Effects estimation and compensation of frequency sweep nonlinearity in fmcw ranging systems
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Effects, Estimation, and Compensation of Frequency Sweep Nonlinearity in FMCW * Ranging Systems. * Frequency-Modulated Continuous-Wave. Contents. Introduction Digital chirp generation and its effect on the performance of a FMCW radar

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Effects estimation and compensation of frequency sweep nonlinearity in fmcw ranging systems

Effects, Estimation, and Compensation of Frequency Sweep Nonlinearity in FMCW*Ranging Systems

* Frequency-Modulated Continuous-Wave


Contents
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
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)



Intercept receivers
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

power

pulse with high peak power

LPI radar

continuous wave with low peak power

  • Low probability of intercept

time

Thales Smart-L

power megaWatt

Thales Scout Mk2

power milliWatt


Fmcw radar

frequency

FMCW radar

bandwidth = 50 MHz

carrier frequency = 10 GHz

  • Frequency-modulated continuous-wave

sweep period = 500 µs

time

amplitude

time


Principle of fmcw ranging

transmitted linear chirp

frequency

Principle of FMCW ranging

received echoes

time

target ‘beat’ frequencies

frequency difference

time


Fmcw transceiver

chirp generator

transmit antenna

FMCW transceiver

coupler

time

LO

RF

mixer

target

receive antenna

IF

power

spectrum analyzer

frequency

frequency


Frequency sweep nonlinearity
Frequency sweep nonlinearity

transmitted non-linear chirp

frequency

received target echoes

time

beat frequency

time


Ghost targets
“Ghost” targets

transmitted non-linear chirp

frequency

received target echo

power

target

“ghost” targets

time

beat frequency

time

frequency


Analog chirp generation
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
Digital chirp generation

  • Direct digital synthesizer (DDS)

address generator

RAM or ROM

D/A converter

low-pass filter

to transmitter

clock

  • Clock speed 1 GSPS

  • Integrated 14-bit DAC

Output of a AD9910 sweeping from 180 MHz to 210 MHz

Source: J. Ledford, Master’s Thesis, University of Kansas (2008).


Quantization of phase
Quantization of phase

‘jump’ size

‘phase accumulator’

sine look-up table (ROM)

clock


Worst case ghost target
Worst-case “ghost” target

  • ‘Spurious-free dynamic range’

  • “Ghost” targets practically negligible

power

SFDR = 92 dB

frequency


Compensation of phase errors
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 non-linearities correction in FMCW SAR, IEEE Conf. on Geoscience and Remote Sensing 2006, 403 (2006).


Remember this
Remember this?

frequency

time

intermediate frequency (IF)

time


Compensation algorithm
Compensation algorithm

collected non-linear deramped data

transmitted non-linearties removal

time

range deskew

time

non-linearities compensation

time

linear deramped data

time


Implementation
Implementation

deskew filter

phase error






Fcmw in optics
FCMW in optics

  • Swept-Source Optical Coherence Tomography

  • Compensation algorithm not in the literature!

3D image of a frog tadpole using a Thorlabs OCS1300SS OCT microscope system.


Conclusions
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




Effect on doppler processing
Effect on Doppler processing

  • Systematic phase errors have negligible effect on Doppler processing

Sinusoidal phase error, 3 cycles per sweep, amplitude 0.1 radian

Sinusoidal phase error, 3.1 cycles per sweep, amplitude 0.1 radian


Spectrum of the complex exponential
Spectrum of the complex exponential

‘signal’

‘replicas’


Spectrum of the analytic signal

‘main’ signal

Spectrum of the analytic signal

‘signal replica’

‘image replica’


Observed beat signal

‘signal ×signal’

Observed beat signal

‘signal × signal replica’

‘image replica × image replica’

‘signal × image replica’


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