Change Detection – An Invitation for
Applying MIMO & Compressive Sensing in
Through Wall Radar Imaging
Moeness Amin
Villanova University, USA
Barcelona-Spain 7-2010
Electromagnetic Waves
Antenna
Array
Front Wall
Scattering Objects
Back Wall
Applications
Imaging of
Building Interiors
and Personnel
Detecting Weapon
Caches
Glass
window
s
M16
Beretta
8357 Cougar
AK47
Weapon
Classification
Detection of Human and
Human Gait Classifications
Motion Detection and
Classifications
One arm
Two arms
No arm
Scene- Without Target
Scene-Without Target
Scene with Target
Experiment I
Signal Processing
DATA ACQUISITION
SIGNAL DIFFERENCE
IMAGE
IMAGE
IMAGE DIFFERENCE
CFAR
CFAR
CFAR
TRACKING
REGISTRATION
TRACKING
Signal Processing Method
-
Results with CFAR
Subtractions of close neighbors
Subtractions from a Reference
Position
Position 1
Two Crossing Targets III
Two Moving Targets
CFAR CD
Observations

With Change Detection
The image is sparse
The target is a Human
Target localization is the goal
Other Strategies
22
Application of CS to CD
Only with 3.5% of the data volume
BP with full set of data
(201 x 21 x 2)
Sparse Constraint Optimization
with limited data (7 x 21 x 2)
Compressed Sensing (CS)

CS is to find sparse solution from under-determined linear
system (J < D)
y

=



s
It is done by l1 norm minimization such that
sˆ  arg min f
f


1
subject to ΦΨf  y
CS is very efficient reconstruction technique

Reconstruction with very few data samples
y R J
Φ R J D
Ψ R DD
s R D
CS in Radar Imaging



Let s[k,l], for k=0,…,K-1 and l=0,…,L-1, be the spatially sampled scene of
interest, s(x,y)
Let M be the number of antenna positions
Let N be the number of frequencies in the stepped-frequency signal
M-1
K-1
…
…
y[m, n]
s[k , l ]
1
1
0
0
f 0 f1
…
f N 1
01
…
L-1
CS in Radar Imaging

We can rewrite the received signal y into a matrix-vector form
s n   s[0, n]
y n   y[0, n]
s[ K  1, n]
T
y[ M  1, n]
y  Ψs

y  y 0H

 y HN 1

H
s  s0H
H

s L
1
H
 is a MN  KL matrix such as
Ψm,n  exp j 4  f a cosb xc  f a sin b yd 

C

a  m modM , b  m / M , c  n modK , d  n / K 
T
Measurement Matrix

Let  be a J  KL measurement matrix that has only one
nonzero element, which is one, at each row

Φ  ei0
ei1  eiJ 1

T
ei  0  0 1 0  0
T
i-th
The indexes i0,…,iJ-1 are randomly chosen in [0,MN-1]
y cs  ΦΨs
Reconstruction by l1 norm
minimization

Given ycs such that
y cs  ΦΨs
s  arg min f
f


1
subject to ΦΨf  y cs
ycs is a J-dimensional vector
 ( > 0) gives robustness

2
Measurement Matrix

Data measurement comparison
 Conventional radar measures MN samples
 CS radar measures only J samples (samples are randomly
chosen)


 N 1
 N 2
 N 1
 N 2


3
2
3
2
1
1
0
0
f
f0
f1
f2
f3

f M 2 f M 1
Conventional measurement
f
f0
f1
f2
f3

f M 2 f M 1
CS measurement
Example
Simulation parameters:
Wall thickness:
d=0.15m
Wall permittivity:
εr=6
Frequency: 1GHz:50MHz:3GHz, Nf=41
Aperture: -1m:0.05m:1m,
Nt=41
Total amount of data:
K=Nt*Nf=1681
Sparse Constraint Optimization
Data
Person Sitting in a Chair
Experimental Setup




Stepped-frequency CW signal
 201 frequency steps
 Step size: 10 MHz
 Bandwidth: 2 GHz centered at 2 GHz
MIMO Radar System
 21-element uniformly spaced receive line array of length 1.5m
 2 Transmitters placed slightly above and on either side of the
receive array
Solid concrete block wall

Thickness: 0.14m
Standoff distance from the wall
 Receivers: 1.06m
 Transmitters: 1.34m
Scene Layout
Background Scene
Target Movements


Person sways his torso backwards, forwards, to
the right, and to the left
Both large and small swaying movements were
Back
measured
Large
Left
Large
Back
Small
Center
Left
Small
Right
Small
Forward
Small
Forward
Large
Right
Large
Large Displacements
Small Displacements
Back Large
Backprojection
Full dataset (201 x 21 x 2)
Compressive Sensing
Limited data (7 x 21 x 2)
Back Small
Backprojection
Full dataset (201 x 21 x 2)
Compressive Sensing
Limited data (7 x 21 x 2)
Forward Large
Backprojection
Full dataset (201 x 21 x 2)
Backprojection
Full dataset (201 x 21 x 2)
Compressive Sensing
Limited data (7 x 21 x 2)
Compressive Sensing
Limited data (7 x 21 x 2)
Forward Small
Backprojection
Full dataset (201 x 21 x 2)
Compressive Sensing
Limited data (7 x 21 x 2)
Left Large
Backprojection
Full dataset (201 x 21 x 2)
Compressive Sensing
Limited data (7 x 21 x 2)
Left Small
Backprojection
Full dataset (201 x 21 x 2)
Compressive Sensing
Limited data (7 x 21 x 2)
Right Large
Backprojection
Full dataset (201 x 21 x 2)
Compressive Sensing
Limited data (7 x 21 x 2)
Right Small
Backprojection
Full dataset (201 x 21 x 2)
Compressive Sensing
Limited data (7 x 21 x 2)
Compressive Sensing –
Taking Advantage of Target
RCS Signatures
Example- AK 47
Frequency: 1.5GHz~3.5 GHz,
Nf=43
Aperture: -1m:0.05m:1m,
Nt=41
Total amount of data:
K=Nt*Nf=1763
Target: AK47
BP with full set of data
SNR=20dB
2.5 % of data
Sparse Constraint Optimization
with limited data J = 41
BP with limited data J = 41
Randomly select one Frequency at each antenna location
SNR = 20dB
2.5 % of data
Sparse Constraint Optimization
with limited data J = 41
BP with limited data J = 41
Randomly select one Frequency at each antenna location
SNR = 10dB
2.5 % of data
Sparse Constraint Optimization
with limited data J = 41
BP with limited data J = 41
Randomly select one Frequency at each antenna location
SNR = 0dB
2.5 % of data
Sparse Constraint Optimization
with limited data J = 41
BP with limited data J = 41
Randomly Measure One Frequency at each antenna location
SNR = -5dB
Frequency Response for all 41 Antenna Locations
Sparse Constraint Optimization
2.5 % of data
SNR = 20dB
Sparse Constraint Optimization
with limited data J = 41
SNR = 10dB
Sparse Constraint Optimization
with limited data J = 41
SNR = 0dB
Sparse Constraint Optimization
with limited data J = 41
Randomly Measure One Frequency at RCS> 0.5* RCS_Max
SNR = -5dB
MIMO-MTI Approach for
TWRI Applications
MIMO Radar System


MIMO Radar System

Synthetic uniform line array of receivers with an
inter-element spacing of 7.49cm

2 Transmitters placed (slightly above and slightly
behind) on either side of the receive array
Virtual Array or Co-Array
Two persons walking across the scene along
different trajectories
Experimental Setup




Stepped-frequency CW signal
 201 frequency steps
 Step size: 10 MHz
 Bandwidth: 2 GHz centered at 2 GHz
MIMO Radar System
 21-element uniformly spaced receive line array of length 1.5m
 2 Transmitters placed slightly above and on either side of the
receive array
Solid concrete block wall

Thickness: 0.14m
Standoff distance from the wall
 Receivers: 1.06m
 Transmitters: 1.34m
Scene Layout
Background Populated Scene
Target Movements

Measurements were made with the targets at the
following ten positions
Target 1
1A 1B
3cm
2A 2B
3A 3B
4A 4B
5A 5B
6A 6B
7A 7B
8A 8B
9A 9B
10A 10B
7A 7B
8A 8B
9A 9B
10A 10B
45cm
Target 2
1A 1B
3cm
2A 2B
35cm
3A 3B
4A 4B
5A 5B
6A 6B
Target Movements – Cont’d
Images before Change
Detection
Position 8A
Position 8B
Change Detection Results
Targets at Position 8
MIMO Radar
SIMO (Tx 2 only) Radar
Two persons walking side by side
Experimental Setup




Stepped-frequency CW signal
 201 frequency steps
 Step size: 10 MHz
 Bandwidth: 2 GHz centered at 2 GHz
MIMO Radar System
 15-element uniformly spaced receive line array of length 1.0m
 2 Transmitters placed slightly above and on either side of the
receive array
Solid concrete block wall

Thickness: 0.14m
Standoff distance from the wall
 Receivers: 1.06m
 Transmitters: 1.34m
Scene Layout
Target Movements
Change Detection Results
Targets at Position 3
MIMO Radar
SIMO (Tx 2 only) Radar
Conclusions

Through wall radar imaging is a fertile area for
emerging techniques in signal analyses and
processing