gr-doa: Direction Finding in GNU-Radio GRCon 2017 Travis F. Collins, PhD Srikanth Pagadarai, PhD September 12, 2017
Sponsors T. Collins 1
Outline Project Background MUSIC Hardware options USRP-N210 X300/X310 FMComms5 Antenna Calibration Test and Results EADF Feasibility Test and Results T. Collins 2
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
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
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
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
DoA Baseline: MUSIC MUSIC: Multiple Signal Classification Gain (db) 70 60 50 40 30 20 10 N=4 N=8 N=12 0 0 20 40 60 80 100 120 140 160 180 angle (degrees) R. Schmidt, Multiple emitter location and signal parameter estimation, in IEEE Transactions on Antennas and Propagation, vol. 34, no. 3, pp. 276-280, Mar 1986. 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
MUSIC: Estimation Performance 10 9 8 SNR=10dB SNR=0dB 1.5 RMSE (Degrees) 7 6 5 4 3 2 1 0 0 20 40 60 80 100 120 140 160 180 DoA (Degrees) Mean RMSE (Degrees) 1 0.5 0 0 20 40 60 80 100 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. 720-741, May 1989. T. Collins 8 [?]
Estimation Blocks T. Collins 9
GUI Real-time visuals QT Compass Pseudo spectrum (MUSIC block only) T. Collins 10
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
Remaining Phase Offset 10 khz tone sent into 3xUSRPs through splitter and matched cabling T. Collins 12
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
Array Cart T. Collins 14
X300/X310 TwinRx Array Still needs calibration Better phase stability Limited to 4-RX Easier to carry around! T. Collins 15
FMComms5 Array Self phase calibrating! T. Collins 16
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
MUSIC: Positioning Error 3 Modified signal model RMSE (Degrees) [40-140] 2.5 2 1.5 1 0.5 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 0 0 0.02 0.04 0.06 0.08 0.1 STD λ T. Collins 18
MUSIC: Testbed Refinement Array 1 Pegboard Array 0 Transmitte r Positioning Moved to pegboard for precise positioning +/-0.125 tolerance 0.028λ (0.7 Degree RMSE) T. Collins 19
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. 973-976, Apr 1994. T. Collins 20
Calibration Flowgraphs: Phase and Antennas Antennas Phase T. Collins 21
MUSIC: Anechoic Chamber Testing 35 30 25 TX Array 20 Inches 15 10 5 0-5 -50-25 0 25 50 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
MUSIC: Chamber Results 11 0 10 9 8 MuSIC RootMuSIC MuSIC Ant RootMuSIC Ant CRLB SNR=20dB -1-2 MUSIC Ant Calib MUSIC 7 CRLB SNR=0dB -3 RMSE (Degrees) 6 5 4 3 2 1 0 Gain (db) -4-5 -6-7 -8-9 40 60 80 100 120 140 Azimuth Angles (Degrees) -10 0 50 100 150 200 Angle (Degrees) Antenna calibration uses target at known position Increase P-Spectrum SNR and DoA estimate T. Collins 23
gr-doa Demo DEMO T. Collins 24
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
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
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 27 2012 IEEE Radio and Wireless Symposium, Santa Clara, CA, 2012, pp. 155-158.
EADF Synthetic Model 50 Magnitude (db) 0-50 -100-150 -100 100 [?][LComm Inc.] EADF Realization -50 0 Azimuth Freq 50 100-100 -50 0 Elevation Freq 50 Monopoles well estimated in azimuth Synthetic model as replacement for B p T. Collins 28
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
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
EFD vs. MUSIC 30 25 Music (Calib) EADF (Calib) Music EADF 20 RMSE (Degrees) 15 10 5 Results 0 40 60 80 100 120 140 DoA (Degrees) Measurements taken in lab environment 1000 packets collected minimal variance among measurements Adopted correction algorithms from MUSIC implementation T. Collins 31
Questions? Repo: https://github.com/ettusresearch/gr-doa Whitepaper: https://github.com/ettusresearch/gr-doa/blob/master/ docs/whitepaper/doa_whitepaper.pdf GitHub: @tfcollins T. Collins 31
References I Images http://www.tut.fi/5g/positioning/ http://www.toyo.co.jp/files/user/img/english/images/ Antenna_Receiver.jpg https: //www.ettus.com/content/images/x300_w_twinrx_large.png http://blogs-images.forbes.com/scottdavis/files/2016/01/ IoT1-1200x900.jpg T. Collins
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