Correlation of Backscattering

1
Physics-based Modelling of Foliage-Camoulaged
Targets
K. Sarabandi and M. Dehmolaian
Radiation Laboratory The University of Michigan,
Ann Arbor, MI 48109-2122 saraband_at_eecs.umich.edu
2
Outline
Progress Since August 2004

• The High frequency GOPOPO foliage and hard target
  model is enhanced by incorporating a PTD method
  to account for edge diffractions on the target.
  The model verification using scaled targets is
  completed.
• 2. A polarization synthesis optimization method
  for improving signal to clutter is performed by
  applying a genetic algorithm for finding an
  optimum polarization that enhances signal to
  clutter ratio.
• 3. The hybrid FDTD and Foliage model is
  completed and verified. The model can be utilized
  in VHF to low UHF bands (20-400 MHz) and is
  developed to investigate the scattering behavior
  of hard targets embedded inside a forest canopy.

3
Enhanced GOPOPO model for Hard Targets

• Fast GOPOPO algorithm is enhanced by including
  the edge effects
• Edge currents are added locally using PTD

Phase
shh
Backscatter
GOPOPOPTD
MoM
z
1st order GOPO
Incidence angle
Length of 10l along the y axis. Frequency 2 GHz
8l
4
Validation Using Scaled Models
UoM Anechoic Chamber
Transmit Antenna
UoM 93-95GHz fully Polarimetric
Radar Coherent-on-receive Dynamic range 100
dB Noise equivalent RCS -30 dBsm
Scaled tank, used for radar measurement in the
anechoic chamber of Radiation Laboratory
5
Comparison of theory with measurement
6
Target Detection Enhancement Using
Multi-Polarization Channels

• Target and clutter backscatter are both strong
  functions of polarization state of the radar
  transmit and receive polarization
• Is there a polarization that minimizes clutter
  response in a statistical sense?
• Is there a polarization that maximizes the
  foliage-embedded target response? Or
  target/clutter response in a statistical sense?
• What are the variability of the optimal
  polarization on a pixel basis?

7
Simulation Scenario A metallic target embedded
in a coniferous forest stand. Ten trees around
the target are considered (tree density0.05
tree/m2) Radar Fully polarimetric operating at
S-band. (amplitude and phase in four polarimetric
channels) Simulation includes near-field
interaction of foliage with target and vice versa
(hybrid GOPOPO/foliage model) Polarimetric
clutter response and target response (including
foliage interaction) are calculated.
8
Metallic Target Inside the Forest
Target on the ground in the absence of foliage
3l
Response of target inside forest Fluctuations are
due to the target-foliage interactions.
3l
4l
10l
Frequency 2 GHz.
8l
9
Cross-pol response
Significant cross-pol is generated from
target-foliage interaction
8l
Cross-pol to co-pol ratio of about -15 dB is
predicted for the target embedded in the forest.
10
Backscatter coefficients of forest (Clutter
Response)
Frequency 2 GHz Number of Realizations
10 Density of trees 0.05 trees/m2
Fluctuation range
Max
Mean value
Min
vertical
horizontal
Note Horizontal polarization has higher RCS
values. This is due to the Brewster angle effect
on tree trunks.
11
Polarization Signature
Plot of target response as a function of radar
polarization state Two special cases Co-pol and
Cross-pol responses
Target Including foliage interaction
CO-POL
CROSS-POL
12
Clutter response generated from Avg. co-variance
matrix
ltCROSS-POLgt
ltCo-POLgt
13

• Backscatter RCS of target Co-pol. response occurs
  at HH polarization.
• Unfortunately clutter Co-Pol. Response also
  occurs at HH-polarization
• Co- or Cross-pol. Configurations are not
  necessarily the best configuration for target
  detection.
• Minimum clutter response occurs at c-30 and
  y50, but the target response is also weak there.
• Need to search for optimal polarization
• that minimizes clutter response
• Or in cases target response is known a priori
  (e.g. through target/forest simulation) a
  polarization that maximizes target-to-clutter
  ratio

14
Problem Statement
1- Clutter minimization
Search for a set of polarizations that minimizes
the maximum clutter response among all forest
realizations (m).
2- Target-to-clutter maximization
Search for a set of polarizations that maximizes
the minimum target/clutter response among all
forest realizations (m).
These cost functions are highly non-linear use a
genetic algorithm search based optimization method
15
Polarization Optimization Procedure Using Genetic
Algorithm
There is a one-to-one correspondence between
and a point on Poincare Sphere
1- Discretization of polarization state Uniform
polarization (Dc10) produces 13-bit Gene.
and require 26-bit Chromosome (226
possibilities) 2- Random generation of initial
population 3- Evaluation of Chromosomes using the
optimization cost function 4- Convergence? 5-
Natural selection (discarding poor performing
Chromosomes) 6- Mating and mutation 7- Recursion
of steps 3 through 6
16
Flowchart of Digital GA
17
Input Data for GA
Number of forest realizations 10 Monte Carlo
simulations Density of forest 0.05
trees/m2 Pixel area 200 m2 Frequency 2
GHz Radar Incidence angle

• 10 Covariance matrices for forest
• 10 Covariance matrices for Target embedded inside
  forest

18
Convergence of GA Algorithm
Convergence Achieved after 20 iterations.
Seed Initial population
Note Clutter response is computed from an area
of 200 m2 (target occupies less than 1 m2 )
19
Optimal Tilt angles
Results of GA for different seeds
Optimal ellipticity angles
Two solutions exist Different initial seeds
produce similar results as expected
20
Optimum Polarization 1
Maximize target to clutter backscattering RCS
ratio
10 dB
Solution2
Solution1
Optimum polarization will provide 10 dB
improvement on target/clutter ratio compared to
tradition pol. configurations.
T
T
R
R
21
Results of GA for Clutter minimization
Optimal Tilt angles
Optimal ellipticity angles
Two solutions exist Different initial seeds
produce similar results as expected
22
Clutter Minimization
Minimize clutter backscattering RCS
-10 dB
Solution2
Solution1
R
R
Optimum polarization will provide 10 dB reduction
in clutter backscatter compared to tradition pol.
configurations.
T
T
23
Summary of Polarization Synthesis

• Polarization agile radars (different polarization
  modality) have the ability to suppress clutter.
• If important polarization signature of desired
  targets are known polarization synthesis can
  drastically enhance S/C.
• Physics-based target foliage model can provide
  foliage-embedded target signature

24
Hybrid FDTD/forest model

• Using the coherent forest model, calculate the
  fields on an FDTD boundary enclosing the target.

h-pol. or v-pol.
2. Using FDTD, compute the scattered fields from
the target on the same grid.
including all interactions
25
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.
26
Hybrid FDTD and Foliage Model
Based on reciprocity
can be any equivalent current
which can generate scattered field from target.
On FDTD Box
Therefore
27
Flow Chart
(1)
(2) Get the time domain response
Incident field from the forest on FDTD box
Fourier Trans.
(3)
Solve scattering from hard target get the
scattered field on the FDTD box
Must be run for two fundamental incident wave
polarizations and at many frequencies over the
desired band
FDTD
Fourier Trans.
(4) Get frequency domain
(5)
Apply reciprocity to find target/foliage
backscatter
28
Validation of Hybrid Method (1)
3m x 3m x 3m Dihedral in free space (no
foliage) VHF band (20-200 MHz)
GOPOPOPTD agree well at high frequencies
Time Domain
Frequency Domain
Very good agreement between direct FDTD and
Hybrid method
29
Validation of Hybrid Method (2)
3m x 3m x 3m Dihedral above a ground plane
5.6 i 0.9
Note An absorber layer is considered just below
the FDTD box to suppress ground reflections from
shadowed area.
30
Target Simulation inside the forest
target response alone
No foliage
shh
Horizontal Polarization
Phase
with foliage
Number of Trees 8 Density of forest
0.05 Simulation area 160 m2 VHF frequency band
Vertical Polarization
No foliage
Phase
svv
with foliage
Note Significant target foliage interaction at
higher frequencies.
31
Comparison in Time Domain
Total response Foliage Target
Horizontal Polarization
Vertical Polarization
Note Forest distorts the target response.
32
Summary

• After 2.5 year we are now in a position to
  consider radar response of varieties of targets,
  foliage at different frequencies, polarizations,
  incidence angles, etc. to try multi-modal target
  detection.
• Phenomenology of target/foliage interaction can
  be carried out most accurately