Noise RADAR and passive RADAR interrogation of passive wireless sensors

Texte intégral

(1)Noise RADAR and passive RADAR interrogation of passive wireless sensors J.-M Friedt & al.. Noise RADAR and passive RADAR interrogation of passive wireless sensors. Spectrum spreading. F. Gégot0 , J.-M Friedt0,1,2 , W. Feng2 , G. Goavec-Mérou1 , G. Martin1 , M. Sato2. Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. 1. 0 SENSeOR SAS, Besançon, France FEMTO-ST Time & Frequency department, Besançon, France 2 CNEAS, Tohoku University, Sendai, Japan. jmfriedt@femto-st.fr slides and references at jmfriedt.free.fr. This work is completed in the framework of the common laboratory PhASES between SENSeOR and FEMTO-ST. 1 / 23.

(2) Noise RADAR and passive RADAR interrogation of passive wireless sensors J.-M Friedt & al. Spectrum spreading Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. What is passive RADAR ? • use the emission of an existing, non cooperative emitter as radiofrequency source for RADAR measurement • since the emitted signal is unknown, a reference channel collects the signal directly transmitted from emitter to receiver • a second surveillance channel, ideally hidden from the direct signal, collects signals reflected by (moving) targets • {range,Doppler} maps computed by correlating Z rd(τ, df ) = meas(t + τ ) · ref (t) exp(j2πfDoppler t)dt. 2 / 23.

(3) Noise RADAR and passive RADAR interrogation of passive wireless sensors. Outline. J.-M Friedt & al.. 1. passive, wireless sensor characteristics (bandwidth, time delay). Spectrum spreading. 2. spectrum spreading of a carrier. Noise RADAR. 3. noise RADAR (2.4 & 4.2 GHz). Passive RADAR. 4. passive RADAR (WiFi). 5. antenna array for spatial separation. DSI Measurement Antenna array. Conclusion Appendix. [0] H. Guo & al., Passive radar detection using wireless networks, International IET Conference on Radar Systems (2007) [1] K. Chetty & al., Through-the-Wall Sensing of Personnel Using Passive Bistatic WiFi Radar at Standoff Distances, IEEE Trans. Geoscience & Remote Sensing (2012) In this paper, we investigate the feasibility of uncooperatively and covertly detecting people moving behind walls using passive bistatic WiFi radar at standoff distances. A series of experiments was conducted which involved personnel targets moving inside a building within the coverage area of a WiFi access point. These targets were monitored from outside the building using a 2.4-GHz passive multistatic receiver, and the data were processed offline to yield range and Doppler information. The results presented show the first through-the-wall (TTW) detections of moving personnel using passive WiFi radar. The measured Doppler shifts agree with those predicted by bistatic theory. Further analysis of the data revealed that the system is limited by the signal-tointerference ratio (SIR), and not the signal-to-noise ratio. 3 / 23.

(4) Noise RADAR and passive RADAR interrogation of passive wireless sensors. Passive, wireless sensor characteristics. J.-M Friedt & al.. • Underlying philosophy: delay sensor response beyond clutter • Convert electromagnetic waves to the 105 times slower acoustic wave • 1-2 µs delay introduced by a 1.5-3 mm long acoustic path • Surface Acoustic Wave (SAW) delay line up to 2.5 GHz (lithography limitation: λ = 1.2 µm) • High-overtone Bulk Acoustic Resonator above (4.2 GHz here). Spectrum spreading Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix Trc1. S11 dB Mag 1 dB/ Ref -6 dB. Cal int. Trc3. S22 dB Mag 0.5 dB/ Ref -3 dB Cal int. Trc1. -1. -3. R 4.306958 GHz -12.5764 dB ΔM1 9.926000 MHz -1.3726 dB. 2 -1. -4. -4. -5. -7. -6-6dB. -10dB -10. RSSI CTR. -7 -8 -9 -10. R ∆M1. -13 -16 -19 -22. -11. -25. Ch1 Start 2.4 GHz Trc2. S11 dB Mag 3 dB/ Ref -10 dB. 5. WiFi chan. 3. -2. Pwr -10 dBm Bw 10 kHz. S11 dB Mag 10 dB/ Ref -80 dB Cal int. -30 -40. M1. Trc4. Stop 2.48 GHz. S22 dB Mag 10 dB/ Ref -80 dB Cal int. 2. M2. M1. -50 -60. M2. M1 863.000 ns -41.9305 dB M2 2.293 µs -41.7276 dB M1 993.200 ns -41.9452 dB M2 2.193 µs -44.3469 dB. -70. Trc2. Pwr -10 dBm Bw 1 kHz. -10 -20. Span 200 MHz. S11 dB Mag 10 dB/ Ref -40 dB. 2 R 302.700 ns -26.2081 dB ΔM1 -102.600 ns 7.7962 dB. 0. ∆M1. R. -30. -80dB -80. -40dB -40. -90. -50. -100. -60. -110. -70. -120 -130. Trc2 Start 100 ns. Ch1 Center 4.307 GHz. 10. Time Domain. Stop 3 µs. -80 -90. Ch1 Center 4.307 GHz. Pwr -10 dBm Bw 1 kHz. Span 200 MHz. Commercial, off the shelf acoustic reflective delay lines provided by RSSI & CTR HBAR characterization Frequency (top) & time (bottom) domain characterization of transducers 4 / 23 Trc2 Start. 100 ns. Time Domain. Stop 2 µs.

(5) Noise RADAR and passive RADAR interrogation of passive wireless sensors. Spectrum spreading numerical experiments. J.-M Friedt & al.. Carrier frequency and bandwidth are two unrelated quantities which can be tuned independently for matching each sensor spectral characteristics. Noise RADAR. Binary Phase shift keying: ϕ ∈ [0; π] for spectrum spreading. Passive RADAR DSI Measurement Antenna array. Conclusion. power (no unit). Spectrum spreading. 60000 50000 40000 30000 20000 10000 0. 200. 400. 800. 1000. 1200. pure sine -1. Appendix. 600. time (no unit). time=[0:0.02:1023];time=time(1:end-1); signal=exp(j*2*pi*time); f=linspace(-1,1,length(time)); plot(f,abs(fftshift(fft(signal))));. -0.5. 0. 0.5. 1. power (no unit). normalized frequency (no unit) 25000. indices=[1:100:length(signal)-50]’... *[ones(1,50)]+[0:49]; signal(indices)=-signal(indices);. 20000 15000 200. 10000. 400. 600. 800. 1000. 1200. time (no unit). periodically modulated sine. 5000 0 -1. -0.5. 0. 0.5. 1. power (no unit). normalized frequency (no unit) 4000 3500 3000 2500 2000 1500 1000 500 0. c=cacode(11,50)*2;c=c-mean(c); signal=signal.*c; 200. 400. 600. 800. 1000. 1200. time (no unit). pseudo randomly modulated sine -1. -0.5. 0. normalized frequency (no unit). 0.5. 1. 5 / 23.

(6) Noise RADAR and passive RADAR interrogation of passive wireless sensors. Spectrum spreading numerical experiments. J.-M Friedt & al.. Carrier frequency and bandwidth are two unrelated quantities which can be tuned independently for matching each sensor spectral characteristics. Noise RADAR. Binary Phase shift keying: ϕ ∈ [0; π] for spectrum spreading. Antenna array. Conclusion Appendix. 1.15 1.1 1.05 1 0.95 0.9 0.85. pure sine (xcorr(signal, ’unbiased’)). 0. 20000. 40000. 60000. 80000. 100000. 80000. 100000. delay (no unit) 1.4 1.2 1 0.8 0.6 0.4 0.2 0. periodically modulated sine. 0. 20000. 40000. 60000. delay (no unit) 60000 50000 40000 30000 20000 10000 0. pseudo randomly modulated sine. autocorr (no unit). Measurement. autocorr (no unit). DSI. autocorr (no unit). Passive RADAR. autocorr (no unit). Spectrum spreading. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 50. 100. 150. 200. delay (no unit). 0. 20000. 40000. 60000. delay (no unit). 80000. 100000. 6 / 23.

(7) Noise RADAR. Range (delay) resolution ∝ bandwidth 1/B ⇒ maximize B, ∀fc • • • • •. short pulse = broadband spectrum (pulse RADAR) frequency sweep and measure scattering coefficient at each frequency (FSCW) linear frequency sweep and beatnote ∝ delay (FMCW) pseudo random phase modulation of carrier: noise RADAR Binary Phase Shift Keying (BPSK) by mixing carrier frequency (LO) with 20-bit long pseudo-random R sequence generator (IF) • Correlation (τ ) = r (t)m(t + τ )dt. J.-M Friedt & al. Spectrum spreading Noise RADAR Passive RADAR DSI Measurement Antenna array. FPGA PRNG. IF LO. surveillance channel. SAW delay line. RF 2.42 GHz. reference channel 3000. HBAR port1. no sensor+40 20 cm 60 cm. 200. HBAR port2 50 ohm load 2000. 150. 1000. |xcorr(ref,mes)| (a.u.). Appendix. auto-correlation imaginary part (a.u.). Conclusion. oscilloscope. Noise RADAR and passive RADAR interrogation of passive wireless sensors. sensor response 100. 0. -1000. 50 -2000. 0 0. 1. 2. time (us). 3. 4. 0.2 and 0.6 m range, SAW delay line. 5. -3000 -0.2. 0. 0.2. 0.4. 0.6. 0.8. 1. time (us). fc = 4.3 GHz, 150 MHz bandwidth, HBAR7 / 23.

(8) Noise RADAR and passive RADAR interrogation of passive wireless sensors. Passive RADAR • Radiofrequency spectrum is a scarce resource ⇒ strong regulations on emission • Solve certification challenge by using existing emitters • Detect time-delayed copies of the emitted signal: static target detection (no frequency transposition SNR improvement).. J.-M Friedt & al. Spectrum spreading Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion. oscilloscope. Appendix. Tx. Rx. ref LO. WiFi. surv. • • • • •. WiFi emitter as (pseudo-random) signal source (monitoring mode) Out-of-band downconversion (prevent WiFi from dropping connection) Collect (coupled channel) the reference signal Observe the suveillance signal Measurement duration improves SNR, while source bandwidth defines timing resolution. 8 / 23.

(9) Noise RADAR and passive RADAR interrogation of passive wireless sensors. Passive RADAR: signal processing • Cross-correlation magnitude for coarse estimate of the echo delays • Each WiFi channel is 15 MHz wide (=67 ns resolution). J.-M Friedt & al. Spectrum spreading. • Multiple channel accumulation for increased bandwidth: WiFi channels 1..11=2.412..2.462 MHz (' 15 ns resolution) • All data collected at the same rate and different carrier frequencies: sum in the frequency domain after mixing with fixed LO. Noise RADAR Passive RADAR DSI Measurement Antenna array. 30000. Appendix. chan 3. power (a.u.). 25000. chan 5. 20000. chan 7. 15000 10000 5000 0 -150. -100. -50. 0. 50. 100. 150. cross-correlation amplitude (a.u.). Conclusion 1e+06 chans 3+5+7 800000 600000 400000 200000 0 0. 1. 2. frequency offset (MHz). chan 3. power (a.u.). 25000 20000 15000 10000 5000 -100. -50. 0. frequency offset (MHz). 50. 100. 150. cross-correlation amplitude (a.u.). 30000. 0 -150. 3. 4. 5. time (us) 250000 chan. 3 200000 150000 100000 50000 0 0. 1. 2. 3. 4. 5. time (us). 8-echo delay line, recorded with WiFi channels 3-5-7 (2422, 2432, 2442 MHz) 9 / 23.

(10) Spectrum spreading Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. • Ideal noise: correlation = Dirac function @ delay 1 • WiFi signal: correlation within signal hides delayed echoes • Least square method for Direct Signal 0.8 Interference removal: t −1 t DSIweights = (X · X ) · X ·meas {z } | pinv(X) with 0.6  ref1  ref2  X =  ref3  ref 4 .... 0 ref1 ref2 ref3. 0 0 ref1 ref2. 0 0 0 ref1. |xcorr|. J.-M Friedt & al.. Direct Signal Interference removal.    . 0.4. 1e+07 no DSI removal 0 delay. cross correlation absolute value (a.u.). Noise RADAR and passive RADAR interrogation of passive wireless sensors. 0-60 ns delay. 8e+06. 0-160 ns delay. 6e+06. 0.2 s oe ch re so. 4e+06. n. se 2e+06. 0 0. 0. 1000. 2000. 3000. delay (ns). 4000. 5000. 6000. 0.5. 1. 1.5. 2. time (us). 2.5. 3 10 / 23.

(11) Noise RADAR and passive RADAR interrogation of passive wireless sensors. Temperature measurement • Fine time delay τ measured as a phase: ϕ = 2πfc τ • Correlation is a linear operation: phase is conserved • Correlation phase difference for acoustic velocity measurement independent of range. J.-M Friedt & al. Spectrum spreading Noise RADAR Passive RADAR. 100. Antenna array. Conclusion Appendix. 80 60 40 20 0. -20. 0. 100. 200. 300. 400. 500. 600. 700. 800. 500. 600. 700. 800. time (s) relative temperature (K). Measurement. -phase (rad). DSI. 100 80. SAW sensor (-76 ppm/K) Pt100 probe. 60. Example of temperature measurement: the sensor is heated twice – temperature sensitivity taken as -76 ppm/K (YXl/128◦ LNO). 40 20 0. -20. std(1:140)=0.1 K 0 100 200. 300. 400. time (s). dϕ/ϕ · (1/T ) , S = 60 ppm/K⇒ T = dϕ/ϕ · (1/S) = dϕ/(S · 2πf τ ) 11 / 23.

(12) Noise RADAR and passive RADAR interrogation of passive wireless sensors J.-M Friedt & al.. Receiver antenna array Problem of collision: how to separate the signals from two sensors visible from the surveillance antenna ? dk. τk =. Spectrum spreading. sin(ϑ). ϑ. Noise RADAR Passive RADAR DSI. d. Measurement Antenna array. dk. .... Conclusion. 1→8. Appendix. Narrowband – B c/(Kd) = 680 MHz h– plane wave approxii mation: mes = ref (t)a(ϑ) with a(ϑ) = exp(j2π kd sin ϑ ) , λ k = 0..K=7 ⇒ mes · conj(a) for focusing in time-ϑ plane ϑ3dB = 0.89λ rad=15◦ since d = λ and K = 7 Kd 2. • antenna array for spatial separation. 1. (8 dipoles separated by λ/2 = 6.25 cm). • all antennas must see all sensors (6= cantennas, too directional) • switch between antennas, extract complex correlation, and apply inverse phase due to time of flight (SAR processing) • ... alternatively, move a single antenna to known positions 1 G.. Charvat, Small and short range RADAR systems, CRC Press (2014), p.300 12 / 23.

(13) Problem of collision: how to separate the signals from two sensors visible from the surveillance antenna ? M1 993.200 ns -41.9452 dB M2 2.193 µs -44.3469 dB. 3. Spectrum spreading. DSI Measurement Antenna array. 2. Time Domain. bistatic time delay (us). Passive RADAR. M2. 2.5. Noise RADAR. Stop 3 µs. J.-M Friedt & al.. Receiver antenna array. 1.5. M1. 1. • antenna array for spatial separation. -120 -130. -100. -110. -90. -70. 50. -50. 0. angle (deg). -30. -50. -60. 0.5. -40. Appendix. -80dB -80. Conclusion. Trc2 Start 100 ns. Noise RADAR and passive RADAR interrogation of passive wireless sensors. 1. (8 dipoles separated by λ/2 = 6.25 cm). • all antennas must see all sensors (6= cantennas, too directional) • switch between antennas, extract complex correlation, and apply inverse phase due to time of flight (SAR processing) • ... alternatively, move a single antenna to known positions 1 G.. Charvat, Small and short range RADAR systems, CRC Press (2014), p.300 13 / 23.

(14) Noise RADAR and passive RADAR interrogation of passive wireless sensors J.-M Friedt & al.. Receiver antenna array Problem of collision: how to separate the signals from two sensors visible from the surveillance antenna ? 3. Spectrum spreading. 500000 2.5. bistatic time delay (us). Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. 400000 2 300000. 1.5 200000. 1 100000. 0.5 -50. 0. 50. angle (deg). • antenna array for spatial separation. 1. (8 dipoles separated by λ/2 = 6.25 cm). • all antennas must see all sensors (6= cantennas, too directional) • switch between antennas, extract complex correlation, and apply inverse phase due to time of flight (SAR processing) • ... alternatively, move a single antenna to known positions 1 G.. Charvat, Small and short range RADAR systems, CRC Press (2014), p.300 14 / 23.

(15) Noise RADAR and passive RADAR interrogation of passive wireless sensors J.-M Friedt & al.. Receiver antenna array Problem of collision: how to separate the signals from two sensors visible from the surveillance antenna ? 3. Spectrum spreading. bistatic time delay (us). 500000. Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. CTR. 2.5. RSSI 400000. 2 300000. 1.5. 200000. 1. 0.5. • antenna array for spatial separation. 100000. -50. 0 angle (deg). 50. 1. (8 dipoles separated by λ/2 = 6.25 cm). • all antennas must see all sensors (6= cantennas, too directional) • switch between antennas, extract complex correlation, and apply inverse phase due to time of flight (SAR processing) • ... alternatively, move a single antenna to known positions 1 G.. Charvat, Small and short range RADAR systems, CRC Press (2014), p.300 15 / 23.

(16) Noise RADAR and passive RADAR interrogation of passive wireless sensors J.-M Friedt & al.. Receiver antenna array Problem of collision: how to separate the signals from two sensors visible from the surveillance antenna ? 3. Spectrum spreading. 600000 2.5. bistatic time delay (us). Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion. 500000. 2. 400000. 300000 1.5. 200000. Appendix. 1 100000. 0.5. 0 -80. -60. -40. -20. 0. 20. 40. 60. 80. angle (deg). • antenna array for spatial separation. 1. (8 dipoles separated by λ/2 = 6.25 cm). • all antennas must see all sensors (6= cantennas, too directional) • switch between antennas, extract complex correlation, and apply inverse phase due to time of flight (SAR processing) • ... alternatively, move a single antenna to known positions 1 G.. Charvat, Small and short range RADAR systems, CRC Press (2014), p.300 16 / 23.

(17) SAR processing Fixed distance (50 cm) from dipole array to sensor axis. Varying distance between sensors with a broader antenna:. Spectrum spreading 3. 3. 400000. DSI. 300000. Measurement. 200000. 600000. CTR. 500000. 2 400000. 300000. 1.5. 200000. Antenna array. 400000 1.5 300000. -20. 0. 20. 40. 60. 0.5. CTR. 2. 1.5. 1. 80. 100000. 0 -80. -60. angle (deg). -40. -20. 0. 20. 40. 60. 0.5. 80. 0 -80. -60. angle (deg). -40. -20. 0. 20. 40. 60. 0.5. 80. -80. -60. -40. angle (deg). -20. 0. 20. 40. 60. 80. angle (deg). 16 cm 39 cm 47 cm 65 cm Varying position with fixed distance between sensors (broader antenna) 3. 3. 3. 700000. 400000 600000 600000. 350000. RSSI CTR. 2.5. RSSI. 2.5 300000. 2. 250000. 200000 1.5 150000. CTR. RSSI CTR. 2.5 500000. 2. 400000. 300000 1.5. 200000. bistatic time delay (us). -40. 500000. 100000. 0. bistatic time delay (us). -60. 600000. 2. RSSI. 2.5. 1. 100000. Conclusion -80. 700000. CTR. 200000 1. 0.5. Appendix. RSSI. 2.5. bistatic time delay (us). bistatic time delay (us). 500000. Passive RADAR. RSSI. 2.5. 2. 1. 3 800000. 600000. Noise RADAR. 1.5. 3. 700000. 700000. RSSI CTR. 2.5. bistatic time delay (us). J.-M Friedt & al.. bistatic time delay (us). bistatic time delay (us). Noise RADAR and passive RADAR interrogation of passive wireless sensors. 500000. 2 400000. 300000. 1.5. 200000. 100000 1. 1. 1 100000. 100000. 50000. 0.5. 0 -80. -60. -40. -20. 0. 20. 40. 60. angle (deg). 28 cm left. 80. 0.5. 0 -80. -60. -40. -20. 0. 20. 40. angle (deg). 28 cm. 60. 80. 0.5. 0 -80. -60. -40. -20. 0. 20. 40. 60. 80. angle (deg). 28 cm right. Emitting & sensor antennas: Huber-Suhner SPA-2400/70/9/0/LCP (8.5 dBi, 70◦ horiz. beamwidth @ 3 dB). 17 / 23.

(18) Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. xcorr (a.u.). Noise RADAR. 40 30 20 10 0 -10 -20 -30. xcorr (a.u.). Spectrum spreading. 40 30 20 10 0 -10 -20 -30. xcorr (a.u.). J.-M Friedt & al.. What about resonators ?. • Delay line: discrete delays easy to interpret • Resonator: continuous exponential decay of returned signal ... • nevertheless, correlation = impulse response of system. • ⇒ noise radar interrogation of resonators exhibits the exponentially decaying response, with an amplitude dependent on emitted signal bandwidth. • Q ' 2000 @ f = 2.4 GHz ⇒ decay time constant is Q/(πf ) = 260 ns' 1/4 MHz ⇒ how to recover a frequency with kHz resolution (Prony, Levenberg-Marquardt [2]) ? SAW Components 2.4 GHz resonator 40 30 20 10 0 -10 -20 -30. xcorr (a.u.). Noise RADAR and passive RADAR interrogation of passive wireless sensors. 40 30 20 10 0 -10. BW=300/16 MHz. 0. 0.2. 0.4. 0.6. 0.8. 1. time (us). BW=300/8 MHz. 0. 0.2. 0.4. 0.6. 0.8. 1. time (us). BW=300/4 MHz. 0. 0.2. 0.4. 0.6. 0.8. 1. time (us). BW=300/2 MHz. 0. 0.2. 0.4. 0.6. 0.8. 1. time (us). [2] J.-M Friedt & al, High-overtone Bulk Acoustic Resonator as passive Ground Penetrating RADAR cooperative targets, J. Appl. Phys 113 (13), 134904 (2013). 18 / 23.

(19) J.-M Friedt & al. Spectrum spreading Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. Conclusion • Demonstrated noise RADAR interrogation of passive wireless sensors using a dedicated, pseudo-random BPSK modulated source • Demonstrated passive RADAR interrogation of passive wireless sensors using a COTS WiFi transceiver • DSI removal to extract useful signal from non-cooperative emitter auto-correlation • Physical quantity measurement through correlation phase analysis • Antenna array for source separation Outlook: fully embedded implementation based on Redpitaya/Zynq 7010 + on-board processing. Redpitaya DSI removal + xcorr. Noise RADAR and passive RADAR interrogation of passive wireless sensors. dipole SLP−200+. 2. 31.25 MHz NCO 2. ZX60−8008E−S+ ZX05−63−LH−S+. ADC1. 1:8. f+31.25 MHz PLL (Windfreak SynthUSB). HMC321 ZX10−2−42−S+. SPA−2400/70/9/0 LCP. ZX60−3018G ZX−30−17−5−S+. ADC2 SLP−200+. ZEM−4300MH+. Wifi dongle. References: [3] W. Feng, J.-M. Friedt, G. Goavec-Merou, M. Sato, Passive RADAR measurement of acoustic delay lines used as passive sensors, accepted IEEE Sensors (Sept. 2018). 19 / 23.

(20) Noise RADAR and passive RADAR interrogation of passive wireless sensors. Appendix. J.-M Friedt & al. Spectrum spreading Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. Least square parameter identification (demonstration by G. Cabodevila): • Output y is a weighted sum of inputs x with noise ε. • We want to identify weights ϑ from observations of y . P 2 • y = xϑ + ε minimizing the error e = e t e with e = y − xϑ • Criteria J = (Y −X Θ)t (Y −X Θ) = Y t Y −(X Θ)t Y − Y t X Θ+(X Θ)t X Θ = Y t Y −Θt X t Y − Y t X Θ + Θt X t X Θ ∂J • ⇒ ∂Θ = 0 − X t Y − (Y t X )t + 2X t X Θ = −2X t Y + 2X t X Θ = 0 at extremum • ⇒ 2X t X Θ = 2X t Y ⇔ Θ = (X t X )−1 X t Y = pinv(X ) Reminder2 :. ∂v t a ∂v. =. ∂at v ∂v. =a. 2 https://atmos.washington.edu/. ~dennis/MatrixCalculus.pdf 20 / 23.

(21) Noise RADAR and passive RADAR interrogation of passive wireless sensors. gr-oscilloscope real time display. J.-M Friedt & al. Spectrum spreading Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. • radiofrequency-grade oscilloscope (100 MHz=10 ns=3 m range resolution) used as real data source • two synchronous channels provide reference and measurement • feed GNURadio with streams of discontinuous measurements from a multi-channel oscilloscope • custom block gr-oscilloscope easily adapted to any oscilloscope (here VXI11, could be GPIB or USBTMC). Autocorrelation ↑ – Crosscorrelation ↓. github.com/jmfriedt/ gr-oscilloscope 21 / 23.

(22) Noise RADAR and passive RADAR interrogation of passive wireless sensors J.-M Friedt & al. Spectrum spreading Noise RADAR Passive RADAR DSI Measurement Antenna array. Conclusion Appendix. github.com/jmfriedt/gr-oscilloscope. 22 / 23.

(23) 60. X is Nsamples ' 216 to 220 long and Ndelay ' 26 wide. 100 samples along 0.5x+3 100 samples: 0.496x+3.834 50. 15 samples 15 samples: 0.505x+3.715. (4 ns sampling ⇒ 104 ns delay or 31 m 1-2.5 µs echoes). 40. • Reduce computation time by selecting a random subset of the Nsamples lines • Reduce computation time by selecting a subset of linear combinations of the Nsamples lines • Improve DSI identification with sub-sampling period accuracy [2] y (no unit). Noise RADAR and passive RADAR interrogation of passive wireless sensors. 30. 20. J.-M Friedt & al.. 10. Spectrum spreading. 0. Noise RADAR. 0. 20. 40. x (no unit). 60. 80. Passive RADAR. Antenna array. Conclusion Appendix. Idx1=0;Idx2=26; X1=zeros(nt,Idx2-Idx1);te=1; for kk=Idx1:Idx2 % full matrix X1(:,te)=[zeros(kk-1,1); ref(1:end-kk+1)]; te=te+1 end. 26 sampling steps (104 ns) indices=randi(length(X1),4096,1); X1s=X1(indices,:); % matrix subset meas=meas-X1*(pinv(X1s)*meas(indices));. X1: 1048576×27 → X1s: 4096× 27 cross-correlation amplitude (a.u.). Measurement. cross-correlation amplitude (a.u.). DSI. 250000 chan. 3 200000 150000 100000 50000 0 0. 1. 2. 3. 4. time (us). Elapsed time is 7.40 seconds.. 5. 500000 chan. 3 400000 300000 200000 100000 0 0. 1. 2. 3. 4. 5. time (us). Elapsed time is 0.08 seconds.. [4] W. Feng, J.-M Friedt & al. Direct path interference suppression for short range passive bistatic SAR imaging based on atomic norm minimization and Vandermonde decomposition, submitted IET Radar, Sonar & Navigation 23 / 23.

(24)