cfo estimation with ici cancellation for ofdm systems
DESCRIPTION
CFO Estimation with ICI Cancellation for OFDM Systems. 吳宗威. Outline. Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions. Outline. Motivations Background knowledge - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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.