[9] S. Bellez, C. Dahon and H. Roussel, "Analysis of the Main. Scattering Mechanisms in Forested Areas: An Integral. Representation Approach for Monostatic ...
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REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
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REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < Each tree has 8 primary branches and their heights vary between 1.2 m to 4.5 m. The relative permittivity and conductivity of the ground are r 5 and 0.07S/m . The tank is 2.6m high, 3.2min length and 1.5m in width. The incident field is a plane wave of frequency f 400MHz .
Fig.11. Geometry of the considered scene.
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Not unexpectedly, for the co-polarization cases of VV and HH, the maxima are in the forward ( obs inc and obs inc ) and backward ( obs inc and obs inc 180 ) directions, when we consider only the forest, the latter being the strongest (the subscript obs refers to the angles of the observation points). This is due to the double bounce of signals between the trunk and the ground. Both of these lobes are relatively narrow. This is the typical bi-static scattering pattern of a single vertical cylinder laying on a flat surface, and by extension the one of a forest patch comprised of vertical trunks and branches with relatively vertical orientations. In the other side concerning the cross-polar HV and VH given in figure 13, the maxima are not in the backward and forward directions. This may be due, at least partly, to the presence of primary branches of the trees. We can also imagine being able to better detect the target for these polarizations if we use bi-static configurations in . We notice also that the level of polar VV is more important than the other polar field; consequently, we use a different scale for this polarization to maintain a contrasting image. It is worthwhile to note that the presence of a metallic target significantly enlarges the aperture of the two main lobes of the pattern. This leads us to the conjecture that the most desirable bi-static angular directions for detecting metallic objects are not in the back- and forward-scattering directions (using HH and VV polarisations) but in the angular ranges that skirt these angles instead.
Fig.12. Influence of the presence of a metallic target in a forest environment on the amplitude of the co-polar VV and HH for the incident angle
(inc , inc ) ( 45, 0) : (a) without the target (dB). (b) in presence of the target (dB).
Figure 12 presents the amplitude of the co-polarisations (VV and HH) of the scattered field calculated at a distance R=2000m with respect to the direction cosines ( uˆ sin cos and vˆ sin sin ), both in presence and absence of the metallic target. This is done in order to investigate the effect of the presence of the target on the field diffracted by the forest. For this example a bi-static configuration is used. The incident angles are inc , inc 45,0 and the observation points are such that s varies from 0° to 89° (with a step of 1°) and the azimuth angle s varies from 0° to 360° (with a step of 5°).
Fig.13. Influence of the presence of a metallic target in a forest environment on the amplitude of the cross-polar VH and HV for the incident angle
(inc , inc ) ( 45,0) : (a) without the target (dB). (b) in presence of the target (dB).
In figure 14, we investigate the effect of the coupling between the tank and the forest. To do so we compare the diffracted field by the scene illustrated in figure 11 by taking into account all the mechanisms present in this case to the coherent addition of the field scattered only by the forest and only the tank. There is a noticeable difference between the two
> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < scattered fields, so we can conclude that the coupling between the tank and the forest is not negligeable for this case.
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of the scattered field using the Huygens principle could be very time-consuming. In fact, it can take more time than the resolution of the linear system. This calculation can be expressed in a matrix form and then compressed using ACA technique. The time consumption versus the number of trees is shown in Figure 16. This simulation has been carried out by using a computer with a CPU Intel® i7 4600U and 16 Gb RAM). We observe that the execution time increases almost linearly with the number of trees, which is directly related to the number of unknowns.
Fig.14. Influence of the coupling between the metallic target and the forest environment on the amplitude of the polar HH for the incident angle
(inc , inc ) ( 45,0) : (a) without the target (dB). (b) in presence of the target (dB).
Additionally, we investigate the effect of the presence of the forest on the radar cross-section of the tank, and we also treat the same scene for a monostatic configuration (HH polarization). The incident field is a plane wave propagating along the direction defined by 0 inc 90 and inc 0 . The results of comparison are given in figure 15. It can be seen from this figure that the presence of the tank affects the RCS of the forest and depends on the position of the tank in the forest and the surrounding trees. For the other case of copolarization (VV), the difference between the RCS of the forest alone and that of the forest in the presence of target is less obvious.
Fig.16. Time consumption in terms of number of trees.
V. CONCLUSION In this paper, an efficient formulation for the analysis of targets placed in a forest environment has been presented. The proposed scheme hybridizes two electromagnetic formulations for dielectric and metallic objects. The model was numerically validated for different test scenarios, obtaining good agreement with the commercial software FEKO. Finally, the effect of metallic targets on the fields diffracted by realistic forest area was investigated from the point of view of detecting these targets, which was the main goal of this study. APPENDIX DYADIC GREEN’SFUNCTION FOR A TWO LAYERED STRATIFIED MEDIA Fig.15. The effect of the forest on the polar HH monostatic RCS on theta of the tank.
The simulation of the scene given in figure 11 has been carried out on a shared memory computer (CPU Intel® CPU E5-1650 v3 with 128 Go RAM). The discretization of the scene leads to 773 670 unknowns (762 240 for the volume formulation and 11430 for the surface one). Using a CBFM-E for the forest the number of unknowns is reduced to 93 223, thus realizing a compression rate (CR defined in [10]) of 8.17. The memory consumption for this complex scene is 96 514 Mb. The entire simulation takes 16h 25min for the bi-static case and 7h30min for the monostatic one. It should be noted that, for a large number of observation points, the calculation
In this appendix we give the elements of the dyadic Green’s function obtained using the image principle combined with the Fresnel reflection coefficients. We have
Gxx (r, r1 ) Gxy (r, r1 ) Gxz (r, r1 ) G (r, r1 ) G yx (r, r1 ) G yy (r, r1 ) G yz (r, r1 ) Gzx (r, r1 ) Gzy (r, r1 ) Gzz (r, r1 ) where
> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < Gxx (r, r1 ) g xx 0 (r, r1 ) g xx1 (r, r2 )
ρ ρ'
2
g
xx1 (r, r2 )( y y ') g yx1 (r, r2 )( x x ') ( y y ')
[6]
Gyx (r, r1 ) g yx 0 (r, r1 ) g yx1 (r, r2 )
ρ ρ'
2
g
xx1
[5]
(r, r2 )( y y ') g yx1 (r, r2 )( x x ') ( x x ')
[7]
Gzx (r, r1 ) g zx 0 (r, r1 ) g zx1 (r, r2 ) [8]
Gxy (r, r1 ) Gyx (r, r1 )
Gyy (r, r1 ) g yy 0 (r, r1 ) g yy1 (r, r2 )
ρ ρ'
2
g
xy1
(r, r2 )( y y ') g yy1 (r, r2 )( x x ') ( x x ')
[9]
Gzy (r, r1 ) g zy 0 (r, r1 ) g zy1 (r, r2 ) Gxz (r, r1 ) g xz 0 (r, r1 ) g xz1 (r, r2 )
ρ ρ'
2
g
xz1
[10]
(r, r2 )( y y ') g yz1 (r, r2 )( x x ') ( y y ') [11]
Gyz (r, r1 ) g yz 0 (r, r1 ) g yz1 (r, r2 )
ρ ρ'
2
g
xz1
(r, r2 )( y y ') g yz1 (r, r2 )( x x ') ( x x ')
[13]
Gzz (r, r1 ) g zz 0 (r, r1 ) g zz1 (r, r2 ) Where
g i (r, ri ) gi (r, ri ) ,
( ,) ( x, y, z) and gi (r, ri ) e jk
0
Green
function
of
free
[12]
1 2 gi (r, ri ) k02 r ri
space.
4 r ri
with
the scalar
r1 x ', y ', z '
[14]
[15]
and
r2 x ', y ', z ' represent the positions of the source point 2 2 and its image respectively. ρ ρ' ( x x ') ( y y ') .
ACKNOWLEDGMENT This work is supported by the French Agence Nationale de la Recherche (ANR) and the French Direction Générale de l’Armement (DGA) under the Project MOBILE.
[16]
[17]
[18]
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