(1)Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping

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(1)Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. J.-M Friedt, W. Feng Introduction. J.-M Friedt1 , W. Feng2. RADAR basics SDR RADAR. 1. Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. 2. FEMTO-ST/Time & Frequency department, Besançon, France National Laboratory of Radar Signal Processing, Xidian University, Xi’an, China [email protected] Slides at http://jmfriedt.free.fr/grcon2020_radar.pdf sequel to http://jmfriedt.free.fr/sdra_radar.pdf SDRA2020. T HE FREE & OPEN SOFT WA RE RA DIO EC OSY ST EM. August 15, 2020. 1 / 24.

(2) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng Introduction. Why a SDR-based RADAR ? Can we range the house opposite to ourbalcony using available hardware, namely • two DVB-T and two WiFi antennas  ⇒ OFDM or noise, • PlutoSDR + Ettus Research B210 frequency swept RADAR1  1 RAdio Detection And Ranging • splitter and attenuator. RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. View from the balcony. Aerial map of the area: balcony to house=48 m ?. French Geographic Institute (geoportail) claims 48 m: is that correct ?. 2 / 24.

(3) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement. RADAR design – general principles Spectrum spreading the emission: ∆R = c/(2B) • could be chirp (LO frequency sweep), • OFDM1 /WiFi (sum of well defined adjacent frequency components), • noise RADAR: pseudo random phase fluctuation while keeping amplitude constant (see GPS/CDMA for PRN phase spread spectrum) • Correlate reference signal with measured (delayed) signal=sum of echoes: FT (xcorr (r , s)) = FT (r ) · FT ∗ (s) ∼ FT (r )/FT (s). TX. RX attenuator. Conclusion. Noise modulated frequency source LO1 GNU Radio I, Q. dual−channel receiver LO2 2xI, Q. 1 M. Braun, OFDM Radar Algorithms in Mobile Communication Networks (2015) at publikationen.bibliothek.kit.edu/1000038892/2987095. R. Bourret, A proposed technique for the improvement of range determination with noise radar, Proc IRE 45 (12) 1744–1744 (1957). 3 / 24.

(4) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR). RADAR design – general principles Spectrum spreading the emission: ∆R = c/(2B) • noise RADAR: pseudo random phase fluctuation while keeping amplitude constant (see GPS/CDMA for PRN phase spread spectrum) Options. Sync: Unknown PPS. Output Language: Python. Samp rate (Sps): 2.7M. Generate Options: No GUI. Ch0: Center Freq (Hz): 860M. Run Options: Prompt for Exit. command. Ch0: AGC: Default. out. in. Ch0: Gain Value: 60. Variable. Variable. Id: samp_rate. Id: f. Value: 2.7M. Value: 860M. freq. Ch0: Gain Type: Absolute (dB) Ch0: Antenna: RX2. bw. QT GUI Frequency Sink FFT Size: 1.024k Center Frequency (Hz): 0. PlutoSDR Sink IIO context URI:. Constant: 1. Random Source Minimum: 0 Num Samples: 1k Repeat: Yes. out. in. Int To Float Scale: 1. DC Blocker out. in. Length: 32 Long Form: True. out. in. LO Frequency: 860M. out. Sample Rate: 2.7M. mag. Multiply Const Constant: 3.1415. Magnitude and Phase To Complex out out. QT GUI Range Id: df Default Value: 10k Start: -1.35M Stop: 1.35M. Conclusion. freq. Bandwidth (Hz): 2.7M. Constant Source. Maximum: 2. Interferometric displacement measurement. UHD: USRP Source. Title: Not titled yet. Step: 1k. phase. in. RF Bandwidth: 20M Buffer size: 32.768k Cyclic: False Attenuation TX1 (dB): 30. Signal Source. Filter:. Sample Rate: 2.7M. Filter Auto: True. Waveform: Cosine. freq Frequency: df. Fixed magnitude (power) and pseudo-random definition of phase in the Magnitude and Phase to Complex block. out. Amplitude: 1 Offset: 0 Initial Phase (Radians): 0. ↑ Flowchart for checking the spectrum spreading capability of the PlutoSDR and simultaneous data collection by the B210 (⇒ max samp rate with no sample loss). Spectrum collected by the B210 −→ 4 / 24.

(5) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng Introduction. RADAR design – GNU Radio implementation B limited by USB to about 2.7 MHz=56 m range resolution: sweep LO to concatenate multiple spectra and extend B following multiple sequential sweeps 1 Options. Variable Id: samp_rate. Id: f. Output Language: Python. Value: 2.7M. Value: 860M. Generate Options: No GUI. in0. Run Options: Prompt for Exit. RADAR basics SDR RADAR. Variable. Title: Not titled yet. Variable. in1. Id: N. UHD: USRP Source. Value: 2k. Sync: Unknown PPS. freq. Samp rate (Sps): 2.7M Ch0: Center Freq (Hz): 860M. Synthetic Aperture RADAR (SAR). out0. freq. Bandwidth (Hz): samp_rate. Interleave out out1. ZMQ PUB Sink Keep 1 in N in N: 10. in0. command Ch0: Gain Type: Absolute (dB) Ch0: Antenna: RX2. Center Frequency (Hz): 0. bw. Ch0: AGC: Default Ch0: Gain Value: 60. QT GUI Frequency Sink FFT Size: 1.024k. in Stream to Vector out. in1. Vec Length: 2k. out. in Address: tcp://127.0.0.1:5555. Vec Length: 2k. Timeout (msec): 100. Ch1: Center Freq (Hz): 860M. Interferometric displacement measurement. Constant Source. Ch1: Gain Value: 60. Constant: 1. Ch1: Gain Type: Absolute (dB) Ch1: Antenna: RX2. in. Conclusion. Random Source Minimum: 0 Maximum: 2 Num Samples: 1k. out. PlutoSDR Sink. Pass Tags: No. Ch1: AGC: Default. in. Int To Float Scale: 1. in. Length: 32 Long Form: True. LO Frequency: 860M. out. Multiply Const Constant: 3.1415. Sample Rate: 2.7M. mag Magnitude and Phase To Complex out out. phase. in. RF Bandwidth: 20M Buffer size: 32.768k Cyclic: False Attenuation TX1 (dB): 30. DC Blocker out. IIO context URI:. out. Filter: Filter Auto: True. Repeat: Yes. • Collect time series → program next LO frequency → repeat until full B has been swept • No known way of synchronizing data collection with LO sweep in GNU Radio Companion ⇒ benefit from external data collection and processing program (GNU Octave): streaming using ZeroMQ from GNU Radio to Octave 1 S. Prager & al., Ultrawideband Synthesis for High-Range-Resolution Software-Defined Radar, IEEE Trans. 5 / 24 Instrumentation and Measurement 69(6), 3789-3803 (2019): “frequency stacking”.

(6) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng. RADAR design – GNU Radio implementation. GNU Octave & ZeroMQ toolbox Python generated by GNU Radio Companion. #! / u s r / b i n / e n v p y t h o n 3 c l a s s t ( gr . top block ) [...] RADAR basics def s e t f ( self , f ) : self . f = f SDR RADAR s e l f . i i o p l u t o s i n k 0 . set params ( s e l f . f , s e l f .→ ,→ s a m p r a t e , 2 0 0 0 0 0 0 0 , 3 0 . 0 , ’ ’ , True ) Synthetic s e l f . u h d u s r p s o u r c e 0 . s e t c e n t e r f r e q ( s e l f . f , 0) Aperture RADAR s e l f . u h d u s r p s o u r c e 0 . s e t c e n t e r f r e q ( s e l f . f , 1) (SAR) Introduction. Interferometric displacement measurement Conclusion. 2. d e f main ( t o p b l o c k c l s=t , o p t i o n s=None ) : tb = t o p b l o c k c l s ( ) d e f s i g h a n d l e r ( s i g=None , f r a m e=None ) : tb . stop ( ) tb . wait ( ) sys . e x i t (0) s i g n a l . s i g n a l ( s i g n a l . SIGINT , s i g h a n d l e r ) s i g n a l . s i g n a l ( s i g n a l . SIGTERM , s i g h a n d l e r ) tb . s t a r t ( ). Callback functions defining PlutoSDR and B210 LO frequency f 2 J.-M.. t o t a l l e n g t h =140000; % [ s a m p l e s / measurement ] N f r e q =50; pkg l o a d zeromq f o r f r e q u e n c y =1: N f r e q s o c k 1 = z m q s o c k e t (ZMQ SUB) ; zmq connect ( s o c k 1 , " tcp : / / 1 2 7 . 0 . 0 . 1 : 5 5 5 5 " ) ; z m q s e t s o c k o p t ( s o c k 1 , ZMQ SUBSCRIBE , " " ) ; r e c v=z m q r e c v ( s o c k 1 , t o t a l l e n g t h ∗8∗2 , 0 ) ; v a l u e=t y p e c a s t ( r e c v , " single complex " ) ; x ( : , f r e q u e n c y )=v a l u e ( 1 : 2 : l e n g t h ( v a l u e ) ) ; m( : , f r e q u e n c y )=v a l u e ( 2 : 2 : l e n g t h ( v a l u e ) ) ; zmq close ( sock1 ) ; end. • zmq recv: number of bytes (*8 complex, *2 interleaved channels) • typecast: char → complex float • socket-connect-opt-close = 130 us. TCP client: sockets toolbox pkg l o a d s o c k e t s s c=s o c k e t ( AF INET , SOCK STREAM , 0 ) ; s=s t r u c t ( " addr " , " 127.0.0.1 " , " port " , 4 2 4 2 ) ; c o n n e c t ( sc , s ) ; f o r f r e q u e n c y =1: N f r e q [...] s e n d ( sc , ’+ ’ ) ; % w a i t PlutoSDR pause ( 1 . 0 ) % to s t a b i l i z e end s e n d ( sc , ’q ’ ) ;. Friedt, W. Feng, Noise RADAR implementation using software defined radio hardware, SDRA 2020. 6 / 24.

(7) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. RADAR design – GNU Radio implementation. J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. Python Module in GNU Radio Companion to add TCP server receiving commands from Octave (LO reset, LO 7 / 24 increment, antenna position with PyGPIO).

(8) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. RADAR design – GNU Radio implementation TX. PlutoSDR/WiFi. noise/OFDM f0+/−2.7 MHz. J.-M Friedt, W. Feng. −10 dB coupler (ZEDC−10−2B). f0 Introduction. PRN. RADAR basics. Synthetic Aperture RADAR (SAR). B210. Conclusion. USB3. Interferometric displacement measurement. RXA. ADC RXB I’ Q’ I Q GNU Radio Companion/Python 0MQ TCP/IP Matlab/Octave. RX. f0’. software. ADC. SDR RADAR. • ⇒ functional frequency sweep ... • ... but need to wait for unknown delay between LO programming and settling ⇒ 1 s between programming the PlutoSDR 3 and recording • if LO not settled, no pseudo-random modulation ⇒ single carrier carrying all energy with no range resolution (threshold test). 8 / 24.

(9) J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. Range measurement (noise, 2450±50 MHz) • Well resolved multiple echoes: 24, 28.5, 46.5, 49.5, 54 m (30 measurements, bold=average) 70. reflecter power (a.u.). Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. 60 50 40 30 20 10 0 -20. 0. 20. 40. 60. 80. 100. range (m). • However, hard to identify the source of the reflections: • '50 m is probably associated with the house/roof (red arrow) • '25 m probably associated with the nearby covered parking boxes (yellow arrow) 9 / 24.

(10) SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement. • USB bandwidth: offset RX LO by 3 MHz wrt WiFi center TX frequency, sample at 6.25 MS/s, keep 5 MHz • OFDM structure creates sidelobes: replace FT (meas) · FT (ref )∗ with FT (meas)/FT (ref ) to cancel varying magnitude 120. 5 MHz 100 80 60 40 20. Conclusion. 8.125 MHz. 6.25 MHz. +27−32 not used. RADAR basics. • 20 MHz/64 = 0.3125 MHz subcarrier spacing. −1 not used +1 not used. Introduction. • 20 MHz-wide OFDM with 64 sub-carrier structure: unused 0 (avoid DC after downconversion), -32 to -27 and 27 to 32. −27−32 not used. J.-M Friedt, W. Feng. Range measurement (WiFi, ch 1 to 11=55 MHz). power (a.u.). Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. 0 -2. 0. 2. 4. 6. frequency (MHz). • ability to combine digital communication with ranging: reflected power (a.u.). 8. 6. 4. 2. 0 -20. 0. 20. 40. range (m). 60. 80. 100. WiFi LO=2412+(channel−1)*5 MHz. -4. B210 LO=WiFi LO−3 MHz. -6. 20 MHz. 10 / 24.

(11) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement. Azimuth measurement • • • •. Focus narrow beam in a known direction to identify azimuth of target Beamwidth ∝ wavelength λ/antenna diameter D Antenna array: replace single wide antenna with array of small antennas Synthetic Aperture RADAR (SAR): simulate D my moving a single small antenna along a path of length D • For an N antenna array with elements separated by distance d: Wikipedia: ASR-9 0.89 × 0.12 0.89λ = = 80 mrad = 4.5◦ ϑ3dB = Nd 1.40 or 8 m azimuth resolution at 100 m at 2.45 GHz (λ = 12 cm) with rail length 1.4 m. Conclusion. Replace one-dimension analysis (range compression by correlation) with two-dimensional analysis (range and azimuth compression). Scale for positioning the antenna every λ/4 → 11 / 24.

(12) Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. • Uniform Linear Array: a plane wave reaches each antenna with an additional phase delay ~k · d~ = 2π d sin(ϑ) λ • For the nth antenna, the received time series St (nd) has become 2πnd ~k St (nd) · exp j λ d ϑ which can be read as the Fourier transform of St with the phase being the translation • ⇒ azimuth compression is inverse Fourier Transform (FT) along the antenna position • Cross-correlation is inverse FT of product of transmitted signal FT with complex conjugate antenna position received signal FT S1(1) S2(1) S3(1) ... • ⇒ range/azimuth compression is inverse Fourier transform of the S1(2) S2(2) S3(2) ... S1(3) S2(3) S3(3) ... matrix with column=time series and line=antenna position ... ... ... • range resolution only determined by signal bandwidth • azimuth resolution only determined by antenna displacement azimuth compression range: no degree of freedom in mapping to real scale 4 4 see. range compression. J.-M Friedt, W. Feng. Signal processing basics. time. Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. last appendix slide for antenna motion step demonstration meeting the sampling theorem 12 / 24.

(13) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. Full demonstration 2D FT. 1 2D-FT of exp(j2πfy · y0 ) × exp(j2πfx · x0 ) − −−−→ δ(x0 , y0 ). RADAR basics. target. and xp (antenna position → azimuth ϑ0 )   2 s(p, q) |{z} ∝ exp j 4π f · Rp (r0 , ϑ0 ) with Rp = c q RCS. SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. we must separate fq (frequency → range r0 ). | {z }. J.-M Friedt, W. Feng Introduction. so5. 3. target. (xp −a) +b. p. +. b2. =. (xp − r0 sin ϑ0 )2 + (r0 cos ϑ0 )2 where x0 = r0 sin ϑ0 and. | {z }. y0 = r0 cos ϑ0 (cartesian → polar coordinates) p x −a ∂ (xp − a)2 + b 2 = √ p 2 2 = √ −a ∂x 2 a2. q. a +b 2. at xp ' 0 ⇒ Taylor expansion Rp ' r0 − xp sin ϑ0 since. r02.     f · (r0 − xp sin ϑ0 ) ' exp j2π(2fq · r0 /c − 2xp sin ϑ0 /λc ) assuming that 4 s(p, q) ∝ exp j 4π c q | {z } | {z } range α azimuth β P fq /c = 1/λ ' 1/λc the wavelength at center frequency since x1 = n (−1)n · (x − 1)n ' 1 around x ' 1 (keep only n = 0) 5 r0 = α × c/(2fq ) and sin θ0 = β/(2λc ) in polar coordinates or 6 x0 = r0 sin ϑ0 = αβ · c · λc /4 and y0 = r0 cos ϑ0 = cα/2 cos(asin(λc β/2)) in cartesian coordinates: conversion from (fq , xp ) to (x0 , y0 ) using 2D-FT thanks to variable separation. 5 https://hforsten.com/synthetic-aperture-radar-imaging.html 13 / 24.

(14) 0. 0 140 120 120. -10. -10 100 100. Range (m). 80. Range (m). Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. -20. 80. -20. -30. -30 40. 40. 20. 20. Introduction. -40. -40. J.-M Friedt, W. Feng. 0. 0 10. 20. 30. -1. 40. 140. 0. Synthetic Aperture RADAR (SAR). 1. 140. 0. 120 -10. -10 100. 80. -20. y (m). -20. 60. 60. Nf=100 % number o f f r e q u e n c i e s Na=73 % number o f a n t . pos , c=3e8 % speed of l i g h t f =2.45 e9 % c e n t e r f r e q u e n c y ( a z i m u t h c o m p r e s s i o n ) d f =1e6 ; % f r e q . sweep s t e p => t o t a l bw i s 100∗1=100 MHz lambda=c / f dx=lambda / 4 ; % a n t e n n a moved by q u a r t e r w a v e l e n g t h s t e p s f s r = 1/ d f ; r = ( 0 : Nf−1)∗ f s r / Nf∗c / 2 ;. -30 -30. 40. 40. 20. 20 -40 -40. Interferometric displacement measurement. Map {angle-range} → X-Y:. 100. 80. y (m). SDR RADAR. 0. Sin(theta). antenna position (*3.14 cm). 120. RADAR basics. Azimuth compression. 60. 60. 0 -150. -100. -50. 0. 50. 100. 0 -150. 150. -100. x (m). -50. 0. 50. 100. f s a = 1/ dx ; a l p h a = ( 0 : Na−1)∗ f s a /Na−f s a / 2 ; s i n t h t a=a l p h a ∗lambda / 2 ;. 150. x (m). 140. 0. Conclusion. [ R , ST]= m e s h g r i d ( r , s i n t h t a ( a b s ( s i n t h t a )<=1)) ; X = R. ∗ST ; Y = R. ∗ s q r t (1−ST . ˆ 2 ) ; Z=I m g f o c u s ( : , ( a b s ( s i n t h t a )<=1)) ; p c o l o r (X . ’ , Y . ’ , 1 0 ∗ l o g 1 0 ( Z ) ) ;. 120 -10 100. 80. y (m). -20. 60 -30 40. 20 -40. 0 -150. -100. -50. 0. x (m). 50. 100. 150. Top left: range-position map Top right: range-angle map (iFFT along antenna pos.) Middle left: range-azimuth map Middle right: range-azimuth backprojection Bottom: range-azimuth backprojection with windowing 14 / 24.

(15) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. Azimuth compression. J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. 15 / 24.

(16) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. Azimuth compression. J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. 16 / 24.

(17) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. Azimuth compression • Targets match geographic features: roof edges & cars • No freedom in scaling image: • azimuth fully defined by Nd/λ + orientation of balcony rail • range given by frequency span. • QGis Freehand raster georeferencer plugin to scale, rotation and translate raster picture over geoereferenced aerial images (Google Maps). 17 / 24.

(18) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. Azimuth compression (WiFi emitter). J.-M Friedt, W. Feng Introduction. • Replace PlutoSDR configured as noise generator with WiFi emitter. RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. • Each WiFi channel is 20 MHz wide with center OFDM sub-carrier unused • Frequency offset between emitted and received signal: 3 MHz • Sampling rate : 5 MHz • Scan 11 channels with 5 MHz steps: 55 MHz=3 m range resolution • WiFi in Monitor mode & continuous emission using B. Bloessl’s PacketSpammer 6. 6 github.com/bastibl/gr-ieee802-11/tree/maint-3.8/utils/packetspammer. 18 / 24.

(19) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR). Interferometric displacement measurement (noise InSAR) • Assuming the antenna is always positioned at the same location, the phase to the target is a fine ( λ) indicator of its position: 4πr · fc 4πr cos ϑ0 = cos ϑ0 ϕ = 2~k~r = λc c ⇒ varying ~r varies ϕ with sub-λ resolution BUT λ/2 (π) uncertainty • Known moving target: corner reflector 7. Interferometric displacement measurement Conclusion. Static target (roof) 7 Corner. 30 cm corner reflector. Positioned corner reflector. reflector and rail fabricated by P. Abbé (FEMTO-ST/Time & Frequency, Besançon, France) 19 / 24.

(20) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR). Interferometric displacement measurement (noise InSAR) • Assuming the antenna is always positioned at the same location, the phase to the target is a fine ( λ) indicator of its position: 4πr · fc 4πr cos ϑ0 = cos ϑ0 ϕ = 2~k~r = λc c ⇒ varying ~r varies ϕ with sub-λ resolution BUT λ/2 (π) uncertainty • Known moving target: corner reflector 7 1. Interferometric displacement measurement. 0.8. Conclusion 0.6. 0.4. 0.2. 0 -0.4. -0.2. 0. 0.2. 0.4. Rail for automated scanning 90 v.s 95◦ angle Motor Microcontroller for motor control receiving cmds from computer (could be Raspberry Pi4) – 1 h/1.4 m sweep (3.2 cm/step: 30 min displacement/30 min acquisition) 7 Corner reflector and rail fabricated by P. Abbé (FEMTO-ST/Time & Frequency, Besançon, France) 20 / 24.

(21) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. Interferometric displacement measurement meas3 60. 0. 60. 50. -10. 50. mag 9-3. J.-M Friedt, W. Feng. -20. 40. 20. 40. Introduction. SDR RADAR Synthetic Aperture RADAR (SAR). -30. y (m). RADAR basics. 30. y (m). 0 30. -40 20. -20. 20. -50 10. 10. • Right: magnitude difference with corner reflector position highlighted (arrow). -40. -60 0. Interferometric displacement measurement. • Left: magnitude (all target reflections). 0 -60. -40. -20. 0. 20. 40. 60. -60. -40. -20. x (m). 0. 20. 40. 60. x (m). angle 1-3. angle 1-7. angle 3-5 (no movement). 60. 0.03. 60. 0.03. 60. 0.03. 50. 0.02. 50. 0.02. 50. 0.02. 40. 0.01. 40. 0.01. 40. 0.01. 0. 20. -0.01. 10. 0 -60. -40. -20. 0. x (m). 20. 40. 60. y (m). 30. y (m). y (m). Conclusion. 30. 0. 30. 0. 20. -0.01. 20. -0.01. -0.02. 10. -0.02. 10. -0.02. -0.03. 0. -0.03. 0. -60. -40. -20. 0. 20. 40. 60. -0.03 -60. x (m). Phase difference with arrow indicating corner reflector location: 1 cm, 2 cm and 0 cm. -40. -20. 0. 20. 40. 60. x (m). 21 / 24.

(22) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. Interferometric displacement measurement 1-0. 2-0. 4-0. 8-0. 50. 50. 50. 50. 100. 100. 100. 100. 150. 150. 150. J.-M Friedt, W. Feng Introduction 50. SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. measured displacement (cm). RADAR basics. 100. 150. 200. 250. 50. 100. 150. 200. 250. 150. 50. 100. 150. 200. 250. 50. 100. 150. 200. 250. 4 2. 4 mm. 0 -2 -4. raw phase to position. -6. 1/2 wavelength =6.12 cm @ 2450 MHz. expe c. ted. unwrapped phase to position. -8. reference position. -10 0. 2 3-0. 4. 6. 8. 10. wanted displacement (cm). Corner reflector range: 40 m Reference=phase at roof position (47.5 m range). 50. 100. 150. 50. 100. 150. 200. 250. 22 / 24.

(23) SDR RADAR Synthetic Aperture RADAR (SAR). Impact of temperature and moisture on velocity of electromagnetic wave in air p pe 5 pe • Minimum delay given by sampling rate (1/b1 = 1/2.7 MHz) N = (n−1)ppm = 77, 6 T −6 T +3, 75·10 T 2 • Maximum delay given by correlation integration duration 22 18 (1/b2 = 20 ms) 14 rain (mm/h) temperature (C). RADAR basics. Weather/propagation. • Integrate oscillator phase noise (measured at output of AD9361) over this frequency offset interval. Interferometric displacement measurement. 4 3 2 1 0. 10. 15. 20. 25. 10. 15. 20. 25. 10. 15. 20. 25. 10. 15. 20. 25. 10. 15. 20. 25. -40 2450 MHz 100 MHz 2450 MHz. -60. TX. phase noise (dBrad2/Hz). Conclusion -80. coupler + attenuator reference. RX received. RH (%). Introduction. • Impact of local oscillator phase noise: TX LO is cancelled but time delay between reference and measured signals allows for phase fluctuations.. P (mbar). J.-M Friedt, W. Feng. Tentative error budget (4 mm/day). Electronics. 100 80 60. 1017 1015 1013 1011. -100 25 dB. TX LO. -120. RX LO DAC. ADC. PRN generator range & azimuth 102. 103. 104. 105. 106. 107. frequency offset (Hz). σϕ =. ADC. xcorr. -140. -160 1 10. dn (ppm). Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping. qR b2 b1. Sϕ (f )df ' 1.3◦ ⇒ dr =. PlutoSDR AD9364. λ dϕ 720. = 0.1 mm. B210 AD9361. 380 340 300 260. time (h). Ambiant pressure (1013 hPa=1013 mbar): temperature variation dK1 = 77, 6 × p/T = 77.6 × 1013/273 = 287 ppm and dK1 /dT = 287/T ' 1 ppm/K around ambiant temperature. 10 ppm=0.6 mm @ 60 m 23 / 24.

(24) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng Introduction RADAR basics SDR RADAR Synthetic Aperture RADAR (SAR) Interferometric displacement measurement Conclusion. Conclusion & perspective Software Defined Radio for active RADAR prototyping (B210 receiver, PlutoSDR or WiFi emitter with carrier frequency sweep) • separate functions and delegate to most efficient framework (GNU Radio, Python, Octave) • Extended range measurement to azimuth measurement by implementing Synthetic Aperture RADAR (SAR) processing • Extended SAR processing to interferometric displacement measurement on corner reflector • 4-mm baseline stability on displacement measurement, mm accuracy with departure from expected displacement attributed to poor corner reflector positioning & weather • github.com/jmfriedt/active_radar Perspective: can we apply this knowledge to Copernicus satellite (Sentinel-1) datasets ? https://scihub.copernicus.eu/dhus/. 24 / 24.

(25) Software defined radio based Synthetic Aperture noise and OFDM (WiFi) RADAR mapping J.-M Friedt, W. Feng. Antenna displacement step Assumption: TX antenna is fixed and RX antenna is moved with xp step: p 2πfc R 1 Received signal phase is ϕ = 2 × where R = (xp − x0 )2 + y02 c 2. We have discussed far field R ' r0 + xp · sin ϑ. 3. ⇒ ϕ ' 2 × 2πfc · r0 /c +2 × 2π fc /c ·xp · sin ϑ0 | {z } |{z} static. 4. λ−1 c. avoid ϕ ambiguity with 2xp /λc < 1 ⇔ xp < λc /2. Notice that if both TX and RX move (as opposed to keeping TX fixed and moving RX), then xp < λc /4 Spatial equivalent to sampling theorem 25 / 24.

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