TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.4, April 201
4, pp. 3208 ~ 3
2
1
3
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i4.4932
3208
Re
cei
v
ed Se
ptem
ber 21, 2013; Revi
se
d No
vem
ber
20, 2013; Accepted Decem
ber 10, 20
13
Iterative Integral Equation Method for Efficient
Computation of Multiple Scattering
Xiao
y
a
n Zha
ng*
1,2
, Zhi
w
e
i Liu
1,2
, S
h
an He
1
, Yingting Liu
1
, Yue
y
uan Zhan
g
1
1
East China Ji
a
o
tong U
n
iv
ersity, Na
ncha
ng, 3
300
13, Ch
ina
2
T
he State Ke
y Labor
ator
y
of Millim
eter W
a
ve, Nanj
ing, 2
1
0
096, Ch
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: xy_zh
ang
31
29@ic
lo
ud.co
m
A
b
st
r
a
ct
An iterative int
egra
l
equ
atio
n
me
tho
d
(IEM) is propose
d
for calc
ul
atio
n of the electro
m
a
g
n
e
tic
(EM) scattering field from
geom
etries with multiple reflections
, suc
h
as rough s
u
rface, dihedr
al
and
trihedr
al. T
he first reflection i
s
comp
uted b
y
physical o
p
ti
cs and the co
upli
ng effects are
c
o
mput
ed by
integr
al e
q
u
a
ti
ons. T
he av
era
ge si
z
e
of the t
r
ian
gul
ar
mesh
es use
d
i
n
the
prop
osed
meth
od is
a co
nsta
nt
valu
e w
h
ile
th
at in
meth
od
of moment is
a li
near f
uncti
on of w
a
ve
len
g
th. As a res
u
lt, compare
d
w
i
th
meth
od
of
mo
me
nt, the pr
o
pose
d
meth
od
w
ill le
ad to
l
e
ss nu
mber
of unkn
o
w
n
s for
electric
ally
lar
g
e
geo
mety. Accordin
gly,
this method is
mor
e
efficient an
d suitab
le
for fast comp
utatio
n of scattering fr
o
m
electric
ally
larg
e ge
o
m
etry. F
u
rther
mor
e
, w
hen c
o
mp
ared
w
i
th hig
h
freq
uency
asy
m
pt
otic
metho
d
, t
h
e
prop
osed
meth
od is
mor
e
ac
curate. T
he n
u
m
er
ical r
e
sult
s
de
mo
nstrate that this
m
e
thod
i
s
a
c
cu
ra
te
fo
r
computati
on sc
attering w
i
th multipl
e
reflecti
o
n
s and effici
ent
for electrical
ly larg
e obj
ect.
Ke
y
w
ords
:
iter
ative
inte
gral e
quati
on meth
o
d
,
multi
p
l
e
scattering, el
ectro
m
a
g
n
e
tics
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Electrom
agn
etic wave
scattering p
r
obl
ems a
ddress the physical
issu
e of det
ecting the
diffraction p
a
ttern of the electroma
gne
tic radi
atio
n scattered fro
m
a large an
d compl
e
x body
whe
n
illumi
n
a
ted by
an
inci
dent i
n
comin
g
wav
e
[1-2]. A good
un
derstanding
of t
hese
phen
omen
a i
s
cru
c
ial to
ra
dar
cross
se
ction (
RCS
) ca
lculatio
n, ant
enna
de
sign,
electroma
gne
tic
comp
atibility, and
so
on.
Gene
rally, the scatte
ri
ng
of arbit
r
ary
geomet
ry ca
n be
accu
rat
e
ly
comp
uted by
method of moment (Mo
M
) [3]. Howe
ve
r, since the multiple ref
l
ection
s exist, the
coupling effects
will l
ead to a
slow
convergence hi
story. Besides,
t
he el
ectri
c
ally
large geom
etry
will lead to
a larg
e num
ber of u
n
kno
w
n
s
, whi
c
h
make
s the
memory
req
u
irem
ent of
MoM
incredibl
e large. Both the conv
e
r
ge
nce
and the me
m
o
ry req
u
irem
ent are the m
a
in bottlene
ck for
MoM. Accord
ingly, an num
erical meth
od
named it
e
r
at
ive integral
e
quation m
e
th
od is
pro
p
o
s
ed
for efficient calcul
ation of scattering fro
m
any elec
tri
c
ally larg
e ge
ometrie
s
with
coupli
ng effe
cts,
su
ch a
s
rou
g
h
surfa
c
e, dih
edral, trih
edral and so on.
At prese
n
t, numeri
c
al met
hod such as
the method
of moments
(MoM
) in [3] has the
spe
c
ialtie
s of
comp
utationa
l com
p
lexity and sl
ow
sp
ee
d whil
e with
the hig
h
p
r
e
c
i
s
ion. Influe
nced
by the
com
p
u
t
er
comp
uting
ability, only
good
condi
to
ned
syste
m
with n
o
t very
large
nu
mbe
r
of
unkno
wn
s co
uld be analy
z
ed by traditional method of
moment. For example, the scatteri
ng fro
m
3D ta
rget o
n
a ro
ugh
su
rf
ace
with the
scale of n
o
more th
an 3
0
λ
×
30
λ
[4],
λ
represent
th
e
wavele
ngth.
Actually, the
roug
h surfa
c
e is u
s
u
a
lly hund
red
s
of t
hou
san
d
s
of wavele
ngth
s
. By
contrast, the
aymptotic me
thod sho
w
s l
o
w p
r
e
c
i
s
ion,
su
ch
as
ki
rchhoff app
roxi
mation (KA
)
[5],
physi
cal
optics
(PO) [6], et
c. Due
to the
sm
all
co
mp
u
t
ational
comp
lexity and fa
st spe
ed, it
ca
n
be further
si
mplified into the app
roxima
te mathem
atical expressio
n
s wh
en
stu
d
ying the far-field
cha
r
a
c
teri
stics of
rou
gh
su
rface
scatte
ri
ng. Hy
b
r
id
al
gorithm
which combin
ed
Analytical m
e
thod
with n
u
me
rical metho
d
wa
s p
u
t forwa
r
d
by G. A. Thi
e
le a
nd oth
e
rs in
197
5. Foll
owe
d
by hyb
r
id
method h
ad
been in
co
ntinuou
s devel
o
p
ment, and it
had ma
de si
gnifica
nt effect on imp
r
ovi
ng
the efficie
n
cy
of alg
o
rithm
.
In 200
8, Ji
n Yaqiu
p
r
op
ose
d
the
hyb
r
id m
e
thod
which
combin
e
d
kirchh
off app
roximation
m
e
thod
with th
e meth
od
of mome
nts
(K
A-MoM) in
[7
]. This
meth
od
impleme
n
ted
the ge
ne
ral
rough
surfa
c
e
,
su
ch
a
s
so
il
and
sea,
efficien
cy
cal
c
ul
ation fo
r ta
rg
et
EM scatteri
ng
field. Howev
e
r, KA or PO
is onl
y appli
c
able to large
-
scale ro
ugh surface with lo
w-
roug
h an
d smooth. When
the ro
ugh
ne
ss i
n
crea
se
s,
the co
uplin
g
effects in
cre
a
s eith
er.
Usi
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Iterative Integ
r
al Equatio
n Method for Ef
ficient Com
p
u
t
ation of Multiple… (Xia
oya
n
Zhang
)
3209
KA or PO on
ly will not lea
d
to rea
s
o
n
a
b
le re
sult
s. Fung an
d othe
rs
com
b
ined
KA with SPM,
putting forwa
r
d the i
n
tegral
equ
ation m
e
thod
(IEM) f
r
o
m
[8-9]
whi
c
h
trial
scope
b
r
oade
r in
19
9
2
.
In 2003, the
algorith
m
is i
m
prove
d
by Che
n
. The im
proved AIEM
can
be u
s
ed
to a wide
r ro
ugh
para
m
eters range. It is ap
plied to ch
ara
c
teri
stics of terrai
n
feature
s
study in [10].
Whethe
r the
traditional IE
M or the AIEM, t
he efficiency mainly e
m
bodie
s
in
consi
deri
ng
only one time about the
effect of mutual co
upling
scattering fiel
d betwe
en the rou
gh a
r
ea
element
s. Actually, the incre
a
se of the se
ve
ral re
peated mutu
al cou
p
ling
scattering fie
l
d
betwe
en th
e
ro
ugh
area
elem
ents can't b
e
ig
no
red
while th
e roug
h
surf
ace
rough
ne
ss
increa
sed. In
this pa
per, b
a
s
ed
on the t
r
aditional
algo
rithms
of IEM, an efficient i
t
erative integ
r
al
equatio
n met
hod
(IEM) is propo
sed,
which
can
cal
c
ulate the
EM
scatteri
ng fo
r the
diel
ectri
c
target. Thi
s
al
gorithm
co
nsi
ders
several t
i
mes
abo
ut
th
e effect of
mu
tual co
uplin
g
scattering
fiel
d
betwe
en th
e
rou
gh
area
eleme
n
ts. It
uses the
n
ear-field radit
i
on
formula
r
to
co
mpute
the
c
o
up
lin
g
fie
l
d. T
h
e
c
h
ar
ac
te
r
i
s
t
ic
o
f
gr
id s
u
bd
iv
isio
n coul
d
not affected by
the influen
ce
of
t
he
diele
c
tric
co
n
s
tant. The
r
ef
ore, IEM ha
s an
a
d
vant
age ove
r
Mo
M whe
n
cal
c
ulating the EM
scattering
pro
b
lem for diel
e
c
tri
c
target. T
he mathem
atical theo
ry of IEM is introd
uce
d
in se
cti
on
2 and then th
e nume
r
ical e
x
perime
n
t pro
v
es the effe
ct
iveness of this algo
rithm in
sectio
n 3. The
con
c
lu
sio
n
is
made in secti
on 4.
2. Iterativ
e I
E
M for Multi
p
le Reflections
Suppo
se t
hat
the g
eom
etry su
rface i
s
d
i
vided into
m
fac
e
ts and
()
a
A
r
is
any on
e of
th
e
element
s whil
e
P(
)
p
r
is the dete
c
ting poi
nt. Whe
n
the incident EM wa
ve
i
E
illuminates the area
element, it will be formed t
he equivale
nt surfa
c
e
current
J
ei
, where
1
,
2,
3....
i=
n
. At this
time
,
apart f
r
om th
e indu
ction
to produ
ce
direct
scattering
d
s
E
, the coupli
n
g indu
ction
b
e
twee
n
ei
J
,
will al
so p
r
od
uce th
e coupl
ing field
c(
)
ss
i
E
, as
is sho
w
n in F
i
gure
1(a). T
herefo
r
e, the
scatterin
g
field of any point inclu
d
ing
point
P
and
A
on the su
rface of the targ
e
t
can be represe
n
ted a
s
:
sd
c
(
)
ss
s
s
1
n
i
i
E
=E
E
(1)
i
E
()
d
s
a
r
E
()
ci
s
s
E
00
,
11
,
()
d
s
p
r
E
()
ci
s
s
E
(a) T
he top ro
ugh surfa
c
e field
i
E
00
,
11
,
()
d
s
a
r
E
()
d
s
p
r
E
()
ci
s
s
E
(b) T
he botto
m roug
h su
rface field
Figure 1. Sch
e
matic Di
ag
ram of IEM Algorithm
Her
e
,
n
refers to the coupl
ing numb
e
r. And
d
s
E
can b
e
calcul
ated accordin
g to the
following formula:
d
s0
0
0
2
0
1
,'
(
'
)
'
IJ
ei
s
j
kG
d
s
k
Er
r
r
(2)
By the formula of (2), we
can
get the direct scatteri
ng
field
d
s
()
p
E
r
of the point
P
and the dire
ct
scattering fiel
d
d
s
()
a
E
r
of the point
A.
When the effect of the
EM mutual couplin
g field betwe
en
Evaluation Warning : The document was created with Spire.PDF for Python.
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02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 3208 – 3
213
3210
the area el
e
m
ents
cann
ot be ignored,
d
s
()
a
E
r
is a new in
ci
dent field for the area el
e
m
ents
P
.
Then
i
E
sho
u
ld
be re
pla
c
ed
by
d
s
()
a
E
r
, and then
the co
upling
field
c(1)
ss
E
co
uld b
e
cal
c
ul
ated.
This
pro
c
e
ss will b
e
count
inued
until th
e co
uplin
g fie
l
ds b
e
twe
en t
he ele
m
ent
s
become
we
a
k
.
Finally, by th
e formulate of
(1) , we can
get
s
s
E
.
Above is targ
eted for a perfect electri
c
al
con
d
u
c
tor (P
EC), the surf
ace do
es n
o
t exist the
equivalent m
agneti
c
curre
n
t, and the
scattering field
cal
c
ulatio
n is
relatively sim
p
le. Accordin
g to
the equivalen
c
e pri
n
ci
ple, there exi
s
ts th
e equivalent
electri
c
curre
n
t
J
e
and magn
etic cu
rrent
J
m
on the homo
gene
ou
s med
i
um target surface. They m
eet the dema
nds of (3) a
s
follows:
J
J
is
m
is
e
nE
E
nH
H
(3)
The sc
attering EM fields
,
s
E
and
s
H
, are listed
below:
s
00
0
0
2
0
1
,'
(
'
)
'
,
'
(
'
)
'
IJ
J
ei
m
i
ss
j
kG
d
s
G
d
s
k
Er
r
r
r
r
r
(4)
s
0
00
2
00
1
,'
(
'
)
'
,'
(
'
)
'
IJ
J
mi
ei
ss
k
j
Gd
s
G
d
s
k
Hr
r
r
r
r
r
(5)
The scatte
rin
g
cha
r
a
c
teri
stics of the di
electr
i
c
o
b
je
cts are
differe
nt from those of the
PEC obje
c
ts. For the diele
c
tric obje
c
ts, the ele
c
trom
a
gnetic
wave can tran
smit in
the inner of the
objects, whi
c
h will cause
the transmission field.
And the transmissi
on filed could occur the
multiple coup
ling field fu
rth
e
r. While, for
the PEC
obj
e
c
ts, the total
reflection
occurs on th
e P
E
C
surfa
c
e of the
target, so the
r
e is no tra
n
smissi
on
field. In this work, only the scatt
ering a
bove the
surfa
c
e
of the obje
c
ts i
s
con
s
id
ere
d
, therefo
r
e, n
o
t all of the transmi
ssion fi
led should
b
e
con
s
id
ere
d
. Ho
wever,
wh
en the an
gle
betwe
en the
incid
ent direction of the EM wave an
d
the
norm
a
l di
re
ction of th
e ta
rget
su
rface
is a
n
a
c
ute
angle,
as is sh
own in
F
i
gure
1
(
b), t
he
contri
bution
of the scattering field fo
r the poi
nt P sho
u
ld be f
r
om the b
o
ttom sp
ace of
the
diele
c
tric ta
rg
et. To cal
c
ula
t
e the co
uplin
g EM field, the inne
r surfa
c
e of in
cid
e
n
c
e EM field
a
n
d
the no
rmal
o
f
the eve
r
y a
r
ea
elem
ent
sho
u
ld
be
rel
e
vant in th
e
oppo
site
dire
ction, a
nd th
e
reflectio
n
a
n
g
l
e should
follo
w the
snell'
s l
a
w.
Here, the
co
upling
EM
field which
sp
read
s f
r
om th
e
se
con
d
half o
f
space is the
transmi
ssion
field.
3. Results a
nd Discu
ssi
on
Figure 2 is a
model of 3
D
roug
h su
rfa
c
e with ro
ugh
ness. Let
L
= 1.0m and
σ
=0.
0
m,
0.2m, 0.5m, whe
r
e
L
is th
e correl
ation length an
d
σ
is the root me
an sq
uare (RMS) height of
the
roug
h su
rface. Calcul
ate the
RCS of the hori
z
o
n
tal
polari
z
ation
rada
r ra
ndo
m rough
su
rface
whi
c
h i
s
me
n
t
ioned a
bove.
The pl
ane i
n
cide
nt wave’
s
frequ
en
cy is 300M
HZ, al
ong the
verti
c
al
dire
ction. Fi
g
u
re
3
sho
w
s t
he
comp
ari
s
o
n
of th
e
nu
m
e
ric
a
l re
sults
of
t
he p
r
o
posed iterative I
E
M
method in thi
s
pap
er
with
MoM and KA
with the in
ci
dent pitch
an
gles
ran
ge from -90 to
90
deg.
From th
e n
u
m
eri
c
al
cal
c
u
l
ation results, it is
n
o
t ha
rd to
se
e, when th
e
surf
ace
ro
ugh
ne
ss
increa
se
s, the cal
c
ulatio
n
pre
c
isi
on
cha
r
acte
ri
stics of
IEM algorith
m
sho
w
s bett
e
r than KA a
nd
clo
s
e to M
o
M. This i
s
b
e
c
au
se KA
do
es n
o
t take i
n
to acco
unt t
he mutu
al co
upling fiel
d when
cal
c
ulatin
g th
e EM
scatteri
ng of
ro
ugh
surfa
c
e,
while la
rge
calcul
ation e
r
ror wi
ll be i
n
tro
duced
becau
se of t
he hig
her ro
u
ghne
ss. And
the erro
r
will increa
se by
followin
g
the mutual cou
p
ling
stren
g
th. In orde
r to de
m
onstrate the
suitabl
e fo
r
use, the
con
t
rast of the t
h
ree
algo
rith
ms’
results di
spla
ys in
Figu
re
4 for dih
e
d
r
al
angl
e a
n
d
tri
hedral
angle
model
with
th
e in
cide
nt pit
c
h
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TELKOM
NIKA
ISSN:
2302-4
046
Iterative Integ
r
al Equatio
n Method for Ef
ficient Com
p
u
t
ation of Multiple… (Xia
oya
n
Zhang
)
3211
angle
s
ran
g
e
from
0 to
90
deg. T
he
cal
c
ulatio
n
resul
t
s sho
w
ed
th
at IEM calcul
ation
re
sults
are
more
con
s
i
s
tent than KA with MoM.
Figure 2. 3D
Rou
gh Surfa
c
e Model
(a) PEC
RS:
L
= 1.0m,
σ
= 0m
(b) PEC
RS:
L
= 1.0m,
σ
= 0.2m
(c
) PEC RS:
L
= 1.0m,
σ
= 0.5m
Figure 3. The
Nume
rical Contra
st of Mo
M, KA,
IEM f
o
r PEC
Ro
ug
h Surface (RS)
(a) PEC
DA
(b) PEC TA
Figure 4. The
Nume
rical Contra
st of MoM, KA,
IEM for PEC Dih
e
d
r
al Angle (DA
)
and T
r
ihed
ral
Angle (TA)
-90
-60
-30
0
30
60
-
1
00
-5
0
0
50
1
0
0
Angle
(
d
e
g)
RC
S
(
d
B
s
m
)
Mo
M
KA
IE
M
-10
0
10
20
30
-100
-5
0
0
5
0
100
An
gle
(
d
e
g)
RCS
(
dB
s
m
)
Mo
M
KA
IEM
-20
-10
0
10
20
30
-
1
00
-50
0
50
10
0
Angl
e(d
e
g)
RCS
(
dB
s
m
)
Mo
M
KA
IEM
-6
0
-3
0
0
30
60
0
2
04
0
6
08
0
1
0
0
An
gl
e(d
e
g)
R
C
S(
dB
s
m
)
Mo
M
KA
IEM
-6
0
-3
0
0
30
60
0
1
02
0
3
04
05
0
6
0
7
08
0
9
0
1
0
0
A
n
gl
e(d
e
g)
RCS
(
d
B
s
m
)
Mo
M
KA
IEM
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 3208 – 3
213
3212
L
= 1.0m
i
s
cha
ngel
ess, by
σ
= 0.0m
, 1.0m, 1.5m
three
group
s of di
ele
c
tri
c
roug
h
surfa
c
e
o
n
th
e ba
ckg
r
ou
n
d
of
ocean
a
s
a
n
exampl
e, whil
e th
e relative diel
ectric
co
nsta
nt
wa
s
4.0. Assume
t
hat the
inci
de
nt wave
for h
o
rizont
al pola
r
izatio
n
i
s
pyramidal wave
and
th
e width
is
2.0
λ
. Th
e incident directio
n rem
a
ine
d
u
n
ch
ang
ed ju
st like the p
r
e
v
ious exam
pl
e. It shows t
he
nume
r
ical results of KA
an
d IEM with
th
e differe
nt
su
rface
roug
hn
ess in
Figu
re
5. It’s not
difficult
to see,
whe
n
the su
rface rough
ne
ss in
crea
se
s,
the di
fference of th
e nume
r
i
c
al result
s bet
we
en
KA and IEM
is g
r
e
a
ter.
As a
re
sult,
the coup
lin
g
field ab
out
the area
ele
m
ents
gradu
ally
enha
ncement
is not allo
we
d to ignore. IEM is also
ap
plica
b
le to ot
her di
ele
c
tric
model. Figu
re 6
sho
w
s the nu
meri
cal re
sult
s of the dihed
ral angl
e and
trihed
ral an
gle in the same
conditio
n
s.
(a) Die-
RS:
L
= 1.0 m,
σ
= 0.0 m
(b) Die-
RS:
L
= 1.0 m,
σ
= 1.0 m
(c
) Die
-
RS:
L
= 1.0 m,
σ
= 1.5 m
Figure 5. The
Nume
rical Contra
st of KA, IEM fo
r Different Diel
ect
r
ic Roug
h Surfa
c
e(Die
-
RS)
(a) Die-
DA
(b) Die-
TA
Figure 6. The
Nume
rical Contra
st of KA, IEM
for Diele
c
tri
c
Dihe
dral Angle (Die-DA) and
Trihedral Angle (Die-TA)
4. Conclusio
n
The propo
se
d IEM has more exten
s
i
v
e app
licabili
ty and high
er accu
ra
cy
due to
con
s
id
erin
g the coupli
ng
field betwee
n
the ta
rget
su
rface are
a
eleme
n
ts.
This
pro
p
o
s
ed
-12
0
-8
0
-4
0
0
40
-
100
-5
0
0
5
0
100
A
n
gl
e(
d
e
g)
RCS
(
d
B
s
m
)
KA
IEM
-4
5
-3
5
-2
5
-1
5
-5
5
-1
00
-
5
0
0
50
10
0
An
gl
e(
d
e
g)
RCS
(
d
B
s
m
)
KA
IEM
-2
5
-1
9
-1
3
-7
-1
5
-1
00
-
5
0
0
50
1
0
0
A
n
gl
e
(
de
g)
RCS
(
d
B
s
m
)
KA
IE
M
-8
0
-5
0
-2
0
10
40
0
2
04
06
0
8
0
1
0
0
A
n
gl
e(deg)
RC
S
(
dB
s
m
)
KA
IE
M
-8
0
-5
0
-2
0
10
40
0
2
04
0
6
08
0
1
0
0
An
gl
e
(
d
e
g
)
RC
S
(
dB
s
m
)
KA
IE
M
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Iterative Integ
r
al Equatio
n Method for Ef
ficient Com
p
u
t
ation of Multiple… (Xia
oya
n
Zhang
)
3213
algorith
m
app
lies to cal
c
ul
a
t
e the target scatteri
ng fiel
d not only for the PEC mod
e
l comp
utatio
n,
but also for di
electri
c
mo
de
l computatio
n
.
The
numeri
c
al experime
n
t result
s sh
ow
that even for a
smooth PE
C target EM scattering
cal
c
u
l
ation, wh
ile
KA produ
ce
s large
r
calcul
ation erro
r, IEM
cal
c
ulatio
n error i
s
sm
all
with MoM, a
nd the
calculation re
sult
s are in g
ood
agre
e
me
nt. Also,
IEM are
not
affected
by th
e influe
nce of
the di
ele
c
tr
ic co
nsta
nt whi
l
e me
shin
g, so it’s l
e
ss tim
e
-
con
s
umi
ng
a
nd mo
re
adv
antage
to
cal
c
ulate
the ta
rget EM
scat
tering
proble
m
. As fo
r la
rge
scale diele
c
tri
c
rou
gh su
rfa
c
e mod
e
l,
its roug
hne
ss d
o
not m
eet the
appli
c
a
b
le
condition
of K
A
,
so the IEM is more a
ppli
c
a
b
ility than KA.
Ackn
o
w
l
e
dg
ements
The auth
o
rs
woul
d like to
thank the
su
pport of
Nati
onal Sci
e
n
c
e
Found
ation
of China
(No: 6
106
10
02, 6126
100
5); Ope
n
Project of St
ate Key Labo
ratory of Millimeter
Wave
(No:
K20132
5, K2013
26); Yo
uth Found
ation of Jiangx
i Provincial
Dep
a
rtme
nt of Science and
Tech
nolo
g
y (No: 2012
2B
AB21101
8); Youth Found
ati
on of Jian
gxi Provincia
l
Depa
rtment
of
Educatio
n (No: GJJ133
52,
GJJ133
21, GJJ13
320
).
Referen
ces
[1]
J Hu,
X Z
h
u
,
L Che
n
. El
ectromag
netic
Enviro
nment
and T
a
rget
Simulat
o
r for
Rad
a
r T
e
st.
T
E
LKOMNIKA Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
ng.
2013; 1
1
(7): 3
699-
370
3.
[2]
X W
u
, L W
ang, L Yan, X F
Xia. Simu
lati
on of
Rad
a
r T
r
ack Based o
n
Data Mini
ng
T
e
chniq
ues
.
T
E
LKOMNIKA Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
ng.
2013; 1
1
(7): 3
780-
378
8.
[3]
RF
H arringto
n
.
F
i
eld Comp
utation b
y
Mom
e
nt
Methods. Mala
bar, F
l
a.: R. E. Krieger. 19
68.
[4]
HX Ye, YQ Ji
n. A H
y
br
id A
nal
ytic
al-n
umer
ical
A
l
g
o
rithm
for Scatterin
g
from a 3-
D T
a
rget a
bove
a
Ran
doml
y
R
o
u
gh Surface.
Ac
ta Physica Sinica.
2008; 5
7
(2)
:
839-84
6.
[5]
EI T
horsos.
T
he V
a
li
dit
y
of
the Kirc
hhoff
A
ppro
x
imati
o
n for R
oug
h
Surface Sc
atterin
g
Usi
ng
a
Gaussia
n
Rou
ghn
ess Spectr
um.
Journa
l of the Acoustica
l Society of Ame
r
ica.
198
8; 83(
1): 78-92.
[6]
PY Ufimtsev. Method
of Ed
ge W
a
ves i
n
the Ph
ysic
al T
heor
y
of Diffraction.
Sovyets
koye Radio,
Moscowj.
1971
.
[7]
GA T
h
iele, T
H
Ne
w
h
ous
e. A
H
y
brid
T
e
chni
q
ue for
C
o
mbi
n
i
ng M
o
ment
Me
thods
w
i
th
the
Geometrica
l
T
heor
y
of Diffraction.
IEEE Trans Antennas
Propagat.
197
5; 23(1): 62-6
9
.
[8]
BF
Apostol. S
c
attering
of th
e Elec
trom
agn
etic W
a
ves fro
m
a Ro
ugh S
u
rface.
Jour
na
l of Mod
e
r
n
Optics.
2012; 5
9
(18): 40
7-4
1
6
.
[9]
Z
Li, AK
F
ung
. A Reformulation of the Surface F
i
eld Inte
gral Eq
uatio
n.
Jo
u
r
na
l
o
f
El
ectro
m
ag
ne
tic
W
a
ves and Ap
plicati
on.
1
991;
5(2): 195-2
0
3
.
[10]
KS Chen, T
D
W
u
, L
T
s
ang.
T
he Emission of Roug
h
Surfaces Ca
lcul
ate
d
b
y
th
e Integ
r
al Equ
a
ti
o
n
Method
w
i
th
a
Comp
ariso
n
to
a T
h
ree-dim
e
nsio
nal
Mome
nt Metho
d
Sim
u
lati
ons.
IEEE Trans
Geosc
i
Rem
o
te Sens.
200
3; 41(1): 90
-101.
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