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CFO Estimation with ICI Cancellation for OFDM Systems
吳宗威
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Outline
Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions
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Outline
Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions
4
Motivations
Motivations
Every OFDM model has a specific form in the carrier frequency offset system.
When we estimate the frequency offset by pilot,the ICI still exists. It is intuitive to decrease the ICI first , then estimate it.
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Outline
Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions
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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(k)} which have been modulated with N modulation
values {X(k)} on every sub-carrier
x ( t )
Channel h ( t)
S ( k)
r (t )ˆ ( )S k
S/P
P/S
X (k ) x ( n)
Adding Pilots C(n) &IFFT
AddingCyclicPrefix & P/S
DACSignal
Mapper
z (t )
( )R k
FFT RemoveCyclicPrefix & S/P
ADC
SignalDemapper
( )r n
AWGN w ( t)
The OFDM system model:
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OFDM System Model
The nth 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 n X k e n NN
[ ( ),..., ( 1), (0),..., ( 1)]gx x N N x N x x N
z x h
( ) ( ) ( )r n z n w n
12 /
0
( ) ( ) ,0 1N
j kn N
n
R k r n e k 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]
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
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Sensitivity for Carrier Frequency Offset
The OFDM system model with CFO:
x ( t )
Channel h ( t)
S ( k )
S/P
X ( k ) x(n)
Adding Pilots C(n)& IFFT
AddingCyclicPrefix & P/S
DACSignal
Mapper
z (t )
r (t )ˆ ( )S k
P/S
( )R k
FFTRemoveCyclicPrefix & S/P
ADC
SignalDemapper
( )r n
AWGN w ( t)
02 /fj n 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 n-th received sample of the m-th symbol is given by
FFT 12 /
0
1 12 ( ) / 2 /2 / 2 /
0 0
1 12 ( ) / 2 ( ) /
0 0
( ) ( ) ,0 1
1 ( )
( )
1 ( )
g g f f
g g f f
Nj kn N
m mn
N Nj mN mN N N j n Nj kn N j in N
m ii n
m
N Nj mN mN N N j n i k N
m ii n
R k r n e k N
e X i H e e eN
W k
e X i H eN
( )mW k
( ) ( ) ( ) ( )m mm mR k S k I k W k
2 ( ) /( ) ( ) (n),0 1f g gj mN mN N n Nm m mr n z n e w n N
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Amplitude reduction: Phase shift:
Sensitivity for Carrier Frequency Offset
2 ( ) / ( 1) /
m
sin( )S ( ) ( ) ( )
sin( )f g g f
f
j mN mN N N j N Nfm m
N
k X k H k e eN
sin( )
sin( )f
f
NN
2( ) ( 1) /f g gmN mN N N N
.
.1
( )( 1) / 2 ( ) /
( )0,
sin( ( ))( ) ( ( ) ( ))
sin( )f f g g
f
Nj i k N N j mN mN N Nf
m mm i ki i k N
i kI k X i H i e e
N
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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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Outline
Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions
15
Matrix form of R(k)
2 ( ) /( ) ( ) (n),0 1f g gj mN mN N n Nm m mr n z n e w n N
12 /
0
( ) ( ) ( ).N
j in N
m m mi
n i i eZ X H
( ) ( )* ( )z n x n h n
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2 ( ( ) 0) /
2 ( ( ) 1) /
.0
0
j f m N Ng Ng N
j f m N Ng Ng N N
r ze
e
2 ( ( ) 0) /
2 ( ( ) 1) /
1
0
1
1
(0) (0)
( 1)( 1)
0
0
0
0
0
0
j f m N Ng Ng N
j f m N Ng Ng N N
N
H X
F
X NH N
F H X
e
e
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R F r
12 /
0
( ) ( ) ,0 1N
j kn Nm m
n
R k r n e k N
0
1
1
0
0N
F F H X
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A math property
A(k) , k=0…N-1 is the DFT of
a(n) , n=0,…,N-1
(0) (1) ( 1)
(0)
( 1) (0) ( 2)1
( 1)(1) ( 1) (0)
0
0
N
N N
NN
F F
a a aA
a a a
A a a a
0
1
1
0 1 1
1 0 2
1 2 1 0
0
0N
N
N N
N N
R F F H X
H X
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The Problem
Can we find a matrix B, such that
0 1 1
1
1 0 2
1 2 1 0
( )
B
( )
0
0
N
N N
N
N N
f
f
1
1
( ) (0) (0)
.
( 1) ( 1)( )
( ) (0) (0)
=
( ) ( 1) ( 1)
0
0 N
N
f H X
B R
H N X Nf
f H X
f H N X N
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B is in fact a matrix that does Gaussian
Reduction to
0 1 1
1 0 2
1 2 1 0
N
N N
N N
( )exp( 2 ( ) ) /
nj m f N Ng Ng n N
( ) ( )( )
k nifft
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The term is the key point .Because if the ratio between each term is irrelevant to , then we can definitely finish the matrix B.
sin( ( ))
sin( ( ) / )
f k
f k N
( )exp( 2 ( ) / ) exp( ( 1) / )
kj m f N Ng Ng N j f N N
sin( ( ))exp( ( 1) / )
sin( ( ) / )
f kj k N N
f k N
f
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The numerator of is actually .
And the denominator because
So, we can regard as
Thus, the ratio between each term is irrelevant to .
sin( ( ))f k sin( )f
/f N 0sin( / )k N
( )k
f
sin( )exp( ( 1) / )
sin( / )
fj k N N
k N
sin( ( ))
sin( ( ) / )
f k
f k N
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However, is zero when k=0 . So we need a estimate for the denominator of
Choose the PTAW estimate for the denominator of
B is the matrix does Gaussian reduction to the cyclic matrix
composed of
sin( / )k N
f̂ (0)
(0)
( )
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sin( / )
( 1)exp( ( 1) / ) 1,...... 1
sin( / )
k k
kf N
j k N N k Nk N
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The Procedure
Step1: Estimate the frequency offset by PTAW
Step2: Substitute the estimate into the denominator of
Step3: multiply the matrix B with the incoming symbol and the previous symbol
Step4: Apply the PTAW again, then we have a more accurate estimate.
(0)
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Outline
Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions
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Different Modulation
0 5 10 15 20 25 30 35 40 45 5010
-6
10-5
10-4
10-3
10-2
SNR(dB)
MS
E
N=128 Np=12 DF=0.1
BPSK-PTAW
BPSK-PTAW-mine
BPSK
270 5 10 15 20 25 30 35 40 45 5010
-6
10-5
10-4
10-3
10-2
SNR(dB)
MS
E
N=128 Np=12 DF=0.1
QPSK-PTAW
QPSK-PTAW-mine
QPSK
280 5 10 15 20 25 30 35 40 45 5010
-6
10-5
10-4
10-3
10-2
SNR(dB)
MS
E
N=128 Np=12 DF=0.1
8PSK-PTAW
8PSK-PTAW-mine
8PSK
290 5 10 15 20 25 30 35 40 45 5010
-6
10-5
10-4
10-3
10-2
SNR(dB)
MS
E
N=128 Np=12 DF=0.1
16PSK-PTAW
16PSK-PTAW-mine
16PSK
300 5 10 15 20 25 30 35 40 45 5010
-6
10-5
10-4
10-3
10-2
SNR(dB)
MS
E
N=128 Np=12 DF=0.1
BPSK-PTAW
BPSK-PTAW-mine
QPSK-PTAWQPSK-PTAW-mine
8PSK-PTAW
8PSK-PTAW-mine
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Recursive
Recursive
0 5 10 15 20 25 30 35 40 45 5010
-6
10-5
10-4
10-3
10-2
SNR(dB)
MS
E
N=128 Np=12 DF=0.1
16PSK-PTAW
16PSK-PTAW-1st
16PSK-PTAW-2nd16PSK-PTAW-3rd
16PSK-PTAW-True
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Random initial condition
0 5 10 15 20 25 30 35 40 45 5010
-6
10-5
10-4
10-3
10-2
SNR(dB)
MS
E
N=128 Np=12 DF=0.1
16PSK-PTAW
16PSK-PTAW-seed1
16PSK-PTAW-seed216PSK-PTAW--seed3
16PSK-PTAW-True
Random initial condition =0.5 Delta_f=0.1
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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 p
rovide more accurate frequency synchronization . Estimate the frequency offset without knowing the ch
annel response first.
Complexity: N*Np multiplier .
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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.