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f
m
u
lti
-
b
an
d
an
ten
n
as.
B
id
ir
ec
tio
n
al
an
ten
n
as
ar
e
cr
u
cial
f
o
r
w
ir
eless
co
m
m
u
n
icatio
n
in
s
p
ec
if
ic
en
v
ir
o
n
m
en
ts
lik
e
s
tr
ee
ts
,
h
ig
h
w
ay
s
,
s
k
y
w
alk
s
,
co
r
r
id
o
r
s
,
tu
n
n
els,
an
d
s
u
b
w
ay
s
tatio
n
s
[
1
4
]
,
[
1
8
]
,
[
2
7
]
,
en
s
u
r
in
g
ad
eq
u
ate
co
v
er
ag
e.
Sev
er
al
tech
n
iq
u
es
ac
h
iev
e
b
id
ir
ec
tio
n
al
p
r
o
p
ag
atio
n
.
T
h
ese
in
clu
d
e
u
tili
zin
g
w
id
e
s
lo
ts
to
m
an
ip
u
late
o
m
n
id
ir
ec
tio
n
al
r
ad
iatio
n
[
1
8
]
,
th
e
s
p
o
o
f
s
u
r
f
ac
e
p
lasm
o
n
p
o
lar
ito
n
(
SP
P
)
m
eth
o
d
f
o
r
w
id
eb
an
d
en
d
-
f
ir
e
an
ten
n
as
[
2
8
]
,
r
esh
ap
in
g
s
lo
t
an
ten
n
a
r
ad
iatio
n
p
atter
n
s
u
s
in
g
ch
ar
ac
ter
is
tic
m
o
d
e
an
aly
s
is
[
2
9
]
,
an
d
co
m
b
in
in
g
tw
o
u
n
id
ir
ec
tio
n
al
an
ten
n
as,
s
u
ch
as
b
ac
k
-
to
-
b
ac
k
f
r
eq
u
en
cy
s
ca
n
n
in
g
tap
e
r
ed
s
lo
t
an
ten
n
a
(
FS
T
SA
)
elem
en
ts
[
3
0
]
.
T
h
e
m
u
lti
-
r
eso
n
an
ce
p
r
in
cip
le,
co
m
b
in
in
g
m
u
ltip
le
b
o
w
-
tie
an
ten
n
as,
is
an
o
th
er
ap
p
r
o
ac
h
[
3
1
]
.
T
h
ese
m
eth
o
d
s
im
p
r
o
v
e
co
m
m
u
n
icatio
n
ef
f
icien
cy
in
en
v
ir
o
n
m
en
ts
r
eq
u
ir
in
g
r
o
b
u
s
t
s
ig
n
al
co
v
er
ag
e.
T
h
is
p
ap
er
p
r
esen
ts
a
b
id
ir
ec
tio
n
al
an
ten
n
a
d
esig
n
in
teg
r
atin
g
a
d
u
al
-
o
v
er
lap
p
in
g
r
ec
tan
g
u
lar
p
atch
(
DORP
)
w
ith
in
a
w
id
e
cir
cu
lar
s
lo
t
(
W
C
S)
an
d
an
in
v
er
ted
-
L
s
h
ap
e
s
tr
ip
(
I
L
SS
)
,
f
ed
b
y
a
co
p
lan
ar
w
av
eg
u
id
e
(
C
P
W
)
.
T
h
is
co
m
p
ac
t
an
ten
n
a
o
p
er
ates
ac
r
o
s
s
f
iv
e
b
an
d
s
,
s
u
p
p
o
r
tin
g
2
.
4
-
2
.
4
8
4
GHz
f
o
r
2
.
4
GHz
W
L
A
N,
3
.
4
-
3
.
6
GHz
f
o
r
W
iMA
X,
5
.
1
5
-
5
.
8
2
5
GHz
f
o
r
5
GHz
W
L
A
N,
7
.
2
5
-
8
.
4
GHz
f
o
r
X
-
b
an
d
,
an
d
1
3
.
4
-
1
7
.
7
GHz
f
o
r
Ku
-
b
an
d
ap
p
licatio
n
s
(
s
atellite
co
m
m
u
n
icatio
n
s
an
d
r
ad
ar
)
.
I
ts
m
u
lti
-
b
an
d
ca
p
ab
ilit
y
m
ak
es
it
s
u
itab
le
f
o
r
u
r
b
an
o
u
td
o
o
r
m
o
b
ilit
y
,
r
ec
eiv
in
g
s
ig
n
als
f
r
o
m
W
L
A
N/W
iMA
X
to
w
er
s
an
d
s
atellites.
I
t
ca
n
also
b
e
u
s
ed
in
h
ig
h
-
g
ain
an
ten
n
a
ar
r
ay
s
f
o
r
s
atellite
co
m
m
u
n
icatio
n
s
.
I
n
itial
th
eo
r
etica
l
d
esig
n
p
ar
am
eter
s
w
er
e
ca
lcu
lated
(
s
ec
tio
n
2
)
an
d
th
en
s
im
u
lated
in
C
ST
m
icr
o
w
av
e
s
tu
d
io
[
3
2
]
.
T
h
e
f
in
al
d
esig
n
p
ar
am
eter
s
w
er
e
d
eter
m
in
ed
th
r
o
u
g
h
an
iter
ativ
e
s
im
u
latio
n
p
r
o
ce
s
s
.
2.
T
H
E
P
RO
P
O
SE
D
M
E
T
H
O
D
2
.
1
.
Ant
enna
la
y
o
ut
a
nd
f
o
r
m
u
la
s
T
h
is
s
ec
tio
n
d
etails
th
e
d
esig
n
o
f
a
f
iv
e
-
b
an
d
b
id
ir
ec
tio
n
al
p
atch
an
ten
n
a
(
FB
B
P
A
)
,
an
ex
te
n
s
io
n
o
f
o
u
r
p
r
ev
io
u
s
ly
d
ev
elo
p
ed
tr
i
-
b
an
d
d
esig
n
(
T
B
B
P
A
)
[
1
8
]
f
o
r
2
.
4
/5
GHz
W
L
A
N
an
d
Ku
-
b
an
d
o
p
er
atio
n
.
T
h
e
T
B
B
P
A
(
Fig
u
r
e
1
(
a)
[
1
8
]
)
co
n
s
is
ted
o
f
a
r
ec
tan
g
u
lar
r
ad
iatin
g
p
atch
(
R
R
P
)
o
f
w
id
th
w
r
an
d
len
g
th
l
r
w
ith
in
a
W
C
S
o
f
r
ad
iu
s
r
.
T
h
is
W
C
S
w
as
em
p
lo
y
ed
to
ac
h
iev
e
b
id
ir
ec
tio
n
al
r
ad
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n
p
atter
n
s
.
A
n
I
L
SS
w
ith
d
im
en
s
io
n
s
l
1
,
l
2
,
an
d
l
3
,
p
o
s
itio
n
ed
at
a
h
eig
h
t
p
ab
o
v
e
th
e
g
r
o
u
n
d
p
lan
e,
w
as
u
s
ed
to
tu
n
e
im
p
ed
an
ce
m
atch
in
g
at
th
e
lo
w
er
f
r
eq
u
en
cy
b
an
d
.
Fo
r
th
e
tr
an
s
itio
n
to
a
f
iv
e
-
b
an
d
o
p
er
atio
n
,
as
d
ep
icted
in
Fig
u
r
e
1
(
b
)
,
a
s
m
aller
R
R
P
(
w
ith
d
im
en
s
io
n
s
w
r1
an
d
l
r1
)
w
as
s
tr
ateg
ically
p
lace
d
ab
o
v
e
th
e
o
r
ig
in
al
R
R
P
.
I
ts
p
r
ec
is
e
p
o
s
itio
n
in
g
,
in
clu
d
in
g
s
p
ac
in
g
(
s
r
)
an
d
ce
n
ter
p
o
in
t
(
p
r
)
,
w
as
m
eticu
lo
u
s
ly
d
esig
n
ed
to
in
tr
o
d
u
ce
ad
d
itio
n
al
r
eso
n
an
ce
s
.
B
o
t
h
a
n
t
e
n
n
a
s
w
e
r
e
f
a
b
r
i
c
a
t
e
d
o
n
a
c
o
s
t
-
e
f
f
e
c
t
i
v
e
F
R
4
s
u
b
s
t
r
a
t
e
(
w
i
d
t
h
w
,
l
e
n
g
t
h
l
,
t
h
i
c
k
n
e
s
s
h
=
1
.
6
m
m
,
r
e
l
a
t
i
v
e
p
e
r
m
i
t
t
i
v
i
t
y
4
.
3
)
a
n
d
f
e
d
b
y
a
50
-
Ω
C
PW
w
i
t
h
a
f
e
e
d
l
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n
e
l
e
n
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t
h
o
f
l
f
,
w
i
d
t
h
of
w
f
,
g
a
p
o
f
g
,
a
n
d
g
r
o
u
n
d
p
l
a
n
e
l
e
n
g
t
h
l
g
b
e
n
e
a
t
h
t
h
e
R
R
P.
T
h
e
T
B
B
PA
a
c
h
i
e
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d
a
1
0
d
B
r
e
t
u
r
n
l
o
s
s
a
c
r
o
s
s
2
-
2
.
5
6
G
H
z
,
4
.
4
2
–
6
.
8
2
G
H
z
,
a
n
d
1
3
.
2
6
-
1
7
.
7
0
G
H
z
,
w
ith
an
ad
d
itio
n
al
r
eso
n
an
ce
o
f
ar
o
u
n
d
8
.
9
GHz
(
Fig
u
r
e
2
,
d
ash
ed
lin
e)
.
T
o
ex
p
an
d
th
is
to
f
iv
e
-
b
an
d
o
p
er
atio
n
an
d
in
tr
o
d
u
ce
tw
o
n
ew
r
eso
n
an
ce
s
a
t
ap
p
r
o
x
im
ately
3
.
5
GHz
an
d
8
GHz
(
r
ep
r
esen
ted
b
y
th
e
s
o
lid
lin
e
in
Fig
u
r
e
2
)
,
th
e
s
m
aller
R
R
P
w
as
ad
d
ed
as
d
escr
ib
ed
.
T
h
e
f
o
llo
w
in
g
s
ec
tio
n
an
aly
ze
s
th
e
im
p
ac
t
o
f
th
e
u
p
p
er
R
R
P
p
ar
am
eter
s
(
l
r1
,
w
r1
,
s
r
,
an
d
p
r
)
.
(
a)
(
b
)
Fig
u
r
e
1
.
Dev
elo
p
m
e
n
t o
f
t
h
e
d
esig
n
ed
an
te
n
n
a:
(
a)
T
B
B
P
A
[
1
8
]
an
d
(
b
)
FB
B
P
A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
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o
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p
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t E
l
C
o
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tr
o
l
,
Vo
l.
23
,
No
.
4
,
A
u
g
u
s
t
20
25
:
9
0
6
-
917
908
Fig
u
r
e
2
.
Si
m
u
lated
|
S
11
|
o
f
th
e
T
B
B
P
A
an
d
FB
B
P
A
I
n
itial
an
te
n
n
a
d
i
m
en
s
io
n
s
w
er
e
ca
lcu
lated
u
s
in
g
estab
l
is
h
ed
f
o
r
m
u
la
s
[
1
8
]
,
[
3
3
]
.
T
h
e
lo
w
er
r
ec
tan
g
u
lar
p
atch
w
id
t
h
(
w
r
)
was c
alcu
lated
f
o
r
a
5
.
5
GHz
r
e
s
o
n
an
ce
:
=
2
√
2
+
1
(
1
)
w
h
er
e
w
r
w
a
s
t
h
e
r
ec
tan
g
u
lar
p
atch
w
id
th
,
c
w
a
s
t
h
e
s
p
ee
d
o
f
li
g
h
t,
f
w
as a
r
eso
n
an
t
f
r
eq
u
e
n
c
y
(
5
.
5
GHz
)
,
an
d
w
a
s
t
h
e
r
elati
v
e
p
er
m
i
tti
v
it
y
o
f
th
e
F
R
4
s
u
b
s
tr
ate
(
a
v
a
lu
e
o
f
4
.
3
)
.
T
h
e
lo
w
er
r
ec
ta
n
g
u
lar
p
atch
le
n
g
t
h
(
l
r
)
w
a
s
th
e
n
ca
lc
u
lated
:
=
2
√
−
0
.
824
ℎ
[
(
+
0
.
3
)
(
+
0
.
264
ℎ
)
(
−
0
.
258
)
(
+
0
.
8
ℎ
)
]
(
2
)
w
h
er
e
l
r
w
a
s
th
e
p
atch
len
g
t
h
;
w
a
s
th
e
ef
f
ec
ti
v
e
d
ielec
tr
ic
co
n
s
tan
t
o
f
t
h
e
s
u
b
s
tr
ate,
an
d
h
w
a
s
th
e
s
u
b
s
tr
ate
t
h
ic
k
n
e
s
s
.
=
+
1
2
+
−
1
2
√
1
+
12
ℎ
(
3
)
T
h
ese
ca
lcu
latio
n
s
,
w
h
ic
h
ac
co
u
n
t
f
o
r
f
r
i
n
g
i
n
g
ef
f
ec
ts
,
y
iel
d
ed
in
itial
d
im
e
n
s
io
n
s
o
f
w
r
=
1
7
m
m
a
n
d
l
r
=1
2
m
m
.
T
h
e
u
p
p
er
r
ec
tan
g
u
lar
p
atc
h
d
i
m
e
n
s
io
n
s
(
w
r1
a
n
d
l
r1
)
f
o
r
a
7
.
5
GHz
r
eso
n
an
ce
w
er
e
ca
lc
u
lated
s
i
m
ilar
l
y
,
r
es
u
lti
n
g
in
w
r1
=1
2
m
m
an
d
l
r1
=8
m
m
.
I
n
ad
d
itio
n
,
th
e
f
ee
d
li
n
e
w
id
th
(
w
f
)
an
d
l
en
g
t
h
(
l
f
)
f
o
r
50
-
Ω
i
m
p
ed
an
ce
m
atch
in
g
w
er
e
ca
l
cu
lated
u
s
in
g
(
4
)
an
d
(
5
)
f
r
o
m
[
1
8
]
,
[
3
3
]
.
=
2
ℎ
{
(
60
2
√
)
−
1
−
(
120
2
√
−
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h
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at
es
t
w
o
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w
r
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s
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n
a
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f
r
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en
cies.
Su
b
s
eq
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h
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f
w
r1
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n
t
h
e
r
ef
le
ctio
n
co
ef
f
icie
n
t
(
|
S
11
|
)
w
as
i
n
itiall
y
a
s
s
e
s
s
ed
b
y
v
ar
y
in
g
it
s
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g
t
h
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d
1
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m
m
)
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ile
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o
ld
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g
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t
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er
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m
eter
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3
.
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a
n
g
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s
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n
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ig
n
i
f
ica
n
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y
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n
f
l
u
en
ce
d
t
h
e
f
o
u
r
th
f
r
eq
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en
c
y
b
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d
(
7
.
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GHz
)
.
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r
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s
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g
w
r1
ca
u
s
e
s
a
d
o
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n
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ar
d
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f
t
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n
th
e
lo
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er
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eso
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n
t
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en
c
y
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p
o
ten
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er
g
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n
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e
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d
an
d
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o
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r
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h
b
an
d
s
.
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h
er
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o
r
e,
w
r1
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m
m
w
a
s
s
elec
ted
f
o
r
f
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r
t
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al
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f
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m
ain
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n
g
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ar
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m
e
ter
s
.
Fig
u
r
e
3
.
T
h
e
ef
f
ec
t o
f
w
r1
o
n
|
S
11
|
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
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23
,
No
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4
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g
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:
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f
ter
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th
e
im
p
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t
o
f
l
r1
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n
|
S
11
|
w
as
in
v
esti
g
ated
b
y
v
ar
y
in
g
its
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g
th
to
6
,
8
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d
1
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m
m
as
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ep
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Fig
u
r
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4
.
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h
e
r
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lts
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h
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w
th
at
l
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p
r
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ar
ily
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f
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ts
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e
s
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o
n
d
,
th
ir
d
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an
d
f
o
u
r
th
f
r
eq
u
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b
an
d
s
.
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r
ea
s
in
g
l
r1
lo
w
er
s
th
e
r
eso
n
an
t
f
r
eq
u
en
cy
,
d
ee
p
en
in
g
th
e
|
S
11
|
an
d
p
o
ten
tially
m
er
g
in
g
th
e
th
ir
d
an
d
f
o
u
r
th
b
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s
b
elo
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6
GHz
.
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o
n
v
er
s
ely
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at
h
ig
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r
eq
u
en
cies,
a
s
h
o
r
ter
l
r1
s
h
if
ts
th
e
h
ig
h
er
r
eso
n
an
t
f
r
eq
u
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u
p
w
ar
d
s
.
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h
ile
l
r1
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m
m
an
d
l
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0
m
m
ac
h
iev
e
a
1
0
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B
r
etu
r
n
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s
s
ac
r
o
s
s
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r
b
an
d
s
,
l
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m
m
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n
d
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th
ir
d
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d
l
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0
m
m
m
er
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es
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e
th
ir
d
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d
f
o
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r
th
.
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h
er
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o
r
e,
l
r1
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m
m
w
as
ch
o
s
en
as
th
e
o
p
tim
al
v
alu
e
f
o
r
s
u
b
s
eq
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en
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aly
s
is
.
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h
e
n
ex
t
s
tep
in
v
o
lv
es
in
v
esti
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g
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e
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o
s
itio
n
in
g
o
f
th
e
u
p
p
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R
R
P
.
Fig
u
r
e
4
.
T
h
e
ef
f
ec
t o
f
l
r1
o
n
|
S
11
|
Fig
u
r
e
5
illu
s
tr
ates
th
e
im
p
ac
t
o
f
th
e
s
p
ac
in
g
(
s
r
)
b
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n
th
e
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er
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an
d
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e
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p
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R
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as
th
e
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R
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P
is
m
o
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u
p
w
ar
d
b
y
d
is
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ce
s
o
f
0
,
1
,
an
d
2
m
m
.
T
h
e
r
esu
lts
in
d
icate
th
at
in
cr
ea
s
in
g
th
e
s
p
ac
e
im
p
r
o
v
es
|
S
11
|
f
o
r
th
e
th
ir
d
b
an
d
;
h
o
w
ev
er
,
it
n
eg
ativ
ely
af
f
ec
ts
|
11
|
f
o
r
th
e
s
ec
o
n
d
b
an
d
an
d
ca
u
s
e
s
an
u
p
w
ar
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s
h
if
t
in
th
e
h
ig
h
er
r
eso
n
an
ce
f
r
eq
u
en
cy
f
o
r
th
e
f
o
u
r
th
b
an
d
.
A
s
a
r
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lt,
a
s
p
ac
in
g
(
s
r
)
o
f
0
m
m
is
ch
o
s
en
as
th
e
o
p
tim
al
co
n
f
ig
u
r
atio
n
.
Fig
u
r
e
5
.
T
h
e
ef
f
ec
t o
f
s
r
o
n
|
S
11
|
Nex
t,
th
e
ef
f
ec
t
o
f
s
h
if
tin
g
th
e
u
p
p
er
R
R
P
h
o
r
izo
n
tally
to
th
e
lef
t
(
-
)
an
d
r
ig
h
t
(
+)
o
n
|
S
11
|
is
ex
am
in
ed
,
as
d
ep
icted
in
Fig
u
r
e
6
.
T
h
e
p
ar
am
eter
p
r
is
ad
j
u
s
ted
to
-
2
,
0
,
an
d
2
-
m
m
v
alu
es.
T
h
e
f
in
d
in
g
s
r
ev
ea
l
th
at
m
o
v
in
g
th
e
u
p
p
er
R
R
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h
o
r
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n
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af
f
ec
ts
th
e
f
ir
s
t,
s
ec
o
n
d
,
an
d
f
o
u
r
th
b
an
d
s
,
w
h
ile
th
e
th
ir
d
an
d
f
if
th
b
an
d
s
r
em
ain
u
n
ch
an
g
ed
.
Sp
ec
if
ically
,
s
h
if
tin
g
to
th
e
lef
t
at
-
2
m
m
r
esu
lts
in
a
d
eter
io
r
atio
n
o
f
|
S
11
|
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Evaluation Warning : The document was created with Spire.PDF for Python.