I
nte
rna
t
io
na
l J
o
urna
l o
f
I
nfo
rm
a
t
ics a
nd
Co
m
m
un
ica
t
io
n T
ec
hn
o
lo
g
y
(
I
J
-
I
CT
)
Vo
l.
1
4
,
No
.
1
,
A
p
r
il
20
2
5
,
p
p
.
1
82
~
194
I
SS
N:
2252
-
8
7
7
6
,
DOI
:
1
0
.
1
1
5
9
1
/
ijict
.
v
1
4
i
1
.
pp
182
-
1
9
4
182
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ict.
ia
esco
r
e.
co
m
The integra
tion
of discre
te
co
ntour
let
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ra
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rm in
O
FDM
framewo
rk
for fu
ture
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M
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us
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Ner
m
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2
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A
da
m
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ed
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ed
Abdo
3
1
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e
p
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p
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a
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a
t
i
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n
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e
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h
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o
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o
g
y
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n
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r
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i
t
y
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a
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b
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k
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a
u
d
i
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h
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h
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t
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a
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t
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o
f
N
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l
a
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y
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l
a
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S
u
d
a
n
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
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y:
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eiv
ed
Au
g
3
0
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2
0
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ev
is
ed
Oct
8
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2
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2
4
Acc
ep
ted
No
v
1
9
,
2
0
2
4
In
th
e
u
p
c
o
m
i
n
g
e
ra
,
t
h
e
fo
r
th
c
o
m
in
g
six
t
h
-
g
e
n
e
ra
ti
o
n
(6
G
)
wire
les
s
c
o
m
m
u
n
ica
ti
o
n
n
e
two
r
k
will
d
e
m
a
n
d
h
ig
h
l
y
e
fficie
n
t
tec
h
n
o
lo
g
y
to
su
p
p
o
r
t
e
x
ten
siv
e
c
a
p
a
c
it
y
,
u
lt
ra
-
h
ig
h
sp
e
e
d
s,
lo
w
late
n
c
y
,
sc
a
lab
il
it
y
,
a
n
d
a
d
a
p
tab
il
it
y
.
Wh
il
e
t
h
e
c
u
rre
n
t
f
if
th
-
g
e
n
e
ra
ti
o
n
(
5
G
)
wire
les
s c
o
m
m
u
n
ica
ti
o
n
sy
ste
m
re
li
e
s
o
n
OFDM
tec
h
n
o
l
o
g
y
,
t
h
e
e
v
o
l
u
ti
o
n
to
wa
rd
s
a
b
e
y
o
n
d
5
G
wire
les
s
c
o
m
m
u
n
ica
ti
o
n
sy
ste
m
n
e
c
e
ss
it
a
tes
a
n
e
w
OFDM
fra
m
e
wo
rk
.
T
h
is
stu
d
y
i
n
tr
o
d
u
c
e
s
a
n
o
v
e
l
OFDM
sy
ste
m
th
a
t
in
teg
ra
tes
th
e
d
isc
re
te
Co
n
t
o
u
rlet
tran
sf
o
rm
.
A
c
o
m
p
a
ra
t
iv
e
a
n
a
l
y
sis h
a
s
b
e
e
n
c
o
n
d
u
c
ted
a
m
o
n
g
t
h
e
p
ro
p
o
se
d
s
y
ste
m
,
c
o
n
v
e
n
ti
o
n
a
l
O
F
DM,
a
n
d
c
u
r
v
e
let
-
b
a
se
d
OFDM
sy
ste
m
s.
Th
e
re
su
lt
s
i
n
d
ica
te
th
a
t
th
e
p
ro
p
o
se
d
s
y
ste
m
o
ffe
rs
imp
ro
v
e
m
e
n
ts
in
b
it
e
rro
r
ra
te
(BER),
re
d
u
c
e
d
c
o
m
p
u
tati
o
n
a
l
c
o
m
p
lex
it
y
,
d
e
c
re
a
se
d
p
e
a
k
-
t
o
-
a
v
e
ra
g
e
p
o
we
r
ra
ti
o
(P
APR),
a
n
d
e
n
h
a
n
c
e
d
p
o
we
r
sp
e
c
tru
m
d
e
n
sity
(P
S
D)
wh
e
n
c
o
n
tras
ted
with
b
o
th
th
e
tra
d
it
io
n
a
l
a
n
d
c
u
r
v
e
let
-
b
a
se
d
sy
ste
m
s.
K
ey
w
o
r
d
s
:
B
E
R
C
o
n
to
u
r
let
t
r
an
s
f
o
r
m
OFDM
PAPR
PSD
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
:
Mo
h
am
ed
Hu
s
s
ien
Mo
h
a
m
ed
Ner
m
a
Dep
ar
tm
en
t o
f
C
o
m
p
u
ter
E
n
g
i
n
ee
r
in
g
,
Facu
lty
o
f
C
o
m
p
u
ter
s
an
d
I
n
f
o
r
m
atio
n
T
ec
h
n
o
lo
g
y
Un
iv
er
s
ity
o
f
T
a
b
u
k
T
ab
u
k
,
Sau
d
i A
r
ab
ia
E
m
ail:
m
n
er
m
a@
u
t.e
d
u
.
s
a
1.
I
NT
RO
D
UCT
I
O
N
I
n
1
9
5
7
,
th
e
n
o
tio
n
o
f
t
r
an
s
m
itti
n
g
a
s
et
o
f
o
r
th
o
g
o
n
al
s
u
b
ca
r
r
ier
s
was
in
tr
o
d
u
ce
d
with
th
e
aim
o
f
ef
f
icien
tly
s
en
d
in
g
th
ese
s
u
b
ca
r
r
ier
s
with
o
u
t
an
y
o
v
er
la
p
o
r
d
is
tu
r
b
an
ce
[
1
]
,
[
2
]
.
I
n
itially
,
th
is
id
ea
wa
s
ex
ec
u
ted
th
r
o
u
g
h
th
e
d
is
cr
ete
f
o
u
r
ier
tr
a
n
s
f
o
r
m
(
DFT)
,
wh
ich
was
s
u
g
g
ested
in
1
9
7
1
[
3
]
.
Su
b
s
eq
u
en
tly
,
th
e
f
ast
f
o
u
r
ier
tr
an
s
f
o
r
m
(
FF
T
)
was
u
tili
ze
d
,
lead
in
g
t
o
th
e
e
m
er
g
en
ce
o
f
t
h
e
o
r
th
o
g
o
n
al
f
r
eq
u
en
c
y
d
iv
is
io
n
m
u
ltip
lex
in
g
(
OFDM)
s
y
s
tem
as
a
p
r
o
m
is
in
g
f
ield
f
o
r
e
x
p
l
o
r
atio
n
an
d
an
aly
s
is
.
Nu
m
er
o
u
s
p
u
b
licatio
n
s
h
av
e
d
elv
ed
in
to
s
u
b
jects a
s
s
o
ciate
d
with
th
is
s
y
s
tem
[
4
]
-
[
7
]
.
As
p
er
r
ef
er
en
ce
s
[
1
]
-
[
4
]
,
OFDM
r
ep
r
esen
ts
a
f
o
r
m
o
f
m
u
lticar
r
ier
m
o
d
u
latio
n
s
y
s
tem
(
MCM)
th
at
em
p
lo
y
s
a
n
o
r
th
o
g
o
n
al
m
u
lti
ca
r
r
ier
to
co
n
cu
r
r
en
tly
tr
an
s
m
it
d
ata
d
ev
o
i
d
o
f
a
n
y
in
ter
-
ca
r
r
ier
in
ter
f
er
e
n
ce
(
I
C
I
)
.
W
h
ile
OFDM
s
y
s
tem
s
wer
e
in
teg
r
al
t
o
f
if
th
-
g
en
er
ati
o
n
(
5G
)
an
d
ea
r
lier
iter
atio
n
s
,
m
o
r
e
s
o
p
h
is
ticated
OFDM
s
y
s
tem
s
ar
e
im
p
er
ativ
e
to
m
ee
t
t
h
e
r
e
q
u
is
ites
o
f
s
ix
th
-
g
en
er
atio
n
(
6G
)
a
n
d
f
o
r
th
c
o
m
in
g
g
en
er
atio
n
s
.
T
h
e
co
n
v
en
tio
n
al
OFDM
s
y
s
tem
,
g
r
o
u
n
d
e
d
in
t
h
e
DFT,
f
ac
ilit
ates
th
e
s
u
cc
ess
f
u
l
tr
an
s
m
is
s
io
n
o
f
m
u
ltip
l
e
o
r
th
o
g
o
n
al
d
ata
s
tr
ea
m
s
with
o
u
t
o
v
er
lap
p
i
n
g
s
y
m
b
o
ls
o
r
i
n
ter
-
ch
an
n
el
in
ter
f
er
en
ce
,
th
e
r
eb
y
o
p
tim
izin
g
th
e
d
ata
r
ate
with
in
t
h
e
lin
ea
r
b
an
d
wid
th
[
8
]
.
T
h
e
s
ch
em
atic
f
o
r
o
r
th
o
g
o
n
al
p
ar
allel
d
ata
tr
an
s
m
is
s
io
n
u
s
in
g
DFT
is
d
ep
icted
in
Fig
u
r
e
1
.
Ass
u
m
in
g
x
(
n
)
s
ig
n
if
ies
th
e
d
is
cr
ete
-
tim
e
r
en
d
itio
n
o
f
a
tim
e
-
d
o
m
ain
s
ig
n
al,
x
(
t)
,
th
e
DFT
tr
an
s
f
o
r
m
atio
n
f
o
r
x
(
n
)
in
th
e
f
r
e
q
u
en
c
y
d
o
m
ain
(
FD)
,
lab
eled
as X(
k
)
,
ca
n
b
e
a
r
ticu
lated
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Th
e
in
teg
r
a
tio
n
o
f
d
is
crete
co
n
to
u
r
let
tr
a
n
s
fo
r
m
in
OF
DM
…
(
Mo
h
a
med
Hu
s
s
ien
Mo
h
a
m
ed
N
erma
)
183
(
)
=
∑
[
]
−
2
−
1
=
−
0
,
=
0
,
1
,
2
,
⋯
,
−
1
(
1
)
T
o
o
b
tai
n
t
h
e
in
v
er
s
e
d
is
cr
ete
-
tim
e
d
o
m
ain
s
ig
n
al
(
x
(
n
)
)
,
w
h
ich
is
th
e
tr
an
s
f
o
r
m
atio
n
o
f
X(
k
)
b
ac
k
in
to
th
e
d
is
cr
ete
d
o
m
ain
,
th
e
f
o
llo
win
g
eq
u
atio
n
ca
n
b
e
u
tili
ze
d
:
(
)
=
1
∑
(
)
2
−
1
=
0
,
=
0
,
1
,
2
,
⋯
,
−
1
(
2
)
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
p
a
r
allel
an
d
o
r
t
h
o
g
o
n
al
d
ata
tr
a
n
s
m
is
s
io
n
C
o
n
s
id
er
in
g
a
s
eq
u
en
ce
o
f
tr
a
n
s
m
itted
d
ata
as
d
0
,
d
1
,
.
.
.
d
m
,
alo
n
g
with
th
e
d
is
cr
ete
im
p
u
ls
e
r
esp
o
n
s
e
o
f
th
e
tr
an
s
m
itter
f
ilter
as
a
i
(
n
)
.
T
h
e
tr
a
n
s
m
is
s
io
n
ch
an
n
el'
s
d
is
cr
ete
im
p
u
ls
e
r
esp
o
n
s
e
a
s
h
(
n
)
,
an
d
th
e
d
is
cr
ete
ch
an
n
el'
s
n
o
is
e
as
g
(
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)
,
it
ca
n
also
b
e
tak
in
g
in
to
ac
co
u
n
t
th
e
r
ec
eiv
er
f
ilter
'
s
d
is
cr
ete
i
m
p
u
ls
e
r
esp
o
n
s
e
as
b
i
(
n
)
,
a
n
d
a
s
eq
u
en
ce
o
f
esti
m
ated
r
ec
eiv
ed
d
ata
as
d
^
0
,
d
^
1
,
.
.
.
d
^
m
.
Un
d
er
th
ese
co
n
d
itio
n
s
,
th
e
ex
p
r
ess
io
n
f
o
r
th
e
t
r
an
s
m
itted
s
ig
n
al
ca
n
b
e
d
er
iv
ed
u
s
in
g
:
(
)
=
1
∑
2
−
1
=
0
(
3
)
T
h
e
s
ig
n
al
th
at
is
u
ltima
tely
r
e
ce
iv
ed
at
th
e
o
u
tp
u
t c
a
n
b
e
d
escr
ib
ed
as:
(
)
=
1
∑
ℎ
(
,
)
(
−
)
+
(
)
−
1
=
0
(
4
)
T
h
e
s
ig
n
als
r
ec
eiv
ed
,
d
en
o
ted
as
y
(
n
)
,
in
clu
d
in
g
y
1
(
n
)
,
y
2
(
n
)
,
.
.
.
y
m
(
n
)
ar
e
o
r
th
o
g
o
n
al,
it
im
p
lies
th
at
th
ey
ar
e
m
u
tu
ally
p
er
p
en
d
icu
lar
to
o
n
e
an
o
th
e
r
.
∫
(
)
(
−
)
∞
−
∞
=
0
,
=
±
1
,
±
2
,
⋯
(
5
)
W
h
er
e,
(
)
=
∫
ℎ
(
−
)
(
)
∞
−
∞
.
I
n
th
e
d
is
cr
ete
tim
e
d
o
m
ain
,
th
e
c
o
r
r
ela
tio
n
b
etwe
e
n
d
i
,
a
i
a
n
d
h
(
n
)
will
r
esu
lt
in
c
o
n
v
o
lu
tio
n
,
wh
er
ea
s
in
t
h
e
d
is
cr
ete
f
r
e
q
u
en
c
y
d
o
m
ain
,
it
will
b
e
r
ep
r
esen
ted
b
y
m
u
ltip
licatio
n
.
I
f
we
ass
u
m
e
f
lawless
ch
an
n
el
esti
m
atio
n
an
d
r
em
o
v
al
o
f
n
o
i
s
e,
th
en
th
e
s
ig
n
al
r
ec
eiv
e
d
ca
n
b
e
ex
p
r
ess
ed
as:
=
+
(
6
)
Nu
m
er
o
u
s
alter
n
ativ
e
tr
an
s
f
o
r
m
atio
n
m
eth
o
d
s
h
av
e
b
ee
n
s
u
g
g
ested
af
ter
th
e
ad
v
en
t
o
f
th
e
FF
T
.
T
h
ese
en
co
m
p
ass
th
e
m
o
d
u
lated
lap
p
ed
tr
a
n
s
f
o
r
m
(
ML
T
)
,
d
is
cr
ete
co
s
in
e
tr
an
s
f
o
r
m
(
DC
T
)
,
d
is
cr
ete
wav
elet
tr
an
s
f
o
r
m
(
DW
T
)
,
wav
elet
p
a
ck
et
tr
an
s
f
o
r
m
(
W
PT)
,
co
m
p
l
ex
wav
elet
tr
an
s
f
o
r
m
(
C
W
T
)
,
co
m
p
lex
wav
elet
p
ac
k
et
tr
an
s
f
o
r
m
(
C
W
PT)
,
d
u
al
-
tr
ee
co
m
p
lex
wav
elet
tr
an
s
f
o
r
m
(
DT
ℂ
W
T
)
,
an
d
cu
r
v
elets
tr
an
s
f
o
r
m
(
C
u
r
T
)
.
Mo
r
eo
v
er
,
a
n
o
v
el
tr
a
n
s
f
o
r
m
a
tio
n
ap
p
r
o
ac
h
k
n
o
wn
as
th
e
d
is
cr
ete
C
o
n
to
u
r
let
tr
a
n
s
f
o
r
m
(
DC
o
n
T
)
h
as
b
ee
n
em
p
lo
y
ed
in
th
is
in
v
esti
g
atio
n
.
T
h
e
MCM
s
y
s
tem
s
ar
e
b
r
o
ad
l
y
d
iv
id
e
d
in
t
o
wir
ed
an
d
wir
e
less
s
y
s
tem
s
,
as
illu
s
tr
ated
in
Fig
u
r
e
2
.
W
ir
eles
s
s
y
s
tem
s
em
p
lo
y
b
lo
ck
-
tr
an
s
f
o
r
m
m
eth
o
d
s
f
o
r
th
ei
r
ex
ec
u
tio
n
,
s
u
ch
as
FF
T
,
M
L
T
,
DC
T
,
W
T
,
an
d
FDC
u
r
T
.
T
h
e
W
T
-
b
ased
s
y
s
tem
s
ca
n
b
e
f
u
r
th
er
s
eg
m
en
ted
in
to
DW
T
,
W
PT,
C
W
PT,
an
d
DT
ℂ
W
T
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
4
,
No
.
1
,
A
p
r
il
20
2
5
:
182
-
1
9
4
184
Similar
ly
,
th
e
C
u
r
T
-
b
ased
s
y
s
tem
s
f
all
in
to
two
ca
teg
o
r
ies
:
FDC
u
r
T
v
ia
USF
FT
an
d
FDC
u
r
T
v
ia
W
r
ap
p
in
g
.
I
n
th
is
r
esear
ch
,
o
u
r
atten
tio
n
is
d
ir
ec
ted
to
war
d
s
th
e
DC
o
n
T
-
b
ased
s
y
s
tem
as
a
tr
an
s
f
o
r
m
ativ
e
p
r
o
p
o
s
itio
n
in
th
is
wo
r
k
.
Fig
u
r
e
2
.
C
lass
if
icatio
n
o
f
th
e
MCM
s
y
s
tem
s
2.
T
H
E
C
O
NS
I
D
E
RE
D
SYS
T
E
M
S M
O
D
E
L
2
.
1
.
T
he
co
nv
ent
io
na
l sy
s
t
e
m
T
h
e
OFDM
s
y
s
tem
is
b
ased
o
n
th
e
DFT,
wh
ich
in
v
o
lv
es
b
o
th
f
o
r
war
d
an
d
in
v
e
r
s
e
tr
an
s
f
o
r
m
atio
n
s
[3
]
-
[
8
]
.
I
n
th
e
tr
an
s
m
itter
,
th
e
in
v
er
s
e
DFT
(
I
DFT)
is
u
s
e
d
,
wh
ile
th
e
r
ec
eiv
er
u
tili
ze
s
th
e
f
o
r
war
d
DFT.
Ass
u
m
in
g
th
at
th
er
e
ar
e
N
s
u
b
ca
r
r
ier
s
,
let
d
N
b
e
th
e
co
m
p
lex
d
is
cr
ete
tr
an
s
m
itted
d
ata.
T
h
e
o
u
tp
u
t
o
f
th
e
I
DFT
r
esu
lts
in
th
e
tr
an
s
m
itted
s
ig
n
al
x
(
n
)
,
wh
ich
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
ws:
(
)
=
1
√
∑
2
;
=
0
,
1
,
2
,
⋯
,
−
1
−
1
=
0
(
7
)
Su
p
p
o
s
e
th
at
th
e
ch
an
n
el
im
p
u
ls
e
r
esp
o
n
s
e
is
d
e
n
o
ted
as
h
(
n
)
a
n
d
th
e
ad
d
itiv
e
wh
ite
Gau
s
s
ian
n
o
is
e
is
r
ep
r
esen
ted
b
y
g
(
n
)
.
O
n
th
e
r
e
ce
iv
in
g
en
d
,
th
e
s
ig
n
al
r
ec
eiv
e
d
is
r
ef
er
r
ed
to
as y
(
t)
.
(
)
=
1
√
∑
2
∗
ℎ
(
)
+
(
)
−
1
=
0
(
8
)
B
y
u
tili
zin
g
th
e
o
r
th
o
g
o
n
ality
ch
ar
ac
ter
is
tic,
it
is
p
o
s
s
ib
le
to
d
etec
t
th
e
tr
an
s
m
itted
s
ig
n
al
x
(
n
)
at
th
e
r
ec
eiv
er
en
d
th
r
o
u
g
h
DFT
wh
en
co
n
s
id
er
in
g
p
e
r
f
ec
t
ch
an
n
e
l
esti
m
atio
n
.
T
h
is
ca
n
b
e
ac
h
i
ev
ed
b
ased
o
n
th
e
in
f
o
r
m
atio
n
o
b
tain
e
d
f
r
o
m
th
e
r
ec
eiv
ed
s
ig
n
al
y
(
n
)
.
=
∑
(
)
−
2
−
1
=
0
(
9
)
T
h
e
r
etr
iev
al
o
f
th
e
co
m
p
le
x
s
et
o
f
t
r
an
s
m
itted
d
ata,
in
a
d
is
cr
ete
f
o
r
m
at
(
b
N
)
,
is
ac
h
i
ev
ab
le
th
r
o
u
g
h
th
e
im
p
lem
en
tatio
n
o
f
th
e
s
u
b
s
eq
u
en
t a
p
p
r
o
ac
h
:
=
∑
⌢
−
1
=
0
(
1
0
)
2
.
2
.
M
L
T
,
DCT,
a
nd
wa
v
ele
t
-
ba
s
ed
s
y
s
t
em
s
I
n
OFDM
s
y
s
tem
s
u
tili
zin
g
ML
T
,
th
e
I
FF
T
f
u
n
ctio
n
was
r
ep
lace
d
with
th
e
i
n
v
er
s
e
M
L
T
(
I
ML
T
)
f
u
n
ctio
n
f
o
r
tr
an
s
m
is
s
io
n
p
u
r
p
o
s
es.
C
o
n
v
er
s
ely
,
th
e
f
o
r
wa
r
d
ML
T
f
u
n
ctio
n
was
u
s
ed
o
n
th
e
r
ec
eiv
e
r
s
id
e
in
s
tead
o
f
t
h
e
DFT
f
u
n
ctio
n
[
9
]
-
[
1
1
]
.
T
o
d
e
n
o
te
t
h
is
s
u
b
s
titu
tio
n
,
β
F
[
n
]
an
d
β
1
[
n
]
wer
e
u
s
ed
as
r
ep
r
esen
tatio
n
s
o
f
th
e
f
o
r
war
d
a
n
d
in
v
er
s
e
ML
T
f
u
n
ctio
n
s
,
r
esp
ec
tiv
ely
.
Fo
r
th
e
N
s
u
b
ca
r
r
ier
s
,
if
[
]
=
−
s
in
[
(
2
+
1
)
4
]
th
en
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Th
e
in
teg
r
a
tio
n
o
f
d
is
crete
co
n
to
u
r
let
tr
a
n
s
fo
r
m
in
OF
DM
…
(
Mo
h
a
med
Hu
s
s
ien
Mo
h
a
m
ed
N
erma
)
185
[
]
=
[
]
√
2
c
os
[
(
2
+
2
+
+
2
2
)
]
(
1
1
)
I
f
we
d
en
o
te
th
e
r
esu
ltin
g
s
ig
n
al
at
th
e
o
u
tp
u
t o
f
th
e
I
ML
T
a
s
x
(
n
)
,
it c
an
b
e
ex
p
r
ess
ed
as f
o
llo
ws:
(
)
=
∑
−
1
=
0
[
]
;
=
0
,
1
,
2
,
⋯
,
−
1
(
1
2
)
In
(
13
)
a
n
d
(
14
)
r
ep
r
esen
t
th
e
r
ec
eiv
ed
s
ig
n
al
y
(
t)
an
d
th
e
o
u
tp
u
t
s
ig
n
al
a
k
attain
e
d
th
r
o
u
g
h
ML
T
o
n
th
e
r
ec
eiv
in
g
en
d
,
r
esp
ec
tiv
el
y
.
(
)
=
∑
−
1
=
0
[
]
ℎ
(
)
+
(
)
(
1
3
)
=
∑
(
)
−
1
=
0
[
]
(
1
4
)
R
esear
ch
h
as
s
h
o
wn
th
at
in
o
r
d
er
to
u
tili
ze
OFDM
-
b
ased
DC
T
,
it
is
n
ec
ess
ar
y
to
ap
p
ly
th
e
f
o
r
war
d
DC
T
f
u
n
ctio
n
(
r
ep
r
esen
ted
as
η
F
[
n
]
)
o
n
th
e
tr
an
s
m
itter
s
id
e
an
d
th
e
in
v
er
s
e
DC
T
f
u
n
ctio
n
(
r
ep
r
esen
ted
as
η
I
[
n
]
)
o
n
t
h
e
r
ec
eiv
e
r
s
id
e
[
1
2
]
-
[
1
5
]
.
T
h
is
en
s
u
r
es
o
p
tim
al
p
er
f
o
r
m
an
ce
o
f
th
e
s
y
s
tem
wh
ile
m
ain
tain
in
g
ef
f
icien
cy
an
d
ac
cu
r
ac
y
.
=
{
√
1
;
=
0
√
2
c
os
[
(
2
+
1
2
)
]
;
=
1
,
2
,
3
,
⋯
,
−
1
(
1
5
)
Af
ter
th
e
tr
an
s
m
is
s
io
n
o
f
th
e
s
ig
n
al
x
(
n
)
,
th
e
s
ig
n
al
y
(
n
)
is
r
ec
eiv
ed
an
d
th
en
th
e
d
ata
is
esti
m
ated
ac
co
r
d
in
g
l
y
.
(
)
=
∑
−
1
=
0
[
]
;
=
0
,
1
,
2
,
⋯
,
−
1
(
1
6
)
(
)
=
∑
−
1
=
0
[
]
∗
ℎ
(
)
+
(
)
(
1
7
)
=
∑
(
)
−
1
=
0
[
]
(
1
8
)
Fo
r
th
e
OFDM
b
ased
o
n
wav
elet
tr
an
s
f
o
r
m
ac
tu
ally
,
v
ar
i
o
u
s
f
am
ilies
o
f
th
e
wav
elet
tr
an
s
f
o
r
m
wer
e
ad
o
p
ted
in
t
h
e
OFDM
s
y
s
tem
.
Star
tin
g
f
r
o
m
th
e
DW
T
[
1
6
]
-
[
1
9
]
,
a
n
d
th
e
n
th
e
W
PT
[
2
0
]
-
[
2
3
]
.
Af
ter
t
h
at
th
e
C
W
PT
[
2
4
]
-
[
2
6
]
,
an
d
f
in
ally
t
h
e
DT
ℂ
W
T
[
2
7
]
-
[
3
6
]
.
Fo
r
th
e
DW
T
,
let
ζ
(
n
)
b
e
th
e
wav
elet
f
u
n
ctio
n
,
an
d
l
b
e
th
e
co
m
p
r
ess
io
n
f
ac
to
r
.
x
(
n
)
at
th
e
o
u
tp
u
t o
f
t
h
e
in
v
e
r
s
e
DW
T
(
I
DW
T
)
is
:
(
)
=
∑
∑
2
2
⁄
(
2
2
⁄
−
)
∞
=
0
∞
=
0
(
1
9
)
At
th
e
r
ec
eiv
in
g
en
d
,
th
e
s
ig
n
al
th
at
h
as
b
ee
n
r
ec
eiv
ed
ca
n
b
e
d
en
o
ted
as
y
(
n
)
g
iv
en
in
(
2
0
)
,
wh
er
ea
s
th
e
s
ig
n
al
th
at
h
as b
ee
n
esti
m
ated
at
th
e
o
u
t
p
u
t o
f
DW
T
ca
n
b
e
ex
p
r
ess
ed
as g
iv
e
n
in
(
2
1
)
:
(
)
=
(
)
∗
ℎ
(
)
+
(
)
(
2
0
)
=
̂
=
∑
2
2
⁄
(
)
(
2
2
⁄
−
)
−
1
=
0
(
2
1
)
I
n
th
e
co
n
tex
t
o
f
DW
PT,
g
iv
e
n
th
e
DW
PT
f
u
n
ctio
n
ψk
(
n
)
,
in
p
u
t
d
ata
d
i,
an
d
in
p
u
t
d
ata
c
o
n
s
tellatio
n
z
i,
j,
th
e
r
esu
ltin
g
o
u
tp
u
t sig
n
al
x
(
n
)
o
b
tain
ed
th
r
o
u
g
h
t
h
e
in
v
e
r
s
e
DW
P
T
(
I
DW
PT)
ca
n
b
e
ca
lcu
lated
as:
(
)
=
∑
∑
,
(
−
)
−
1
=
0
(
2
2
)
T
h
e
s
ig
n
al
th
at
is
r
ec
eiv
ed
at
t
h
e
r
ec
eiv
er
s
id
e,
y
(
t)
,
ca
n
b
e
e
x
p
r
ess
ed
in
wr
itin
g
as:
(
)
=
(
)
∗
ℎ
(
)
+
(
)
=
∑
ℎ
(
)
(
−
)
+
(
)
(
2
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
4
,
No
.
1
,
A
p
r
il
20
2
5
:
182
-
1
9
4
186
T
h
e
esti
m
atio
n
o
f
th
e
d
i c
an
b
e
ac
h
iev
ed
b
y
tak
in
g
th
e
in
n
er
p
r
o
d
u
ct
(
‹
.
,
.
›
)
o
f
f
u
n
ctio
n
s
,
wh
ich
is
p
er
f
o
r
m
ed
at
th
e
en
d
o
f
th
e
p
r
o
ce
s
s
.
=
〈
(
−
)
,
(
)
〉
(
2
4
)
I
n
co
r
p
o
r
atin
g
th
e
in
t
r
icate
iter
atio
n
o
f
wav
elet
tr
a
n
s
f
o
r
m
atio
n
,
th
e
OFDM
s
y
s
tem
u
ti
lized
th
r
ee
d
is
tin
ct
m
eth
o
d
s
-
t
h
e
C
W
T
,
C
W
PT,
an
d
DT
ℂ
W
T
.
T
h
e
tr
an
s
m
is
s
io
n
o
f
s
ig
n
al
x
(
n
)
was
p
en
n
ed
d
o
wn
u
tili
zin
g
th
e
C
W
T
an
d
C
W
PT
m
o
d
els.
(
)
=
∑
∑
(
)
,
(
−
)
∞
=
0
=
(
2
5
)
T
h
e
f
u
n
ctio
n
γ
l,
m
(
n
)
o
f
eith
er
th
e
C
W
T
o
r
th
e
C
W
PT
d
eter
m
in
es
th
e
r
ec
eiv
ed
s
ig
n
al
y
(
n
)
,
r
ep
r
esen
ted
in
eq
u
atio
n
(
2
0
)
.
Su
b
s
eq
u
e
n
tly
,
t
h
e
r
esu
lt y
ield
s
an
esti
m
atio
n
o
f
th
e
d
ata.
̂
(
)
=
∑
∑
(
)
∗
,
(
−
)
∞
=
0
=
(
2
6
)
Up
o
n
ca
r
ef
u
l
a
n
aly
s
is
,
it
h
as
b
ee
n
d
is
co
v
er
e
d
th
at
th
e
f
o
r
war
d
tr
an
s
f
o
r
m
(
ϒ)
f
o
r
th
e
DT
ℂ
W
T
ca
n
b
e
r
ep
r
esen
ted
in
t
h
e
f
o
llo
win
g
m
an
n
er
:
ϒ
=
[
ℎ
]
(
2
7
)
T
h
e
r
ea
l
an
d
im
a
g
in
ar
y
DT
ℂ
W
T
ar
e
r
e
p
r
esen
ted
b
y
F
h
an
d
F
g
r
esp
ec
tiv
el
y
.
T
o
o
b
tain
t
h
e
in
v
er
s
e
DT
ℂ
W
T
(
DT
ℂ
W
T
)
,
th
e
f
o
llo
win
g
f
o
r
m
u
la
ca
n
b
e
u
s
ed
:
ϒ
−
1
=
[
ℎ
−
1
−
1
]
(
2
8
)
Su
b
s
e
q
u
en
tly
,
th
e
s
ig
n
al
x
(
n
)
th
at
h
as
b
ee
n
tr
a
n
s
m
itted
w
ill
ap
p
ea
r
at
th
e
o
u
tp
u
t
o
f
th
e
in
v
er
s
e
Dis
cr
ete
T
im
e
C
o
m
p
lex
W
av
elet
T
r
an
s
f
o
r
m
(
I
DT
-
C
W
T
)
in
th
e
f
o
llo
win
g
m
an
n
e
r
:
(
)
=
ϒ
−
1
(
2
9
)
In
(
2
0
)
p
r
o
v
id
es
th
e
v
alu
e
o
f
th
e
r
ec
eiv
ed
s
ig
n
al,
y
(
n
)
.
C
o
n
s
id
e
r
in
g
p
er
f
ec
t
ch
a
n
n
el
esti
m
atio
n
an
d
n
o
is
e
elim
in
atio
n
,
th
e
d
ata
esti
m
ated
b
y
DT
ℂ
W
T
ca
n
b
e
o
b
tain
ed
f
r
o
m
th
e
o
u
tp
u
t.
=
∑
ϒ
∗
(
)
−
1
=
0
(
3
0
)
2
.
3
.
T
he
curv
elet
t
ra
ns
f
ro
m
ba
s
ed
s
y
s
t
em
Sin
ce
th
e
c
u
r
v
elets
tr
an
s
f
o
r
m
(
C
u
r
T
)
was
in
tr
o
d
u
ce
d
[
3
7
]
-
[
3
9
]
,
it
ap
p
r
o
v
e
d
t
h
at
it’s
a
v
er
y
ef
f
ec
tiv
e
tech
n
iq
u
e
in
d
if
f
e
r
en
t
f
ield
s
in
clu
d
in
g
im
ag
e
p
r
o
ce
s
s
in
g
,
s
eismic
p
r
o
ce
s
s
in
g
,
tu
r
b
u
len
ce
an
aly
s
is
in
f
lu
id
m
ec
h
an
ics,
s
o
lv
in
g
o
f
p
a
r
tial
d
if
f
er
en
t
eq
u
atio
n
s
,
co
m
p
r
ess
ed
s
en
s
in
g
o
r
co
m
p
r
ess
iv
e
s
am
p
lin
g
,
an
d
r
ec
en
tly
in
th
e
wir
eless
co
m
m
u
n
icatio
n
s
[
4
0
]
-
[
4
2
]
.
Fig
u
r
e
3
illu
s
tr
ates
th
e
f
ast
d
is
cr
ete
c
u
r
v
elet
tr
an
s
f
o
r
m
(
FDC
u
r
T
)
an
d
its
f
o
r
war
d
an
d
r
ev
er
s
e
co
n
v
er
s
io
n
s
u
tili
zin
g
wr
a
p
p
in
g
b
ased
o
n
t
h
e
FF
T
.
T
h
e
f
o
r
war
d
co
n
v
e
r
s
io
n
in
clu
d
es
th
e
co
n
v
er
s
io
n
o
f
d
at
a
in
to
th
e
f
r
eq
u
e
n
cy
d
o
m
ain
t
h
r
o
u
g
h
FF
T
.
Su
b
s
eq
u
en
tly
,
t
h
e
d
ata
is
m
u
ltip
lied
b
y
a
s
eq
u
en
ce
o
f
win
d
o
w
f
u
n
ctio
n
s
.
T
h
e
FF
T
co
ef
f
icien
ts
ar
e
th
en
'
wr
ap
p
ed
'
o
r
f
o
ld
e
d
in
to
a
r
ec
tan
g
u
lar
f
o
r
m
b
ef
o
r
e
b
ein
g
a
p
p
lied
t
o
th
e
in
v
er
s
e
FF
T
(
I
FF
T
)
.
T
h
e
cu
r
v
elet
co
ef
f
icien
ts
ar
e
d
e
r
iv
ed
b
y
ex
ec
u
tin
g
th
e
I
FF
T
o
n
t
h
e
win
d
o
wed
d
ata.
T
h
e
r
ev
er
s
e
tr
a
n
s
f
o
r
m
atio
n
u
n
d
o
es th
e
s
tep
s
o
f
th
e
f
o
r
war
d
c
o
n
v
er
s
io
n
p
r
o
ce
s
s
.
Ass
u
m
e
th
at
φ
μ
is
th
e
cu
r
v
elet
f
u
n
ctio
n
th
e
n
th
e
cu
r
v
elet
co
ef
f
icien
t
(
C
μ
)
ca
n
b
e
o
b
tai
n
ed
b
y
t
h
e
in
n
er
p
r
o
d
u
ct
b
etwe
en
th
e
s
ig
n
al
x
(
t)
a
n
d
th
e
c
u
r
v
elet
f
u
n
cti
o
n
as:
=
〈
(
)
,
〉
(
3
1
)
T
h
e
s
ig
n
al
x
(
t)
ca
n
b
e
r
ec
o
v
e
r
ed
b
ac
k
a
g
ain
b
y
(
3
2
)
.
(
)
=
∑
(
)
(
3
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Th
e
in
teg
r
a
tio
n
o
f
d
is
crete
co
n
to
u
r
let
tr
a
n
s
fo
r
m
in
OF
DM
…
(
Mo
h
a
med
Hu
s
s
ien
Mo
h
a
m
ed
N
erma
)
187
Fo
r
th
e
OFDM
b
ased
o
n
C
u
r
T
,
th
e
tr
an
s
m
itted
s
ig
n
al
x
(
t)
at
th
e
o
u
tp
u
t o
f
th
e
in
v
e
r
s
e
ass
u
m
e
th
at
th
e
C
u
r
T
(
I
C
u
r
T
)
is
:
(
)
=
∑
(
)
−
1
,
=
0
(
3
3
)
T
h
e
r
ec
eiv
ed
s
ig
n
al
y
(
n
)
is
g
iv
en
as
in
(
2
0
)
.
At
th
e
o
u
tp
u
t
o
f
C
u
r
T
,
th
e
esti
m
ated
d
ata
u
n
d
er
p
e
r
f
ec
t
ch
an
n
el
esti
m
atio
n
an
d
n
o
is
e
elim
in
ati
o
n
ca
n
b
e
g
iv
en
b
y
th
e
in
n
er
p
r
o
d
u
ct
b
etwe
en
th
e
s
ig
n
al
y
(
n
)
an
d
t
h
e
cu
r
v
elet
f
u
n
c
tio
n
as:
=
〈
(
)
,
(
)
〉
(
3
4
)
Fig
u
r
e
3
.
T
h
e
f
o
r
war
d
a
n
d
th
e
in
v
er
s
e
wr
ap
p
in
g
FDC
u
r
T
2
.
4
.
T
he
pro
po
s
ed
s
y
s
t
em
T
h
e
d
r
awb
ac
k
s
r
elate
d
to
wav
elet
tr
an
s
f
o
r
m
h
a
v
e
b
ee
n
o
v
er
co
m
e
b
y
u
s
in
g
th
e
c
o
n
to
u
r
let
tr
an
s
f
o
r
m
(
C
o
n
T
)
[
4
3
]
.
T
h
e
C
o
n
T
[
4
4
]
i
s
a
p
r
o
m
is
in
g
tr
a
n
s
f
o
r
m
atio
n
t
h
at
h
as
b
ee
n
u
s
ed
in
m
an
y
f
iel
d
s
in
clu
d
in
g
s
ig
n
al
p
r
o
ce
s
s
in
g
,
s
eismic
p
r
o
ce
s
s
in
g
,
an
d
im
a
g
e
p
r
o
ce
s
s
in
g
[
4
5
]
-
[
4
9
]
.
T
o
ad
d
r
ess
th
e
co
n
s
tr
ai
n
ts
o
f
th
e
wav
elet
tr
an
s
f
o
r
m
,
th
e
C
o
n
T
was
in
tr
o
d
u
ce
d
[
4
3
]
-
[
4
4
]
.
T
h
is
i
n
n
o
v
ativ
e
tech
n
iq
u
e
h
as
b
ee
n
ap
p
l
ied
in
d
iv
er
s
e
f
ield
s
s
u
ch
as
s
ig
n
al
p
r
o
ce
s
s
in
g
,
s
eismic
p
r
o
ce
s
s
in
g
,
an
d
im
ag
e
p
r
o
ce
s
s
in
g
[
4
5
]
-
[
4
9
]
.
Fu
r
th
er
m
o
r
e,
in
th
is
s
tu
d
y
,
i
t
was
u
tili
ze
d
with
in
wir
eless
co
m
m
u
n
icatio
n
s
.
T
h
e
f
o
r
w
ar
d
(
d
ec
o
m
p
o
s
itio
n
)
DC
o
n
T
is
co
n
s
tr
u
cted
b
y
co
m
b
in
in
g
th
e
L
ap
lacia
n
p
y
r
am
id
(
L
P)
an
d
th
e
d
ir
ec
tio
n
al
f
ilter
b
an
k
(
DFB
)
,
as
d
ep
icted
in
Fig
u
r
e
4
.
T
h
e
o
u
tp
u
t
f
r
o
m
th
e
L
P
s
er
v
es
as
th
e
in
p
u
t
to
t
h
e
DFB
,
r
esu
ltin
g
in
a
d
u
al
-
iter
ate
d
f
i
lter
b
an
k
s
tr
u
ctu
r
e
r
ep
r
esen
tin
g
t
h
e
d
is
cr
ete
c
o
n
t
o
u
r
let
f
ilter
b
an
k
.
C
o
n
v
e
r
s
ely
,
th
e
in
v
er
s
e
(
r
ec
o
n
s
tr
u
ctio
n
)
DC
o
n
T
(
I
DC
o
n
T
)
in
v
o
lv
es r
ev
e
r
s
in
g
th
e
p
r
o
ce
s
s
o
f
th
e
f
o
r
war
d
DC
o
n
T
(
FDC
o
n
T
)
,
as illu
s
tr
ated
in
Fig
u
r
e
5
[
4
4
]
,
[
5
0
]
.
Fig
u
r
e
4
.
T
h
e
Dec
o
m
p
o
s
itio
n
C
o
n
T
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
4
,
No
.
1
,
A
p
r
il
20
2
5
:
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-
1
9
4
188
Fig
u
r
e
5
.
T
h
e
r
ec
o
n
s
tr
u
ctio
n
C
o
n
T
Fig
u
r
e
6
s
h
o
ws
th
e
D
C
o
n
T
-
b
ased
OFDM
s
y
s
tem
.
Fo
r
th
e
p
r
o
p
o
s
ed
s
y
s
tem
,
th
e
I
n
v
er
s
e
D
C
o
n
T
(
I
DC
o
n
T
)
is
u
s
ed
o
n
t
h
e
tr
an
s
m
itter
s
id
e
wh
ile
th
e
f
o
r
wa
r
d
DC
o
n
T
(
FDC
o
n
T
)
is
u
s
ed
o
n
th
e
r
ec
eiv
er
s
id
e.
Ass
u
m
e
th
at
th
e
C
o
n
T
f
u
n
ctio
n
is
g
iv
in
g
b
y
:
,
,
(
)
=
1
√
[
1
co
s
+
2
s
i
n
−
]
(
3
5
)
Mo
r
eo
v
er
,
th
e
f
o
r
war
d
a
n
d
th
e
in
v
er
s
e
C
o
n
T
ca
n
b
e
g
i
v
en
r
e
s
p
ec
tiv
e
ly
b
y
:
(
,
,
)
=
∫
,
,
(
)
(
)
(
3
6
)
(
)
=
∫
∫
∫
(
,
,
)
,
,
(
)
∞
0
∞
−
∞
3
2
0
4
(
3
7
)
wh
er
e
r
is
th
e
s
ca
lin
g
f
ac
to
r
,
p
is
th
e
tr
an
s
latio
n
f
ac
to
r
,
a
n
d
θ
is
th
e
o
r
ien
tatio
n
f
ac
to
r
.
I
n
th
e
p
r
o
p
o
s
ed
s
y
s
tem
th
e
d
is
cr
ete
v
er
s
io
n
o
f
C
o
n
T
h
as
b
ee
n
u
s
ed
,
an
d
th
e
in
teg
r
atio
n
i
n
th
e
c
o
n
tin
u
o
u
s
tim
e
C
o
n
T
will
b
e
co
n
v
er
ted
to
s
u
m
m
atio
n
in
th
e
d
is
cr
ete
-
tim
e
C
o
n
T
.
O
n
th
e
tr
an
s
m
itter
s
id
e,
th
e
I
DC
o
n
T
is
u
s
ed
,
wh
ile
th
e
r
ec
eiv
er
s
id
e
u
tili
ze
s
th
e
FDC
o
n
T
.
Fig
u
r
e
6
.
B
lo
ck
d
iag
r
am
o
f
th
e
OFDM
b
ased
o
n
th
e
DC
o
n
T
Ass
u
m
in
g
th
at
th
e
r
e
a
r
e
N
s
u
b
ca
r
r
ier
s
,
let
d
N
b
e
t
h
e
c
o
m
p
l
ex
d
is
cr
ete
tr
an
s
m
itted
d
ata.
T
h
e
o
u
tp
u
t
o
f
th
e
in
v
er
s
e
d
is
cr
ete
C
o
n
T
r
esu
lts
in
th
e
tr
an
s
m
itted
s
ig
n
al
x
(
n
)
,
wh
ich
ca
n
b
e
e
x
p
r
ess
ed
as f
o
llo
ws:
(
)
=
∑
∑
,
,
(
)
∞
0
2
0
(
)
(
3
8
)
At
th
e
r
ec
eiv
e
r
'
s
en
d
,
th
e
r
ec
eiv
ed
s
ig
n
al
y
(
n
)
will
b
e
as
g
iv
en
in
(
20
)
,
t
h
e
s
ig
n
al
y
’
(
n
)
at
th
e
o
u
tp
u
t
o
f
th
e
f
o
r
war
d
d
is
cr
ete
C
o
n
T
is
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Th
e
in
teg
r
a
tio
n
o
f
d
is
crete
co
n
to
u
r
let
tr
a
n
s
fo
r
m
in
OF
DM
…
(
Mo
h
a
med
Hu
s
s
ien
Mo
h
a
m
ed
N
erma
)
189
′
(
)
=
∑
∑
,
,
(
−
)
∞
0
2
0
(
,
,
)
(
)
(
3
9
)
Fig
u
r
e
7
s
u
m
m
ar
izes
th
e
s
et
o
f
tr
an
s
f
o
r
m
atio
n
s
th
at
wer
e
u
s
ed
in
th
e
OFDM
s
y
s
tem
in
clu
d
in
g
th
e
p
r
o
p
o
s
ed
C
o
n
T
.
Fig
u
r
e
7
.
B
lo
ck
d
iag
r
am
o
f
th
e
OFDM
b
ased
o
n
n
u
m
er
o
u
s
tr
an
s
f
o
r
m
atio
n
m
eth
o
d
s
3.
SI
M
UL
A
T
I
O
N
P
RO
C
E
DU
RE
T
h
e
f
lo
wc
h
ar
t
d
ep
icted
in
Fig
u
r
e
8
o
u
tlin
es
an
d
en
ca
p
s
u
lates
th
e
s
im
u
latio
n
m
eth
o
d
o
lo
g
ie
s
ad
o
p
te
d
in
th
is
s
tu
d
y
,
with
MA
T
L
AB
®
b
ein
g
t
h
e
p
latf
o
r
m
f
o
r
im
p
lem
en
tatio
n
.
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
u
n
d
er
wen
t
a
co
m
p
ar
ativ
e
an
aly
s
is
with
b
o
t
h
th
e
c
o
n
v
e
n
tio
n
al
s
y
s
tem
r
eli
an
t
o
n
th
e
FF
T
-
OFDM
an
d
t
h
e
s
y
s
tem
b
ased
o
n
t
h
e
f
a
s
t
d
is
c
r
et
e
c
u
r
v
e
l
e
ts
t
r
a
n
s
f
o
r
m
u
t
i
l
i
z
i
n
g
t
h
e
u
n
e
q
u
is
p
a
c
ed
f
a
s
t
f
o
u
r
i
e
r
t
r
a
n
s
f
o
r
m
(
U
SF
FT
)
(
C
u
r
T
-
O
FD
M
)
.
Fig
u
r
e
8
.
Simu
latio
n
p
r
o
ce
d
u
r
es f
lo
w
ch
ar
t
T
h
e
p
er
f
o
r
m
a
n
ce
e
v
alu
atio
n
o
f
t
h
ese
th
r
ee
s
y
s
tem
s
was
co
n
d
u
cted
u
n
d
e
r
th
e
AW
GN
ch
an
n
el
s
ettin
g
,
f
o
cu
s
in
g
o
n
asp
ec
ts
s
u
ch
as
co
m
p
u
tatio
n
al
c
o
m
p
le
x
ity
,
b
it
er
r
o
r
r
ate
(
B
E
R
)
,
an
d
p
ea
k
-
to
-
av
er
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e
p
o
wer
r
atio
(
PAPR
)
.
Utilizin
g
6
4
s
u
b
ca
r
r
ie
r
s
an
d
two
m
o
d
u
latio
n
s
ch
em
es
(
b
in
ar
y
p
h
ase
s
h
if
t
k
ey
in
g
(
PS
K)
an
d
eig
h
t
-
p
h
ase
s
h
if
t k
e
y
in
g
(
PS
K)
)
,
t
h
e
s
im
u
latio
n
p
ar
am
et
er
s
ar
e
s
u
cc
in
ctly
o
u
tlin
e
d
in
T
ab
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
4
,
No
.
1
,
A
p
r
il
20
2
5
:
182
-
1
9
4
190
T
ab
le
1
.
T
h
e
s
im
u
latio
n
p
a
r
a
m
eter
s
P
a
r
a
me
t
e
r
s
D
i
sce
r
p
t
i
o
n
M
o
d
u
l
a
t
i
o
n
t
y
p
e
B
P
S
K
,
8
P
S
K
C
h
a
n
n
e
l
A
W
G
N
c
h
a
n
n
e
l
C
y
c
l
i
c
p
r
e
f
i
x
1
/
4
N
u
mb
e
r
o
f
sy
mb
o
l
s
1
0
4
s
y
m
b
o
l
s
N
u
mb
e
r
o
f
su
b
c
a
r
r
i
e
r
s
6
4
su
b
c
a
r
r
i
e
r
s
P
A
P
R
t
h
r
e
s
h
o
l
d
2
d
B
F
F
T
O
F
D
M
s
y
st
e
m
U
si
n
g
t
h
e
F
F
T
C
u
r
T
O
F
D
M
s
y
s
t
e
m
U
si
n
g
t
h
e
U
S
F
F
T
C
o
n
T
O
F
D
M
s
y
st
e
m
U
si
n
g
t
h
e
p
y
r
a
mi
d
a
l
d
i
r
e
c
t
i
o
n
a
l
f
i
l
t
e
r
b
a
n
k
(
P
D
F
B
)
4.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
T
o
co
m
p
a
r
e
th
e
p
r
o
p
o
s
ed
s
y
s
tem
with
th
e
co
n
v
en
tio
n
al
s
y
s
tem
b
ased
o
n
th
e
FF
T
an
d
t
h
e
OFDM
s
y
s
tem
b
ased
o
n
th
e
C
u
r
T
,
t
h
e
f
o
llo
win
g
c
o
n
s
id
er
atio
n
s
a
r
e
tak
in
g
in
to
ac
c
o
u
n
t:
t
wo
t
y
p
es
o
f
m
o
d
u
latio
n
(
B
PS
K
an
d
8
PS
K)
h
av
e
b
ee
n
u
s
ed
in
th
is
wo
r
k
u
n
d
e
r
th
e
A
W
GN
ch
an
n
el
u
s
in
g
6
4
an
d
2
5
6
s
u
b
ca
r
r
ier
s
,
with
a
2
d
B
PAPR
th
r
esh
o
ld
,
1
0
4
s
y
m
b
o
ls
,
¼
cy
clic
p
r
e
f
i
x
,
an
d
5
2
b
it p
er
OFDM
s
y
m
b
o
l.
4
.
1
.
T
he
co
m
pu
t
a
t
io
na
l c
o
mp
lex
it
y
C
o
m
p
u
tatio
n
al
co
m
p
lex
ity
is
an
ess
en
tial
f
ac
to
r
in
th
e
s
y
s
t
em
’
s
d
esig
n
,
th
er
ef
o
r
e
in
th
is
wo
r
k
,
t
h
is
f
ac
to
r
h
as
b
ee
n
tak
en
in
to
ac
c
o
u
n
t.
C
o
n
s
id
er
in
g
N
is
th
e
n
u
m
b
er
o
f
s
u
b
ca
r
r
ier
s
(
s
u
b
ch
a
n
n
els),
th
e
tr
a
d
itio
n
al
s
y
s
tem
i.e
.
OFDM
b
ased
o
n
th
e
FF
T
an
d
th
e
OFDM
b
ased
o
n
th
e
C
u
r
T
h
av
e
a
c
o
m
p
u
tatio
n
al
co
m
p
lex
ity
o
f
o
r
d
er
O(
N
l
o
g
N)
.
At
th
e
s
a
m
e
tim
e,
th
e
p
r
o
p
o
s
ed
OFD
M
s
y
s
tem
i.e
.
OFDM
b
ased
o
n
th
e
C
o
n
T
h
as
a
co
m
p
u
tatio
n
al
co
m
p
lex
ity
o
f
o
r
d
er
O(
N)
[
4
4
]
.
T
h
e
f
ir
s
t
b
lu
e
cu
r
v
e
r
e
p
r
esen
ts
th
e
FF
T
-
b
a
s
ed
OFDM
s
y
s
tem
,
th
e
s
ec
o
n
d
b
lack
cu
r
v
e
r
ep
r
e
s
en
ts
th
e
C
u
r
T
-
b
ased
OFDM
s
y
s
tem
,
an
d
th
e
th
ir
d
r
ed
c
u
r
v
e
r
ep
r
esen
ts
th
e
C
o
n
T
-
b
ased
OFDM
s
y
s
tem
.
Fo
r
N=
2
5
6
s
u
b
ca
r
r
ier
s
,
OFDM
b
ased
o
n
th
e
FF
T
an
d
th
e
OFDM
b
ased
o
n
th
e
C
u
r
T
n
ee
d
s
1
,
4
2
0
o
p
er
ati
o
n
s
wh
ile
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e
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ased
o
n
t
h
e
C
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n
T
n
ee
d
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o
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ly
2
5
6
o
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er
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th
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m
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er
o
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b
ca
r
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ier
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.
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h
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ea
n
s
th
e
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ased
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e
C
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e
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Fig
u
r
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Fig
u
r
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tatio
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o
m
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lex
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o
r
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e
d
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4
.
2
.
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itted
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u
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s
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ates
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ile
Fig
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1
1
d
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ig
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r
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ased
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r
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ased
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e
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ir
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r
e
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e
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icts
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ased
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Fig
u
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ased
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ates
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ased
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tem
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d
th
e
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u
r
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a
s
ed
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tem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Th
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Fig
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1
1
.
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ple
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itted
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r
r
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r
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u
r
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1
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u
r
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1
2
illu
s
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ates
th
e
C
C
D
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f
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r
th
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s
y
s
tem
s
em
p
lo
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in
g
B
PS
K
with
6
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b
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ith
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th
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v
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n
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e
f
ir
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t
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l
u
e
c
u
r
v
e
c
o
r
r
esp
o
n
d
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to
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e
FF
T
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ased
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r
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e
r
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r
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C
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ased
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al
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r
v
e
s
ig
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e
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n
T
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ased
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tem
.
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aly
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is
o
f
Fig
u
r
e
1
2
r
ev
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ls
th
at
th
e
OF
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y
s
tem
b
ased
o
n
C
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n
T
y
ield
s
s
u
p
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th
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ased
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tem
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d
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e
C
u
r
T
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b
a
s
ed
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y
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tem
s
.
4
.
4
.
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he
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pect
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h
is
s
ec
tio
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p
r
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th
e
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p
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tr
u
m
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en
s
ity
(
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D)
attr
ib
u
tes.
Fig
u
r
e
1
3
illu
s
tr
ates
th
at
th
e
s
u
p
p
r
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io
n
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m
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d
at
-
3
7
d
B
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3
2
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B
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n
d
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2
8
d
B
f
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e
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r
o
p
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ed
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em
,
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e
C
u
r
T
-
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ased
s
y
s
tem
,
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d
th
e
FF
T
-
b
ased
s
y
s
tem
,
r
esp
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.
T
h
e
p
r
o
p
o
s
ed
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tem
d
em
o
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s
tr
ates
s
u
p
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io
r
PS
D
o
u
tco
m
es
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m
p
ar
ed
to
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e
FF
T
-
b
ased
s
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tem
an
d
th
e
C
o
n
T
-
b
ased
s
y
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tem
in
r
eg
ar
d
to
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n
h
an
ce
d
o
u
t
-
of
-
b
an
d
atten
u
atio
n
s
u
p
p
r
ess
io
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.