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’