Virtual multi-antenna arrays for radio transmitter bearing estimation or How to do synthetic aperture radar with cell phones ? François Quitin Université libre de Bruxelles (ULB), Belgium Brussels School of 1 Engineering
Virtual AOA estimation / Synthetic aperture radar we want to measure the AOA of a Tx • Tx sends multiple packets (e.g. synch ’ signal) • Rx receives packets at multiple points along its trajectory each received packet can be seen as a « virtual » antenna element conventional MIMO AOA techniques Brussels School of 2 Engineering
Outline Virtual AOA estimation • Method description Difference with conventional MIMO AOA • Algorithms for LO offset and AOA estimation • IMU sensor processing • Implementation and results Brussels School of 3 Engineering
Difference between V-AOA and MIMO-AOA 2 main differences in V-AOA case: 1) Position of « virtual antenna elements » depends on the λ /2 movement of Rx Tx λ /2 2) LO offset introduce phase Rx rotation in received trajectory packets Tx Brussels School of 4 Engineering
LO offset between Tx and Rx … introduces a phase rotation in Rx packets • LO offset between Tx and Rx net effect: frequency difference/offset 𝜕 0 between Tx and Rx • Receiver receives different packets (suppose no movement): – at time 𝑢 0 : 𝑠 𝑛 – at time 𝑢 1 : 𝑠 𝑛 𝑓 𝑘2𝜌𝑔 0 𝑢 1 −𝑢 0 – at time 𝑢 2 : 𝑠 𝑛 𝑓 𝑘2𝜌𝑔 0 𝑢 2 −𝑢 0 Rx does Tx not move Brussels School of 5 Engineering
AOA estimation: system description System model • Transmitter sends packet with known header • Receiver correlates received baseband samples with (known) header Phase of peak of correlation function corresponds to the phase of the channel • In a Line-of-Sight case (and periodic Tx), the angle is given by 0 + 2𝜌 𝜒 𝑜 = 𝜒 0 + 2𝜌𝑔 0 𝑜𝑈 𝑦 𝑜 cos 𝜄 + 𝑧 𝑜 sin 𝜄 𝜇 𝑢 𝑜 time elapsed between packet 0 and n 𝑦 𝑜 change in x-coordinates between packet 0 and n 𝑧 𝑜 change in y-coordinates between packet 0 and n Brussels School of 6 Engineering
AOA estimation: system description Difference with conventional MIMO 𝜒 𝑜 = 𝜒 0 + 2𝜌 𝑦 𝑜 cos 𝜄 + 𝑧 𝑜 sin 𝜄 𝜇 λ /2 Tx λ /2 Rx trajectory Tx 0 𝑜𝑈 0 + 2𝜌 𝜒 𝑜 = 𝜒 0 + 2𝜌𝑔 𝑦 𝑜 cos 𝜄 + 𝑧 𝑜 sin 𝜄 𝜇 Brussels School of 7 Engineering
Outline Virtual AOA estimation • Method description Difference with conventional MIMO AOA • Algorithms for LO offset and AOA estimation • IMU sensor processing • Implementation and results Brussels School of 8 Engineering
LO offset and angle estimation Start- and-stop (SaS) approach • Step 1: Receiver stands still Only LO frequency offset cause phase to change Rx does Tx not move • Step 2: Receiver starts moving Rx trajectory LO frequency offset is compensated: Conventional MIMO estimation can be used Tx (MUSIC, ESPRIT, …) • Works if LO frequency offset does not change during movement phase Movement should be short Compatible with WSSUS assumption! Brussels School of 9 Engineering
LO offset and angle estimation Joint estimation The signal model used in MUSIC can be augmented to accound for LO frequency offset 𝐳 𝑛 = 𝐛 𝑔 0 , 𝜄 𝑦 𝑛 + 𝐱[𝑛] with 0 𝑢 1 + 2𝜌 exp 𝑘 2𝜌𝑔 𝑦 1 cos 𝜄 + 𝑧 1 sin 𝜄 𝜇 0 𝑢 2 + 2𝜌 exp 𝑘 2𝜌𝑔 𝑦 2 cos 𝜄 + 𝑧 2 sin 𝜄 𝐛 𝑔 0 , 𝜄 = 𝜇 ⋮ 0 𝑢 𝑂 + 2𝜌 exp 𝑘 2𝜌𝑔 𝑦 𝑂 cos 𝜄 + 𝑧 𝑂 sin 𝜄 𝜇 MUSIC (or beamforming) can use this signal model and do joint search over 𝑔 0 and 𝜄 Brussels School of 10 Engineering
Outline Virtual AOA estimation • Method description Difference with conventional MIMO AOA • Algorithms for LO offset and AOA estimation • IMU sensor processing • Implementation and results Brussels School of 11 Engineering
LO offset and angle estimation Determining 𝒚 𝒐 and 𝒛 𝒐 • Fraction of wavelength accuracy required Rx trajectory D-GPS insufficient! • If antenna non-isotropic: orientation required • Only relative position is required • WSSUS assumption Movement should be limited • We use a 3D-Inertial Measurement Unit (IMU) Contains accelerometers and gyroscopes Solution will drift from truth, but integration time is short due to WSSUS, so error will remain limited Brussels School of 12 Engineering
Strap-down IMU = IMU attached to vehicle • accelerometers => measures acceleration along each axis • gyroscope => measures angular speed around each axis – Measurements are done in body frame , but positions needs to be known in navigation frame – Note: gravitation of ~9.78 m/s^2 (along D-axis) is always measured by accelerometer(s) Brussels School of 13 Engineering
IMU processing Can be processed in EKF/UKF • Initial position/orientation need to be known Initial Orientation Angular speeds (rad/s) Accelerations (m/s^2) • Problems: 1) how to estimate initial orientation ? => use gravitation vector 2) how to estimate IMU biases ? => calibration procedure 3) Augment stability by using nonholonomic constraints Brussels School of 14 Engineering
Outline Virtual AOA estimation • Method description Difference with conventional MIMO AOA • Algorithms for LO offset and AOA estimation • IMU sensor processing • Implementation and results Brussels School of 15 Engineering
Implementation Transmitter and receiver: USRP-N210 • Carrier frequency: 1 GHz • Tx and Rx use GPSDO with OCXO LO (20 ppb accuracy) • Tx sends 3G primary sequence – 128 samples long @ 1.8 MHz sample rate – Periodicity: 0.667 ms, but only one transmitter packet out of 15 considered 𝑈 0 = 10 ms • Rx sample rate = 3.6 MHz Brussels School of 16 Engineering
Implementation Receiver details • Rx performs correlation in FPGA Sends both correlation function (« peaks ») and BB samples to host • Rx accumulates 3 peaks (host processor) Increased SNR • Peak detector in host processor receiver Phase of peak is written to output file • IMU: XSens MTi-10 (automotive- grade) • Parallel thread to read IMU data @ 200 Hz IMU values written to output file Brussels School of 17 Engineering
Experimental setup in anaechoic chamber => only LOS • IMU z-axis placed parallel to vertical axis Error of few ° cannot be avoided! • Turntable still for 30 s then turned by 180° (about 5 s) Radius of 30, 40 and 50 cm Brussels School of 18 Engineering
Experimental setup note the « vertical » IMU placement antenna IMU USRP-N210 turntable Brussels School of 19 Engineering
IMU processing Initial orientation: (pitch,roll)=( -0.79°, 3.18°) g along z-axis Small acceleration Rotation around and deceleration z-axis along x-axis Speeds mainly along x-axis Yaw changes from 180° to 0° Speeds along y-axis: - Centrifugal force - Integration errors Brussels School of 20 Engineering
IMU processing Final estimated trajectory • Estimated trajectory drifts off at the end of movement • Room for improvement! – Introduce nonholonomic constraints (already done for standstill) – Improve bias estimation – Improve EKF/UKF parameters (requires to know process model accurately) Brussels School of 21 Engineering
AOA estimation Stop-and-Start approach Phase noise and Phase before freq. offset compensation 7 Packet phases drift 6 5 after LO offset Phase (rad) 4 3 compensation 2 1 Packet phases 0 16 16.5 17 17.5 Time (s) before LO offset Phase change due compensation to movement Rx movement MUSIC spectrum from IMU with peak close to 90° Brussels School of 22 Engineering
AOA estimation SaS approach: notes about MUSIC AOA estimation error – Zero-mean – Standard deviation Larger (virtual) arrays have better accuracy Consistent with conventional MIMO theory Brussels School of 23 Engineering
AOA estimation Joint estimator • Augmented signal model – joint search over 𝑔 0 and 𝜄 Brussels School of 24 Engineering
AOA estimation Joint estimator AOA estimation error – Zero-mean – Standard deviation Larger (virtual) arrays have better accuracy Performance of joint estimation worse than SaS approach, but more flexible ! Brussels School of 25 Engineering
E-310 implementation Why? • Why not ? • Use embedded IMU and SDR • Test with low(er)-quality IMU and TCXO • Possible to mount on (autonomous) vehicles Brussels School of 26 Engineering
E-310 implementation Architecture USRP E310 Filter AD 9361 XILINX ZYNQ 7020 banks RFIC Artix-7 FPGA PS-Dual Core ARM A9 Capturing IMU and RF Correlator and peak detector data IMU processing MUSIC algo. Tx chains and 2 nd Rx chain deactivated GPS receiver IMU Brussels School of 27 Engineering
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