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s
tellatio
n
s
,
an
d
e
y
e
p
atter
n
d
ia
g
r
a
m
s
.
T
h
e
s
i
m
u
latio
n
i
s
p
o
w
er
f
u
ll
y
p
r
ej
u
d
iced
b
y
th
e
a
d
j
u
s
t
m
e
n
t o
f
t
h
e
v
al
u
e
o
f
ea
c
h
p
ar
am
eter
to
g
et
t
h
e
b
est B
E
R
.
R
esear
ch
o
n
i
n
ter
f
er
e
n
ce
ca
n
b
e
d
o
n
e
b
y
lo
o
k
in
g
at
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
d
ev
ice
t
h
r
o
u
g
h
t
h
e
B
E
R
m
eter
,
e
y
e
p
atter
n
,
an
d
co
n
s
te
llatio
n
d
ia
g
r
a
m
.
W
ir
ast
u
ti
et
a
l.
[
4
]
,
r
ed
u
ctio
n
o
f
in
ter
-
ca
r
r
ie
r
in
ter
f
er
e
n
ce
(
I
C
I
)
is
d
o
n
e
b
y
s
i
m
u
lati
n
g
t
h
e
cir
cu
it
f
o
r
m
ed
b
y
th
e
o
r
th
o
g
o
n
a
l
f
r
eq
u
e
n
c
y
-
d
i
v
is
io
n
m
u
ltip
le
x
in
g
(
O
FDM
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p
u
l
s
e
s
h
ap
i
n
g
s
y
s
te
m
.
T
h
e
r
esu
lt
o
f
th
e
s
i
m
u
latio
n
in
ter
m
s
o
f
B
E
R
v
s
.
E
b
/No
s
u
g
g
es
ted
th
at
r
ec
tan
g
u
lar
(
R
E
C
)
i
m
p
r
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v
ed
s
in
c
-
p
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w
er
(
I
SP
)
p
u
ls
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h
ap
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g
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n
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I
SP
p
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ls
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s
h
a
p
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o
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ter
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ier
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ter
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le
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f
o
r
m
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elati
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O
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te
m
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An
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th
er
w
a
y
i
s
to
d
o
a
r
elativ
e
a
n
al
y
s
i
s
.
C
o
m
p
ar
is
o
n
o
f
t
h
e
p
er
f
o
r
m
an
ce
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f
v
ar
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u
s
t
y
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e
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f
b
asic
m
o
d
u
la
tio
n
tech
n
iq
u
es
is
ca
r
r
ied
o
u
t in
v
ar
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s
s
tu
d
ie
s
to
s
ee
th
e
p
er
f
o
r
m
an
ce
o
f
B
E
R
,
E
y
e
d
i
ag
r
a
m
,
a
n
d
co
n
s
tellatio
n
d
iag
r
a
m
r
esp
ec
ti
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el
y
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ad
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itiv
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h
ite
Ga
u
s
s
ia
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n
o
is
e
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A
W
GN)
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R
a
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leig
h
a
n
d
R
ici
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c
h
an
n
el
s
u
s
i
n
g
M
A
T
L
A
B
Si
m
u
li
n
k
,
g
r
ap
h
ical
u
s
er
in
ter
f
ac
e
(
GUI
)
,
an
d
B
E
R
to
o
l
o
n
OFDM
s
y
s
te
m
s
,
c
o
d
e
d
iv
is
io
n
m
u
ltip
le
ac
ce
s
s
(
C
DM
A
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to
o
p
tica
l
s
y
s
te
m
s
.
T
h
e
g
o
al
i
s
to
s
ee
th
e
ef
f
o
r
ts
to
s
u
p
p
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ess
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n
ter
s
y
m
b
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ter
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ce
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SI
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d
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r
m
u
ltip
at
h
f
ad
in
g
w
it
h
th
e
s
i
m
u
la
tio
n
[
6
]
-
[
1
3
]
.
P
er
f
o
r
m
an
ce
co
m
p
ar
is
o
n
o
f
o
p
tical
f
ib
er
is
f
o
u
n
d
i
n
[
1
4
]
,
[
1
5
]
.
On
e
t
h
i
n
g
th
a
t
is
also
i
m
p
o
r
tan
t
f
r
o
m
t
h
e
ex
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g
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p
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at
t
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A
W
GN
c
h
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n
el
i
s
b
etter
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n
R
a
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lei
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h
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d
R
icia
n
ch
a
n
n
el
o
n
t
h
e
O
FDM
s
y
s
te
m
.
[
1
6
]
-
[
2
0
]
.
Me
an
w
h
i
le
[
2
1
]
o
b
s
er
v
ed
B
E
R
i
n
o
r
th
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g
o
n
al
f
r
eq
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en
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iv
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u
ltip
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ter
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m
u
ltip
le
ac
ce
s
s
(
OF
DM
-
I
DM
A
)
o
f
5
G
s
y
s
te
m
.
Kad
h
u
m
a
n
d
Haith
a
m
[
2
2
]
,
th
e
b
est B
E
R
r
esu
lt is
1
.
0
e
-
3.
2.
K
E
Y
CO
M
P
O
NE
NT
S
2
.
1
Dif
f
er
ent
ia
l Q
P
SK
T
h
e
DQP
SK
to
g
eth
er
w
it
h
OQP
SK
is
a
ty
p
e
o
f
d
if
f
er
e
n
tial
m
o
d
u
la
tio
n
th
a
t
is
w
id
el
y
u
s
e
d
in
d
ig
ita
l
co
m
m
u
n
icatio
n
s
[
2
2
]
.
I
n
DQ
P
SK,
in
f
o
r
m
at
io
n
is
ca
r
r
ied
b
y
th
e
estab
li
s
h
m
e
n
t
o
f
a
ce
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t
ain
s
tep
o
f
a
s
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n
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le
s
y
m
b
o
l
co
m
p
ar
ativ
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to
t
h
e
p
r
ec
ed
in
g
s
y
m
b
o
l.
T
h
e
p
h
ase
v
ar
iatio
n
b
et
w
ee
n
n
ei
g
h
b
o
r
in
g
s
y
m
b
o
ls
is
u
s
ed
b
y
DQP
SK
to
p
r
ev
en
t
i
s
s
u
es
a
s
s
o
ciate
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w
i
th
t
h
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ab
s
e
n
ce
o
f
p
h
ase
s
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n
ch
r
o
n
iza
tio
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et
wee
n
tr
an
s
m
itter
an
d
r
ec
eiv
er
.
T
h
e
DQP
SK
co
n
s
tel
latio
n
e
x
p
r
ess
es
f
o
u
r
d
is
s
i
m
i
la
r
s
y
m
b
o
ls
(
M=
4
)
s
o
t
h
at
2
b
it
s
ar
e
o
r
g
an
ized
p
er
s
y
m
b
o
l.
T
h
e
b
it e
r
r
o
r
p
r
o
b
a
b
ilit
y
o
f
DQP
SK i
s
ex
p
r
es
s
ed
in
(
1
)
.
=
1
2
.
2
∫
ex
p
(
(
ϒ
.
2
)
.
(
1
−
/
.
)
)
(
1
−
/
.
)
/
2
−
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2
d
θ
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1
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W
ith
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E
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E
b
d
en
o
tes th
e
en
er
g
y
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er
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s
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it
ted
b
it a
n
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No
is
th
e
n
o
is
e
ad
d
ed
b
y
t
h
e
ch
a
n
n
e
l [
1
]
.
2
.
2
.
Dis
cr
et
e
F
I
R
f
ilte
r
A
f
i
n
ite
-
d
u
r
atio
n
i
m
p
u
ls
e
r
esp
o
n
s
e
o
r
FIR f
il
ter
tak
es a
s
y
s
te
m
f
u
n
ctio
n
o
f
th
e
f
o
r
m
:
(
)
=
0
+
1
−
1
+
2
−
2
+
⋯
…
…
…
…
…
+
−
1
1
−
(
2
)
w
h
er
e
M
is
t
h
e
n
u
m
b
er
o
f
co
e
f
f
icien
ts
a
n
d
M
-
1
is
th
e
o
r
d
er
o
f
th
e
f
ilter
.
FI
R
f
ilter
s
tr
u
ct
u
r
es
ar
e
o
f
ten
s
tab
le
an
d
co
m
p
ar
ed
to
in
f
i
n
ite
-
d
u
r
a
tio
n
i
m
p
u
ls
e
r
esp
o
n
s
e
(
I
I
R
)
s
t
r
u
ctu
r
es,
t
h
e
y
ar
e
r
elati
v
el
y
s
i
m
p
le
[
2
3
]
.
T
h
e
FIR
f
ilter
i
s
b
r
o
ad
ly
u
s
ed
i
n
cl
u
d
in
g
in
t
h
e
co
m
m
u
n
icatio
n
s
f
ie
ld
.
An
ex
a
m
p
le
o
f
i
ts
u
s
e
i
s
f
o
r
a
b
an
d
-
li
m
it
in
g
f
ilter
.
T
o
r
ea
ch
t
h
e
id
ea
lis
m
o
f
t
h
e
tr
a
n
s
m
it
ted
s
p
ec
tr
u
m
s
i
g
n
al,
t
h
e
d
is
cr
ete
FIR
f
ilter
is
u
s
ed
f
o
r
th
is
b
a
n
d
r
estrictin
g
[
5
]
.
2
.
3
.
Ada
ptiv
e
f
ilte
r
Usi
n
g
ad
ap
ti
v
e
f
ilter
al
g
o
r
ith
m
s
,
t
h
e
f
il
ter
co
ef
f
icie
n
t
ca
n
b
e
m
o
d
if
ied
.
T
h
e
ad
ap
tiv
e
f
ilt
er
h
as
x
(
n
)
in
p
u
t,
w
ei
g
h
t
w
(
n
)
an
d
o
u
tp
u
t
y
(
n
)
.
T
h
e
o
u
tp
u
t
y
(
n
)
is
p
r
o
d
u
ce
d
as
a
lin
ea
r
m
ix
t
u
r
e
o
f
th
e
d
ela
y
ed
i
n
p
u
t
s
eq
u
en
ce
s
a
m
p
le
s
x
(
n
)
ac
co
r
d
i
n
g
to
t
h
e
eq
u
atio
n
.
T
h
e
eq
u
ati
o
n
is
ac
co
r
d
in
g
to
[
2
4
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
T
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L
KOM
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A
T
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1477
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(
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0
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3
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T
h
e
least
m
ea
n
s
q
u
ar
e
(
L
M
S
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alg
o
r
ith
m
is
i
n
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l
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asi
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ed
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o
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h
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is
i
n
co
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ast
to
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th
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al
g
o
r
ith
m
s
th
at,
s
u
ch
a
s
th
e
L
M
S,
ai
m
t
o
r
ed
u
ce
th
e
m
ea
n
s
q
u
ar
e
er
r
o
r
.
T
h
e
in
p
u
t
s
i
g
n
a
ls
ar
e
ca
lled
d
eter
m
in
i
s
tic
f
o
r
th
e
d
er
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o
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th
e
R
L
S,
alth
o
u
g
h
th
e
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ar
e
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s
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s
to
ch
asti
c
f
o
r
th
e
L
MS
an
d
r
elate
d
alg
o
r
ith
m
s
[
2
4
]
.
A
d
ap
tiv
e
f
il
ter
in
g
is
w
id
el
y
u
s
ed
i
n
b
o
th
id
en
ti
f
icat
io
n
,
p
r
ed
ictio
n
,
an
d
in
ter
f
er
en
ce
ca
n
ce
llatio
n
s
y
s
te
m
s
.
I
n
cl
u
d
ed
in
th
e
in
ter
f
er
en
ce
ca
n
ce
lla
tio
n
i
s
a
n
ad
ap
tiv
e
b
ea
m
f
o
r
m
in
g
s
y
s
te
m
[
2
5
]
.
A
d
ap
ti
v
e
f
ilter
i
n
g
w
it
h
L
MS
a
n
d
N
L
M
S
al
g
o
r
it
h
m
s
is
a
ls
o
u
s
ed
f
o
r
i
n
ter
f
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ce
ca
n
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li
n
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th
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m
ar
t
a
n
ten
n
a
s
y
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te
m
i
n
t
h
e
s
tu
d
y
[
2
6
]
.
T
h
e
co
m
p
ar
is
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n
o
f
L
MS,
N
L
M
S,
an
d
R
L
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f
o
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n
o
is
e
ca
n
ce
l
latio
n
i
s
c
ar
r
ied
o
u
t
in
[
2
4
]
.
Me
an
w
h
ile,
th
e
R
L
S
al
g
o
r
it
h
m
i
s
u
s
ed
,
f
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r
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th
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ter
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n
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itio
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(
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etti
n
g
its
f
o
r
g
etti
n
g
f
ac
to
r
to
v
alu
e
≤
1
[
2
7
]
.
3.
SYST
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M
M
O
DE
L
AND
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B
SE
RVA
T
I
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P
RO
P
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y
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m
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li
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k
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th
at
w
e
p
r
o
p
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s
e
in
Fig
u
r
e
1
,
w
h
er
e
th
e
co
m
p
lete
p
ar
a
m
eter
s
ar
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as
s
h
o
w
n
i
n
T
ab
le
1
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h
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m
ain
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s
tar
t
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w
it
h
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r
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d
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m
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SK
m
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k
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te
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h
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ch
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n
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t
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p
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e
w
as
AW
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s
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t
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s
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h
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ter
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ab
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h
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i
m
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atter
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t
h
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e
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d
b
o
th
b
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o
r
e
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d
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ter
th
e
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i
lt
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an
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f
o
r
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tiv
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co
m
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ar
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et
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r
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m
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h
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/No
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m
u
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r
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2
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1
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d
B
an
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d
is
p
la
y
th
e
f
u
ll
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r
o
r
s
i
m
u
latio
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r
e
s
u
l
ts
i
n
T
ab
le
2
.
W
e
ad
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ed
Sco
p
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to
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p
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o
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s
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d
t
h
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s
h
ap
e
o
f
th
e
ad
ap
tiv
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f
ilter
s
i
g
n
al.
I
n
Fig
u
r
e
1
,
as
a
s
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b
-
b
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we
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d
tw
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ter
m
in
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v
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R
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h
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ca
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L
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µ
=
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=
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=
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Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
R
o
b
u
s
t in
terf
eren
ce
ca
n
ce
lla
ti
o
n
fo
r
d
iffer
en
tia
l q
u
a
d
r
a
tu
r
e
p
h
a
s
e
-
s
h
ift ke
yin
g
…
(
R
a
h
ma
d
Hid
a
ya
t
)
1479
Fo
r
DQP
SK c
o
n
s
tellatio
n
ch
e
ck
in
g
,
w
e
i
n
clu
d
e
t
h
e
f
o
llo
w
i
n
g
p
s
eu
d
o
co
d
e:
data = zeros(1,bit);
I = zeros(1,S); Q = zeros(1,S);
II = zeros(1,S); QQ = zeros(1,S);
theta = zeros(1,S);
thetaout = zeros(1,NT*S);
data=round(rand(1,bit));
II=data(1:2:bit
-
1); QQ=data(2:2:bit);
theta(1)=iph;
thetaout(1:NT)=theta(1)*ones(1,NT);
for k=2:S
if II(k)==1
phi_k=(2*QQ(k)
-
1)*pi/4;
else
phi_k=(2*QQ(k)
-
1)*3*pi/4;
end
theta(k)=phi_k+theta(k
-
1);
for i=1:NT
j=(k
-
1)*NT+i;
thetaout(j)=theta(k);
end
end
I=cos(thetaout);Q=sin(thetaout);
[b,a]=butter(fo,nb);
If=filter(b,a,I);
Qf=filter(b,a,Q);
kk=0;
figure
constel(If,Qf)
plot(If,Qf)
axis('equal')
xlabel('In
-
phase')
ylabel('Quadrature')
4.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
h
e
s
tab
ilit
y
o
f
t
h
e
s
elec
ted
d
is
cr
ete
FIR
f
ilter
is
s
h
o
w
n
b
y
all
t
h
e
p
o
les
i
n
s
id
e
th
e
u
n
it
cir
cle
i
n
Fig
u
r
e
2
.
T
h
e
s
p
ec
tr
u
m
an
al
y
ze
r
d
is
p
la
y
s
t
h
e
s
h
ap
e
o
f
th
e
in
ter
f
er
en
ce
s
o
u
r
ce
at
th
e
1
0
0
Hz
an
d
3
0
0
Hz
p
o
s
itio
n
s
in
F
ig
u
r
e
3
.
T
h
e
r
esu
lts
o
b
tain
ed
f
r
o
m
t
h
e
B
E
R
-
m
eter
co
r
r
esp
o
n
d
to
th
e
co
n
s
tellatio
n
p
lo
t
an
d
ey
e
p
atter
n
d
iag
r
a
m
.
Fi
g
u
r
e
4
s
h
o
w
s
t
h
e
f
o
r
m
o
f
a
n
e
y
e
d
iag
r
a
m
w
it
h
a
n
o
p
ti
m
u
m
e
y
e
-
o
p
en
i
n
g
w
it
h
an
er
r
o
r
r
ate
o
f
6
.
6
0
1
e
-
0
5
o
r
2
e
r
r
o
r
s
.
T
h
is
h
ap
p
en
ed
at
t
h
e
s
tep
s
ize
s
e
tt
in
g
(
µ)
0
.
0
1
o
f
th
e
ad
ap
tiv
e
N
L
MS
f
i
lter
;
E
b
/No
o
f
1
0
d
B
an
d
2
b
its
p
er
s
y
m
b
o
l
o
n
th
e
A
W
GN
ch
a
n
n
el.
I
t
ca
n
b
e
clea
r
l
y
co
m
p
ar
ed
w
it
h
th
e
ap
p
ea
r
an
ce
o
f
th
e
e
y
e
d
iag
r
a
m
a
f
ter
th
e
N
L
MS
f
ilter
an
d
b
ef
o
r
e
th
e
N
L
MS
f
i
lter
.
L
ik
e
w
i
s
e,
th
e
co
n
s
tellat
i
o
n
d
is
p
la
y
af
ter
t
h
e
NL
M
S
f
ilter
ag
ai
n
s
t
b
ef
o
r
e
th
e
NL
MS
f
ilter
in
Fi
g
u
r
e
5
.
T
h
e
co
n
s
tella
tio
n
s
h
o
w
n
h
er
e
is
a
s
ig
n
al
tr
aj
ec
to
r
y
f
r
o
m
DQP
SK.
T
h
e
tr
aj
ec
to
r
y
ap
p
ea
r
an
ce
af
ter
N
L
M
S b
ea
r
s
a
r
ese
m
b
la
n
ce
to
t
h
e
o
ctag
o
n
s
h
ap
e
o
f
t
h
e
th
eo
r
y
.
An
d
t
h
is
is
ev
id
e
n
ce
d
b
y
th
e
MA
T
L
A
B
s
i
m
u
la
tio
n
r
e
s
u
l
ts
i
n
F
ig
u
r
e
6
.
Me
a
n
w
h
ile,
Fi
g
u
r
e
7
s
h
o
w
s
t
h
e
tap
s
o
f
th
e
ad
ap
tiv
e
f
ilter
ac
co
r
d
in
g
to
th
e
f
i
lter
len
g
t
h
s
etti
n
g
s
t
h
at
h
av
e
b
ee
n
d
o
n
e.
T
h
e
r
esu
lts
o
f
t
h
e
f
il
ter
ad
ap
tatio
n
p
r
o
ce
s
s
u
s
ed
ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
8
w
h
er
e
th
e
er
r
o
r
w
a
s
o
b
s
er
v
ed
to
d
ec
r
ea
s
e
af
ter
1
s
ec
o
n
d
,
in
d
icatin
g
th
e
s
tab
ilit
y
o
f
th
e
s
y
s
t
e
m
th
at
o
cc
u
r
r
ed
.
T
h
is
s
tab
ilit
y
ca
n
also
b
e
s
ee
n
f
r
o
m
F
ig
u
r
e
9
w
h
er
e
th
e
r
e
s
u
l
ts
s
h
o
w
ed
th
at
th
e
N
L
MS
f
ilt
er
w
as
ab
le
to
ad
ap
t
to
ch
an
g
es
in
f
r
eq
u
e
n
c
y
an
d
r
esp
o
n
s
e
ac
co
r
d
in
g
l
y
.
T
h
e
er
r
o
r
r
ate
r
esu
lts
i
n
T
ab
le
2
clea
r
l
y
ill
u
s
tr
ate
t
h
e
co
m
p
ar
i
s
o
n
b
et
w
ee
n
b
ef
o
r
e
an
d
af
ter
t
h
e
ad
ap
ti
v
e
f
ilter
.
T
h
e
s
m
alle
s
t
n
u
m
b
er
o
f
b
it e
r
r
o
r
s
i
s
in
th
e
N
L
MS
f
ilter
,
a
n
d
t
h
e
m
o
s
t e
r
r
o
r
(
u
p
to
1
6
2
b
its
er
r
o
r
)
o
f
th
e
th
r
ee
ar
e
in
th
e
L
MS
f
ilter
.
R
L
S
f
o
r
g
et
tin
g
f
ac
to
r
s
et
tin
g
i
s
tak
e
n
f
o
r
th
e
co
m
m
o
n
l
y
u
s
ed
v
alu
e
(
0
.
9
8
)
u
p
to
a
m
a
x
i
m
u
m
v
al
u
e
o
f
1
.
0
.
I
f
t
h
e
co
n
f
i
g
u
r
atio
n
is
w
it
h
o
u
t
a
d
is
cr
ete
FIR
f
ilter
,
it
i
s
clea
r
t
h
a
t
th
e
er
r
o
r
r
ate
is
w
o
r
s
e
t
h
a
n
h
a
v
in
g
a
d
is
cr
ete
FI
R
f
ilter
as
a
b
an
d
-
li
m
iti
n
g
f
ilter
.
T
h
is
ap
p
li
es to
t
h
e
t
h
r
ee
t
y
p
es
o
f
ad
ap
tiv
e
f
ilter
s
u
s
ed
.
W
h
en
co
m
p
ar
ed
w
it
h
r
esear
ch
[
2
2
]
w
it
h
t
h
e
b
est
B
E
R
v
alu
e
o
f
1
.
0
e
-
3
,
o
v
er
all
in
th
is
s
tu
d
y
t
h
er
e
is
a
n
i
m
p
r
o
v
e
m
e
n
t.
I
n
th
is
ca
s
e,
b
y
ta
k
i
n
g
th
e
s
a
m
e
f
il
ter
len
g
t
h
o
f
3
2
,
t
h
e
b
est
ad
ap
tiv
e
f
ilter
a
m
o
n
g
t
h
e
th
r
ee
t
y
p
e
s
test
ed
is
th
e
f
ilter
w
it
h
t
h
e
N
L
MS
alg
o
r
ith
m
w
it
h
B
E
R
3
.
3
e
-
0
5
;
m
ea
n
w
h
ile
B
E
R
3
.
3
e
-
0
4
f
o
r
R
L
S a
n
d
3
.
4
e
-
0
3
f
o
r
L
MS.
Fig
u
r
e
2
.
P
o
le
-
ze
r
o
o
f
d
is
cr
ete
FIR f
il
ter
p
r
o
p
o
s
ed
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
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
19
,
No
.
5
,
Octo
b
e
r
2
0
2
1
:
1
4
7
5
-
1483
1480
Fig
u
r
e
3
.
A
s
p
ec
tr
u
m
o
f
in
ter
f
er
en
ce
s
o
u
r
ce
s
(
a)
(
b
)
Fig
u
r
e
4
.
E
y
e
d
ia
g
r
a
m
(
µ=
0
.
0
1
; E
b
/No
=1
0
d
B
)
: (
a)
b
ef
o
r
e
NL
M
S f
il
ter
an
d
(
b
)
af
ter
NL
MS
f
il
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
R
o
b
u
s
t in
terf
eren
ce
ca
n
ce
lla
ti
o
n
fo
r
d
iffer
en
tia
l q
u
a
d
r
a
tu
r
e
p
h
a
s
e
-
s
h
ift ke
yin
g
…
(
R
a
h
ma
d
Hid
a
ya
t
)
1481
(
a)
(
b
)
Fig
u
r
e
5
.
Sig
n
al
tr
aj
ec
to
r
y
o
f
DQP
SK (
NL
MS
: µ
=0
.
0
1
; E
b
/
No
=1
0
d
B
)
: (
a)
b
ef
o
r
e
NL
MS
f
ilter
an
d
(
b
)
af
ter
NL
MS
f
ilter
Fig
u
r
e
6
.
E
r
r
o
r
s
ig
n
a
l o
f
th
e
f
i
lter
Fig
u
r
e
7
.
Mo
d
u
lato
r
an
d
ad
ap
t
iv
e
f
ilter
s
i
g
n
a
l
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
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
19
,
No
.
5
,
Octo
b
e
r
2
0
2
1
:
1
4
7
5
-
1483
1482
Fig
u
r
e
8
.
A
d
ap
tiv
e
f
ilter
tap
s
Fig
u
r
e
9
.
C
o
n
s
tel
latio
n
c
h
ec
k
5.
CO
NCLU
SI
O
N
Ob
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a
n
d
an
al
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s
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s
o
f
th
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co
m
m
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n
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ar
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est
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atter
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ca
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h
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n
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.
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w
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o
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co
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3
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-
0
5
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ch
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est
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tiv
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lter
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ith
m
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el
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x
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in
g
DQP
SK s
y
s
te
m
.
RE
F
E
R
E
NC
E
S
[1
]
J.
R.
L
u
q
u
e
,
M
.
J.
M
o
ró
n
,
a
n
d
E.
Ca
silari,
“
A
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m
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latio
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s
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p
lo
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d
b
y
Blu
e
to
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th
E
n
h
a
n
c
e
d
Da
ta
Ra
tes
,
”
EURA
S
IP
J
o
u
rn
a
l
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n
W
ire
les
s
Co
mm
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6
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6
8
7
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.
[2
]
A
.
S
u
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in
,
R.
A
.
R
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sh
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,
M
.
A
.
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e
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sc
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m
e
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o
r
w
irele
s
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s
e
n
so
r
n
e
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rk
,
"
T
EL
KOM
NIKA
T
e
lec
o
mm
u
n
ica
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io
n
Co
m
p
u
t
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El
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]
P
.
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.
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n
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.
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.
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.
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.
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L
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t
,
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6
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[4
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N.
M
.
A
.
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D.
W
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tu
ti
,
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P
.
L
.
A
n
g
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n
d
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P
ra
m
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it
a
,
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p
in
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,
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[5
]
F
.
F
a
y
d
h
e
A
l
-
A
z
z
a
w
i,
"
LT
E
RF
re
c
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m
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d
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im
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li
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k
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d
o
n
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si
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trica
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[6
]
A
.
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sa
n
v
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n
d
,
A
.
Kh
a
leg
h
i,
a
n
d
I.
Ba
las
in
g
h
a
m
,
"
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h
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t
q
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e
ry
sc
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m
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s
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ta
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,
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EUR
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IP
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[7
]
M
.
G
.
S
a
d
e
q
u
e
,
“
Bit
Err
o
r
Ra
te
(BER)
Co
m
p
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o
f
AWGN
C
h
a
n
n
e
ls
f
o
r
Diffe
re
n
t
Ty
p
e
’s
Dig
it
a
l
M
o
d
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latio
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Us
in
g
M
ATLA
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S
i
m
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li
n
k
,
”
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ric
a
n
S
c
ien
ti
fi
c
Res
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a
rc
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o
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c
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[8
]
B.
O.
Om
ij
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h
a
n
d
K.
S
a
ro
-
w
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,
"
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Err
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LAB
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[9
]
T
.
P
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v
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th
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G
.
M
o
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sig
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ter
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p
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0
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P
.
N.
M
a
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sw
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ri,
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s,”
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ter
n
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n
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o
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in
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tro
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1
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Ko
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a
,
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sig
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n
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ly
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ss
Co
m
m
u
n
ica
ti
o
n
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
En
g
in
e
e
rin
g
Res
e
a
rc
h
&
T
e
c
h
n
o
lo
g
y
(
IJ
ER
T
)
,
v
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l.
1
,
n
o
.
3
,
p
p
.
1
-
5
,
2
0
1
2
.
[1
2
]
D.
S
h
a
rm
a
a
n
d
P
.
S
riv
a
sta
v
a
,
“
O
F
DM
S
im
u
lato
r
Us
i
n
g
M
A
TL
A
B
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Eme
rg
in
g
T
e
c
h
n
o
lo
g
y
a
n
d
Ad
v
a
n
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e
d
E
n
g
in
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g
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l.
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o
.
9
,
p
p
.
4
9
3
-
4
9
6
,
2
0
1
3
.
[1
3
]
J.
M
a
n
ik
a
n
d
a
n
,
V
.
M
a
n
g
a
iy
a
r
k
a
ra
si,
a
n
d
P
.
S
u
b
ra
m
a
n
ian
,
“
P
e
rf
o
r
m
a
n
c
e
Ex
a
m
in
a
ti
o
n
o
f
OFDM
M
o
d
u
latio
n
T
e
c
h
n
iq
u
e
s
in
L
T
E
4
G
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
a
n
d
Ad
v
a
n
c
e
d
T
e
c
h
n
o
lo
g
y
(
IJ
EA
T
)
,
v
o
l.
9
,
n
o
.
2
,
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p
.
3
4
0
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4
0
4
,
2
0
1
9
,
d
o
i:
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0
.
3
5
9
4
0
/i
jea
t.
B
4
9
1
2
.
1
2
9
2
1
9
[1
4
]
A
.
S
in
g
h
a
n
d
S
.
S
riv
a
sta
v
,
"
S
im
u
latio
n
-
b
a
se
d
c
o
m
p
a
ra
ti
v
e
a
n
a
ly
sis
o
f
BER
u
sin
g
S
im
u
li
n
k
,
"
In
ter
n
a
ti
o
n
a
l
Res
e
a
rc
h
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
(
IRJET
)
,
p
p
.
1
2
1
5
-
1
2
1
8
,
2
0
1
5
.
[1
5
]
I.
A
li
,
“
Bit
-
Err
o
r
-
Ra
te
(BER)
S
i
m
u
latio
n
Us
in
g
M
A
TL
A
B,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
Res
e
a
rc
h
a
n
d
Ap
p
li
c
a
ti
o
n
s (
IJ
ER
A)
,
v
o
l.
3
,
n
o
.
1
,
p
p
.
7
0
6
-
7
1
1
,
2
0
1
3
.
[1
6
]
P
.
M
a
n
h
a
sa
a
n
d
M
.
K.
S
o
n
ib
,
"
P
e
rf
o
r
m
a
n
c
e
o
f
OFDM
s
y
ste
m
u
n
d
e
r
d
if
fe
re
n
t
fa
d
in
g
c
h
a
n
n
e
ls
a
n
d
c
o
d
in
g
,
"
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ll
.
El
e
c
tr.
En
g
.
In
fo
rm
a
t
ics
,
v
o
l.
6
,
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o
.
1
,
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p
.
5
4
-
6
1
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0
1
7
,
d
o
i:
1
0
.
1
1
5
9
1
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i.
v
6
i
1
.
5
9
1
[1
7
]
P
.
M
a
n
h
a
s
a
n
d
M
.
K.
S
o
n
i,
"
Be
r
A
n
a
l
y
sis
o
f
Bp
sk
,
Qp
sk
&
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m
Ba
se
d
Of
d
m
S
y
ste
m
Us
in
g
S
im
u
li
n
k
,
"
In
t.
J
.
El
e
c
tr.
El
e
c
tro
n
.
En
g
.
,
v
o
l.
7
,
n
o
.
2
,
p
p
.
5
4
-
6
0
,
2
0
1
5
.
[1
8
]
A
.
A
g
a
r
wa
l
a
n
d
K.
A
g
a
r
w
a
l,
“
I
m
p
le
m
e
n
tatio
n
a
n
d
P
e
rf
o
rm
a
n
c
e
Ev
a
lu
a
ti
o
n
o
f
OFDM
S
y
ste
m
in
Div
e
rs
e
T
ra
n
s
m
issio
n
Ch
a
n
n
e
l
Us
in
g
S
im
u
li
n
k
,
”
Ame
ric
a
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
El
e
c
tro
n
i
c
En
g
in
e
e
rin
g
,
v
o
l.
3
,
n
o
.
5
,
p
p
.
1
1
7
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2
3
,
2
0
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5
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d
o
i:
1
0
.
1
2
6
9
1
/aje
e
e
-
3
-
5
-
2
[1
9
]
P
.
Ko
g
ias
,
K.
Ov
a
li
a
d
is,
a
n
d
F
.
Ko
g
ia,
“
Co
m
p
a
ra
ti
v
e
P
e
rf
o
r
m
a
n
c
e
Ev
a
lu
a
ti
o
n
o
f
M
-
A
r
y
Q
a
m
,
”
AR
P
N
J
.
En
g
.
A
p
p
l
.
S
c
i.
,
v
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l
.
1
2
,
n
o
.
2
2
,
p
p
.
6
3
2
0
–
6
3
2
6
,
2
0
1
7
.
[2
0
]
A
.
M
u
sta
f
a
e
t
a
l.
,
“
BER
Re
d
u
c
ti
o
n
in
Q
P
S
K,”
J
.
A
p
p
l.
E
n
v
iro
n
.
Bi
o
l.
S
c
i.
,
v
o
l
.
7
,
n
o
.
6
,
p
p
.
4
7
-
5
5
,
2
0
1
7.
[
2
1
]
H
.
M
a
r
n
e
a
n
d
P
.
M
u
k
h
e
r
j
i
,
“
P
e
r
f
o
r
m
a
n
c
e
e
n
h
a
n
c
e
m
e
n
t
o
f
b
i
t
e
r
r
o
r
r
a
t
e
w
i
t
h
i
n
c
r
e
a
s
e
d
c
a
p
a
c
i
t
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s
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n
g
m
o
d
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f
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e
d
S
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C
-
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D
f
o
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b
a
s
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d
O
F
D
M
-
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D
M
A
s
y
s
t
e
m
f
o
r
5
G
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
I
n
n
o
v
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t
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v
e
T
e
c
h
n
o
l
o
g
y
a
n
d
E
x
p
l
o
r
i
n
g
E
n
g
i
n
e
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r
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n
g
(
I
J
I
T
E
E
)
,
v
o
l
.
8
,
n
o
.
9
S
p
e
c
i
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s
s
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e
3
,
p
p
.
1
9
2
-
2
0
0
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2
0
1
9
,
d
o
i
:
1
0
.
3
5
9
4
0
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i
j
i
t
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e
.
I
3
0
3
7
.
0
7
8
9
S
3
1
9
.
[2
2
]
E.
Ka
d
h
u
m
a
n
d
R.
Ha
it
h
a
m
,
“
P
e
rf
o
r
m
a
n
c
e
A
n
a
l
y
sis
o
f
IEE
E
8
0
2
.
1
5
.
4
T
ra
n
sc
e
iv
e
r
S
y
ste
m
u
n
d
e
r
A
d
a
p
ti
v
e
W
h
it
e
G
a
u
ss
ian
Ch
a
n
n
e
l,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
n
o
.
6
,
p
p
.
4
1
8
4
-
4
1
9
6
,
2
0
1
8
,
d
o
i
:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
8
i
6
.
p
p
4
1
8
4
-
4
1
9
6
.
[2
3
]
V
.
K.
I
n
g
le
a
n
d
J.
G
.
P
ro
a
k
is,
Dig
it
a
l
S
i
g
n
a
l
Pr
o
c
e
ss
in
g
u
si
n
g
M
AT
L
AB
,
T
h
ird
e
d
i
t.
S
tam
f
o
rd
:
CENGA
G
E
L
e
a
rn
in
g
,
2
0
1
2
.
[2
4
]
I.
C.
De
e
p
ik
a
,
“
A
S
im
u
latio
n
&
P
e
rf
o
rm
a
n
c
e
A
n
a
l
y
sis
o
f
A
N
C
u
sin
g
A
d
a
p
ti
v
e
F
il
ters
,
”
IJ
EIT
,
v
o
l.
3
,
n
o
.
2
,
p
p
.
2
8
3
-
2
8
7
,
2
0
1
3
.
[2
5
]
R.
Hid
a
y
a
t,
Ru
sh
e
n
d
ra
a
n
d
E.
A
g
u
stin
a
,
"
Dig
it
a
l
b
e
a
m
f
o
rm
in
g
o
f
s
m
a
rt
a
n
ten
n
a
in
m
il
li
m
e
ter
wa
v
e
c
o
m
m
u
n
ica
ti
o
n
,
"
2
0
1
7
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
Br
o
a
d
b
a
n
d
Co
mm
u
n
ic
a
ti
o
n
,
W
ire
les
s
S
e
n
so
rs
a
n
d
Po
we
rin
g
(
BCW
S
P)
,
Ja
k
a
rta,
In
d
o
n
e
sia
,
2
0
1
7
,
p
p
.
1
-
5
,
d
o
i:
1
0
.
1
1
0
9
/BCW
S
P
.
2
0
1
7
.
8
2
7
2
5
6
4
.
[2
6
]
S
.
S
i
n
g
h
,
"
A
n
L
M
S
a
n
d
NL
M
S
A
l
g
o
rit
h
m
A
n
a
l
y
sis
f
o
r
S
m
a
rt
An
ten
n
a
,
"
IJ
AR
CS
S
E
,
v
o
l.
5
,
n
o
.
4
,
p
p
.
3
8
0
–
3
8
4
,
2
0
1
5
.
[2
7
]
A
.
A
l
Ri
k
a
b
i
a
n
d
T
.
A
l
S
h
a
ra
b
a
ti
,
"
M
it
ig
a
ti
n
g
in
terf
e
re
n
c
e
to
G
P
S
o
p
e
ra
ti
o
n
u
sin
g
v
a
riab
le
f
o
rg
e
tt
i
n
g
f
a
c
to
r
-
b
a
se
d
re
c
u
rsiv
e
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st
sq
u
a
re
s
e
sti
m
a
ti
o
n
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
mp
u
ter
Ne
two
rk
s
&
Co
mm
u
n
ica
ti
o
n
s
(
IJ
CNC)
,
v
o
l.
9
,
n
o
.
2
,
p
p
.
1
9
-
2
8
,
2
0
1
7
,
d
o
i
:
1
0
.
5
1
2
1
/i
jcn
c
.
2
0
1
7
.
9
2
0
2
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