estimator
Phase
compensation
Hard decision
Outer receiver

15. Channel estimation by least square error
Lk,l : transmitted training sequence
Rk,l : received training sequence
: equalized training sequence
Hk : channel
Nk,l : noise
: equalizer initial coefficient
Equalized training sequence 
l : 2 long training symbol
k : 52 subcarrier
In a

16. Channel estimation by least square error
Error between transmitted signal and equalized signal
Find optimal Heq,k for minimum value of ek
 Setting the partial derivative of ek

17. k is the step size that modified by channel condition
LMS algorithm
Filtering output: Yk=wkHXk
Error estimation: ek=dk-Yk
Tap-weight vector adaptation *
After hard decision
k is the step size that modified by channel condition

18. selection of  Normalized-LMS & time average Training sequence
0 <  < 1

19. Pilot-based phase estimator
Received pilots
After giving the
appropriate weight
Maximum ratio combination (MRC) pilot C’ Im Im A’ C A B B’ ∠2 ∠1 O Re O Re

20. Simulation by Simulink 5.0
從MathWork網站上download下來

21. 1.沒有包括MAC/PHY介面和PLCP 標頭，傳送封包未含短訓練符元，每個OFDM symbol之間沒有時間加窗法
2.接收端的部分，不考慮訊框偵測、CFO估測和符元同步細調

22. Unequalized signal spacing plot
Channel A (Ts=50ns, TRMS=50ns )
SNR=10dB
Residual CFO =0.01
SFO=800Hz
(Ts=1/(20MHz-400), =1/(20MHz+400 )
Code rate=1/2, QPSK
44 OFDM symbol per packet
1000 packet

23. Applied the proposed inner receiver structure
After channel equalization 紅點

24. IEEE 802.11a PER v.s. SNR =0.15 =0.3 Channel A (Ts=50ns, TRMS=50ns )
Residual CFO =0.01
SFO=800Hz
(Ts=1/(20MHz-400), =1/(20MHz+400 )
PSDU=256 bytes
1000 packet
每次傳256bytes,而不同調變會有不同的OFDM symbol數目產生,但是在這download下來的Simulink 5.0只適用在偶數個OFDM symbol的情況,所以某些調變為了配合會多或少一個OFDM symbol,經過測試之後結果並不會因為多或少一個OFDM symbol而有很大差異
曲線顯示的效能不理想 只以AWGN通道作測試時就是這樣,所以並非程式有誤

25. IEEE 802.11a PER v.s. SNR Channel B (Ts=50ns, TRMS=100ns )
Channel C (Ts=50ns, TRMS=150ns )

26. IEEE 802.11a PER v.s. SNR Channel D (Ts=50ns, TRMS=200ns )
Channel E (Ts=50ns, TRMS=250ns )

27. PER v.s. SNR with different 
=0.3
Channel A (Ts=50ns, TRMS=50ns )
Residual CFO =0.01
SFO=800Hz
(Ts=1/(20MHz-400), =1/(20MHz+400 )
44 OFDM symbol per packet
1000 packet

28. PER v.s. SNR with different 
Channel C (Ts=50ns, TRMS=150ns )
Channel E (Ts=50ns, TRMS=250ns )

29. PER v.s. SNR with different 
=0.3
Channel A (Ts=50ns, TRMS=50ns )
Residual CFO =0.01
SFO=800Hz
(Ts=1/(20MHz-400), =1/(20MHz+400 )
200 OFDM symbol per packet
1000 packet

30. PER v.s. SNR with different 
Channel C (Ts=50ns, TRMS=150ns )
Channel E (Ts=50ns, TRMS=250ns )

31. PER v.s.  with different channel
=0.3
Channel A (Ts=50ns, TRMS=50ns )
Channel C (Ts=50ns, TRMS=150ns )
Channel E (Ts=50ns, TRMS=250ns )
SNR=10dB
Residual CFO =0.01
SFO=800Hz
(Ts=1/(20MHz-400), =1/(20MHz+400 )
44 OFDM symbol per packet
1000 packet

32. PER v.s.  with different channel
=0.3
Channel A (Ts=50ns, TRMS=50ns )
Channel C (Ts=50ns, TRMS=150ns )
Channel E (Ts=50ns, TRMS=250ns )
SNR=10dB
Residual CFO =0.01
SFO=800Hz
(Ts=1/(20MHz-400), =1/(20MHz+400 )
200 OFDM symbol per packet
1000 packet

33. Conclusion A Robust Inner Receiver Structure
Simulink 5.0
 pilot-based phase estimator
1. Compensate the residual CFO
2. Assist the LMS equalizer in phase tracking
 Dynamic simulation

34. Future work At present The future work
Frequency selective fading channel
LMS algorithm
The future work
Slow fading channel
Other adaptive algorithms
Decoding block of Simulink 5.0

35. Reference
IEEE Std a-1999, Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: High Speed Physical Layer in the 5GHz Band.
Yung-An Kao; Chia-Hung Su; Shih-Kai Lee; Chung-Lung Hsiao; Po-Lin Chio, “A robust design of inner receiver structure for OFDM systems,” IEEE Conference. on Consumer Electronics, pp , Jan
S. Haykin, Adaptive Filter Theory, Englewood Cliffs, NJ: Prentice-Hall, 2002, 4th Ed.
M. Speth, S. A. Fechtel, G. Fock and H. Meyr, “Optimum Receiver Design for Wireless Broad-band Systems Using OFDM-Part I,” IEEE Trans. Commun., vol. 47, pp , Nov
M. Speth, S. A. Fechtel, G. Fock and H. Meyr, “Optimum Receiver Design for Wireless Broad-band Systems Using OFDM-Part II,” IEEE Trans. Commun., vol. 49, pp , Apr
Doufexi, A.; Armour, S.; Butler, M.; Nix, A.; Bull, D.; McGeehan, J.; Karlsson, P., “A comparison of the HIPERLAN/2 and IEEE a wireless LAN standards,” IEEE Magazine on Comm. Vol. 40, pp , May 2002.
黃凡維, 2004, “一揭最小均方差頻域等化器應用於正交分頻多工系統之特性分析,” 長庚大學電機工程研究所碩士論文

36. Any Questions?

37. Channel estimation by LSE

38. Channel estimation by LSE
Applying
we obtain
and
R:real part
I:imaginary part

39. Channel estimation by LSE

40. Comparison between the MRC pilot and the original pilot multiplication
Only add
MRC pilot

41. Comparison between the MRC pilot and the original pilot addition
Original pilot multiplication
After mutual multiplying

42. Channel A
MRC pilot
4 pilot multiplying