UWB Base-band Time/Freq. Synchronization for SFO

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UWB Base-band Time/Freq.Synchronization for SFO

Reporter : 黃彥欽指導教授 : 吳仁銘博士

2007/01/05通訊工程研究所國立清華大學

Proprietary of NTHU Communication SOC Lab, Copyright @ 2006 2

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Outline

• MB-OFDM UWB Introduction• Tx / Rx Block Diagram• Synchronization of SFO

– Time-domain effect– SFO analysis– Freq-domain effect

• Simulation Result• Future Work


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MB-OFDM UWB

• Spectrum:– 14 sub-bands– 5 band groups

f3432MHz

3960MHz

4488MHz

5016MHz

5544MHz

6072MHz

6600MHz

7128MHz

7656MHz

8184MHz

8712MHz

9240MHz

9768MHz

Band #1

Band #2

Band #3

Band #4

Band #5

Band #6

Band #7

Band #8

Band#9

Band #10

Band #11

Band #12

Band #13

10296MHz

Band #14

Band Group #1 Band Group #2 Band Group #3 Band Group #4 Band Group #5


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MB-OFDM UWB

Data Rate

(Mb/s)

Modulation

Coding Rate

FDS TDS Coded Bits/ 6 Symbols

Info Bits/ 6 Symbols

53.3 QPSK 1/3 YES YES 300 100

80 QPSK 1/2 YES YES 300 150

106.7 QPSK 1/3 NO YES 600 200

160 QPSK 1/2 NO YES 600 300

200 QPSK 5/8 NO YES 600 375

320 DCM 1/2 NO NO 1200 600

400 DCM 5/8 NO NO 1200 750

480 DCM 3/4 NO NO 1200 900


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Timing-related parameters

Parameter

Description Value

Sampling frequency 528 MHz

Total number of data subcarriers ( FFT size ) 128

Number of data subcarriers 100

Number of pilot subcarriers 12

Number of guard subcarriers 10

Total number of subcarriers used 122

Subcarrier frequency spacing 4.125MHz

IFFT and FFT period 242.42ns

Number of samples in zero-padded suffix 37

Zero-padded suffix duration in time 70.08ns

Symbol interval 312.5ns

Symbol rate 3.2MHz

Total number of samples per symbol 165

s

FFT

D

P

G

T

FFT

ZPS

ZPS

SYM

SYM

SYM

f

N

N

N

N

N

f

T

N

T

T

F

N

1

( / )

( )

s FFTf N

f

1

( / )

( )

( )

( )

ZPS s

FFT ZPS

SYM

FFT ZPS

N f

T T

T

N N


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Info. Data rate (Mbps) 53.3 80 106.7 160 200 320 400 480

Mod./ Constellation OFDM / QPSK or DCM

FFT Size 128

Coding Rate 1/3 1/2 1/3 1/2 5/8 1/2 5/8 3/4

Conjugate Symmetric Input to IFFT (FDS)

Yes Yes No No No No No No

Time Spreading Factor 2 2 2 2 2 1 1 1

Overall Spreading Gain 4 4 2 2 2 1 1 1

Data Tones 100

Info. Length 242.42 nsec

Zero-padded Prefix 70.08 nsec

Symbol Length 312.5 nsec

Channel Bit Rate 640 Mbps

Multi-path Tolerance 70.08 nsec

(The version 4/2005 post at MBOA web page)

System Parameters


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PA

2 cj f te

DataSource

P

D+PChannel encoder

Inter-leaver

Signal Mapping

GenerateTraining Symbol

AddGuard Tone

128-point IFFT

Insert Preamble

Pulse Shaping

PAPR ClippingDAC

Time-Freq Code

MB-OFDM UWB Tx

Insert Guard Interval


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MB-OFDM UWB Rx

LPFSymbol WindowControl

PacketDetection

Symbol Timing

Estimation+

Freq.HoppingSignal

ADC

Coarse carrier phase

Estimation

RemoveGuard Interval

N-pointFFT

ChannelEstimation

Channel Equalization

Pilot TrackingEstimation

Sampling ClockSync

P/SSignal

De-mapping

De-Inter-leaver

ChannelDecoder

LNA

2 cj f te

N

P

D

N

D

P

D

DecodedInformationBits

PhaseOffset

Estimation

Coarse carrier phasecompensation

s/p


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Sampling Freq. Offset (SFO)

• SFO is caused by sampling instant mismatch between DAC and ADC.

SFO , (1 )

1 sampling period

s s s s

s ss

s s

T T T T

T TT

T f

DAC ADCchannel,l ns s t r t ,l nr

T T

2T 3TT 4T

T’ 2T’ 3T’

T 2 T 3 T


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SFO Effects Simulation (Time Domain)


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Sampling Freq. Offset (SFO) (cont.)

• Effect in Time Domain

OFDM Symbol Window DriftOFDM Symbol Window Drift

0

0 symlN 1 syml N

syml N

FFT window

This leads to irreducible ISI !

max

3max

20 for UWB

40

128 37 165

6.6 10 samples per OFDM symbol

drift 1 sample after about 151 OFDM symbols

sym FFT ZPS

sym

ppm

ppm

N N N

N

Need to add/drop 1 sample after every 151 OFDM symbols !


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SFO analysis

FFTT ZPST

SYMT

FFTk S

FFT FFT

k Tf t nT n

T N= = =

{ }1

0

[ ] ( )

1 [ ] [ ] exp 2

t nTs

t nTs

l

N

kkFFT

y n y t

X k H k j f tN

p

=

=

-

=

=

= å

1

0

1

0

1 [ ] ( ) [ ]exp 2

[ ] [ ]exp 2

:

:

t nTs

N

kFFT FFT

N

n FFT

nkx n x t X k j

N N

nkX k x n j

IFFT

FFTN

p

p

=

-

=

-

=

ì üï ïï ï= = í ýï ïï ïî þì üï ïï ï= -í ýï ïï ïî þ

å

å


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SFO analysis (cont)

1

0

1

0

1[ ] [ ] exp 2 [(1 ) ]

1[ ] [ ] exp 2 exp 2 exp 2

NFFT

symkFFT FFT FFT

Nsym

kFFT FFT FFT FFT

k TX k H k j n lT

N T N

Tkn knX k H k j j j k l

N N N T

p z z

p p z p z

-

=

-

=

ì üï ïï ï= + +í ýï ïï ïî þì ü ì ü ì üï ï ï ï ï ïï ï ï ï ï ï= í ý í ý í ýï ï ï ï ï ïï ï ï ï ï ïî þ î þ î þ

å

å

{ }(1 )

'

1

0

[ ] ( )

1[ ] [ ] exp 2

t nTs

t nT lTs sym

l

N

kkFFT

y n y t

X k H k j f tN V V

p

¢=

= + +

-

=

=

= å

(1 )s s s sT T T T


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SFO analysis (cont)

'

1

0

1

'

[

0

]

[ ] exp 2

1[ ] [ ] exp

...... (

2

exp 2 exp 2

FF )[ ] T

l

N

ln FFT

N

FFT FFT

sym

FFT F

l

y n

k

FT

npY p j

N

knX k H k j

N N

Tknj j k l

n

N

y

T

p

p

p z p z

-

=

-

=

æ ö÷ç ÷= -ç ÷ç ÷çè ø

ì üï ïï ïí ýï ïï ïî þ=ì ü ì üï ï ï ïï ï ï ïí ý í ýï ï ï ïï ï ï ïî þ î þ

å

å

1444444444444444424444444444 3

{

1

0

1

0

exp 2

1[ ] [ ] exp 2 exp 2

1exp 2 [ ] [ ] exp 2

N

n FFT

Nsym

n FFT FFT FFT

sym

FFT FFT FFT

k p

npj

N

TknX k H k j j k l ICI

N N T

T knj k l X k H k j

T N N

p

p z p z

p z p z

-

¹

=

-

=

æ ö÷ç ÷-ç ÷ç ÷çè ø

ì ü ì üï ï ï ïï ï ï ï= +í ý í ýï ï ï ïï ï ï ïî þ î þì ü ìï ï ïï ï ï= í ý íï ïï ïî þ

å

å

444444

{1

0

k p

N

n

ICI-

= ¹

üïï +ýï ïï ïî þå


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SFO analysis (cont)

{ }{

{ }

1 exp 21exp 2 [ ] [ ]

1 exp 2

exp1 sin( )exp 2 [ ] [ ]

sin( )exp

k p

sym

FFT FFT

FFT

sym

FFT FFT

FFTFFT

T j kj k l X k H k ICI

T N kj

N

T j k kj k l X k H k

kT N kj NN

p zp z

p z

p z p zp z

p zp z

¹

ì ü -ï ïï ï= +í ý ì üï ï ï ïï ïï ïî þ - í ýï ïï ïî þì üï ïï ï= í ý ì üï ï ï ïï ïï ïî þ í ýï ïï ïî þ

{

{

{,

1exp 2 [ ] [ ] exp (1 ) sinc( )

;

sym

FFT FFT

FFT FFT ZPSl

k p

k

k FFT sym FFT ZPSs s

p

k p s

ICI

Tj k l X k H k j k k ICI

T N

N N NS ICI T T T T

f f f

p z p z p z

¹

¹

¹

+

ì ü ì üï ï ï ïï ï ï ï= - +í ý í ýï ï ï ïï ï ï ïî þ î þ

= + = = + = +

, is very small kkLet kf z= ×


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Residual Carrier Freq. Offset (RCFO)

• RCFO is caused by non-exact carrier freq. offset (CFO) correction before FFT.

( )/ : normalized RCFO

wher : RCFO

e

rx tx

k

FFT FFT s

f f f

f T f f

k

N

d

f z

e

e

=D × =D ×

D = -

® » + ×

PacketDetection

CFOCorrection

Coarse CFOEstimator

Symbol TimingEstimator

Remove CP FFT

Data

Preamble


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Sampling Freq. Offset (SFO) (cont.)

• Effect in Freq. Domain

1l +( )

, , , ,

, , , k

',,

where

1exp 1 sinc

: normalized residual

exp 2

ex

carrier

p 2

l k l k l k l k

l k k l k lsym k

FFT

sym k

FFT

k

k

FFT

lk kl

Y S ICI V

S j XlN

jN

lNj

N

H

k

N

X H

p f pf

e

f e z

fp

fp

æ ö÷ç ÷ç ÷ç ÷çè ø

æ ö÷ç ÷ç ÷ç

= + +

é ùæ ö÷çê ú÷= × - ×

÷çè ø

×ç ÷ê úç ÷çè øê úë û

=

» +

× ×

×

freq. offset (NRCFO)

: symbol (time) indexl

Sub-carrier Symbol RotationSub-carrier Symbol Rotation

The rotated phase is the functionof time and different between sub-carriers ! So the receiver has to track and compensate SFO and RCFO continuously in time !

k

12

N-

2

N-

l

2l +

Phase Rotation

3l +

ez

pilot


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SFO Effects Simulation (Frequency Domain)

•Timing offset in time domain resulting in phase rotation in the freq domain


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General Method

• Use Pilots to estimate SFO– Symmetrically distributed around middle subcarrier– Use the knowledge of the linear relationship between p

hase rotation of negative (C1) and positive (C2) set.

• Received pilot subcarriers

• Calculate the rotation of the pilot from this symbol to the previous

[ ] exp 2 [ ] [ ] syml l l

FFT

NR k j k l P k H k

Np z

ì üï ïï ï= í ýï ïï ïî þ

*21

*1

[ ] [ ][ ] [ ] exp 2

[ ] [ ]syml l

ll l FFT

NR k R kZ k H k j k

P k P k Np z-

-

ì üï ïï ï= = í ýï ïï ïî þ


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General Method (cont)

• Take the cumulative phase of for the two sets C1 and C2

• SFO estimation is given by

[ ]lZ k

1

2

1,

2,

( [ ])

( [ ])

l lk C

l lk C

Z k

Z k

f

f

Î

Î

=

=

å

å

R

R

2 1

2 1

2, 1,( )1

2 ( )

where ( ) is the normalization factor

l lFFT

symk C k C

k C k C

N

N k k

k k

ffz

pÎ Î

Î Î

-=

-

-

å å

å å


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Our Proposed Method

• Estimation Method– We use Least-Square (LS) algorithm to

estimate the SFO and RCFO

k

12

N-

2

N-

3,55lb+

( )intercept 3l e= +

( )slope 3l z= +


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LS estimation

• No probabilistic assumptions about data, only a signal model is assumed

• Data Model ：

• Least Squares error

Signalmodel

θ

s[n]

Perturbation

NoiseModel

inaccuracies

x[n]

Signalmodel

θ

s[n]

x[n]

Error=ε[n]

Σ


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LS estimation (cont)

• LS error criterion– The value of θthat minimizes J(θ) is the LSE.

• If the signal s is linear, we can use matrix notation:

12

0

( ) ( [ ] [ ])N

n

J x n s n

12

0

( ) ( [ ] [ ])

( ) ( )

N

n

T

s H

J x n s n

x H x H


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LS estimation (cont)

1

( )

2

( )Let 2 2 0

ˆ ( )

T T T T T T

T T T T

T T

T T

J x x x H H x H H

x x x H H H

JH x H H

H H H x

• To find the minimum LS error, setting the gradient equal to error :

minˆ( )

ˆ ˆ ( ) ( )

ˆ ( )

T

T

J J

x H x H

x x H


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T

where

55 45 35 25 15 5 5 15 25 35 45 55

1 1 1 1 1 1 1 1 1 1 1 1A

é ù- - - - - -ê ú= ê úë û

Proposed Method (cont.)

( )2, 2, 2, 2,Initial 0, m m m mR Pa b *= = ×R

, , ,exp 2 sym kl k l k l k

FFT

lNS j X H

N

fp

æ ö÷ç ÷= ×ç ÷ç ÷çè ø

, 2 sym kl k

FFT

N

N

fa p=

( ), ,2lsym k

l k l kFFT

lN

N

fb p a= =

2 12

2

( )H HA A Az

be

-æ ö÷ç ÷=ç ÷ç ÷çè ø

For each subcarreier of data 64 ~ 63k =- +

2, 2 2k kf z e= × +

( )'2, 2, 2,expk k kR R jf= × -

For each instant of time 3,4,5...l =*

, 1,, *

, 1,

l m l ml m

l m l m

R R

P Pa -

-

é ù×ê ú= ê ú×ê úë ûR

( ) *, 1, , , ,(1 ) ( )l m l m l m l m l mR Pb l b a l-= × + + - × ×R

1( )l H Hl

l

A A Az

be

-æö÷ç ÷=ç ÷ç ÷çè ø

For each subcarreier of data 64 ~ 63k =- +

,l k l lkf z e= × +

( )', , ,expl k l k l kR R jf= × -

End

Enhance the BER performance by Using LS algorithm !

, 55 , 45 , 35 , 25 , 15 , 5 ,5 ,15 ,25 ,35 ,45 ,55 l l l l l l l l l l l lb b b b b b b b b b b b b- - - - - -é ù=ë û


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Simulation of using LS algorithm to estimate the slope and intercept


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SFO Simulation (without other noise)


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SFO Simulation (with AWGN & CFO)


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Sampling Frequency Offset Sampling Frequency Offset RecoveryRecovery

FFTAdd/DropADCChannelEqualizer

Pilot extraction

SFO estimator

2,l kz

l : symbol index k : subcarrier index

SFO Compensation

• Digital approach in Baseband


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Future Work

• Continue completing all the simulation• Make sure the sync. part will work successfully :

– Combine with other parts in Rx-end– Consider the multi-path effect

• Chip implementation ：– Design the micro-architecture and write RTL code– Verify the system by FPGA board– Tapeout


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Thanks for your attention…

Documents

UWB Base-band Time/Freq. Synchronization for SFO