1. Physics-based Modelling of Foliage-Camoulaged Targets
K. Sarabandi and
M. Dehmolaian
Radiation Laboratory
The University of Michigan, Ann Arbor, MI

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 ( MHz) and is developed to investigate the scattering behavior of hard targets embedded inside a forest canopy.

3. Phase shh 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
GOPOPO+PTD
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 density=0.05 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. 3l 3l 4l 10l 8l 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. Including foliage interaction
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
<CROSS-POL>
<Co-POL>

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 y=50, 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 (Dc=10) 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
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. +10 dB 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. -10 dB Clutter Minimization Minimize clutter backscattering RCS
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.
Observation point
Source point
exchanging
Note: Using this procedure, interaction between forest & target is inherently taken into account.

26. Based on reciprocity: On FDTD Box: Hybrid FDTD and Foliage Model
can be any equivalent
current which can generate
scattered field from target.
On FDTD Box:
Therefore:

27. (2) Get the time domain response
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 ( MHz)
GOPOPO+PTD 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
= i 0.9
Note: An absorber layer is considered just below
the FDTD box to suppress ground reflections from shadowed area.

30. target response alone Target Simulation inside the forest
No foliage
Horizontal Polarization:
shh
Phase
with foliage
Number of Trees = 8
Density of forest = 0.05
Simulation area = 160 m2
VHF frequency band
Vertical Polarization:
No foliage
svv
Phase
with foliage
Note: Significant target foliage interaction at higher frequencies.

31. Total response = Foliage + Target
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