Graduation_presentation - Complex Photonic Systems | COPS

Report
Effects, Estimation, and
Compensation of Frequency Sweep
Nonlinearity in FMCW* Ranging
Systems
Committee members
Applied Physics
Prof. dr. A.P. Mosk (COPS), ir. R. Vinke (Thales), prof. dr.
W.L. Vos (COPS), ir. H.T. Griffioen (Thales)
Applied Mathematics
Dr. G. Meinsma (MSCT), prof. dr. A.A. Stoorvogel (MSCT),
dr. A. Zagaris (AAMP)
*
Frequency-Modulated Continuous-Wave
Contents
• Introduction
• Digital chirp generation and its effect on the
performance of a FMCW radar
• Compensation of frequency sweep
nonlinearity by digital post-processing
• Applications of FMCW to optics
• Conclusions
Radar
• Radio Detection And Ranging
• “To see and not be seen”
Heinkel HE-111 bombers
RAF Chain Home radar site
German U-boat surrendering
(depth charge in profile)
Pulsed radar
Intercept receivers
• Jamming
• Direction finding (DF)
• Anti-radiation missiles (ARMs)
DRS ZA-4501 shipboard
DF antenna array
Prowler armed with HARM high-speed anti-radiation missiles
LPI radar
• Low probability of intercept
power
pulse with high peak power
continuous wave with low
peak power
Thales Smart-L
power ~ megaWatt
time
Thales Scout Mk2
power ~ milliWatt
FMCW radar
• Frequency-modulated continuous-wave
frequency
carrier
frequency
 = 10
GHz
bandwidth
 = 50 MHz
sweep period
 = 500 µs
time
amplitude
time
1
chirp  = cos 2   +  2
2
,
where  =


Principle of FMCW ranging
frequency
transmitted linear
chirp
received echoes
time
frequency
difference
target ‘beat’
frequencies
time
FMCW transceiver
chirp
generator
frequency
transmit
antenna
coupler
LO
time
RF
mixer
target
IF
power
spectrum
analyzer
frequency
receive
antenna
Frequency sweep nonlinearity
transmitted
non-linear
chirp
frequency
received
target
echoes
time
beat
frequency
time
“Ghost” targets
frequency
transmitted
non-linear
chirp
received
target echo
power
target
time
“ghost”
targets
beat
frequency
time
frequency
Analog chirp generation
• YIG (Yttrium, Iron, and Garnet)-tuned oscillator
A.G. Stove, Measurement of Spectra of
Microwave FMCW Radars, Thales
Aerospace UK, working paper (2006).
Digital chirp generation
• Direct digital synthesizer (DDS)
address
generator
RAM or
ROM
clock
• Clock speed 1 GSPS
• Integrated 14-bit DAC
D/A
converter
low-pass
filter
to
transmitter
Output of a AD9910 sweeping from 180
MHz to 210 MHz
Source: J. Ledford, Master’s Thesis, University of Kansas (2008).
Quantization of phase
‘phase accumulator’
sine look-up table
(ROM)
‘jump’ size
0000 … 0
1111 … 1
Δ
clock
2
radians
2
 = number of bits of the phase accumulator
Δ =
AD9910 synthesizer
 = 19
Δ ≈ 1.2 × 10−5 radians
Worst-case “ghost” target
• ‘Spurious-free dynamic range’
SFDR = 20 log10 2Δ ≈ 92 dB
• “Ghost” targets practically negligible
power
SFDR = 92 dB
frequency
Compensation of phase errors
• Burgos-Garcia et al., Digital
on-line compensation of
errors induced by linear
distortion in broadband FM
radars, Electron. Lett. 39(1),
16 (2002).
• Meta et al., Range nonlinearities correction in FMCW
SAR, IEEE Conf. on Geoscience
and Remote Sensing 2006,
403 (2006).
Remember this?
frequency
time
intermediate
frequency (IF)
time
Compensation algorithm
collected non-linear
deramped data
transmitted nonlinearties removal

time

range deskew
time

non-linearities
compensation
linear deramped
data

time
time
Implementation
− ()
2

deskew filter
∗ 
3
4
  ∗  
“Peek”
  ∗ − 
“Meta”
 
1
chirp  = cos 2   +  2 +  
2
phase error
“Burgos-Garcia”
  = exp 2 
−
 2
 = exp  

Sinusoidal phase error (low frequency)
2  =  sin 2  ,
Parameter Value Unit


0
uncompensated
compensated (narrowband)
compensated (wideband)
ideal
10 GHz
-10
50 MHz
-20
500 μs

15 km

0.1 Rad

4 kHz
Power spectrum (dB)

 ≪ 
-30
-40
-50
-60
-70
-80
14.94
14.96
14.98
15
Range (km)
15.02
15.04
15.06
Sinusoidal phase error (high frequency)
2  =  sin 2  ,
Parameter Value Unit


0
uncompensated
compensated (narrowband)
compensated (wideband)
ideal
10 GHz
-10
50 MHz
-20
500 μs

15 km

0.1 Rad

63 kHz
Power spectrum (dB)

 ~ 
-30
-40
-50
-60
-70
-80
14.9
14.95
15
Range (km)
15.05
15.1
Cubic phase error
2  = 3  3




3
Value
Unit
0
uncompensated
compensated (narrowband)
compensated (wideband)
ideal
10 GHz
-10
50 MHz
-20
500 μs
15 km
4 × 1011 Hz/s2
Power spectrum (dB)
Parameter
-30
-40
-50
-60
-70
-80
14.94
14.96
14.98
15
Range (km)
15.02
15.04
15.06
Quartic phase error
2  = 4  4




4
Value
Unit
0
uncompensated
compensated (narrowband)
compensated (wideband)
ideal
10 GHz
-10
50 MHz
-20
500 μs
15 km
4 × 1011 Hz/s2
Power spectrum (dB)
Parameter
-30
-40
-50
-60
-70
-80
14.94
14.96
14.98
15
Range (km)
15.02
15.04
15.06
FCMW in optics
• Swept-Source Optical Coherence Tomography
3D image of a frog tadpole using a
Thorlabs OCS1300SS OCT
microscope system.
• Compensation algorithm not in the literature!
Conclusions
• Phase quantization effects in digital chirp
synthesizers have negligible effect on
performance
• Frequency sweep nonlinearity can be
compensated by digital post-processing of the
beat signal
• Algorithm is also applicable to optics, but not
mentioned in optics literature
Thank you for your attention!
Questions?
Extra slides
Effect on Doppler processing
Sinusoidal phase error, 3.1
3
cycles per sweep,
amplitude 0.1 radian
• Systematic phase errors have negligible effect
on Doppler processing
Spectrum of the complex exponential
‘signal’
‘replicas’
0,1, … , 7
 =
radians
8
Spectrum of the analytic signal
‘main’ signal
‘signal replica’
‘image replica’
Observed beat signal
‘signal ×signal’
‘signal × signal replica’
‘image replica ×
image replica’
‘signal × image replica’

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