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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

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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

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Serial to

Parallel

Parallelto

Serial IFFT

D/AConver

ter

CH

Parallelto

Serial

Serialto

ParallelFFT

A/DConver

ter

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

TxData

Transmitter

Receiver

RxData yn,l

xn,l

Yk,l

Xk,l

OFDM system block diagram

EqEq...

Eq

SFO

Up convert

Down convert

CFO

n: n-th sample pointk: k-th subcarrierl: l-th subcarrier

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Carrier Frequency Offsets CFO is due to the

oscillator mismatch from up convert and down convert

f

CFO simulation

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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

620 20 10 250 1000.32

312.5 312.5

ppm

kHz

2 n l

N

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Sampling Frequency Offsets SFO is caused by the

oscillator mismatch between A/D & D/A converter

SFO simulation

t

TTX

TRX

When TRX > TTX

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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

2 ( )180TX RX

SFOTX

k T T l

NT

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OFDM baseband signal model OFDM baseband signal after IFFT at the

transmitter side The received OFDM baseband signal

before FFT -------- (2)

12 /

, ,0

1 Nj kn N

n l k lk

x X eN

12 /

, ,0

1 Nj kn N

n l k lk

y Y eN

n: n-th sample pointk: k-th subcarrierl: l-th subcarrier

-------- (1)

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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

''( )( )

{2 [ ( ) ] }

, ,

, ,

d s s ss s k

u u

kT k T T N l Gj f N l G T

T Tk l k l k

k l k l

Y X H e

N I

OFDM baseband signal model

f

k

CFOSFO

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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)

''( )( )

{2 [ ( ) ] }

, ,

arg[ ],

d s s ss s k

u u

k

kT k T T N l Gj f N l G T

T Tk l k l k

j Hk l

Y X e H

e N

,k lN

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OFDM baseband signal model The effect of CFO and SFO can be

represented as :

-------- (5)

and

'' '

,

'

( )( )2 [ ( ) ]s s

k l s ku

k k

k T T N G lf N G lT

T

l

' arg[ ] 2 /k k k d uH kT T

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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.571-578, Apr. 2001.

Decoding &demodulation

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Inner receiver structure

Frame Detection

Carrier FrequencyOffset Estimation

Symbol Timing

Buffer

Frequency OffsetCompensation

Remove Prefix

S/P

Input signal

FFT

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Inner receiver structure

,k ld,k lY

FFTInitial coefficient

FrequencyDomain

Equalizer

Pilot-based phase estimator

Phase compensation

Outer receiver

Hard decision

Update coefficientof equalizer

Phase compensation

Training sequenceData

Pilot

,k lX

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Channel estimation by least square error Lk,l : transmitted training sequence

Rk,l : received training sequence

: equalized training sequenceHk : channel

Nk,l : noise

: equalizer initial coefficient Equalized training sequence

,k lR

,eq kH

, , ,

, , ,

k l k l eq k

k l k k l eq k

R R H

L H N H

In 802.11al : 2 long training symbol

k : 52 subcarrier

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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

2 2

,1 ,1 ,2 ,2k k k k ke R L R L

,1 ,1 ,2 ,2

2 2

,1 ,2

k k k keq

k k

L R L RH

R R

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LMS algorithm Filtering output: Yk=wk

HXk

Error estimation: ek=dk-Yk Tap-weight vector adaptation

*, 1 , , ,k l k l k k l k lw w e X

*

k is the step size that modified by channel condition

After hard decision

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selection of Normalized-LMS & time average

, 1 , , ,

, ,

, 1 , 1

1

0

1 1

k l k l k k l k l

kk

k l k l

kk k

k l k l

w w l e Y

R R

l lY Y

0 < < 1

Training sequence

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Pilot-based phase estimator

After giving the

appropriate weight

Re

Im

Re

Im

Received pilots

∠ 1 ∠ 2

Maximum ratio combination (MRC) pilot

O

A

B

A’

B’

O

C

C’

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Simulation by Simulink 5.0

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Unequalized signal spacing plot

Channel A (Ts=50ns, TRMS=50ns )SNR=10dBResidual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 )Code rate=1/2, QPSK44 OFDM symbol per packet1000 packet

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After channel equalization

Applied the proposed inner receiver structure

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IEEE 802.11a PER v.s. SNR =0.15=0.3Channel A (Ts=50ns, TRMS=50ns )Residual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 )PSDU=256 bytes1000 packet

sT

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

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

TRMS=250ns )

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PER v.s. SNR with different

=0.3Channel A (Ts=50ns, TRMS=50ns )Residual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 )44 OFDM symbol per packet1000 packet

sT

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PER v.s. SNR with different

Channel C (Ts=50ns, TRMS=150ns ) Channel E (Ts=50ns, TRMS=250ns )

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PER v.s. SNR with different

=0.3Channel A (Ts=50ns, TRMS=50ns )Residual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 )200 OFDM symbol per packet1000 packet

sT

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PER v.s. SNR with different

Channel C (Ts=50ns, TRMS=150ns ) Channel E (Ts=50ns, TRMS=250ns )

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PER v.s. with different channel

=0.3Channel A (Ts=50ns, TRMS=50ns )Channel C (Ts=50ns, TRMS=150ns )Channel E (Ts=50ns, TRMS=250ns )SNR=10dBResidual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 )44 OFDM symbol per packet1000 packet

sT

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PER v.s. with different channel

=0.3Channel A (Ts=50ns, TRMS=50ns )Channel C (Ts=50ns, TRMS=150ns )Channel E (Ts=50ns, TRMS=250ns )SNR=10dBResidual CFO =0.01 SFO=800Hz (Ts=1/(20MHz-400), =1/(20MHz+400 )200 OFDM symbol per packet1000 packet

sT

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A Robust Inner Receiver Structure

Simulink 5.0

Conclusion

pilot-based phase estimator

2. Assist the LMS equalizer in phase tracking

1. Compensate the residual CFO

Dynamic simulation

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Future work At present

Frequency selective fading channel LMS algorithm

The future work Slow fading channel Other adaptive algorithms Decoding block of Simulink 5.0

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Reference IEEE Std 802.11a-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. 377-378, Jan. 2005.

S. Haykin, Adaptive Filter Theory, Englewood Cliffs, NJ: Prentice-Hall, 2002, 4 th 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. 1668-1677, Nov. 1999.

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.571-578, Apr. 2001.

Doufexi, A.; Armour, S.; Butler, M.; Nix, A.; Bull, D.; McGeehan, J.; Karlsson, P., “A comparison of the HIPERLAN/2 and IEEE 802.11a wireless LAN standards,” IEEE Magazine on Comm. Vol. 40, pp.172-180, 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

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Any Questions?

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Channel estimation by LSE

2 2

,1 ,1 ,2 ,2

*,1 ,1 ,1 ,1*

,1 ,1 ,1 ,1

*,2 ,2 ,2 ,2*

,2 ,2 ,2 ,2

( ) ( )( ) ( )

( ) ( )( ) ( )

k k k k

eq eq

k k k kk k k k

eq eq

k k k kk k k k

eq eq

R L R L

H H

R L R LR L R L

H H

R L R LR L R L

H H

2 2

,1 ,1 ,2 ,2k k k k ke R L R L

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Channel estimation by LSE Applying we obtain

and

eq

CH

eqR IeqH H

, ,,

, ,

1 ( ) 1 1 0eq

eq k eq kCH eq k

eq k eq kR I

H HH j j j

H H

* *, ,*

,, ,

1 ( ) 1 1 2eq

eq k eq kCH eq k

eq k eq kR I

H HH j j j

H H

R:real partI:imaginary part

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Channel estimation by LSE* *

,1 ,1 ,2 ,2,1 ,1 ,2 ,2

* *1, , 1, 2, , 2,

1, , 1, 2, , 2,

1, , 1, 1, 2, ,

( ) ( )( ) 0 ( ) 0

( ) ( )( ) ( )

( ) (

k k k kk k k k

eq eq

k eq k k k eq k kk eq k k k eq k k

eq eq

k eq k k k k eq k

R L R LR L R L

H H

R H L R H LR H L R H L

H H

R H L R R H

2, 2,)k kL R

,1 ,1 ,2 ,2

2 2

,1 ,2

k k k keq

k k

L R L RH

R R

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Comparison between the MRC pilot and the original pilot multiplication

MRC pilot 21 7 7 21

, , ,CFO SFO CFO SFO CFO SFO CFO SFOj j j jA B Ce De e e

21 7 7 21CFO SFO SFO SFO SFO CFO SFOj j j j j j je e e eA B C EeDe e

21 7 7 21CFO SFO SFO SFO SFO CFO SFOj j j j j j je e e e e eC D E eA B

Only add

MRC pilot

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Comparison between the MRC pilot and the original pilot addition

Original pilot multiplication 21 7 7 21

, , ,CFO SFO CFO SFO CFO SFO CFO SFOj j j jA B Ce De e e

4 21 7 7 21CFO SFO SFO SFO SFOjA eBCD

After mutual multiplying

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Channel A

MRC pilot 4 pilot multiplying

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