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CFO Compensation in Frequency Domain. Presenter: Pin-Hsun Lin Advisor: Prof. Tzi-Dar Chiueh Date: Aug. 18 th 2003. Outline. Motivation Time-delay in a loop What are the impacts of delay in a loop? How the error performance degrades with the prolonged settling time? - PowerPoint PPT Presentation
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NTU Confidential 1
CFO Compensation in Frequency CFO Compensation in Frequency DomainDomain
Presenter: Pin-Hsun LinAdvisor: Prof. Tzi-Dar Chiueh
Date: Aug. 18th 2003
2NTU Confidential
Outline Outline
• Motivation• Time-delay in a loop
– What are the impacts of delay in a loop? – How the error performance degrades with the
prolonged settling time?– Under what condition the conventional method is
improper? – Loop filter design for a stable system
• With/without consideration of phase error variance• Preliminary remedies
– Frequency domain compensation• Circular convolution, interpolator, rotation
• Conclusion
3NTU Confidential
Motivation Motivation
• In the 802.11a project the time domain CFO tracking is said to be unstable since there’s a large delay (FFT block)• Find out how the delay affects the burst communication and how to solve the problem caused by the effect efficiently.
4NTU Confidential
Model of delay in a loopModel of delay in a loop
FFTFFT
CFO Estimato
r
CFO Estimato
r
NCO
NCO
Up to 2 OFDM symbols delay
• Pipeline registers• Latency of signal processing blocks:
―FFT, CFO estimation, TFO estimation, etc.
Some causes of the delay in feedback loop in a communication system include:
ACC
ACC
22
11NCO
NCO
ACC
ACC
If symbol based estimator is used
Example: CFO compensation of OFDM and CP-SC system
5NTU Confidential
Impacts of delay in a loop: Impacts of delay in a loop:
The optimal natural frequency is decreased [1]
The optimal natural frequency is decreased [1]
The error variance increases [1]
The error variance increases [1]
Delay in a loop increases
Delay in a loop increases
Trade-offThe settling time increases [3] [4].The settling time increases [3] [4].
6NTU Confidential
Impacts of delay in a loop:Impacts of delay in a loop: the model of loop with delay [1] the model of loop with delay [1]
[2][2]
LO,RLO,T φφ -KDKD
K0/S
K0/S F(s)F(s)
VCO,Rφ
)t(n
∫∫∞
∞-
∞
∞-- dffHfSdffHfS WNPN
WNPN
22
222
|)(|)(|)(1|)(
2
)(
)(
sHs
kksF fp
LOWNPN kPSf
fS ,
2 2
Close loop transfer function
0LPf is the laser line-width
Delay τ
Delay τ
is the LO signal power
7NTU Confidential
Impacts of delay in a loop:Impacts of delay in a loop: the increased error variance and the the increased error variance and the decreased optimal natural frequency decreased optimal natural frequency
[1][2][1][2]
Bit rate=565Mbps
MHz1=fδ
Optimal loop design
No modification according to the loop delay
8NTU Confidential
How the error rate performance How the error rate performance degrades with the prolonged settling degrades with the prolonged settling
time?time?
The length of settling time The length of settling time
Accuracy of coarse synchronization
Accuracy of coarse synchronization
Length of training sequence
Length of training sequence
Error rate performance Error rate performance
Delay in a loop Delay in a loop
9NTU Confidential
Under what condition the Under what condition the conventional method is conventional method is
improper?improper?
If the previous relationship is valid, then under the following conditions the conventional methods are improper:
• In burst communication (not such long time for convergence)• When training symbol is very short like 802.11a
10NTU Confidential
Loop filter design for a stable system:Loop filter design for a stable system:w/o consideration of phase error w/o consideration of phase error
variance variance [3][3]
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
1.5
2
2.5
3
3.5
4
Kp
Kf
)]12/(,0[
))2/1cos(()2/tan()2/sin(4)(
)2/tan())1sin((2)(
0
M
Mk
Mk
k
f
p
f
Analytical method:
The stable region is enclosed by:
M is the samples of delay
M=0
M=1M=2
(only for 2nd order loop)
11NTU Confidential
Loop filter design for a stable system:Loop filter design for a stable system:w/o consideration of phase error w/o consideration of phase error
variance variance [4][4]
• Replacing z=exp(u+jv) into the denominator of the loop transfer function.• scan u>0 and v=0~2*pi• The region doesn’t cover by the spirals is the stable region as the right figure shows. 0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
kp
kf
Numerical method:
M=1, 2nd order loop
12NTU Confidential
Loop filter design for a stable system:Loop filter design for a stable system:with consideration of phase error with consideration of phase error
variance [5]variance [5]
• Given delay want to find an F(s) that minimizes the phase error variance:
1)()()()(
)(
)(
'
`
sYsMSXsN
sM
sNe
theoremsCauchy
ionapproximatePads
Then F (S) stabilizes the loop iff: NQY
MQXsF
)(
where Q is any stable proper and rational function.
Then find Q by minimizing .2(The solution is complicated so isn’t shown here.)
1.
2.
3.
NTU Confidential 13
Preliminary Remedies Preliminary Remedies
14NTU Confidential
Compensate the error in Compensate the error in frequency domainfrequency domain
FFTFFTCFO
compensator
CFOcompensat
or
CFO Estimator
CFO Estimator
• The latency of the frequency domain compensator must be smaller than the time domain one.• The additional complexity must be moderate.
Design criterion:
15NTU Confidential
Frequency domain Frequency domain compensation: compensation:
Circular convolution Circular convolution
• Time domain rotation is equivalent to frequency domain circular convolution.
)n+YHW(E=rn+YHW=r Hd
H ⇒
)n+YHW(AWE
)n+YHW(EEWH
H1-Time domain compensation:
Frequency domain compensation:
H11 WEWN1
=A⇒EW=AW --⇒
A is circulant with 1st row= 1EW -
16NTU Confidential
Frequency domain Frequency domain compensation: compensation:
Circular convolution (cont’d)Circular convolution (cont’d)
Trunc
ation
17NTU Confidential
Frequency domain Frequency domain compensation: compensation:
Circular convolution (cont’d)Circular convolution (cont’d)
• The length to be truncated can be determined by:
• The computational complexity can be further optimized by the Chinese remainder theory (CRT) and the latency can be further improved.
• Low latency architecture is under researched.
<σ,|hh|=σ 22truncideal
2 - Required SNR degradation
18NTU Confidential
Interpolator [6]Interpolator [6]
FFT
FFT
N NP NPinterpolatorinterpolator
N
CFOEstimator
CFOEstimator
Zero padding
Zero padding P P
1st stage 2nd stage
19NTU Confidential
Interpolator (cont’d)Interpolator (cont’d)
• The constant BER degradation between no CFO and the cubic interpolator may be because not enough information is included to do the compensation.• The sufficient and necessary conditions for the usage of interpolator is needed be investigated.
~0.001
~0.001
CFO normalized to the sub-carrier spacing
20NTU Confidential
Rotation [7] Rotation [7]
• Rotation is the easiest method with the lowest latency and the worst error performance.
• When CFO is small, the effect of CFO can be considered as a phase rotation.the residual CFO can be compensated by frequency
domain rotation.• The ICI can’t be removed by the rotation.• The resulted SNR degradation is related to how accuracy the
coarse synchronization can achieve.
21NTU Confidential
Rotation (cont’d)Rotation (cont’d)
0
s2
NE
)R
fΔNπ(
10ln310
2)R
fΔπ(
10ln310D≈
OFDM
SC
BERMlog
SER
2
≤
• Given BER, we can get SER by the following approximation for M-ary modulation :
• Using the SER we can get the corresponding SNR. With the SNR and the following approximation we can get the SNR degradation (SINRnon-ideal-SNRideal in dB).
R is the clock rate
22NTU Confidential
Conclusion Conclusion
• The impacts of delay in a loop were introduced. • 3 Loop filter design methods for a stabilize a time-
delay system were introduce.• 3 frequency domain compensation methods were
introduced
• Research the relationship between the error rate performance degradation and the prolonged settling time.• Validate the sufficient and necessary conditions for the usage of interpolator.• Merge the circular convolution and the interpolator and find a low latency architecture.
Future work:
23NTU Confidential
Reference Reference • [1] M. A. Grant, W. C. Michie and M. J. Fletcher, “The performance of optical phase-locked
loops in the presence of nonnegligible loop propagation delay,” IEEE Journal of Lightwave Technology, Vol. 5, No.4, April, 1987, pp. 592-597.
• [2] S. Norimatsu and K. Iwashita, “PLL propagation Delay-time influence on linewidth requirements of optical PSK homodyne detection,” IEEE Journal of Lightwave Technology, Vol. 9, No.10, Oct, 1991, pp. 1367-1375.
• [3] J.W.M. Bergmans, “Effect of loop delay on stability of discrete-time PLL, “Circuits and Systems I: Fundamental Theory and Applications. IEEE Transactions on, Volume: 42 Issue: 4, April 1995, pp. 229 -231
• [4] A. D. Gloria, D. Grosso and M. Olivieri and G. Restani, “A novel stability analysis of a PLL for timing recovery in hard disk drives,” Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on , Volume: 46 Issue: 8 , Aug. 1999 pp. 1026 -1031
• [5] O. Yaniv and D. Raphaeli, “Near-optimal PLL design for decision-feedback carrier and timing Recovery,” IEEE Trans, Commu. Vol. 49, No. 9, Sept 2001, pp. 1669-1678
• [6] M. Luise, M. Marselli and R. Reggiannini, “Low-complexity blind carrier frequency recovery for OFDM signals over frequency-selective radio channels,” Communications, IEEE Transactions on, Vol. 50, No. 7, July 2002 pp. 1182 -1188
• [7] T. Pollet, M. V. Bladel and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise,” IEEE Trans, Commu. Vol. 43, No. 2, Feb 1995
• [8] J. R. Barry and J. M. Kahn, “Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying,” IEEE Journal of Lightwave Technology, Vol. 10, No.12, Dec, 1992.