Correlation of Backscattering

1
Sequential Adaptive Multi-Modality Target
Detection and Classification Using Physics-Based
Models
K. Sarabandi, I. Koh, M. Dehmolaian, M. Casciato
Radiation Laboratory The University of Michigan,
Ann Arbor, MI 48109-2122 saraband_at_eecs.umich.edu
2

• Outline
• Motivation
• Detection of targets camouflaged under foliage
  using multi-frequency, -polarization, -incidence
  angle SAR/INSAR sensors.
• Phenomenological study
• Physics-based scattering and propagation
  modeling of clutter
• Scattering models for targets under trees
  including interaction
• High resolution SAR/INSAR image simulator
• Time reversal methods for foliage camouflaged
  target detection
• Simulation results
• Iterative method
• Forest channel estimation using frequency
  correlation function

3

• Motivation
• A reliable approach for detection and
  identification of targets camouflaged under
  foliage with an acceptable false alarm rate and
  probability of detection has not yet been
  developed.
• Due to the complexity of the problem, i.e.
• Signal attenuation, phase-front distortion, poor
  signal-to-clutter ratio, etc., single sensor
  approaches (optical, IR, radar) do not produce
  satisfactory results.
• Capable sensors operating in diverse modality
  in conjunction with novel algorithms can
  drastically enhance FAR and PD.
• Polarization diversity, Multi-frequency,
  Multi-static, Multi-incidence angle,
  Interferometric

4
Phenomenological Study
Physics-based Scattering and Propagation Modeling
of Forest

• Forest is a complex random medium composed of
  lossy scatterers arranged a semi-deterministic
• Foliage cause significant attenuation,
  scattering, field fluctuation
• Target is in the close proximity of many
  scatterers (strong field fluctuations and phase
  front distortion)

• Signal level, fluctuations, polarization state,
  impulse response, spatial coherence etc. depend
  on Tree density, type, height, and structure

• Goal
• To develop an accurate EM model for forest stands
  to allow performance assessment of radar sensors
  and target detection algorithms.

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Scattering Model for Forest Canopies
Scattering from discrete scatterers- Trunk
stratified dielectric cylinder- Branch
homogeneous dielectric cylinder- Leaf
dielectric disk or needle- Ground layered
dielectric half-space Single Scattering is
invoked Four Scattering Mechanisms are
included
Attenuation rate NP/m
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Observation Point in the Forest
Phenomenological Study

• Near-field calculation is required
• Approximate analytical formulations for
  near-field scattering from branches and tree
  trunks are derive.
• Coherent summation of scattered field from all
  tree components. (Coherence is important at
  S-band and lower)

Single scattering theory Interaction among
tree structures are ignored.
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Time-domain Response
Simulation Results
Observation point is 1m above the ground inside a
pine forest. v-pol. wave is incident at 40o, and
BW 1GHz (1GHz 2GHz).
15m
Mean Field
Direct
Ground bounce
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Simulation Results
Backscattering Coefficient
Red pine Tree height 15.3 m, Crown Height 9.5 m
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Bistatic Scattering Response the Pine Forest
Simulation Results
Freq. 1.25GHz (L-band), 10 pine trees, ?i 45o,
?i 0o, 100 realizations.
qs
Co-pol
Cross-pol
HH
VV
Backscatter Enhancement
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Phenomenological Study
Model Enhancement for High Frequencies

• Standard method for the calculation of mean-field
  attenuation constant is based on single
  scattering theory (Foldys approximation), which
  is valid for sparse media.
• Needles are placed very close to each other
  causing significant multiple scattering effects.
• Inclusion of the effect of multiple scattering
  for dense foliage.

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Measurement Setup at 35GHz

• 13 pine trees occupying 15m 25m
• Rx/Tx Ka-band (35GHz) horn antennas with 10o
  HPBW
• Tx 20m away from tree stand, giving 3m 3m
  footprint at the tree stand
• Rx first set in front of tree stand for
  calibration, then moved behind tree stand
• 84 independent spatial samples collected

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Measurement Results

• Histogram shows a close match to the
  exponential PDF.
• More statistical samples needed to obtain more
  accurate PDF.

Measurement mean -24.8 dB, std. -23.8 dB
Simulation mean -33.1 dB, std. -32.3 dB

• Single scattering model for pine trees is not
  accurate at millimeter wave frequencies.
• To reduce the discrepancy, multiple scattering
  effects should be included.

Note Single scattering theory overestimates the
attenuation.
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Multiple Scattering Effect of Needle Clusters
Model Enhancement

• Forward scattering for two cluster structures.
• Frequency 35 GHz.
• Average needle radius 0.6 mm, and length 3.5 cm
  minimum distance between needles 5.5 mm.
• Dense distribution of needles ( 100/cluster).
• Rayleigh-Gans approximation is invalid.

Note lower forward scattering ? lower
attenuation rate.
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• Challenges Application of MoM is impractical.
• Required memory gt 500 MB for 6000 unknowns for
  96 needles.
• Time for inversion of MoM matrix 1 hour using
  2.4 GHz dual processor Linux machine. Calculation
  time for scattered field from all needle clusters
  in one tree 15 min using pre-stored inverse
  MoM matrix. Forest simulation requires 100
  realizations for tens of trees.
• Storage for bistatic S matrix gt 1 GB
• Solution Macro-modeling multiple scattering
  effects.
• Macro-model of bistatic scattering from a needle
  cluster.
• Shape of needle cluster is almost deterministic,
  can be treated as a dielectric block with
  effective permittivity to calculate near forward
  scattering.
• Scattering power at directions far from forward
  scattering direction is much lower.

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Macro-modeling Multiple Scattering from a Needle
Clusters
dB

• Rotation angle around central stem is random
  macro-model the averaging effect.
• For scattering directions away from forward
  scattering direction, the scattered power level
  is much lower and the phase of S parameters is
  random, ? ltS2gt can be modeled as a constant and
  ltSgt can be given a random phase.
• At near forward scattering, S parameters
  determined by the effective dielectric structure,
  which can be modeled by using DBA (Distorted Born
  Approximation).

Fwd. Scat. Cone
?s degrees
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Analytical Computation of Mean Field Using DBA

• Shape of dielectric block is a body of
  revolution determined by the shape of the
  cluster.
• Incident field is attenuated by the effective
  dielectric block during path Li(r?), then
  scattered by the local differential volume with
  effective permittivity.
• Effective permittivity is calculated based on
  dielectric mixing formula, could be inhomogeneous
  due to different needle density at different
  locations.

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Validity Region of DBA comparison with known
solutions
S2
?S
dB
degrees
k0a
k0a

• Forward scattering of a dielectric sphere
  (?r1.5j0.5) with radius a versus size factor k0
  a, where k0 is free space wave number.
• DBA compared with Mie solution lt 0.5 dB error
  in scattered power up to k0 a 50 lt 2o phase
  difference for most k0 a.

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Effective Permittivity Calculation Using
Dielectric Mixing Formula

• Inhomogeneous needle density ?

• Clausius-Mossotti dielectric mixing formula

where, ?h is the permittivity of background
medium,
is the polarizability tensor averaged over
orientation angles, and
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DBA Macro-model Compared with Monte-Carlo
Simulation Using MoM Forward Scattering
Shh
Svv

• Forward scattering of a needle cluster
  consisting of 96 needles versus incident angle
  ?i, averaged over the self-rotation angle.
• DBA compared with MoM (multiple scattering)
  simulation results lt 0.5 dB error in scattered
  power and lt 10o phase difference.

20
DBA Macro-model Compared with Monte-Carlo
Simulation Using MoM Bistatic Pattern
Shh
Svv

• Bistatic scattering (normal incidence) of a
  needle cluster consisting of 96 needles versus
  scattered angle ?s, averaged over the
  self-rotation angle.
• DBA compared with MoM (multiple scattering)
  simulation results pattern and phase matched
  well for the main lobe.

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Multiple Scattering Model Compared with Measured
Results
Mean (dB) Std. (dB)
Measurement -24.8 -23.8
Multiple Scattering -26.4 -25.6
Single Scattering -33.1 -32.3
Rayleigh-Gans -51.7 -51.9
Note

• Rayleigh-Gans approximation is invalid at
  millimeter-wave frequencies.
• Multiple scattering model improves the
  simulation result by 7 dB.

Note Multiple scattering simulation takes
1600s, about 30 faster than RG simulation
(2300s).
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New Model for Broad Leaves

• Motivation
• Thin dielectric disks are used to model broad
  leaves for deciduous trees.
• Two approximate solutions, Rayleigh-Gans VIPO
  are not valid for the entire region of interest
  like frequency, size, observation direction.
• A new scattering model is developed.

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Examination of Two Approximate Solutions
Note VIPO doesnt include diffraction from edge.
From this point diffraction becomes dominant.
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New Formulation for Scattering from Thin
Dielectric Disk
Note Current (J) can be approximated as a
function of only (x,y), and constant w.r.t. z.
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Taking Fourier transform w.r.t (x,y) using
mid-point rule w.r.t. z?
To obtain explicit current expression, taking
Fourier transform again w.r.t (x?,y?)
For Far-field,
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Infinite Dielectric Strip
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Circular Dielectric Disk
Forward scattering
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Circular Dielectric Disk (Continued)
Freq. 20GHz
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Scattering Models for Targets Under Trees

• Challenges
• Hard targets and clutter constitute a
  computationally very large problem.
• Target and clutter are structurally complex
  (features vary from small to very large objects).

• Requirements
• Accurate estimation of scattering from various
  type of forest target for a wide bandwidth.
• Statistical description of scattering for signal
  processing applications.

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Proposed Approaches

• Low frequencies (flt100 MHz) brute force
  Full-wave methods can be used (FDTD, FMM, FEM)
• Scattering from foliage can be ignored
• Mid-frequency range (100 MHzltflt1 GHz) Hybrid
  FDTD and single scattering forest code
• Near-field interaction between foliage and target
  are included.
• High frequency (fgt1GHZ) Hybrid PO and improved
  forest code
• Near-field interaction between foliage and target
  are included.
• Iterative PO for target

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Hybrid FDTD/forest model

1. Using the coherent forest model, calculate the
   fields on an FDTD boundary given in the proximity
   of target.

2. Using FDTD, compute the scattered fields from
the target on the same grid.
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Hybrid FDTD/forest model

• To calculate the effect of the forest on the
  scattered field, apply the reciprocity theorem.
• So source observation are exchanged.

Note Using this procedure, interaction between
forest target is inherently taken into account.
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Forest Response at Low Frequencies
Frequency 30MHz 100MHz 10 trees are
considered. Dielectric constants 21.7 i14.6
for branch 9.8
i1.7 for ground. Height of tree 15m, Diameter of
trunk 22cm. 45o Incidence angle.
Note Effect from trees is can be ignored.
34
Bistatic Scattering from HUMVEE
Discretized HUMVEE for FDTD Analysis
Note Scattering from target is much larger than
that from forest at low frequency band.
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Field Distribution
H-Pol, f180
V-Pol, f180
Freq. 1GHz 10 pine trees. Dimension of the
plane 5 ? 3m. Height of the plane 1m.
f185
Note Due to multi-path, field distribution on
the plate is very sensitive to incidence angle at
high frequency range.
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High-frequency Model

• Calculate scattering from the target inside a
  forest using PO approximation
• Valid for targets large compared to l
• Valid near specular directions where scattering
  amplitude is large.
• Forest scattering at high frequencies is very
  significant, hence the target is illuminated from
  all directions.
• Independent of observation point there will be
  many specular contributions.
• Process
• Calculation of field distribution on the
  scatterer using the coherent forest model.
• Based on these calculated fields derive PO
  currents on the target.
• Apply the reciprocity theorem to calculate
  scattered field from the target that includs the
  effects of trees.

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Reciprocity approach recovers the ground effects
PO current
Note 4-rays Model
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Backscattering Calculation based on Reciprocity
Theorem
Freq. 2GHz Size ? ? ?
For free space
With ground plane
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Validity of PO Solution
Freq. 10GHz Radius of disks 2cm ?r 26.6
i11.56 ?i 31.22o, ?i 258.8o
Discrepancy
?s Degrees
?s Degrees
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PO Approximation inside Random Medium
In a random medium
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Validation of PO Solution (Contd)
2000 sources (plane wave) around scatterer
Note PO estimates scattering accurately over a
wide range.
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Target inside Foliage Co-pol.
Freq. 2GHz 4 realizations, 10 pine trees with
15m height ? ? ? plate 1m above ground plane
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Target inside Foliage Cross-pol.
s0 of forest
s0 of forest
Plate in forest
Plate in forest
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Field Distribution on Plate
Freq. 2GHz, 10 pine trees 3?? 3? plate, ?/4
sampling points
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Time Reversal Methods

• Preliminary study using the coherent foliage
  model
• Point-to-point secure communication using TRM
• Achieving super-resolution focusing through
  proper use of multi-path.

Region of influence
Region of influence
Transmit array
Highly scattering random medium

• Procedure
• transmit from receiver and measure amplitude,
  phase, and polarization at the array points
• transmit from the array elements with matched
  polarization and amplitude but conjugate the
  phase.

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• Foliage camouflaged target detection using TRM
• Due to scattering and attenuation, wave phase
  front is distorted. Conventional SARs point
  spread function is smeared.

SAR track
Multi-path, attenuation, fading, etc.
Beam pattern is broaden or lost.

• Application of TRM using a recursive method in
  conjunction with a first-order channel estimation

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Point-to-point secure communication

• Array in the forest, observation point outside 60
  deg. from normal.
• The antenna is a 17-element array with 1l spacing
  and in cross configuration
• Simulation is done at 10 GHz
• TRM produces a beam with 0.5deg. beamwidth
• element spacing could be increased with no
  grating lobes

Array beam without foliage
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SAR Simulation
Focusin beam inside foliage using time reversal
method
Assume a fictitious source

• Excite fictitious source on ground through forest
  (determine Greens function of medium)
• Complex conjugate reradiate the signal through
  foliage (using reciprocity theorem).
• ? Due to channel, fading, multipath, forest will
  act as a lens to focus energy at the fictitious
  source point.

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1 Km
3 dB
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Array Distribution for a Polarimetric SAR That
can Focus Inside the pine Forest
Amplitude distribution
Phase distribution
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Iterative TRM
I(x,y) L S(u,t) S(u,t) L 1I(x,y)
Phase conjugate the array
Array distribution
Reprocess
This process may not converge
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Forest Channel Estimation Using Frequency
Correlation Function

• Need to retrieve
• Tree structure (height, density)
• Attenuation profile
• Volume scattering

L
C
Side-looking SARs cant directly provide target
vertical struvture
Np/m
53
FCF of a Statistically Homogeneous Random Layer

• Random media parameters
• Layer of sparse or dense (small albedo)
  scattering above a ground plane
• Effective propagation constant

Volume Scattering
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Note It contains system target dependent terms.
.
20o incidence angle vv-polarization No 500/m3
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Experimental Results Random Layer (Dry Snow)
Target Parameters ? 0.34, Crystal diam.
0.5mm, mv 0 System Parameters f0 93.5GHz, BW
1GHz, Beamwidth 1.4o of independent
samples 100
Can estimate ? directly from measured target
dependence component
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Backscattering Decomposition
Where Cd, Cb are constant.
In ? domain
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Uniform Layer
For a layer of d 1m, B 0.5GHz, 15o or 45o
incident HH polarization
3600 disks/m2
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Non-Uniform Layer
Alternating stack of uniform layers and free
space. Layer 1, 3 3600 disks/m2 Layer 2, 4 free
space B 1GHz, 15o VV incident polarization.
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Accomplishments/Future Activities

• Clutter model improvement inclusion of effect of
  multiple scattering among needles, generalized
  formulation for scattering from broad leaf.
• Development of model for estimation of scattering
  from targets embedded in forested environment
• Hybrid forest/FDTD
• Hybrid forest/PO
• Investigation on the application of TRM for beam
  focusing through foliage. (communication, target
  detection)
• 4. Investigation on the application of FCF for
  retrieving response of a forest.
• 5. High frequency SAR simulator.