1

Data-carrier Aided Frequency Offset Estimation for OFDM Systems

2

Outline

Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

3

Outline

Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

4

Motivations

Motivations The conventional carrier frequency offset estimation

methods: pilot, cyclic prefix, training symbol Our proposed schemes: adopting the received signal on

data-carriers Providing more accurate frequency synchronization, or

reducing the pilot numbers to raise transmitted data rate.

5

Outline

Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

6

Carrier Frequency Offset

What result in carrier frequency offset (CFO)? Mismatch between the oscillators at the TX and RX Doppler frequency

Carrier frequency offset can be divided into: Integral part Fractional part

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OFDM System Model

C is pilot sequence h is time domain channel impulse response w is additive white Gaussian noise. N data information {S(n)} which have been modulated with N modulation

values {X(n)} on every sub-carrier

x ( t )

Channel h ( t)

S ( n )

r (t )ˆ ( )S n

S/P

P/S

X ( n ) x ( k )

Adding Pilots C(n) &IFFT

AddingCyclicPrefix & P/S

DACSignal

Mapper

z (t )

( )R n

FFT RemoveCyclicPrefix & S/P

ADC

SignalDemapper

( )r n

AWGN w ( t)

The OFDM system model:

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OFDM System Model

The k sample of an OFDM block generated by IFFT :

N: number of subcarriersNg: length of cyclic prefix

12 /

0

1( ) ( ) ,0 1

Nj kn N

k

x k X n e k NN

[ ( ),..., ( 1), (0),..., ( 1)]gx x N N x N x x N

z x h

( ) ( ) ( )r k z k w k

12 /

0

( ) ( ) ,0 1N

j kn N

k

R n r k e n N

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UWB Channel Model

Four environments in this UWB channel model: CM1 model is based on LOS (0-4m) channel measurements in [2] CM2 model is based on NLOS (0-4m) channel measurements in [2] CM3 model is based on NLOS (4-10m) channel measurements in [2],

and NLOS in [3] CM4 the model generated to fit a 25nsec RMS delay spread.

Time

Signal strength

: cluster decay factor : path decay factor : cluster arrival rate : the arrival rate of path within each cluster

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Outline

Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

11

Sensitivity for Carrier Frequency Offset

The OFDM system model with CFO:

x ( t )

Channel h ( t)

S ( n )

S/P

X ( n ) x ( k )

Adding Pilots C(n)& IFFT

AddingCyclicPrefix & P/S

DACSignal

Mapper

z (t )

r (t )ˆ ( )S n

P/S

( )R n

FFTRemoveCyclicPrefix & S/P

ADC

SignalDemapper

( )r k

AWGN w ( t)

02 /fj k Ne

is the ratio of the actual frquency offset to the sub-carrier spacing/f f f

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Sensitivity for Carrier Frequency Offset

The k-th received sample of the m-th symbol is given by

FFT 12 /

0

1 12 ( ) / 2 /2 / 2 /

0 0

12 ( ) / 2 ( ) /

0 0

( ) ( ) ,0 1

1 ( )

( )

1 ( )

g g f f

g g f f

Nj kn N

m mk

N Nj mN mN N N j k Nj kn N j ik N

m ii k

m

N Nj mN mN N N j k i n N

m ii k

R n r k e n N

e X i H e e eN

W n

e X i H eN

1

( )mW n

( ) ( ) ( ) ( )m mm mR n S n I n W n

2 ( ) /( ) ( ) (k),0 1f g gj mN mN N k Nm m mr k z k e w k N

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Pilot tone - aided CFO Estimation

PTA CFO estimation:

( ) / ( )

2 arg ,( ) / ( )

i

g m D i m D if PTA i

n P m i m i

N N R n C nD n P

N R n C n

( ) / ( )1 1arg

2 ( ) / ( )i

m D i m D if PTA

n Pg m i m i

R n C nN

N N D R n C n

R1 R2

Pilot1 (n1)

Pilot2 (n2)

Pilot3 (n3)

f

t

Rm Rm+D

Let P denote the set of indexes of the Np pilot carriers

I

Q

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Pilot tone - aided CFO Estimation

PTA with weighting (PTAW) CFO estimation:

* *2 arg ( ) ( ) ( ) ( ) ,gf PTAW m m D m m D i

n P

N ND R n R n C n C n n P

N

* *1 1arg ( ) ( ) ( ) ( )

2f PTAW m m D m m Dn Pg

NR n R n C n C n

N N D

f

Let P denote the set of indexes of the Np pilot carriers

I

QR1 R2

Pilot1 (n1)

Pilot2 (n2)

Pilot3 (n3)

t

Rm Rm+D

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CP (Ng)

Symbol 1 Symbol 2(N+Ng)

(CL-1)

(L)

Cyclic Prefix - based CFO Estimation

CL is the channel length

*

0

2 arg ( ) ( )gN CL

f CPB m ml

r k l r k l N

*

0

1arg ( ) ( )

2

gN CL

f CPB m ml

r k l r k l N

*

0

2 arg ( ) ( )gN L

f CPB m ml

r k l r k l N

*

0

1arg ( ) ( )

2

gN L

f CPB m ml

r k l r k l N

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Outline

Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

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Modified PTAW

R1 R2

t

Rm Rm+D

f

Step1 :

*( ) ( ) ( )

( ) is the modulation phase difference of ( )

d m m D

m d

M n R n R n

n M n

2 /

:

( , ) ( ) , 1 ~

case

j i Md d

For MPSK

V i n M n e i M

2 ( , )

( ) arg ( , )fdg d

i nN N D V i n

N

1 1( , ) arg ( , )

2fd dg

Ni n V i n

N N D

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Modified PTAW

Step2 :

2 arg ( )gf PTAW p

n p

N ND V n

N

* *( ) ( ) ( ) ( ) ( ) ,p m m D m m DV n R n R n C n C n n p

1 1arg ( )

2f PTAW pn pg

NV n

N N D

f

R1 R2

Pilot1 (n1)

Pilot2 (n2)

Pilot3 (n3)

t

Rm Rm+D

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Modified PTAW

Find ( ), which is the closest ( , ) to for each fd fd f PTAWn i n n

( , )fd i n

Step4 :

Step3 :

2 ˆ( ) arg ,f MPTAWg p dN N D V V

N

1 1 ˆarg ,2f MPTAW p d

g

NV V

N N D

Each data-subcarrier d(n) has M candicates ,i=1…M

ˆ is the set of all ( ) ( )d d fdV V n corresponding to each n

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Modified CPB

Step2 :

*

0

2 arg ( ) ( )gN CL

f CPB m ml

r k l r k l N

*

0

1arg ( ) ( )

2

gN CL

f CPB m ml

r k l r k l N

Step1 :

*( ) ( ) ( )

( ) is the modulation phase difference of ( )

d m m D

m d

M n R n R n

n M n

2 /

:

( , ) ( ) , 1 ~

case

j i Md d

For MPSK

V i n M n e i M

2 ( , )

( ) arg ( , )fdg d

i nN N D V i n

N

1 1( , ) arg ( , )

2fd dg

Ni n V i n

N N D

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Modified CPB

Step4 :

Step3 :

2 ˆ( ) argf MCPBg dN N D V

N

1 1 ˆarg2f MCPB d

g

NV

N N D

Each data-subcarrier d(n) has M candicates ,i=1…M

Find ( ), which is the closest ( , ) to for each fd fd f PTAWi i n n

ˆ is the set of all ( ) ( )d d fdV V i corresponding to each i

( , )fd i n

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Outline

Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

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Optimum L for CPB Method

CM1

0 5 10 15 20 25 30 3510

-6

10-5

10-4

10-3

10-2

L

MS

E

N=128 Np=12 DF=0.1 SNR=50

CPB for BPSKCPB for QPSKCPB for 8PSKMCPB for BPSKMCPB for QPSKMCPB for 8PSK

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Optimum L for CPB Method

CM3

0 5 10 15 20 25 30 3510

-3

10-2

10-1

L

MS

E

N=128 Np=12 DF=0.1 SNR=50

CPB for BPSKCPB for QPSKCPB for 8PSKMCPB for BPSKMCPB for QPSKMCPB for 8PSK

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Discussion of Pilot Numbers

CM1

0 20 40 60 80 100 120 14010

-6

10-5

10-4

10-3

Np

MS

E

N=128 DF=0.1 SNR=50

PTAW for BPSKPTAW for QPSKPTAW for 8PSKMPTAW for BPSKMPTAW for QPSKMPTAW for 8PSK

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Discussion of Pilot Numbers

CM3

0 20 40 60 80 100 120 14010

-5

10-4

10-3

Np

MS

E

N=128 DF=0.1 SNR=50

PTAW for BPSKPTAW for QPSKPTAW for 8PSKMPTAW for BPSKMPTAW for QPSKMPTAW for 8PSK

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Performance Comparison

CM1 BPSK

0 5 10 15 20 25 30 35 40 45 5010

-6

10-5

10-4

10-3

10-2

10-1

SNR(dB)

MS

E

BPSK N=128 Np=12 DF=0.1

CPBMCPBPTAPTAWMPTAW

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Performance Comparison

CM1 QPSK

0 5 10 15 20 25 30 35 40 45 5010

-5

10-4

10-3

10-2

10-1

SNR(dB)

MS

E

QPSK N=128 Np=12 DF=0.1

CPBMCPBPTAPTAWMPTAW

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Performance Comparison

CM1 8PSK

0 5 10 15 20 25 30 35 40 45 5010

-5

10-4

10-3

10-2

10-1

SNR(dB)

MS

E

8PSK N=128 Np=12 DF=0.1

CPBMCPBPTAPTAWMPTAW

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Performance Comparison

CM3 BPSK

0 5 10 15 20 25 30 35 40 45 5010

-5

10-4

10-3

10-2

10-1

SNR(dB)

MS

E

BPSK N=128 Np=12 DF=0.1

CPBMCPBPTAPTAWMPTAW

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Performance Comparison

CM3 QPSK

0 5 10 15 20 25 30 35 40 45 5010

-5

10-4

10-3

10-2

10-1

SNR(dB)

MS

E

QPSK N=128 Np=12 DF=0.1

CPBMCPBPTAPTAWMPTAW

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Performance Comparison

CM3 8PSK

0 5 10 15 20 25 30 35 40 45 5010

-5

10-4

10-3

10-2

10-1

SNR(dB)

MS

E

8PSK N=128 Np=12 DF=0.1

CPBMCPBPTAPTAWMPTAW

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Outline

Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

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Conclusions

Advantages: The key advantages of our proposed algorithms is to provide mor

e accurate frequency synchronization and reduce pilot numbers to raise bandwidth efficiency.

Comparison with conventional methods: The MCPB performs better than CPB (lower MSE). The MPTAW performs better than two traditional pilot tone-aide

d methods, and we can achieve the same performance as PTAW by less pilot numbers.

The best choices: If there is acceptable ISI, the MCPB will be the most suitable me

thod to estimate CFO because it can provide excellent MSE with its superior resistance of ICI and constellation size.

If there is serious ISI, the MPTAW is the best choice under this condition since it is robust to time domain interference.

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Thank you ~

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Reference

[1] J. R. Foerster, Ed., “Channel Modeling Sub-committee Report Final,” IEEE P802.15 SG3a contribution.

[2] H. Chen and G.J. Pottie, "A Comparison of Frequency Offset Tracking Algorithms for OFDM", GLOBECOM '03, vol.2, pp. 1069-1073, Dec. 2003.

[3] K. Shi, E. Serpedin, and P. Ciblat, “Decision-directed fine synchronization for coded OFDM systems,” in Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing. (ICASSP’04), vol. 4, pp. 365-368, 17-21 May 2004.