I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
15
,
No
.
5
,
Octo
b
er
20
25
,
p
p
.
4
6
4
2
~
4
6
5
2
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/ijece.
v
15
i
5
.
pp
4
6
4
2
-
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4642
J
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ti
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a
l
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n
ts
fo
r
d
irec
ti
o
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-
of
-
a
rriv
a
l
(DO
A)
e
stim
a
ti
o
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is
p
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o
p
o
se
d
.
Esp
e
c
ially
t
h
is
a
p
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a
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h
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a
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p
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n
a
a
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with
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se
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a
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wh
ich
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s
d
ig
it
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tral
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fter
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a
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rm
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g
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e
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e
d
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x
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li
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it
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Cra
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r
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w
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ter
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i
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o
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h
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A
-
e
stim
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ti
o
n
a
n
d
a
n
ten
n
a
e
lem
e
n
t
s'
ra
d
iatio
n
p
a
tt
e
r
n
s,
a
rra
y
g
e
o
m
e
try
,
h
a
s
b
e
e
n
u
se
d
.
M
a
i
n
i
d
e
a
o
f
th
e
p
ro
p
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se
d
tec
h
n
iq
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is t
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t
it
tak
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s in
to
a
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c
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ti
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n
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g
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f
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h
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n
ten
n
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e
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ts.
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e
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g
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g
a
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m
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ts
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r
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tere
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t
d
istan
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e
is
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m
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st
imp
o
r
tan
t
fa
c
to
r
w
h
ich
a
ll
o
w
s
re
d
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c
in
g
th
e
v
a
lu
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o
f
th
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A
-
e
stim
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ti
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e
rro
rs.
A
c
o
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p
le
o
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t
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x
a
m
p
les
o
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lcu
latin
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iati
o
n
p
a
tt
e
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s
o
f
a
n
ten
n
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e
lem
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n
ts
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ro
v
in
g
a
c
c
u
ra
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y
o
f
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stim
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ti
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su
p
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-
re
so
l
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ti
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re
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th
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p
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a
a
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g
t
o
t
h
e
m
e
th
o
d
o
f
m
o
m
e
n
ts
(M
o
M
).
Th
e
v
a
lu
e
s
o
f
th
e
ro
o
t
m
e
a
n
sq
u
a
re
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fter
th
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A
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e
sti
m
a
ti
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n
a
re
o
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tai
n
e
d
.
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t
is
s
h
o
w
n
t
h
a
t
t
h
e
re
su
lt
in
g
h
y
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sy
ste
m
s
c
a
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re
d
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c
e
th
e
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v
a
lu
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in
DO
A
-
e
stim
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ti
o
n
wit
h
su
p
e
r
-
re
so
lu
ti
o
n
.
K
ey
w
o
r
d
s
:
C
r
am
er
-
R
ao
lo
wer
b
o
u
n
d
Dir
ec
tio
n
-
of
-
a
r
r
iv
al
esti
m
atio
n
Hy
b
r
id
an
te
n
n
a
ar
r
ay
Sm
ar
t a
n
ten
n
a
Su
p
er
-
r
eso
lu
tio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
I
lia
Pes
h
k
o
v
Dep
ar
tm
en
t o
f
Ph
y
s
ics,
R
ad
io
en
g
in
ee
r
in
g
an
d
E
lectr
o
n
ics,
I
n
s
titu
te
o
f
Ma
th
em
atics,
Natu
r
e
Scien
ce
an
d
T
ec
h
n
iq
u
e,
B
u
n
in
Yele
ts
State
Un
iv
er
s
ity
3
9
Ko
m
m
u
n
ar
o
v
s
tr
ee
t,
Yele
ts
3
9
9
7
7
0
,
R
u
s
s
ia
E
m
ail: ilv
p
esh
k
o
v
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
s
ta
t
e
-
of
-
a
r
t
t
e
c
h
n
o
l
o
g
i
es
ac
t
i
v
e
l
y
u
s
e
m
u
l
t
i
a
n
te
n
n
a
wi
r
e
le
s
s
s
y
s
t
e
m
s
.
T
h
e
a
n
a
l
y
s
is
o
f
th
e
s
p
a
ti
a
l
s
p
e
c
t
r
u
m
o
f
s
i
g
n
a
ls
u
n
d
e
r
l
i
es
t
h
e
s
e
d
e
v
i
c
es
[
1
]
.
D
OA
-
e
s
t
im
a
t
i
o
n
is
c
r
it
i
c
al
i
n
a
p
p
li
c
a
tio
n
s
r
e
q
u
i
r
i
n
g
s
p
at
i
a
l
a
w
a
r
e
n
e
s
s
,
m
i
n
i
m
a
l
d
el
a
y
a
n
d
e
x
c
e
p
t
i
o
n
a
l
r
el
i
a
b
il
i
t
y
.
F
o
r
e
x
a
m
p
l
e
,
in
5
G
d
i
r
e
c
ti
o
n
-
of
-
a
r
r
i
v
a
l
e
s
t
i
m
at
i
o
n
c
o
n
t
r
i
b
u
t
e
s
i
n
b
e
a
m
f
o
r
m
i
n
g
b
y
i
d
e
n
t
i
f
y
i
n
g
u
s
e
r
d
i
r
e
ct
i
o
n
s
f
o
r
o
p
t
i
m
a
l
s
i
g
n
a
l
t
r
a
n
s
m
is
s
i
o
n
[
2
]
.
D
e
t
e
ct
i
n
g
a
n
g
l
es
o
f
i
n
c
o
m
i
n
g
s
i
g
n
a
ls
f
r
o
m
o
b
s
t
ac
l
e
s
/
v
e
h
i
c
l
es
is
u
t
il
i
z
e
d
i
n
a
u
t
o
m
o
t
i
v
e
r
a
d
a
r
(
s
e
l
f
-
d
r
i
v
i
n
g
c
a
r
s
)
[
3
]
.
L
o
w
ac
cu
r
ac
y
an
d
r
eso
lu
tio
n
ar
e
th
e
m
o
s
t
s
er
io
u
s
p
r
o
b
le
m
s
o
f
th
ese
s
y
s
tem
s
u
s
in
g
m
eth
o
d
s
an
d
alg
o
r
ith
m
s
f
o
r
esti
m
atin
g
s
p
at
ial
co
o
r
d
in
ates,
w
h
ich
ar
e
lim
ited
b
y
ar
r
ay
ap
er
tu
r
e
[
4
]
.
T
h
u
s
,
th
e
p
r
im
ar
y
g
o
al
o
f
th
e
p
ap
er
is
h
o
w
to
im
p
r
o
v
e
th
e
ac
cu
r
ac
y
o
f
DOA
-
esti
m
atio
n
alg
o
r
ith
m
s
.
Ho
wev
er
,
th
e
ac
cu
r
ac
y
o
f
th
e
esti
m
ates
ca
n
n
o
t
b
e
i
n
cr
ea
s
ed
in
a
ea
s
y
way
an
d
h
as
a
l
o
t
o
f
ch
allen
g
es.
T
o
d
a
y
,
th
e
r
e
ar
e
s
ev
er
al
b
asic
ap
p
r
o
ac
h
es r
eg
ar
d
in
g
th
e
ac
cu
r
ac
y
o
f
DOA
-
esti
m
atio
n
.
T
h
e
m
o
s
t
co
m
m
o
n
way
th
e
r
esear
ch
er
s
ap
p
ly
to
im
p
r
o
v
e
ac
cu
r
ac
y
is
to
en
lar
g
e
th
e
a
p
er
tu
r
e
with
ad
d
itio
n
al
elem
en
ts
[
5
]
.
T
h
e
a
ttit
u
d
e
is
wid
esp
r
ea
d
in
th
e
m
i
llime
ter
r
an
g
e
ap
p
licatio
n
s
o
r
m
ilit
ar
y
r
ad
ar
s
[
6
]
.
Nev
er
th
eless
,
th
e
co
m
p
lex
ity
o
f
th
e
m
u
lti
-
an
ten
n
a
s
y
s
tem
ar
ch
itectu
r
e
in
cr
ea
s
es
wh
ich
r
esu
lts
in
a
d
r
am
atic
escalatio
n
o
f
o
v
e
r
all
d
ev
ice
c
o
s
ts
[
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
On
d
esig
n
o
f
a
s
ma
ll
-
s
iz
ed
a
r
r
a
ys fo
r
d
ir
ec
tio
n
-
of
-
a
r
r
iva
l
-
esti
ma
tio
n
ta
kin
g
…
(
I
lia
P
esh
k
o
v
)
4643
An
o
th
er
way
im
p
r
o
v
in
g
th
e
a
cc
u
r
ac
y
wh
ich
h
as
g
ain
ed
p
a
r
ticu
lar
p
o
p
u
lar
ity
is
r
elate
d
to
th
e
d
esig
n
o
f
an
in
n
o
v
ativ
e
DOA
-
esti
m
atio
n
alg
o
r
ith
m
.
Usu
ally
,
I
t
is
tailo
r
ed
to
p
ar
ticu
lar
u
s
e
-
ca
s
e
r
eq
u
ir
em
en
ts
(
f
o
r
in
s
tan
ce
,
a
m
u
ltip
ath
p
r
o
p
a
g
at
io
n
ch
an
n
el)
,
a
ce
r
tain
g
eo
m
etr
y
o
f
a
n
ten
n
a
a
r
r
ay
(
s
u
ch
as
li
n
ea
r
an
ten
n
a
ar
r
a
y
an
d
esti
m
atio
n
o
f
s
ig
n
al
p
ar
am
eter
s
v
ia
r
o
tatio
n
al
in
v
ar
i
an
ce
tech
n
iq
u
e
(
E
SP
R
I
T
)
[
8
]
)
,
o
r
f
o
r
a
s
ig
n
al
wav
ef
o
r
m
(
s
o
-
ca
lled
b
lin
d
m
eth
o
d
s
)
[
9
]
.
T
h
e
m
ain
d
is
ad
v
an
tag
e
o
f
th
is
ap
p
r
o
ac
h
is
th
at
n
ew
alg
o
r
ith
m
s
p
o
s
s
ess
h
ig
h
co
m
p
u
tatio
n
al
c
o
m
p
lex
ity
.
Fo
r
ex
a
m
p
le,
th
e
well
-
k
n
o
wn
MU
SIC
alg
o
r
ith
m
h
as
O
(
N
2
)
,
at
th
e
s
am
e
tim
e
E
SP
R
I
T
an
d
o
th
er
s
O
(
N
3
)
d
ep
en
d
in
g
o
n
t
h
e
n
u
m
b
er
o
f
an
ten
n
as
[
1
0
]
.
I
n
o
th
er
wo
r
d
s
,
th
e
l
o
ad
in
cr
ea
s
es a
lo
t.
T
h
is
f
ac
t m
ak
e
s
it d
if
f
icu
lt to
im
p
lem
en
t
f
o
r
r
ea
l
-
tim
e
ap
p
licatio
n
s
.
A
s
im
ilar
ly
wid
esp
r
ea
d
tech
n
iq
u
e
in
cr
ea
s
in
g
ac
c
u
r
ac
y
is
b
ased
o
n
th
e
o
p
tim
al
ar
r
an
g
em
en
t
o
f
an
ten
n
a
ele
m
en
ts
[
1
1
]
.
Sev
er
a
l
d
if
f
er
e
n
t
cr
iter
ia
h
av
e
b
ee
n
i
n
tr
o
d
u
ce
d
s
u
c
h
as
r
an
d
o
m
d
is
tr
ib
u
tio
n
o
f
an
ten
n
a
co
o
r
d
in
ates
[
1
2
]
o
r
co
m
p
lex
co
o
r
d
in
ate
ex
p
r
ess
io
n
o
f
an
ten
n
as
[
1
3
]
,
o
r
u
s
in
g
ar
r
ay
s
co
m
p
o
s
ed
o
f
o
m
n
id
ir
ec
tio
n
al
r
a
d
iato
r
s
[
1
4
]
,
[
1
5
]
.
T
h
e
m
ain
d
is
ad
v
an
tag
e
o
f
th
e
m
en
tio
n
e
d
ap
p
r
o
ac
h
es
is
th
e
co
n
s
id
er
atio
n
o
f
id
ea
l
ar
r
ay
p
atter
n
s
b
ec
au
s
e
o
m
n
id
ir
ec
tio
n
al
a
n
ten
n
as
ar
e
ab
s
en
t
in
r
ea
l
ap
p
licatio
n
s
.
I
n
o
th
er
wo
r
d
s
,
th
ey
ar
e
h
ar
d
l
y
im
p
lem
en
te
d
.
T
h
e
m
ain
id
ea
o
f
th
e
p
r
o
p
o
s
e
d
m
eth
o
d
o
l
o
g
y
f
o
r
en
h
a
n
cin
g
DOA
est
im
atio
n
p
r
ec
is
io
n
is
t
h
e
o
p
tim
al
p
lace
m
en
t
o
f
d
ir
ec
tio
n
al
an
te
n
n
as
,
as
well
as
th
eir
s
p
atial
p
atter
n
s
.
T
h
e
n
o
v
elty
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
ar
is
es
b
ec
au
s
e
th
at
th
e
d
ir
ec
tio
n
al
s
p
atial
p
atter
n
s
o
f
an
ten
n
a
elem
en
ts
ar
e
tak
en
in
to
ac
co
u
n
t
.
So
th
at
th
e
p
r
o
ce
d
u
r
e
f
o
r
d
esig
n
in
g
a
d
u
al
-
elem
en
t
ar
r
a
y
c
o
n
f
ig
u
r
atio
n
f
o
r
esti
m
atin
g
s
p
atial
p
ar
a
m
eter
esti
m
atio
n
b
y
m
ea
n
s
o
f
m
a
n
u
ally
f
o
r
m
i
n
g
t
h
e
b
ea
m
p
atter
n
s
an
d
co
o
r
d
in
ates
o
f
th
e
ar
r
ay
elem
en
ts
to
g
r
ea
tly
r
ed
u
ce
th
e
v
ar
ian
ce
.
I
n
th
is
way
,
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
h
ig
h
lig
h
ts
t
h
e
g
ain
o
f
an
te
n
n
a
elem
e
n
ts
en
ab
lin
g
th
e
s
en
s
o
r
ar
r
ay
to
b
e
d
e
v
elo
p
ed
f
o
r
3
6
0
° r
an
g
e
s
ca
n
n
in
g
b
y
m
ea
n
s
o
f
s
y
n
th
esizin
g
th
e
r
ad
iatio
n
p
atter
n
s
.
Mic
r
o
s
tr
ip
an
ten
n
as
ca
n
b
e
d
esig
n
ed
u
s
in
g
th
e
m
et
h
o
d
o
f
m
o
m
en
ts
b
y
d
em
o
n
s
tr
atin
g
t
h
e
p
r
ac
tical
im
p
lem
en
tatio
n
o
f
th
e
p
r
esen
ted
m
eth
o
d
.
Fu
r
th
er
m
o
r
e,
t
h
e
p
ap
er
d
escr
ib
es
an
ex
am
p
le
o
f
cr
ea
tin
g
an
a
n
ten
n
a
ar
r
ay
p
r
o
to
ty
p
e
f
o
r
s
u
p
e
r
-
r
es
o
lu
tio
n
DOA
-
esti
m
atio
n
,
wh
i
ch
is
co
m
p
u
ted
u
s
in
g
th
e
cl
o
s
ed
-
f
o
r
m
a
n
aly
tical
f
o
r
m
u
latio
n
s
o
f
C
r
am
ér
–
R
ao
l
o
wer
b
o
u
n
d
(
C
R
L
B
)
co
m
p
ar
i
n
g
to
th
e
o
p
tim
izatio
n
o
r
n
eu
r
al
n
etwo
r
k
s
wh
ich
ar
e
b
lack
b
o
x
s
o
l
u
tio
n
s
.
T
h
e
elab
o
r
ate
d
ar
r
ay
co
n
s
is
ts
o
f
an
a
n
alo
g
b
ea
m
f
o
r
m
i
n
g
s
ch
em
e,
wh
ich
allo
ws
r
ed
u
cin
g
th
e
n
u
m
b
er
o
f
d
ig
ital
p
r
o
ce
s
s
in
g
ch
an
n
els
with
o
u
t
d
ec
r
ea
s
in
g
th
e
ac
cu
r
ac
y
o
f
D
OA
-
esti
m
atio
n
[
1
6
]
.
T
h
u
s
,
th
e
p
ap
e
r
d
is
cu
s
s
es
th
e
s
tep
-
by
-
s
tep
p
r
o
ce
s
s
o
f
an
ten
n
a
ar
r
ay
d
esig
n
,
s
tar
tin
g
f
r
o
m
a
co
n
ce
p
t
b
ased
o
n
an
aly
tical
ex
p
r
ess
io
n
s
an
d
e
n
d
in
g
with
th
e
p
r
ac
tical
im
p
lem
en
tatio
n
o
n
th
e
b
asis
o
f
p
atch
an
ten
n
as.
A
co
m
p
leted
d
ev
ice
is
u
s
ed
to
d
em
o
n
s
tr
ate
th
e
f
ea
s
ib
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
E
s
p
ec
ially
,
th
er
e
is
n
o
u
n
if
ied
m
eth
o
d
o
l
o
g
y
f
o
r
d
esig
n
in
g
th
at
k
in
d
o
f
d
e
v
ices
wh
ich
ar
e
b
u
ilt
o
n
s
u
b
-
ar
r
ay
p
r
ep
r
o
ce
s
s
in
g
n
etwo
r
k
s
[
1
7
]
o
r
b
ea
m
s
elec
tio
n
s
ch
em
e
s
[
1
8
]
.
2.
SYST
E
M
M
O
D
E
L
2
.
1
.
DO
A
-
esti
m
a
t
io
n
f
o
rm
ul
a
t
io
n
I
n
th
is
s
ec
tio
n
t
h
e
m
o
d
el
o
f
a
n
ten
n
a
s
y
s
tem
s
wid
esp
r
ea
d
i
n
d
ir
ec
tio
n
f
in
d
in
g
is
d
escr
ib
ed
.
T
h
e
ar
r
a
y
s
ca
n
b
e
c
o
n
f
ig
u
r
ed
in
d
if
f
er
e
n
t
way
s
in
f
lu
en
ci
n
g
o
n
s
u
ch
p
r
o
p
er
ties
as
ac
cu
r
ac
y
a
n
d
r
eso
lu
tio
n
.
Fig
u
r
e
1
s
h
o
ws s
u
ch
an
ar
r
a
y
,
wh
ich
c
o
n
s
is
ts
o
f
a
ce
r
tain
n
u
m
b
e
r
o
f
a
n
ten
n
a
elem
en
ts
.
Fig
u
r
e
1
.
An
te
n
n
a
ar
r
ay
v
iew
i
n
th
e
C
ar
tesi
an
s
y
s
tem
I
n
th
e
p
ap
er
it
is
ass
u
m
ed
th
at
th
e
s
ig
n
al
is
n
ar
r
o
w
-
b
a
n
d
a
n
d
h
as
th
e
f
o
llo
win
g
s
p
atial
co
o
r
d
in
ates
o
n
az
im
u
th
θ
a
n
d
elev
atio
n
φ
r
e
lativ
e
to
th
e
x
,
y
,
an
d
z
ax
es
in
th
e
C
ar
tesi
an
s
y
s
tem
,
r
esp
ec
tiv
ely
.
T
h
u
s
,
th
e
co
o
r
d
in
ates
θ
an
d
φ
h
as
to
b
e
esti
m
ated
with
m
ax
im
u
m
ac
cu
r
ac
y
.
T
h
e
an
al
y
tical
m
o
d
el
o
f
th
e
an
ten
n
a
ar
r
ay
is
ex
p
r
ess
ed
in
th
e
f
o
llo
win
g
m
an
n
er
[
1
9
]
:
(
,
)
=
[
1
(
,
)
1
⋯
(
,
)
]
(
1
)
s
(t
)
φ
θ
z
y
x
(
х
1
,
у
1
, z
1
)
(x
2
,
y
2
, z
2
)
(
х
3
,
у
3
, z
3
)
(
х
4
,
у
4
, z
4
)
(x
n
,
y
n
, z
n
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
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&
C
o
m
p
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n
g
,
Vo
l.
15
,
No
.
5
,
Octo
b
e
r
20
25
:
4
6
4
2
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4
6
5
2
4644
wh
er
e
=
2
(
,
,
)
=
(
s
in
φ
co
s
θ
,
s
i
n
φ
,
co
s
φ
)
is
th
e
s
p
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f
r
eq
u
en
c
y
s
p
ec
if
y
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g
th
e
o
s
cillatin
g
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f
th
e
p
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ase
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p
r
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a
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tio
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z
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th
e
p
o
s
itio
n
v
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to
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in
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icate
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to
th
e
n
th
an
ten
n
a
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m
en
t a
n
d
g
n
(
θ
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φ
)
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th
e
p
atter
n
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f
th
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th
an
ten
n
a
elem
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h
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an
ten
n
a
elem
en
t o
u
tp
u
t si
g
n
als ar
e
r
ep
r
esen
ted
b
y
th
e
c
o
m
p
lex
v
ec
to
r
[
1
9
]
:
⃗
(
)
=
(
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⋅
⃗
(
)
+
⃗
⃗
(
)
,
(
2
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wh
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⃗
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=
[
1
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,
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]
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th
e
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to
r
o
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th
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im
en
s
io
n
1
×
N
,
wh
ich
d
escr
i
b
es
th
e
an
ten
n
a
ar
r
ay
o
u
tp
u
t
s
ig
n
als;
⃗
(
)
=
[
1
(
)
,
.
.
.
,
(
)
]
is
th
e
N
-
d
im
en
s
io
n
al
o
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th
e
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ig
n
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(
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e
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(
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th
e
N
M
d
im
en
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al
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atr
ix
o
f
th
e
s
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r
in
g
v
ec
to
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s
[
⃗
(
1
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,
…
,
⃗
(
)
]
.
I
n
p
r
ac
tical
ap
p
licatio
n
s
,
th
e
s
p
atial
co
v
a
r
ian
ce
m
atr
ix
is
esti
m
ated
f
r
o
m
a
co
llectio
n
o
f
K
tim
e
s
am
p
les
[
1
9
]
:
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=
1
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⃗
(
)
⃗
(
)
=
1
=
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̂
+
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̂
,
(
3
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wh
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e
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d
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en
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p
le
at
th
e
d
ig
ital
a
n
ten
n
a
a
r
r
ay
o
u
tp
u
t,
th
e
s
y
m
b
o
l
“
”
d
escr
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e
a
v
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ag
in
g
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er
K
s
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p
les,
̂
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th
e
s
ig
n
al
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en
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m
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ix
,
̂
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th
e
n
o
i
s
e
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en
v
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to
r
m
atr
ix
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d
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th
e
eig
en
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e
s
m
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ices.
Sp
atial
s
p
ec
tr
u
m
b
y
th
e
m
eth
o
d
MU
SIC is
ca
lcu
lated
as
[
2
0
]
:
(
,
)
=
1
⃗
⃗
(
)
⃗
⃗
(
)
.
(
4
)
2
.
2
.
Reduct
io
n o
f
DO
A
-
esti
m
a
t
io
n v
a
ria
nce
T
h
e
v
ar
ian
ce
o
f
th
e
b
ea
r
in
g
s
θ
an
d
φ
is
ass
ess
ed
u
s
in
g
th
e
C
r
am
er
-
R
ao
lo
wer
b
o
u
n
d
cr
iter
i
o
n
,
wh
ich
is
d
eter
m
in
ed
b
y
th
e
am
o
u
n
t
o
f
n
o
is
e,
th
e
p
o
s
itio
n
in
g
o
f
t
h
e
an
ten
n
a
elem
en
ts
in
s
p
ac
e
an
d
th
eir
r
ad
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n
p
atter
n
s
.
I
n
th
is
ca
s
e,
an
ar
b
i
tr
ar
y
d
ir
ec
tio
n
-
of
-
a
r
r
iv
al
esti
m
atio
n
alg
o
r
ith
m
ca
n
n
o
t
h
a
v
e
v
alu
es
o
f
v
ar
ian
ce
b
elo
w
th
is
lim
it,
b
u
t
o
n
ly
ap
p
r
o
ac
h
in
g
it.
C
o
v
ar
ian
ce
e
r
r
o
r
m
atr
ix
f
o
r
esti
m
atin
g
th
e
an
g
u
lar
co
o
r
d
in
ates
o
f
s
ig
n
als with
s
u
p
er
-
r
eso
lu
tio
n
i
n
b
o
th
az
im
u
th
al
an
d
elev
atio
n
s
ca
n
n
in
g
p
lan
es c
an
b
e
wr
itten
as
(
5
)
[
1
9
]
:
=
2
2
ℜ
[
{
[
1
2
3
4
]
∘
[
]
}
]
−
1
(
5
)
h
er
e
1
=
⊥
,
2
=
⊥
,
3
=
⊥
,
4
=
⊥
,
=
−
1
,
D
θ
и
D
φ
ar
e
th
e
m
atr
ices
o
f
s
teer
in
g
v
ec
t
o
r
d
i
f
f
er
en
tiatio
n
a
(
θ
,
φ
)
alo
n
g
th
e
co
r
r
esp
o
n
d
in
g
p
lan
es,
K
is
th
e
n
u
m
b
er
o
f
th
e
s
am
p
les.
C
o
n
s
eq
u
en
tly
,
it
is
p
o
s
s
ib
le
to
r
e
d
u
ce
th
e
v
alu
es
B
S
TO
b
y
in
f
lu
e
n
cin
g
th
e
co
o
r
d
in
a
tes
o
f
th
e
an
te
n
n
as
an
d
th
e
s
h
ap
e
o
f
t
h
eir
r
ad
iatio
n
p
atter
n
s
o
f
DOA
-
esti
m
ato
r
.
T
h
er
ef
o
r
e,
let
u
s
ex
am
i
n
e
th
e
C
R
L
B
ex
p
r
ess
io
n
g
iv
en
i
n
(
5
)
in
g
r
ea
ter
d
etail
.
Pre
v
io
u
s
ly
,
a
n
ex
p
licit
g
en
er
al
f
o
r
m
u
la
of
th
e
C
R
L
B
was
o
b
tain
ed
f
o
r
esti
m
atin
g
th
e
co
o
r
d
in
ates
o
f
th
e
r
ad
iatio
n
s
o
u
r
ce
v
ia
Mu
lti
-
s
en
s
o
r
an
ten
n
a
a
r
r
ay
s
with
d
ir
ec
tio
n
al
s
en
s
o
r
s
,
also
o
r
ien
ted
in
s
p
ac
e
in
an
a
r
b
itra
r
y
m
an
n
e
r
[
2
1
]
:
(
,
)
≈
2
2
ℜ
{
(
∑
2
2
(
′
−
′
)
2
+
∑
(
′
−
′
)
2
)
−
1
}
(
6
)
wh
er
e
'
d
en
o
tes
a
d
er
iv
ativ
e
alo
n
g
θ
or
φ
d
e
p
en
d
in
g
o
n
th
e
s
ca
n
n
in
g
d
ir
ec
tio
n
,
i
a
n
d
j
ar
e
th
e
an
te
n
n
a
elem
en
ts
in
d
ex
es
.
T
h
e
a
n
ten
n
a
ar
r
ay
is
s
u
p
p
o
s
ed
c
o
n
s
is
t
in
g
o
f
two
an
ten
n
a
elem
en
ts
,
th
en
th
e
eq
u
atio
n
(
6
)
ca
n
b
e
r
ewr
itten
i
n
th
e
f
o
llo
win
g
f
o
r
m
[
2
2
]
:
(
,
)
=
2
2
{
(
1
2
2
2
(
1
′
−
2
′
)
2
+
(
2
′
1
−
1
′
2
)
2
)
−
1
}
(
7
)
As
d
e
m
o
n
s
tr
ate
d
i
n
t
h
e
e
q
u
a
ti
o
n
'
s
le
f
t
-
h
a
n
d
s
i
d
e
(
7
)
in
cu
r
l
y
b
r
ac
k
ets
,
t
h
e
m
ai
n
p
h
y
s
i
ca
l
f
a
ct
o
r
s
d
et
e
r
m
i
n
i
n
g
th
e
v
a
r
ia
n
c
e
ar
e
t
h
e
s
q
u
ar
e
o
f
th
e
g
ai
n
s
o
f
th
e
s
e
n
s
o
r
e
le
m
e
n
ts
,
j
u
s
t
li
k
e
th
e
ar
ea
o
cc
u
p
ie
d
b
y
t
h
e
e
m
p
lo
y
ed
an
t
e
n
n
a
ar
r
a
y
.
T
h
er
ef
o
r
e,
it
is
p
o
s
s
ib
le
to
in
cr
ea
s
e
th
e
ac
cu
r
a
cy
o
f
DOA
-
esti
m
ates
b
y
ch
an
g
in
g
o
n
e
o
r
b
o
th
o
f
th
ese
f
ac
to
r
s
.
On
th
e
c
o
n
t
r
a
r
y
,
t
h
e
s
m
al
lest
p
o
s
s
i
b
l
e
n
u
m
b
e
r
o
f
an
te
n
n
a
e
le
m
e
n
ts
ca
n
b
e
co
m
p
e
n
s
at
e
d
b
y
a
lar
g
er
g
a
in
,
o
r
b
y
b
ei
n
g
l
o
ca
te
d
o
n
a
la
r
g
e
r
a
r
e
a.
F
o
r
e
x
a
m
p
l
e,
i
f
t
h
e
g
a
in
o
f
e
ac
h
a
n
t
en
n
a
is
i
n
cr
ea
s
ed
twic
e,
th
e
n
t
h
e
v
a
r
ia
n
c
e
o
f
DOA
-
es
ti
m
at
es
ca
n
b
e
r
e
d
u
c
ed
r
a
d
i
ca
ll
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
On
d
esig
n
o
f
a
s
ma
ll
-
s
iz
ed
a
r
r
a
ys fo
r
d
ir
ec
tio
n
-
of
-
a
r
r
iva
l
-
esti
ma
tio
n
ta
kin
g
…
(
I
lia
P
esh
k
o
v
)
4645
T
h
er
ef
o
r
e
,
t
h
e
p
r
o
p
o
s
e
d
m
et
h
o
d
o
lo
g
y
f
o
r
d
esi
g
n
i
n
g
a
n
te
n
n
a
ar
r
ay
s
f
o
r
DOA
-
est
im
ati
o
n
co
n
s
is
ts
o
f
s
y
n
th
esi
zi
n
g
t
h
e
d
i
r
e
cti
o
n
a
l
p
a
tte
r
n
s
o
f
in
d
i
v
i
d
u
a
l
e
le
m
e
n
ts
g
1
a
n
d
g
2
i
n
o
r
d
e
r
t
o
m
i
n
i
m
iz
e
v
a
r
i
an
ce
v
a
r
(
θ,
φ
i
n
th
e
w
o
r
k
s
f
a
m
ili
ar
t
o
th
e
a
u
t
h
o
r
s
,
wh
ic
h
c
o
n
ce
r
n
t
h
e
o
p
ti
m
i
za
ti
o
n
o
f
th
e
an
te
n
n
a
a
r
r
a
y
t
o
p
o
l
o
g
y
t
o
i
n
c
r
ea
s
e
ac
c
u
r
a
cy
,
th
e
g
ai
n
an
d
t
h
e
r
a
d
i
ati
o
n
p
at
te
r
n
s
o
f
t
h
e
ar
r
a
y
el
e
m
e
n
ts
a
r
e
n
o
t
a
cc
o
u
n
te
d
f
o
r
at
all
.
C
o
n
s
id
er
a
n
e
x
am
p
l
e
,
tw
o
c
ir
c
u
la
r
ar
r
ay
c
o
n
f
i
g
u
r
ati
o
n
s
ar
e
s
t
u
d
ie
d
:
a
3
-
el
em
en
t a
n
d
a
2
-
ele
m
e
n
t
ar
r
a
y
o
f
d
i
r
e
cti
o
n
a
l
a
n
te
n
n
as
.
T
h
e
t
a
s
k
is
t
h
e
v
a
r
i
an
ce
o
f
th
e
est
im
ates
o
f
th
e
t
h
r
ee
-
el
em
e
n
t
a
r
r
a
y
v
a
r
(
θ
,
φ
)
3
m
u
s
t
b
e
eq
u
a
l
t
o
t
h
e
v
a
r
ia
n
c
e
o
f
t
h
e
tw
o
-
el
em
en
t o
n
e
v
a
r
(
θ
,
φ
)
2
.
I
n
t
h
is
ca
s
e
t
h
e
s
u
m
o
f
t
h
e
g
ai
n
s
o
f
th
e
el
em
e
n
ts
o
f
t
h
e
s
ec
o
n
d
a
r
r
ay
m
u
s
t
b
e
c
o
n
s
is
t
en
t
t
o
th
e
s
u
m
o
f
t
h
e
g
ai
n
s
o
f
t
h
e
t
h
r
ee
-
e
le
m
e
n
t
ci
r
c
u
l
ar
an
t
e
n
n
a
ar
r
a
y
.
T
h
e
f
o
r
m
u
la
o
f
t
h
e
C
r
a
m
e
r
-
R
ao
l
o
we
r
b
o
u
n
d
f
o
r
t
h
e
t
wo
-
e
le
m
en
t
an
te
n
n
a
a
r
r
a
y
m
u
s
t
b
e
r
e
m
e
m
b
er
e
d
(
7
)
a
n
d
ex
p
r
ess
i
o
n
f
o
r
t
h
e
t
h
r
e
e
-
ele
m
e
n
t
a
r
r
a
y
:
va
r
(
θ
,
φ
)
3
≈
σ
2
2K
{
(
(
g
1
2
g
2
2
(
a
1
'
-
a
2
'
)
2
+
g
3
2
g
1
2
(
a
1
'
-
a
3
'
)
2
+
g
2
2
g
3
2
(
a
2
'
-
a
3
'
)
2
+
(
g
2
'
g
1
-
g
1
'
g
2
)
2
…
+
(
g
3
'
g
1
-
g
1
'
g
3
)
2
+
(
g
2
'
g
3
-
g
3
'
g
2
)
2
)
)
-
1
}
(
8
)
Acc
o
r
d
in
g
t
o
t
h
e
co
n
d
it
io
n
t
h
e
f
o
l
lo
w
i
n
g
e
q
u
at
io
n
m
u
s
t
b
e
m
et
:
(
,
)
2
=
(
,
)
3
(
9
)
I
n
ad
d
itio
n
,
i
t
is
ass
u
m
e
d
t
h
a
t
two
-
an
d
t
h
r
e
e
-
ele
m
e
n
t
cir
cu
l
ar
ar
r
ay
s
ar
e
l
o
c
at
ed
at
t
h
e
s
a
m
e
r
a
d
i
u
s
f
r
o
m
t
h
e
ce
n
te
r
,
as we
l
l
as th
e
n
o
is
e
p
o
wer
2
an
d
t
h
e
n
u
m
b
er
o
f
s
am
p
l
es
K
o
f
t
h
e
c
o
r
r
ela
ti
o
n
m
at
r
ic
e
s
ar
e
t
h
e
s
a
m
e
f
o
r
(
,
)
2
a
n
d
(
,
)
3
.
T
h
u
s
,
2
2
{
1
(
1
2
2
2
(
1
′
−
2
′
)
2
+
(
2
′
1
−
1
′
2
)
2
}
=
2
2
{
1
+
}
(
1
0
)
=
(
1
2
2
2
(
1
′
−
2
′
)
2
+
3
2
1
2
(
1
′
−
3
′
)
2
+
2
2
3
2
(
2
′
−
3
′
)
2
(
1
1
)
=
(
2
′
1
−
1
′
2
)
2
+
(
3
′
1
−
1
′
3
)
2
+
(
2
′
3
−
3
′
2
)
2
)
(
1
2
)
h
er
e
an
d
f
u
r
th
er
2
an
d
3
ar
e
th
e
r
ad
iativ
e
ch
ar
ac
ter
is
tics
o
f
th
e
elem
en
ts
o
f
th
e
co
n
s
id
er
ed
two
-
an
d
th
r
ee
-
elem
en
t a
r
r
ay
s
r
esp
ec
tiv
ely
.
T
h
e
e
q
u
al
ter
m
s
,
i.e
.
,
th
e
n
o
is
e
p
o
wer
an
d
th
e
n
u
m
b
er
o
f
s
am
p
les
o
f
t
h
e
co
r
r
elatio
n
m
at
r
ix
ca
n
b
e
elim
in
ated
,
th
er
ef
o
r
e
it c
an
b
e
wr
itten
th
at:
1
1
2
2
2
(
1
′
−
2
′
)
2
+
(
2
′
1
−
1
′
2
)
2
=
1
1
2
2
2
(
1
′
−
2
′
)
2
+
3
2
1
2
(
1
′
−
3
′
)
2
+
2
2
3
2
(
2
′
−
3
′
)
2
…
+
(
2
′
1
−
1
′
2
)
2
+
(
3
′
1
−
1
′
3
)
2
+
(
2
′
3
−
3
′
2
)
2
(
1
3
)
C
o
n
s
id
er
o
n
ly
th
e
d
en
o
m
in
ato
r
s
o
f
th
e
ex
p
r
ess
io
n
(
13)
:
12
2
22
2
+
(
22
′
12
−
12
′
22
)
2
=
13
2
23
2
+
33
2
13
2
+
23
2
33
2
+
(
23
′
13
−
13
′
23
)
2
+
(
33
′
13
−
13
′
33
)
2
+
(
23
′
13
−
23
′
33
)
2
(
1
4
)
Sin
ce
it
i
s
clea
r
th
at
th
e
p
r
o
d
u
ct
o
f
th
e
s
q
u
ar
es
o
f
th
e
r
ad
iatio
n
p
atter
n
s
is
m
u
ch
g
r
ea
ter
th
an
th
e
o
th
er
ter
m
s
,
th
e
s
im
p
li
f
i
ca
ti
o
n
ca
n
b
e
c
o
n
ti
n
u
ed
a
n
d
:
12
2
22
2
≈
13
2
23
2
+
33
2
13
2
+
23
2
33
2
(
1
5
)
No
w
it
is
r
e
q
u
ir
e
d
t
o
d
e
te
r
m
in
e
t
h
e
g
ai
n
o
f
t
h
e
p
att
e
r
n
o
f
th
e
s
y
n
t
h
es
ize
d
a
n
te
n
n
a
a
r
r
a
y
.
I
t
i
s
h
y
p
o
th
esiz
e
d
t
h
a
t
th
e
m
ax
im
u
m
v
al
u
e
o
f
th
e
p
at
ter
n
o
f
t
h
e
r
ec
t
a
n
g
u
l
ar
a
n
te
n
n
a
ele
m
e
n
t
is
e
q
u
a
l
t
o
6
,
a
n
d
t
h
e
m
i
n
i
m
u
m
v
a
lu
e
t
o
b
e
0
.
1
.
T
h
en
i
t
ca
n
b
e
w
r
it
te
n
t
h
at
:
12
2
0
.
1
22
2
≈
6
13
2
0
.
1
23
2
+
0
.
1
33
2
6
13
2
+
0
.
1
23
2
0
.
1
33
2
(
1
6
)
12
2
≈
6
13
2
0
.
1
23
2
+
0
.
1
33
2
6
13
2
+
0
.
1
23
2
0
.
1
33
2
0
.
1
22
2
(
1
7
)
Af
t
er
s
i
m
p
le
c
al
cu
lati
o
n
s
it
c
a
n
b
e
cla
im
e
d
t
h
at
12
=
8
.
5
.
T
h
e
v
alu
e
m
ak
es
it
p
o
s
s
i
b
le
t
o
o
b
t
ai
n
t
h
e
ac
c
u
r
a
cy
u
s
i
n
g
a
s
m
a
lle
r
n
u
m
b
e
r
o
f
an
ten
n
a
ele
m
e
n
ts
.
He
r
e
,
th
e
m
is
s
in
g
e
le
m
e
n
ts
a
r
e
c
o
m
p
e
n
s
at
ed
b
y
m
e
a
n
s
o
f
a
h
i
g
h
e
r
g
a
in
,
as
it
ca
n
b
e
s
e
en
f
r
o
m
t
h
e
C
R
L
B
f
o
r
m
u
l
a
(
8
,
1
0
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
5
,
Octo
b
e
r
20
25
:
4
6
4
2
-
4
6
5
2
4646
I
t
m
a
y
b
e
s
t
ate
d
;
th
e
p
r
o
p
o
s
e
d
a
p
p
r
o
ac
h
al
lo
ws
d
esi
g
n
i
n
g
an
t
e
n
n
a
a
r
r
a
y
s
h
a
v
i
n
g
r
ad
iat
i
o
n
p
att
er
n
s
wh
i
ch
m
i
n
i
m
iz
e
th
e
v
ar
i
a
n
ce
i
n
s
p
atia
l
c
o
o
r
d
i
n
at
e
esti
m
a
tes
.
O
n
th
e
c
o
n
tr
ar
y
,
it
ca
n
b
e
u
t
il
ize
d
t
o
ev
al
u
at
e
t
h
e
ac
c
u
r
a
cy
o
f
e
x
is
t
in
g
a
r
r
a
y
s
b
y
m
ea
n
s
o
f
t
h
e
cl
o
s
e
d
f
o
r
m
eq
u
a
ti
o
n
s
.
T
h
e
v
ar
ian
ce
b
ase
d
o
n
(
7
)
-
(
8
)
f
o
r
th
e
s
p
atial
co
o
r
d
in
ate
in
az
im
u
th
e
q
u
al
to
9
0
° ca
n
b
e
ca
lc
u
l
ate
d
u
s
in
g
(
1
8
)
an
d
(
1
9
)
:
(
=
9
0
∘
)
2
−
_
≈
1
12
2
22
2
≈
1
2
.
3
12
2
1
.
4
22
2
≈
0
.
096
4
∘
(
1
8
)
(
=
9
0
∘
)
3
≈
1
13
2
23
2
+
33
2
13
2
+
23
2
33
2
≈
1
4
.
6
13
2
0
.
2
23
2
+
0
.
2
33
2
4
.
6
13
2
+
0
.
2
23
2
0
.
2
33
2
≈
0
.
590
2
∘
(
1
9
)
As
it
ca
n
b
e
s
ee
n
f
r
o
m
ex
p
r
e
s
s
io
n
s
(
1
8
)
-
(
1
9
)
,
ac
co
r
d
in
g
to
th
e
C
R
L
B
an
d
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
y
,
th
e
v
ar
ian
ce
o
f
th
e
esti
m
ates u
s
in
g
th
e
d
u
al
-
elem
en
t a
r
r
a
y
will p
r
o
m
o
te
s
m
aller
v
alu
es in
co
m
p
ar
is
o
n
with
th
e
tr
i
-
elem
en
t
d
ig
ital
an
ten
n
a
ar
r
a
y
.
W
ith
all
th
is
,
th
er
e
will
o
n
ly
b
e
m
u
tu
al
r
elatio
n
s
h
ip
s
b
etwe
en
d
if
f
er
en
t
g
eo
m
etr
ies
o
f
an
ten
n
a
ar
r
ay
s
,
am
o
n
g
wh
ich
c
o
m
p
a
r
is
o
n
s
ca
n
b
e
m
ad
e
an
d
th
en
th
e
b
est
o
n
e
ca
n
b
e
s
elec
ted
f
r
o
m
th
e
p
o
in
t
o
f
v
iew
o
f
o
b
ta
in
in
g
h
ig
h
ac
cu
r
ac
y
o
f
th
e
DO
A
-
esti
m
atio
n
.
No
w,
b
ased
o
n
th
e
o
b
tain
ed
a
n
ten
n
a
g
ain
v
alu
e
,
a
r
ad
iatio
n
p
atter
n
m
u
s
t
b
e
s
y
n
th
esized
s
atis
f
y
in
g
th
e
r
eq
u
ir
em
e
n
ts
.
I
n
ad
d
itio
n
,
th
e
p
r
o
p
o
s
ed
h
y
p
o
th
esis
will
b
e
co
n
f
ir
m
ed
b
y
f
u
lf
illi
n
g
c
o
m
p
ar
ativ
e
m
o
d
elin
g
.
T
h
e
r
esu
lts
ar
e
g
iv
en
b
elo
w
in
th
e
s
ec
tio
n
3
.
3.
P
E
RF
O
RM
A
NCE A
NAL
YS
I
S
3
.
1
.
Sim
ula
t
i
o
n study
o
f
t
he
pro
po
s
ed
m
et
ho
do
lo
g
y
I
n
t
h
e
s
ec
ti
o
n
t
h
e
in
tr
o
d
u
ce
d
s
tr
a
te
g
y
o
f
d
esi
g
n
i
n
g
a
n
th
e
d
u
al
-
elem
en
t
ar
r
a
y
f
o
r
D
OA
-
esti
m
ati
o
n
wit
h
s
u
p
e
r
-
r
eso
lu
ti
o
n
is
will
b
e
a
p
p
r
o
v
ed
v
ia
s
im
u
latio
n
s
tu
d
y
.
A
c
ir
cu
la
r
a
n
t
en
n
a
a
r
r
a
y
o
u
t
o
f
t
h
r
ee
d
i
r
e
cti
o
n
al
ele
m
e
n
ts
is
u
s
ed
f
o
r
th
e
c
o
m
p
ar
is
o
n
.
I
n
o
r
d
e
r
t
o
o
b
t
ai
n
t
h
e
s
am
e
ac
c
u
r
ac
y
a
s
t
h
e
th
r
e
e
-
el
em
en
t
ar
r
a
y
.
E
a
ch
an
te
n
n
a
o
f
t
h
e
d
u
al
-
ele
m
e
n
t
a
r
r
a
y
wil
l
h
av
e
g
ai
n
e
q
u
a
l
to
12
=
8
.
5
as
it
was
p
r
o
v
en
in
th
e
p
r
ev
io
u
s
p
a
r
t
.
T
h
e
f
o
ll
o
w
in
g
a
n
te
n
n
a
a
r
r
a
y
s
t
r
u
ct
u
r
e
is
p
r
o
p
o
s
e
d
f
o
r
DO
A
-
esti
m
a
ti
o
n
,
as
r
e
p
r
es
en
te
d
i
n
Fig
u
r
e
2.
As
c
a
n
b
e
s
e
en
f
r
o
m
Fi
g
u
r
e
2
,
ea
ch
a
n
te
n
n
a
o
f
t
h
e
ar
r
a
y
m
u
s
t
h
av
e
r
a
d
ia
ti
o
n
p
att
er
n
s
w
h
i
ch
h
a
v
e
t
o
b
e
s
y
n
t
h
esi
ze
d
a
n
d
p
o
s
s
ess
t
h
e
g
ai
n
12
=
8
.
5
in
o
r
d
er
t
o
m
i
n
im
iz
e
(
7
)
.
T
h
e
p
r
o
p
o
s
ed
p
a
tte
r
n
s
d
e
cr
ea
s
i
n
g
DOA
-
esti
m
a
ti
o
n
e
r
r
o
r
s
a
r
e
s
h
o
wed
i
n
Fi
g
u
r
e
3
.
Fig
u
r
e
2
.
Pro
p
o
s
ed
d
ig
ital a
n
t
en
n
a
ar
r
a
y
d
esig
n
f
o
r
DOA
-
es
tim
atio
n
with
two
an
ten
n
a
elem
en
ts
f
o
r
3
6
0
°
s
ca
n
n
in
g
o
n
az
im
u
th
Fig
u
r
e
3
(
a
)
r
e
v
e
als
th
e
p
e
ak
v
a
lu
es
a
r
e
p
ic
k
e
d
u
p
i
n
s
u
ch
a
w
ay
t
h
at
t
h
e
y
c
o
i
n
ci
d
e
wit
h
th
e
m
i
n
im
al
o
f
th
e
p
at
te
r
n
o
f
t
h
e
n
e
ig
h
b
o
r
i
n
g
ele
m
e
n
t
.
At
t
h
e
s
a
m
e
ti
m
e
,
t
h
e
m
ai
n
p
a
r
t
o
f
t
h
e
g
ai
n
is
f
o
c
u
s
ed
i
n
a
wi
d
e
az
i
m
u
th
r
a
n
g
e.
A
tem
p
late
r
a
d
ia
ti
o
n
p
att
er
n
is
s
h
o
wn
i
n
Fi
g
u
r
e
3
(
a
)
t
h
at
wil
l
b
e
u
s
e
d
f
o
r
a
n
t
e
n
n
a
s
y
n
th
esis
.
Fu
r
th
e
r
t
h
es
e
r
a
d
ia
ti
o
n
p
att
e
r
n
s
a
r
e
u
til
ize
d
to
s
y
n
t
h
esiz
e
a
li
n
e
ar
a
n
t
en
n
a
a
r
r
a
y
,
w
h
ic
h
is
c
o
n
s
is
ts
o
f
t
e
n
d
i
r
e
cti
o
n
al
el
em
en
ts
wi
th
a
u
n
i
f
o
r
m
h
al
f
-
wa
v
e
i
n
t
er
ele
m
e
n
t
d
is
ta
n
c
e.
T
h
e
li
n
e
ar
a
n
t
en
n
a
ele
m
e
n
t
s
h
o
w
n
in
Fig
u
r
e
2
c
o
n
s
is
ts
o
f
d
ir
ec
t
io
n
al
a
n
t
e
n
n
a
ele
m
e
n
ts
.
Ma
t
h
e
m
at
ica
ll
y
,
t
h
e
s
p
ati
al
p
att
er
n
o
f
ea
ch
e
le
m
e
n
t
is
d
e
f
i
n
e
d
as
(
20
)
[
2
3
]
:
(
,
)
=
2
2
(
1
+
(
)
)
(
1
+
(
−
2
)
)
,
(
2
0
)
wh
er
e
D
is
th
e
d
ir
ec
tiv
ity
,
m
c
o
n
tr
o
ls
D
.
DOA
-
e
sti
m
atio
n
p
rocess
o
r
An
ten
n
a E
lem
en
t
1
An
ten
n
a E
lem
en
t
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
On
d
esig
n
o
f
a
s
ma
ll
-
s
iz
ed
a
r
r
a
ys fo
r
d
ir
ec
tio
n
-
of
-
a
r
r
iva
l
-
esti
ma
tio
n
ta
kin
g
…
(
I
lia
P
esh
k
o
v
)
4647
T
h
e
r
a
d
ia
ti
o
n
p
atter
n
of
th
e
lin
ea
r
ar
r
ay
c
o
n
s
is
tin
g
o
f
(
N
=
1
0
)
d
ir
ec
tio
n
al
elem
en
ts
with
o
u
t
tak
in
g
in
to
ac
co
u
n
t m
u
tu
al
c
o
u
p
lin
g
ca
n
b
e
o
b
tain
ed
as
(
21
)
:
(
)
=
∑
(
)
⋅
(
(
−
1
)
(
+
)
)
=
1
,
(
2
1
)
T
h
e
lin
ea
r
ar
r
a
y
h
as
in
ter
-
ele
m
en
t
s
p
ac
in
g
d
,
w
h
er
e
ea
ch
n
-
th
elem
en
t
is
weig
h
ted
b
y
am
p
litu
d
e
aₙ
a
n
d
p
h
ase
βₙ.
T
h
eir
in
d
iv
id
u
al
r
ad
iatio
n
p
atter
n
s
g
ₙ(
θ)
is
ch
a
r
ac
ter
ized
b
y
(
8
)
.
A
g
en
etic
o
p
ti
m
i
za
ti
o
n
alg
o
r
i
th
m
is
a
p
p
li
ed
t
o
s
y
n
th
esi
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g
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d
(
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th
r
ee
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e
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ts
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(
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Fig
u
r
e
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im
u
lated
r
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iatio
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ch
ar
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ter
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e
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ig
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al
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ten
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ar
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ay
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a
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ep
icted
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Fig
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r
e
4
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b
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illu
s
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ated
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Fig
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e
4
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,
a
n
d
(
c)
p
r
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ted
i
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Fig
u
r
e
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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On
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ll
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r
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ys fo
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4649
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ig
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2
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Sim
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A
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t
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No
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Me
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ip
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atter
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atter
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ac
h
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ep
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7
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atter
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ated
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Fig
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h
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atter
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e
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atter
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icted
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Fig
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c)
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e
o
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lf
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2
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e
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2
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t D
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etch
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atter
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alo
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Ph
ases
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Am
p
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
8
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8
I
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&
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m
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15
,
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5
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Octo
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6
I
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5
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atch
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s
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ig
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r
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atter
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b
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.
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ee
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Fig
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i
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u
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c)
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ates w
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th
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atter
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en
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u
r
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8
.
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lectr
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d
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n
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ic
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th
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a
a
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atch
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te
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ased
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7
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ielec
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ic
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ir
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atter
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As
it
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b
e
s
ee
n
f
r
o
m
Fig
u
r
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9
,
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e
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elem
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t
an
ten
n
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ar
r
ay
s
h
o
wn
in
Fig
u
r
e
7
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a)
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o
s
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ess
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th
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elem
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ts
r
ad
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n
p
atter
n
s
d
ep
icted
in
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r
e
7
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c)
,
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ws
o
b
tain
in
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s
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atial
p
s
eu
d
o
s
p
ec
tr
a
as
s
h
ar
p
as
th
e
th
r
ee
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elem
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t
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cu
lar
an
ten
n
a
ar
r
ay
.
T
h
is
is
ex
p
lain
ed
b
y
th
e
f
ac
t
th
at
th
e
elem
en
ts
“
An
ten
n
a
1
”
an
d
“
An
ten
n
a
2
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h
av
e
th
e
g
ain
s
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ich
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e
g
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ter
th
a
n
th
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en
ts
o
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cu
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n
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ay
,
i.e
.
,
7
d
B
i
(
Fig
u
r
e
7
(
c)
)
an
d
4
.
7
d
B
i
(
Fig
u
r
e
8
(
b
)
)
r
esp
ec
tiv
ely
.
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h
u
s
,
as
d
ep
icted
in
Fig
u
r
e
9
,
h
ig
h
er
g
ai
n
r
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lts
in
h
ig
h
er
ac
cu
r
ac
y
in
DOA
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esti
m
atio
n
.
B
ased
o
n
th
e
p
r
o
ce
d
u
r
e
d
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in
s
ec
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s
2
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d
3
th
e
an
ten
n
a
ar
r
ay
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r
o
to
ty
p
e
is
im
p
lem
en
ted
a
n
d
th
e
r
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lts
ar
e
co
n
s
is
ten
t
.
T
h
e
im
p
lem
en
te
d
s
ch
em
e
ca
n
b
e
n
a
m
ed
as
b
ea
m
s
p
ac
e
[
2
7
]
,
[
2
8
]
.
Fig
u
r
e
9
.
T
h
e
p
s
eu
d
o
s
p
ec
tr
u
m
o
f
MU
SIC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
On
d
esig
n
o
f
a
s
ma
ll
-
s
iz
ed
a
r
r
a
ys fo
r
d
ir
ec
tio
n
-
of
-
a
r
r
iva
l
-
esti
ma
tio
n
ta
kin
g
…
(
I
lia
P
esh
k
o
v
)
4651
4.
CO
NCLU
SI
O
N
T
h
e
p
ap
e
r
d
etails
a
m
eth
o
d
f
o
r
d
esig
n
in
g
t
h
e
d
ig
ital
an
te
n
n
a
ar
r
ay
s
f
o
r
in
cr
ea
s
in
g
DOA
-
esti
m
atio
n
ac
cu
r
ac
y
with
s
u
p
er
-
r
eso
lu
tio
n
.
Un
lik
e
th
e
r
ef
er
e
n
ce
d
m
et
h
o
d
s
,
th
e
p
r
o
p
o
s
ed
d
esig
n
a
p
p
r
o
ac
h
ac
co
u
n
ts
f
o
r
th
e
g
ain
an
d
d
ir
ec
ti
o
n
al
p
atter
n
s
o
f
in
d
i
v
id
u
al
a
n
ten
n
a
ele
m
en
ts
.
C
o
m
m
o
n
l
y
,
th
e
y
f
o
cu
s
o
n
c
r
ea
tin
g
n
ew
DOA
-
esti
m
atio
n
m
eth
o
d
s
,
ad
d
in
g
m
o
r
e
an
te
n
n
as,
o
r
o
p
ti
m
izin
g
ar
r
ay
lay
o
u
ts
,
wh
ile
n
eg
lectin
g
an
ten
n
a
-
s
p
ec
if
ic
p
r
o
p
er
ties
b
y
tr
ea
ti
n
g
th
em
as
o
m
n
id
ir
ec
tio
n
al.
I
t
h
as
b
ee
n
s
h
o
wn
b
ased
o
n
s
im
u
latio
n
s
an
d
an
aly
tical
ex
p
r
ess
io
n
s
th
at
th
e
h
ig
h
er
g
ain
c
o
m
p
e
n
s
ates
f
o
r
th
e
lack
o
f
a
n
ten
n
as.
Fo
r
ex
am
p
le,
th
e
g
ain
eq
u
alin
g
to
8
.
5
m
ak
es
it
p
o
s
s
ib
le
to
o
b
tain
th
e
s
am
e
DOA
-
esti
m
atio
n
ac
cu
r
ac
y
as
an
an
te
n
n
a
ar
r
ay
co
m
p
o
s
ed
o
f
m
o
r
e
elem
en
ts
h
av
in
g
th
e
g
ain
eq
u
alin
g
to
6
.
Ad
d
itio
n
ally
,
th
is
tech
n
i
q
u
e
h
as
b
ee
n
u
tili
ze
d
f
o
r
d
esig
n
in
g
a
h
y
b
r
id
ar
r
a
y
ar
c
h
itectu
r
e
f
o
r
d
ir
ec
tio
n
-
of
-
ar
r
i
v
al
esti
m
atio
n
with
s
u
p
er
-
r
eso
lu
ti
o
n
.
M
o
d
elin
g
b
ased
o
n
th
e
Me
th
o
d
-
of
-
Mo
m
en
ts
in
co
n
test
ab
ly
d
em
o
n
s
tr
ated
th
at
th
e
h
y
b
r
id
ar
r
ay
with
f
ewe
r
a
n
ten
n
a
ele
m
en
ts
d
o
es
n
o
t
r
esu
lt
in
a
d
e
clin
e
in
th
e
DOA
-
esti
m
atio
n
ac
cu
r
ac
y
.
As
a
r
e
s
u
lt,
th
e
r
ed
u
ce
d
-
elem
en
t
a
n
t
en
n
a
ar
r
a
y
allo
ws
ac
h
iev
in
g
th
e
s
am
e
lev
el
o
f
ac
cu
r
ac
y
in
DOA
esti
m
atio
n
.
I
n
o
th
er
w
o
r
d
s
,
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
ca
n
b
e
im
p
lem
en
ted
in
p
r
ac
tice
as
b
ea
m
s
p
ac
e
h
y
b
r
i
d
co
n
s
tr
u
ctio
n
.
T
h
u
s
,
it
ca
n
b
e
a
r
g
u
e
d
th
at
th
e
c
o
n
s
id
er
ed
tech
n
iq
u
e
ca
n
b
e
u
s
ed
as
a
th
eo
r
etica
l
s
u
b
s
tan
tiatio
n
f
o
r
th
e
d
esig
n
o
f
s
en
s
o
r
ar
r
a
y
s
f
o
r
s
p
ec
tr
al
s
p
atial
p
r
o
ce
s
s
in
g
.
T
h
u
s
,
in
th
e
p
ap
er
t
h
e
m
eth
o
d
o
l
o
g
y
o
f
th
e
d
esig
n
f
l
o
w
o
f
ar
r
ay
s
f
o
r
DOA
-
esti
m
atio
n
with
s
u
p
er
-
r
eso
lu
tio
n
h
as
b
ee
n
r
ep
r
esen
ted
,
b
eg
in
n
in
g
f
r
o
m
th
e
an
aly
tic
al
an
aly
s
is
o
n
th
e
clo
s
ed
-
f
o
r
m
eq
u
atio
n
s
u
p
to
th
e
p
r
o
to
ty
p
in
g
clo
s
e
to
ex
p
er
im
en
tal
s
o
lu
tio
n
s
.
Ad
d
itio
n
ally
,
it
h
an
d
les
th
e
lo
ca
tio
n
o
f
th
e
a
n
ten
n
as,
th
e
r
a
d
iatio
n
p
atter
n
s
o
f
th
e
elem
en
ts
,
th
e
v
alu
e
o
f
DOA
-
esti
m
atio
n
er
r
o
r
s
s
im
u
ltan
eo
u
s
l
y
.
All
th
at
allo
ws
m
o
v
in
g
f
r
o
m
an
ab
s
tr
ac
t
m
o
d
el
to
a
f
in
al
p
r
o
to
ty
p
e
v
iv
id
l
y
.
RE
F
E
R
E
NC
E
S
[
1
]
B
.
Y
a
n
g
,
Z.
Y
u
,
J.
La
n
,
R
.
Z
h
a
n
g
,
J.
Zh
o
u
,
a
n
d
W
.
H
o
n
g
,
“
D
i
g
i
t
a
l
b
e
a
mf
o
r
mi
n
g
-
b
a
s
e
d
m
a
ssi
v
e
M
I
M
O
t
r
a
n
sc
e
i
v
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r
f
o
r
5
G
mi
l
l
i
m
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t
e
r
-
w
a
v
e
c
o
mm
u
n
i
c
a
t
i
o
n
s
,
”
I
EEE
T
r
a
n
sa
c
t
i
o
n
s
o
n
M
i
c
r
o
w
a
v
e
T
h
e
o
ry
a
n
d
T
e
c
h
n
i
q
u
e
s
,
v
o
l
.
6
6
,
n
o
.
7
,
p
p
.
3
4
0
3
–
3
4
1
8
,
J
u
l
.
2
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8
,
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o
i
:
1
0
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1
1
0
9
/
t
m
t
t
.
2
0
1
8
.
2
8
2
9
7
0
2
.
[
2
]
N
.
R
u
a
n
,
H
.
W
a
n
g
,
F
.
W
e
n
,
a
n
d
J
.
S
h
i
,
“
D
O
A
e
s
t
i
m
a
t
i
o
n
i
n
B
5
G
/
6
G
:
Tr
e
n
d
s
a
n
d
c
h
a
l
l
e
n
g
e
s,
”
S
e
n
s
o
rs
,
v
o
l
.
2
2
,
n
o
.
1
4
,
p
.
5
1
2
5
,
Ju
l
.
2
0
2
2
,
d
o
i
:
1
0
.
3
3
9
0
/
s2
2
1
4
5
1
2
5
.
[
3
]
W
.
Y
i
,
S
.
W
e
i
,
a
n
d
Y
.
X
u
,
“
A
n
i
mp
r
o
v
e
m
mW
a
u
t
o
m
o
t
i
v
e
r
a
d
a
r
D
O
A
e
st
i
m
a
t
i
o
n
a
p
p
r
o
a
c
h
:
J
o
i
n
t
m
a
t
r
i
x
c
o
m
p
l
e
t
i
o
n
a
n
d
sp
e
c
t
r
u
m
e
x
t
r
a
p
o
l
a
t
i
o
n
,
”
i
n
2
0
2
4
I
EE
E
1
7
t
h
I
n
t
e
r
n
a
t
i
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
S
i
g
n
a
l
Pr
o
c
e
ssi
n
g
(
I
C
S
P)
,
O
c
t
.
2
0
2
4
,
p
p
.
1
6
–
1
9
,
d
o
i
:
1
0
.
1
1
0
9
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c
sp
6
2
1
2
9
.
2
0
2
4
.
1
0
8
4
6
2
4
5
.
[
4
]
Y
.
F
a
n
g
,
X
.
W
e
i
,
a
n
d
J.
M
a
,
“
H
i
g
h
-
p
r
e
c
i
si
o
n
D
O
A
e
st
i
ma
t
i
o
n
b
a
se
d
o
n
sy
n
t
h
e
t
i
c
a
p
e
r
t
u
r
e
a
n
d
s
p
a
r
se
r
e
c
o
n
st
r
u
c
t
i
o
n
,
”
S
e
n
so
rs
,
v
o
l
.
2
3
,
n
o
.
2
1
,
p
.
8
6
9
0
,
O
c
t
.
2
0
2
3
,
d
o
i
:
1
0
.
3
3
9
0
/
s
2
3
2
1
8
6
9
0
.
[
5
]
Y
.
W
a
n
g
,
G
.
G
u
i
,
H
.
G
a
c
a
n
i
n
,
T.
O
h
t
su
k
i
,
O
.
A
.
D
o
b
r
e
,
a
n
d
H
.
V
.
P
o
o
r
,
“
A
n
e
f
f
i
c
i
e
n
t
sp
e
c
i
f
i
c
e
m
i
t
t
e
r
i
d
e
n
t
i
f
i
c
a
t
i
o
n
met
h
o
d
b
a
se
d
o
n
c
o
m
p
l
e
x
-
v
a
l
u
e
d
n
e
u
r
a
l
n
e
t
w
o
r
k
s
a
n
d
n
e
t
w
o
r
k
c
o
m
p
r
e
ss
i
o
n
,
”
I
EEE
J
o
u
rn
a
l
o
n
S
e
l
e
c
t
e
d
Are
a
s
i
n
C
o
m
m
u
n
i
c
a
t
i
o
n
s
,
v
o
l
.
3
9
,
n
o
.
8
,
p
p
.
2
3
0
5
–
2
3
1
7
,
A
u
g
.
2
0
2
1
,
d
o
i
:
1
0
.
1
1
0
9
/
j
sac
.
2
0
2
1
.
3
0
8
7
2
4
3
.
[
6
]
V
.
Ja
n
o
u
d
i
e
t
a
l
.
,
“
A
n
t
e
n
n
a
a
r
r
a
y
d
e
s
i
g
n
f
o
r
c
o
h
e
r
e
n
t
M
I
M
O
r
a
d
a
r
n
e
t
w
o
r
k
s,”
i
n
2
0
2
3
I
EEE
R
a
d
a
r
C
o
n
f
e
re
n
c
e
(
R
a
d
a
rC
o
n
f
2
3
)
,
M
a
y
2
0
2
3
,
p
p
.
1
–
6
,
d
o
i
:
1
0
.
1
1
0
9
/
r
a
d
a
r
c
o
n
f
2
3
5
1
5
4
8
.
2
0
2
3
.
1
0
1
4
9
7
8
9
.
[
7
]
D
.
B
o
n
a
c
c
i
,
F
.
V
i
n
c
e
n
t
,
a
n
d
B
.
G
i
g
l
e
u
x
,
“
R
o
b
u
st
D
o
A
e
st
i
ma
t
i
o
n
i
n
c
a
se
o
f
mu
l
t
i
p
a
t
h
e
n
v
i
r
o
n
m
e
n
t
f
o
r
a
s
e
n
s
e
a
n
d
a
v
o
i
d
a
i
r
b
o
r
n
e
r
a
d
a
r
,
”
I
ET
Ra
d
a
r,
S
o
n
a
r
&
N
a
v
i
g
a
t
i
o
n
,
v
o
l
.
1
1
,
n
o
.
5
,
p
p
.
7
9
7
–
8
0
1
,
M
a
y
2
0
1
7
,
d
o
i
:
1
0
.
1
0
4
9
/
i
e
t
-
r
sn
.
2
0
1
6
.
0
4
4
6
.
[
8
]
L.
C
.
G
o
d
a
r
a
,
“
A
p
p
l
i
c
a
t
i
o
n
o
f
a
n
t
e
n
n
a
a
r
r
a
y
s
t
o
mo
b
i
l
e
c
o
m
mu
n
i
c
a
t
i
o
n
s.
I
I
.
B
e
a
m
-
f
o
r
mi
n
g
a
n
d
d
i
r
e
c
t
i
o
n
-
of
-
a
r
r
i
v
a
l
c
o
n
si
d
e
r
a
t
i
o
n
s,
”
Pr
o
c
e
e
d
i
n
g
s
o
f
t
h
e
I
EEE
,
v
o
l
.
8
5
,
n
o
.
8
,
p
p
.
1
1
9
5
–
1
2
4
5
,
1
9
9
7
,
d
o
i
:
1
0
.
1
1
0
9
/
5
.
6
2
2
5
0
4
.
[
9
]
J.
-
F
.
G
u
,
S
.
C
.
C
h
a
n
,
W
.
-
P
.
Z
h
u
,
a
n
d
M
.
N
.
S
.
S
w
a
m
y
,
“
D
O
A
e
s
t
i
m
a
t
i
o
n
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