gr-doa: Direction Finding in GNU-Radio

Transcription

1 gr-doa: Direction Finding in GNU-Radio GRCon 2017 Travis F. Collins, PhD Srikanth Pagadarai, PhD September 12, 2017

2 Sponsors T. Collins 1

3 Outline Project Background MUSIC Hardware options USRP-N210 X300/X310 FMComms5 Antenna Calibration Test and Results EADF Feasibility Test and Results T. Collins 2

4 WiFiUS Project Collaboration Collaboration Outline Phase 1: Baseline DoA SDR implementation and analysis (gr-doa) Phase 2: Link based DoA with TUT DoA modeling specifics (EADF) T. Collins 3

5 Algorithms in gr-doa DoA Algorithms Classical (Beamformers) Subspace Noise Subspace Signal Subspace Search Algebraic Search Algebraic Delay-and-Sum MuSIC Minimum Variance ESPIRIT MVDR FFT-EADF MODE Pisarenko Root-MuSIC Subspace Finding Autoregressive LS-ESPIRIT TLS-ESPIRIT T. Collins 4

6 Phased Array Direction Finding Basics Basics: Signal is planar (far field) Antenna elements have a fixed and known phase Antenna positions are known Signal has limited correlation between elements T. Collins 5

7 ULA: Phased Array Model Element positioning in reference to array center: ( p zn = 0, p yn = 0, p xn = n N 1 ) d, n = 0, 1,..., N 1, 2 Received signal cascaded delays: u z = sin(θ) cos(φ), u y = sin(θ) sin(φ), u x = cos(θ), u := [u z u y u x ] T k(θ, φ) = 2π λ u = 2π λ [sin(θ) cos(φ) sin(θ) sin(φ) cos(θ)]t. Array manifold vector: ] T v(k) = [e jkt p 0 e jkt p 1... e jkt p N 1 T. Collins 6

8 DoA Baseline: MUSIC MUSIC: Multiple Signal Classification Gain (db) N=4 N=8 N= angle (degrees) R. Schmidt, Multiple emitter location and signal parameter estimation, in IEEE Transactions on Antennas and Propagation, vol. 34, no. 3, pp , Mar Received signal model: x(t) = D u d (t)v(k d ) + n(t) d=1 MUSIC subspace principles: [ R xx = E x x H] = V R uu V H + I σ 2 U N C (N D)xN, U S C DxN v H (k d )U N = 0 1 P MUSIC = v H (k(θ, φ))u N U H Nv H (k(θ, φ)) T. Collins 7

9 MUSIC: Estimation Performance SNR=10dB SNR=0dB 1.5 RMSE (Degrees) DoA (Degrees) Mean RMSE (Degrees) L { L [ var(θ) σ2 Re [u (k) vh 2 θ I N v(v H v) 1 v H] ] } 1 v θ u(k) k=1 L = snapshot length P. Stoica and A. Nehorai, MUSIC, maximum likelihood, and Cramer-Rao bound, in IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 5, pp , May T. Collins 8 [?]

10 Estimation Blocks T. Collins 9

11 GUI Real-time visuals QT Compass Pseudo spectrum (MUSIC block only) T. Collins 10

12 N210 Based Array Construction (First Try) Array Fixture d= λ 2 for fc = 2.45 GHz Same length cabling between components Radios and Software Utilizing 4xUSRP N210 radios Octoclock provides MB frequency and PPS sampling signals Not phased aligned GNURadio prototyping platform T. Collins 11

13 Remaining Phase Offset 10 khz tone sent into 3xUSRPs through splitter and matched cabling T. Collins 12

14 USRP Phase Correction Harness System Details OctoClock X8 REF and X8 PPS REF SMA Splitter 0 USRP TX REF Outputs PPS Degree Two Phase Start: REF TX/RX 1. Transmit tone into secondary port (TX/RX) 2. Once corrected disable Sync TX PPS REF PPS USRP USRP RX TX/RX RX Can calibrate any daughterboard(s) REF PPS USRP TX/RX RX φ n = tan 1 (r n ) tan 1 (r k ) REF TX/RX ˆr n = r n exp(j φ n ) PPS USRP RX Open and closed loop versions T. Collins 13

15 Array Cart T. Collins 14

16 X300/X310 TwinRx Array Still needs calibration Better phase stability Limited to 4-RX Easier to carry around! T. Collins 15

17 FMComms5 Array Self phase calibrating! T. Collins 16

18 DOA: Error Sources Remaining Possible Sources of Error Phase drift between radios over time (Physical) Positioning error (Physical) Antenna gain and phase missmatches (Physical) Reflections in environment (Physical) Possible errors in software implementation (Software) T. Collins 17

19 MUSIC: Positioning Error 3 Modified signal model RMSE (Degrees) [40-140] x(t) = D u d (t)ˆv(k d ) + n(t) d=1 Position Error s k = N(0, σ 2 ) ] T ˆv(k d ) = v(k d ) + [s 1, s 2,..., s D STD λ T. Collins 18

20 MUSIC: Testbed Refinement Array 1 Pegboard Array 0 Transmitte r Positioning Moved to pegboard for precise positioning +/ tolerance 0.028λ (0.7 Degree RMSE) T. Collins 19

21 MUSIC: Antenna Calibration Implemented subspace processing method for antenna calibration Only phase mismatches between elements cause estimation error Utilize a target placed at a known position R xx = ΓV R uu V H Γ H + I σ 2. C xx,eig = E s Λ s E H s Γ H + I σ 2 E N E H N, E s E H s ΓV = ΓV. V d true response of target at known position diag{γ} = γ [?] E s E H s V d γ = V d γ V H d E s E H s V d γ = γ, V. C. Soon, L. Tong, Y. F. Huang and R. Liu, A Subspace Method for Estimating Sensor Gains and Phases, in IEEE Transactions on Signal Processing, vol. 42, no. 4, pp , Apr T. Collins 20

22 Calibration Flowgraphs: Phase and Antennas Antennas Phase T. Collins 21

23 MUSIC: Anechoic Chamber Testing TX Array 20 Inches Inches Testing in 4x4x4m (W,L,H) room with a single target Array positioned away from walls X310 dual TwinRX (4 receivers) Measurements include MUSIC and Root-MUSIC T. Collins 22

24 MUSIC: Chamber Results MuSIC RootMuSIC MuSIC Ant RootMuSIC Ant CRLB SNR=20dB -1-2 MUSIC Ant Calib MUSIC 7 CRLB SNR=0dB -3 RMSE (Degrees) Gain (db) Azimuth Angles (Degrees) Angle (Degrees) Antenna calibration uses target at known position Increase P-Spectrum SNR and DoA estimate T. Collins 23

25 gr-doa Demo DEMO T. Collins 24

26 Repository Apps Hardware Specific gr-doa/apps estimate X310 TwinRX constant phase offsets and save.grc: TwinRX phase correction run MUSIC calib lin array X310 TwinRX.grc: TwinRX antenna calibration Run estimation flowgraphs run MUSIC lin array X310 TwinRX.grc: MUSIC run RootMUSIC lin array X310 TwinRX.grc: Root-MUSIC Octave Simulations and QA gr-doa/examples Algorithmic examples for MUSIC,Root-MUSIC, and calibrations T. Collins 25

27 DOA Research: Effective Aperture Distribution Function Effective Aperture Distribution Function (EADF) Alternative and compact representation of antenna angular response Applicable to generic array geometrics Computationally convenient form (CRLB,DoA) T. Collins 26

28 EADF Antenna Model Antenna response matrices and EADF representation [ ] B B p =, G = FFT 2D (B p ) -B G N M A M E, M A and M E are the number of azimuth and elevations modes s Mapping vectors are: [ ] d(θ) = exp( jθ(m A 1)/2),..., exp(jθ(m A 1)/2) [ ] d(φ) = exp( jφ(m E 1)/2),..., exp(jφ(m E 1)/2) d(θ, φ) = d(θ) d(φ) Polarimetric array response: [ ] C(θ, φ) = G H d(θ, φ) G V d(θ, φ) A. Schmitz, T. Karolski and L. Kobbelt, Using spherical harmonics for modeling antenna patterns, T. Collins IEEE Radio and Wireless Symposium, Santa Clara, CA, 2012, pp

29 EADF Synthetic Model 50 Magnitude (db) [?][LComm Inc.] EADF Realization Azimuth Freq Elevation Freq 50 Monopoles well estimated in azimuth Synthetic model as replacement for B p T. Collins 28

30 EADF-FFT DoA (EFD) The channel between the transmitting node and receiving array in terms of the polarimetric response is: h = C(θ, φ) γ + n DoA Algorithm 1. Perform channel estimate: ĥ 2. Correlate: A H = ĥg H, A V = ĥg V 3. Convert coordinates: B H = FFT 3D (A H ) 2, B V = FFT 3D (A V ) 2 [ T 4. Search Max: θ, φ] = argmax(bh + B V ) T. Collins 29

31 Channel Estimation Platform USRP Phase Synced OFDM Sync Header Correlator and Equalizer Payload Equalizer and Packet Framer EADF FFT DoA Estimate Scopes (Constellation) OFDM System Parameterized system (2 Arrays at 5 MHz each with TUT Config) N supported coherent receive channels (4x per radio) One directional link Successful packets (Header and CRC Check) produce channel estimates Verified through simulation and cabling T. Collins 30

32 EFD vs. MUSIC Music (Calib) EADF (Calib) Music EADF 20 RMSE (Degrees) Results DoA (Degrees) Measurements taken in lab environment 1000 packets collected minimal variance among measurements Adopted correction algorithms from MUSIC implementation T. Collins 31

33 Questions? Repo: Whitepaper: docs/whitepaper/doa_whitepaper.pdf T. Collins 31

34 References I Images Antenna_Receiver.jpg https: // IoT1-1200x900.jpg T. Collins

35 Theme Get the source of this theme and the demo presentation from github.com/matze/mtheme The theme itself is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. cba T. Collins