Wireless Communication Systems @CS.NCTU Lecture 6: Localization Instructor: Kate Ching-Ju Lin ( 林靖茹 ) 1
Type of Approaches • RSSI-based • Angle of Arrival (AoA) • Time of Flight (ToF) • Time Difference of Arrival (TDoA) 2
RF-based Localization • See through walls ⎻ WiVi (SIGCOMM’13) • ToF-based localization ⎻ WiTrack (NSDI’14, NSDI’15) • AoA-based localization ⎻ ArrayTrack (NSDI’13) 3
Can you use WiFi to get X-ray vision?
Key Idea Tracking people from their reflections
Challenges Wall refection is 10,000x stronger than reflections coming from behind the wall How to separate the person’s reflections from the reflections of other objects?
WiVi [SIGCOMM’13] • How to eliminate the wall’s reflections? ⎻ Leverage multiple antennas to perform interference nulling • How to track users using reflections? ⎻ Deem a mobile user as a virtual antenna array reflecting the signals 7
Eliminating Static Reflection • Idea: transmit two waves that cancel each other when they reflect off static objects but not moving objects disappears Wall is static People tend detectable to move
Eliminating via Multiple Antennas Receive antenna x Transmit antennas α x
Eliminating via Multiple Antennas 0 Cancel strong y = h 1 x + h 2 α x reflections from walls h 1 x α = -h 1 / h 2 α x h 2
Eliminating All Static Reflections Only the reflections from mobile users survive à Why? ✘ ✘
Eliminating All Static Reflections h 1 x y = h 1 x + h 2 α x α x h 2 People move, therefore Static objects (wall, furniture, their channels change etc.) have constant channels 0 y = h 1 x + h 2 (- h 1 / h 2 )x y = h ’1 x + h ’2 (- h 1 / h 2 )x Not Zero
WiVi [SIGCOMM’13] • How to eliminate the wall’s reflections? ⎻ Leverage multiple antennas to perform interference nulling • How to track users using reflections? ⎻ Deem a mobile user as a virtual antenna array reflecting the signals 13
Tracking Motion RF source θ Direction of reflection Antenna Array
Tracking Motion Direction of motion At any point in time, we θ have a single measurement Antenna Array
Tracking Motion Direction of motion θ θ Direction of motion Antenna Array
Tracking Motion Direction of motion θ θ Human motion emulates antenna array à Inverse synthetic aperture radar ( ISAR ) Antenna Array
How to Calculate the Direction? • Say we have w consecutive channel measures h [ n ], …, h [ n + w ] from time n to ( n + w ) • The signal along the direction θ at time n is given by w h [ n + i ] e j 2 π X λ i ∆ sin θ A [ θ , n ] = spatial separation between i =1 successive antennas • The direction can be found by θ ∗ = arg max How to get Δ given that A [ θ , n ] θ user location is unknown? 18
��������������� � � �������� �������� �������� ����� ����� ����� ������� Tracking Users ��������������� � � • Rough estimation Δ = vT , where v is user mobility (~1m/s) • WiVi only tracks users, instead of localizing them � � � � ������������� ⎻ Only need to know whether the user is moving closer or away from the device positive angle, decreasing à moving closer negative angle, increasing à moving away 19
Tracking Multiple Persons • Human mobility is continuous! user 1 user 2 20
RF-based Localization • See through walls ⎻ WiVi (SIGCOMM’13) • ToF-based localization ⎻ WiTrack (NSDI’14, NSDI’15) • AoA-based localization ⎻ ArrayTrack (NSDI’13) 21
Applications Gaming Gesture Control First Responders Elderly Monitoring
ToF-based Localization Tx Rx Distance = Reflection time x Speed of light
How to Measure ToF? Option1: Transmit short pulse and listen for echo Tx pulse Rx pulse time Reflection Time
How to Measure ToF? Option1: Transmit short pulse and listen for echo Tx pulse Rx pulse signal samples time reflection time (3.33ns per meter) capturing the pulse needs sub-nanosecond sampling Need multi-GHz samplers à expensive and with high noise
How to Measure ToF? Option2: Frequency Modulated Carrier Wave (FMCW) Transmitted Frequency Received Δ F Δ F ToF ToF = slope t t+ Δ T time How to measure Δ F ?
Measuring Δ F • To find Δ F = f Rx – f Tx , 1. Use mixer to subtract f Tx from the received signal à the signal whose frequency is Δ F 2. Take FFT and identify the frequency with peak power power Transmitted Mixer FFT received Δ F Δ F à Reflection Time à Distance
How to Deal with Multiple Reflections? Tx Rx Reflections from different objects Reflection à which one is Power from the person? Distance
Subtract Static Paths • Static objects don’t move ⎻ Eliminate by subtracting consecutive measurements multi-path power @ time t distance multi-path power @ time t+30ms - distance power 2 meters = Why 2 peaks? distance
Dynamic Multipath Tx Rx Moving Person Dynamic Power Multi-path Distance Find the first peak since the direct reflection arrives before other dynamic multipaths
From Distances to Localization • Person can be anywhere on an ellipse whose foci are (Tx,Rx) • One ellipse is not enough to localize! d Rx Tx
From Distances to Localization • Use two Rx antennas to find the intersection • WiTrack uses directional antennas so only one point is in-beam • Extend to 3D by using 3 Rx antennas and taking the intersection of ellipsoids in beam d d’ Rx’ Rx Tx
Key Issue of FMCW • Don’t need a high sampling rate • But, need a very wide band channel Bandwidth of 1.69GHz to support a distance resolution of 8.8cm Transmitted Frequency Received Δ F Δ F ToF ToF = slope t t+ Δ T time Cannot be applied in the unlicensed WiFi band 33
RF-based Localization • See through walls ⎻ WiVi (SIGCOMM’13) • ToF-based localization ⎻ WiTrack (NSDI’14, NSDI’15) • AoA-based localization ⎻ ArrayTrack (NSDI’13) 34
Angle of Arrival • Determine the direction of propagation of a radio-frequency wave using an antenna array • Key idea: ⎻ The phase of the received signal is determined by the length of a path ⎻ The path lengths to different elements of an antenna array vary slightly ⎻ Leverage TDOA (time difference of arrival) at individual elements of the array to measure AoA 35
Time Difference of Arrival Rx d A d A … Δ 2 Δ 3 Δ ≈ d ≈ d ≈ d N Δ ≈ d ≈ d Assumption: d ≫ d A ! Then, the distance from Tx Tx to the k-th Rx antennas is close do (d+k Δ ) 36
Time Difference of Arrival Access point 1 2 λ /2 x 1 Q 2 π d / λ π sin θ d θ θ I ½ λ sin θ λ x 2 Client exp( − 2 j π d Signal received at 1 st antenna: ) λ exp( − 2 j π ( d + ∆ ) Signal received at 2 nd antenna: ) λ = exp( − 2 j π d ) exp( − 2 j π ∆ ) λ λ … exp( − 2 j π ( d + N ∆ ) ) Signal received at N th antenna: λ = exp( − 2 j π d ) exp( − 2 j π N ∆ ) λ λ
Time Difference of Arrival Access point 1 2 λ /2 x 1 Q 2 π d / λ π sin θ d θ θ I ½ λ sin θ λ x 2 Client 1 exp( − j π sin θ ) a ( θ ) = exp( − j 2 π d exp( − j π 2 sin θ ) Signal from angle θ : ) . λ . . exp( − j π ( N − 1) sin θ ) 38
Combined Signals from D paths • If the Rx receives signals from D different paths s 1 ( t ) s 2 ( t ) Final received signal: x ( t ) = [ a ( θ 1 ) a ( θ 2 ) · · · a ( θ D )] . + n . . s D ( t ) 1 1 · · · s 1 ( t ) e − j π sin θ 1 e − j π sin θ D · · · s 2 ( t ) e − j π 2 sin θ 1 e − j π 2 sin θ D − j 2 π d x ( t ) = e . + n · · · λ . . ... . . . · · · s D ( t ) e − j π ( N − 1) sin θ 1 e − j π ( N − 1) sin θ D · · · 39
MUSIC Algorithm • MUltiple SIgnal Classification (MUSIC) • Find the direction of the LOS path from s 1 ( t ) s 2 ( t ) x ( t ) = [ a ( θ 1 ) a ( θ 2 ) · · · a ( θ D )] . + n . . s D ( t ) • High level idea: ⎻ We collect N received signals ( N equations) ⎻ Assume there exist only D paths, D ≤ N , ( D unknowns) ⎻ Use linear algebra to find the D components from N measures 40
MUSIC Algorithm • Find the N x N source correlation matrix R xx = E [ xx ∗ ] = E [( As + n ) ( s ∗ A ∗ + n ∗ )] = A E [ ss ∗ ] A ∗ + E [ nn ∗ ] = AR ss A ∗ + σ 2 n I source correlation matrix sorted • N eigenvalues of R xx à E = [e 1 e 2 … e N-D e N-D+1 … e N ] ⎻ D components with large eigenvalues à from D paths (angles) ⎻ (N – D) components with near-zero eigenvalues à noise 41
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