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53
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e
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n
d
q
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d
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tu
re
a
m
p
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m
o
d
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lati
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QA
M
)
to
a
ss
e
ss
G
F
DM
sig
n
a
l
p
e
rfo
rm
a
n
c
e
.
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sid
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g
i
ts
sp
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n
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y
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s
a
s
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rf
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a
n
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v
a
lu
a
ti
o
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o
f
t
h
e
P
S
F
s
e
n
tails
a
n
a
ly
z
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n
g
sy
m
b
o
l
e
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ra
te
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S
ER)
a
g
a
in
st
si
g
n
a
l
to
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o
ise
ra
ti
o
(S
NR) ac
ro
ss
d
iffere
n
t
m
o
d
u
latio
n
sc
h
e
m
e
s.
K
ey
w
o
r
d
s
:
GFDM
Mo
d
u
latio
n
t
ec
h
n
iq
u
es
Pu
ls
e
s
h
ap
in
g
f
ilter
s
SER
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
:
Sair
am
Vam
s
i
T
ad
ik
am
alla
Dep
ar
tm
en
t o
f
E
lectr
o
n
ics an
d
C
o
m
m
u
n
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n
E
n
g
in
ee
r
i
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g
C
en
tu
r
io
n
Un
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s
ity
o
f
T
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n
o
lo
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y
an
d
Ma
n
ag
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e
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t
Od
is
h
a,
I
n
d
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m
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am
s
i.0
4
3
8
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g
m
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co
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
ec
en
t y
ea
r
s
,
s
ig
n
if
ican
t tr
a
n
s
f
o
r
m
atio
n
s
h
av
e
o
cc
u
r
r
e
d
in
b
o
th
wir
ed
an
d
wir
eless
co
m
m
u
n
icatio
n
s
y
s
tem
s
,
lar
g
ely
d
r
iv
en
b
y
th
e
d
o
m
in
an
ce
o
f
d
ig
ital
tech
n
o
lo
-
g
y
.
T
h
is
s
h
if
t
h
as
cr
ea
ted
a
p
r
ess
in
g
d
em
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f
o
r
h
ig
h
d
ata
r
ates,
in
c
r
ea
s
ed
th
r
o
u
g
h
p
u
t,
a
n
d
m
in
im
ized
late
n
cy
[
1
]
.
Va
r
io
u
s
s
ec
to
r
s
,
in
cl
u
d
in
g
s
atellite
an
d
m
ilit
ar
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ap
p
licatio
n
s
,
r
ely
o
n
ex
ce
p
tio
n
ally
h
i
g
h
d
ata
r
ates
to
s
u
p
p
o
r
t
r
ea
l
-
tim
e
co
n
n
ec
tiv
i
ty
am
o
n
g
n
u
m
e
r
o
u
s
d
ev
ices
[
2
]
.
Similar
ly
,
ap
p
lic
atio
n
s
lik
e
v
e
h
icle
au
to
m
atio
n
n
ec
ess
itate
m
in
im
al
laten
c
y
to
s
wif
tly
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x
ec
u
te
o
p
er
atio
n
s
,
wh
ile
b
an
k
in
g
s
y
s
tem
s
r
eq
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ir
e
h
ig
h
t
h
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o
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g
h
p
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t.
E
m
b
r
ac
in
g
th
e
p
r
in
cip
les
o
f
I
n
d
u
s
tr
y
4
.
0
,
wh
ich
ad
v
o
ca
tes
f
o
r
in
ter
co
n
n
ec
ted
in
d
u
s
-
tr
ies,
m
an
d
ates
m
ee
tin
g
th
ese
cr
iter
ia
[
3
]
.
T
h
e
ad
v
en
t
o
f
5
th
Gen
er
atio
n
(
5
G)
wir
eless
s
y
s
tem
s
is
p
o
is
ed
to
f
u
lf
ill
th
e
d
em
an
d
s
o
f
I
n
d
u
s
tr
y
4
.
0
an
d
g
lo
b
al
au
to
m
atio
n
[
4
]
.
Ho
wev
e
r
,
5
G
tech
n
o
lo
g
y
m
u
s
t
ad
d
r
ess
s
p
ec
if
ic
r
eq
u
ir
em
e
n
ts
,
in
clu
d
i
n
g
m
in
im
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o
u
t
-
of
-
b
an
d
(
OOB)
ra
-
d
iatio
n
an
d
ad
jace
n
t c
h
an
n
el
in
ter
f
er
e
n
ce
,
r
ed
u
cin
g
p
ea
k
to
a
v
er
ag
e
p
o
w
er
r
atio
(
PAPR
)
,
an
d
en
ab
lin
g
u
ltra
-
r
eliab
le,
lo
w
-
laten
cy
co
m
m
u
n
icatio
n
with
a
n
en
h
a
n
ce
d
m
o
b
ile
b
r
o
ad
b
a
n
d
b
an
d
[
5
].
I
n
th
e
r
ea
lm
o
f
5
G
tech
n
o
lo
g
y
,
r
esear
ch
er
s
f
ac
e
th
e
ch
alle
n
g
e
o
f
ac
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v
in
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h
i
g
h
d
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r
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wh
ile
m
in
im
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in
ter
f
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r
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,
p
ar
ti
cu
l
ar
ly
in
th
e
co
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tex
t
o
f
m
u
lti
-
ca
r
r
ier
m
o
d
u
latio
n
tec
h
n
iq
u
es
[
6
]
.
Or
th
o
g
o
n
al
f
r
eq
u
e
n
cy
d
iv
is
io
n
m
u
ltip
lex
i
n
g
(
OFDM)
,
a
well
-
k
n
o
wn
m
eth
o
d
em
p
l
o
y
ed
in
4
G
an
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lu
tio
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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f
&
C
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m
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T
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l
,
Vo
l.
1
4
,
No
.
1
,
A
p
r
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20
2
5
:
153
-
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6
3
154
(
L
T
E
)
s
y
s
tem
s
,
ex
em
-
p
lifie
s
th
is
[
7
]
.
OFDM'
s
u
s
e
o
f
o
r
th
o
g
o
n
ality
an
d
C
y
clic
P
r
ef
i
x
(
C
P)
en
h
a
n
ce
s
r
o
b
u
s
tn
ess
an
d
r
e
d
u
ce
s
f
r
e
q
u
en
cy
-
s
elec
tiv
e
f
ad
in
g
co
m
p
ar
ed
to
s
in
g
le
-
ca
r
r
ier
tech
n
i
q
u
e
s
.
Ho
wev
er
,
OFDM
h
as
d
r
awb
ac
k
s
s
u
ch
as
h
i
g
h
P
APR
,
in
ter
-
ca
r
r
ier
in
ter
f
er
e
n
ce
(
I
C
I
)
,
OOB
em
is
s
io
n
s
,
an
d
r
e
lian
ce
o
n
CP
u
s
ag
e
[
8
]
.
C
o
n
s
e
-
q
u
e
n
tly
,
OFDM
h
as
n
o
t
b
ee
n
ad
o
p
ted
f
o
r
n
ex
t
-
g
en
er
atio
n
(
5
G)
s
y
s
tem
s
d
u
e
to
th
ese
lim
itatio
n
s
.
T
h
e
5
G
n
o
w
g
r
o
u
p
is
ex
p
lo
r
i
n
g
f
o
u
r
alter
n
ativ
e
wav
ef
o
r
m
s
f
o
r
ef
f
icien
t
air
in
ter
f
ac
e
d
e
s
ig
n
,
wh
ich
d
o
n
o
t
r
ely
o
n
o
r
th
o
g
o
n
ality
an
d
s
y
n
ch
r
o
n
izatio
n
r
eq
u
ir
e
m
en
ts
[
9
]
.
T
h
ese
in
clu
d
e
f
ilter
b
an
k
m
u
lticar
r
ier
(
FB
MC),
g
en
er
alize
d
f
r
eq
u
en
cy
d
iv
is
i
o
n
m
u
ltip
lex
in
g
(
GFDM)
,
u
n
iv
er
s
al
f
ilter
ed
m
u
lticar
r
ier
(
UFMC),
an
d
B
i
-
o
r
th
o
g
o
n
al
f
r
e
q
u
en
c
y
d
iv
is
io
n
m
u
ltip
lex
in
g
(
B
FDM)
[
1
0
]
.
E
ac
h
o
f
th
ese
tech
n
i
q
u
es
aim
s
to
r
ed
u
ce
I
n
te
r
-
Sy
m
b
o
l
I
n
ter
f
er
en
ce
(
I
S
I
)
a
n
d
in
cr
ea
s
e
s
p
ec
tr
al
ef
f
icien
cy
.
Ho
wev
er
,
GFDM
s
tan
d
s
o
u
t
as
th
e
o
n
ly
m
u
ltip
lex
in
g
tech
n
iq
u
e
o
f
f
er
in
g
s
ig
n
if
ican
tly
lo
w
OOB
r
ad
iatio
n
,
a
d
d
r
ess
in
g
a
cr
u
cial
co
n
ce
r
n
in
5
G
tech
n
o
lo
g
y
[
11
].
GFDM,
a
p
r
o
m
in
en
t
m
u
ltip
le
x
in
g
tech
n
iq
u
e
in
th
e
r
ea
lm
o
f
5
G,
r
ep
r
esen
ts
th
e
ev
o
lu
tio
n
o
f
OFDM.
I
ts
k
ey
d
is
tin
ctio
n
f
r
o
m
OFDM
lies
in
th
e
u
s
e
o
f
n
o
n
-
r
ec
tan
g
u
lar
p
u
ls
es
in
s
tead
o
f
r
ec
tan
g
u
lar
o
n
es,
elim
in
atin
g
th
e
o
r
t
h
o
g
o
n
ality
ch
ar
ac
ter
is
tic.
GFDM
co
m
p
r
is
es
m
u
ltip
le
in
d
iv
id
u
al
b
lo
c
k
s
,
ea
ch
m
o
d
u
lated
s
ep
ar
ately
with
m
u
lti
p
le
s
u
b
-
c
ar
r
ier
s
,
an
d
ea
c
h
s
u
b
ca
r
r
ier
ca
r
r
y
in
g
v
ar
io
u
s
s
y
m
b
o
ls
[
12
]
.
Du
e
to
th
e
ab
s
en
ce
o
f
o
r
-
th
o
g
o
n
ality
,
GFDM
em
p
lo
y
s
p
u
ls
e
s
h
ap
in
g
f
ilter
s
(
PS
Fs
)
to
m
itig
ate
in
ter
f
er
en
ce
.
T
h
ese
PS
F
s
p
lay
a
cr
u
cial
r
o
le
in
alter
in
g
th
e
c
h
ar
ac
ter
is
tics
o
f
th
e
m
o
d
u
lat
ed
s
ig
n
al
to
b
e
tr
an
s
m
itted
th
r
o
u
g
h
th
e
ch
a
n
n
el,
ess
en
tial
f
o
r
m
in
im
izin
g
I
SI
ca
u
s
ed
b
y
h
i
g
h
m
o
d
u
latio
n
s
i
g
n
als
th
r
o
u
g
h
b
a
n
d
-
lim
ited
c
h
an
n
els
[
1
3
]
.
W
h
ile
co
n
v
en
tio
n
al
f
ilter
s
lik
e
r
aised
co
s
in
e
f
ilter
(
R
C
F)
an
d
r
o
o
t
r
aised
co
s
in
e
f
ilter
(
R
R
C
F)
ar
e
co
m
m
o
n
ly
a
p
p
lied
in
m
u
ltip
lex
in
g
s
ch
e
m
es,
th
e
y
m
ay
n
o
t
ef
f
ec
tiv
ely
r
ed
u
ce
in
ter
f
er
en
ce
.
T
h
is
p
ap
er
in
tr
o
d
u
ce
s
n
o
v
el
PS
Fs
s
u
ch
as
b
etter
th
an
r
aised
c
o
s
in
e
f
ilter
(
B
R
C
F)
an
d
m
o
d
if
ied
b
a
r
tlett
h
an
n
in
g
f
ilter
(
MBHF),
o
f
f
er
i
n
g
s
ig
n
if
ican
t in
ter
f
er
en
ce
r
ed
u
ctio
n
co
m
p
ar
ed
t
o
ex
is
tin
g
tech
n
iq
u
es
[
1
4
]
.
T
h
e
u
p
co
m
in
g
s
ec
tio
n
s
o
f
t
h
e
p
ap
er
d
elv
e
in
to
t
h
e
GFDM
s
y
s
tem
m
o
d
el,
ac
co
m
p
a
n
ied
b
y
its
p
er
f
o
r
m
an
ce
an
aly
s
is
.
T
h
is
will
b
e
f
o
llo
wed
b
y
a
d
is
cu
s
s
io
n
o
n
ex
is
tin
g
an
d
p
r
o
-
p
o
s
ed
PSFs
,
alo
n
g
with
a
co
m
p
ar
ativ
e
a
n
aly
s
i
s
o
f
r
esu
lt
s
.
2.
G
F
DM
SYS
T
E
M
F
RA
M
E
WO
RK
GFDM
em
p
lo
y
s
n
o
n
-
o
r
th
o
g
o
n
al
m
u
lticar
r
ier
m
o
d
u
lati
o
n
,
tr
an
s
m
itti
n
g
in
f
o
r
-
m
ati
o
n
ac
r
o
s
s
K
s
u
b
ca
r
r
ier
s
an
d
N
s
u
b
-
s
y
m
b
o
ls
.
Un
lik
e
tr
ad
itio
n
al
m
eth
o
d
s
,
GFDM
u
s
er
s
o
p
er
ate
with
in
th
e
s
am
e
b
an
d
an
d
f
r
eq
u
e
n
cy
s
im
u
ltan
eo
u
s
ly
,
wi
th
ea
ch
u
s
er
'
s
in
f
o
r
m
atio
n
d
is
tin
g
u
is
h
ed
b
y
p
o
wer
lev
els
[
1
5
]
.
C
o
n
s
eq
u
e
n
tly
,
GFDM
d
em
an
d
s
s
u
b
-
s
tan
tial
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
.
Ad
d
itio
n
ally
,
it
lev
e
r
ag
es
th
e
s
u
p
er
p
o
s
itio
n
p
r
in
cip
le
at
th
e
tr
an
s
m
itter
an
d
im
p
lem
en
ts
s
u
cc
ess
iv
e
in
ter
f
er
en
ce
ca
n
ce
llatio
n
at
th
e
r
ec
eiv
er
,
allo
win
g
f
o
r
th
e
u
tili
za
tio
n
o
f
th
e
s
am
e
s
p
ec
tr
u
m
f
o
r
all
u
s
er
s
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
b
lo
ck
d
iag
r
am
o
f
th
e
GFDM
m
o
d
el
[
1
6
]
.
Fig
u
r
e
1
.
GFDM
s
y
s
tem
m
o
d
e
l
I
n
th
e
tr
an
s
m
itter
p
ar
t
o
f
G
FDM,
s
ev
er
al
o
p
er
atio
n
s
ar
e
co
n
d
u
cte
d
in
clu
d
in
g
d
ata
g
en
er
atio
n
,
Ma
p
p
in
g
,
GFDM
m
o
d
u
latio
n
,
an
d
th
e
a
d
d
itio
n
o
f
a
CP
.
C
o
n
-
s
tellatio
n
m
ap
p
in
g
is
p
er
f
o
r
m
ed
o
n
b
in
ar
y
d
ata
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
E
n
h
a
n
ce
d
p
u
ls
e
s
h
a
p
in
g
filt
ers
fo
r
min
imiz
in
g
in
terf
e
r
en
ce
in
GF
DM
…
(
S
a
ir
a
m
V
a
msi
Ta
d
ika
ma
lla
)
155
to
f
ac
ilit
ate
tr
an
s
m
is
s
io
n
o
v
e
r
th
e
ch
a
n
n
el.
Am
o
n
g
th
e
t
h
r
ee
m
ap
p
in
g
s
av
ailab
le,
q
u
ad
r
atu
r
e
am
p
litu
d
e
m
o
d
u
latio
n
(
QAM
)
m
ap
p
er
is
co
m
m
o
n
l
y
p
r
ef
er
r
ed
f
o
r
its
ab
ilit
y
to
tr
an
s
m
it t
wo
-
b
it st
r
ea
m
s
o
r
an
alo
g
s
ig
n
als
with
v
ar
y
in
g
a
m
p
litu
d
es
in
a
s
in
g
le
tr
an
s
m
is
s
io
n
.
At
th
e
r
ec
eiv
er
,
th
ese
s
ig
n
als
ar
e
s
ep
ar
at
ed
an
d
e
x
tr
ac
ted
to
re
-
co
n
s
tr
u
ct
t
h
e
o
r
ig
in
al
m
o
d
u
latin
g
s
ig
n
al
[
1
7
]
.
T
h
e
GFDM
Mo
d
u
lato
r
u
n
d
er
ta
k
es
two
p
r
i
-
m
ar
y
o
p
er
atio
n
s
:
Up
s
am
p
lin
g
an
d
p
u
ls
e
s
h
a
p
in
g
.
U
p
s
am
p
lin
g
in
c
r
ea
s
es
th
e
m
o
d
u
latio
n
o
f
th
e
tr
a
n
s
m
itted
s
ig
n
al
b
y
p
ad
d
in
g
ze
r
o
s
,
m
ain
tain
i
n
g
t
h
ein
teg
r
ity
o
f
t
h
e
co
n
-
ten
t.
Ad
d
itio
n
ally
,
o
n
e
o
f
th
e
PSFs
is
ap
p
lied
to
g
e
n
er
ate
th
e
GFDM
s
ig
n
al.
C
P
is
ad
d
ed
to
th
e
GFDM
s
ig
n
al
t
o
m
itig
ate
I
SI
d
u
r
i
n
g
tr
a
n
s
m
is
s
io
n
th
r
o
u
g
h
th
e
ch
an
n
el.
C
P
in
s
er
tio
n
in
v
o
lv
es
ap
p
en
d
-
in
g
th
e
last
M
s
a
m
p
les
o
f
th
e
GFDM
s
y
m
b
o
l
to
th
e
f
r
o
n
t
o
f
th
e
s
y
m
b
o
l
[
1
8
]
.
T
h
is
GFDM
s
ig
n
al
will
b
e
tr
a
n
s
m
itted
th
r
o
u
g
h
th
e
ad
d
itiv
e
wh
ite
g
au
s
s
ian
n
o
is
e
(
AW
GN
)
ch
an
n
el
an
d
at
r
ec
eiv
e
r
e
q
u
aliza
tio
n
is
p
er
f
o
r
m
ed
to
r
ec
o
v
e
r
tr
an
s
m
itted
s
y
m
b
o
ls
b
y
r
ed
u
cin
g
I
SI
[
1
9
]
.
-
C
alcu
latio
n
o
f
SER f
o
r
GFD
M
I
n
o
r
d
er
t
o
in
v
esti
g
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
d
if
f
er
en
t
PSFs
alo
n
g
with
d
if
f
e
r
en
t
m
o
d
u
la
tio
n
s
,
it
is
n
ec
ess
ar
y
to
g
en
er
ate
GFDM
m
atr
ix
with
th
e
h
elp
o
f
an
y
PS
Fs
.
T
h
e
p
r
ev
io
u
s
s
ec
tio
n
d
is
cu
s
s
es d
if
f
er
en
t PSF
s
an
d
th
ey
ar
e
in
d
i
-
ca
te
d
as
P
r
cf
,
Pb
r
cf
,
an
d
Pm
b
h
f
an
d
s
ize
o
f
th
e
f
ilter
is
1
x
NS
C
M
[
2
0
]
.
T
h
e
c
ir
cu
la
r
co
n
v
o
l
u
tio
n
h
as
to
b
e
p
er
f
o
r
m
ed
o
n
th
e
m
atr
ix
o
b
tain
ed
d
u
e
to
PSF
in
o
r
d
er
to
g
en
e
r
ate
G
FDM
s
ig
n
al
m
atr
ix
o
f
s
ize
NSC
Mx
N
SC
M
an
d
it
is
in
d
icate
d
as
P
C
=
cir
c
s
h
if
t(
P),
wh
er
e
P
=
Prc
f
/Pb
r
cf
/Pmb
h
f
an
d
PC
is
th
e
p
u
ls
e
s
h
ap
in
g
m
atr
ix
af
ter
ap
p
ly
in
g
c
ir
cu
lar
co
n
v
o
lu
tio
n
[
21
]
.
I
n
GFDM
ea
ch
s
y
m
b
o
l is th
e
tr
an
s
m
itter
with
a
co
r
r
esp
o
n
d
in
g
p
u
ls
e
s
h
ap
e
wh
ich
is
wr
itten
as
,
x
[
k
]
=
∑
∑
,
,
[
]
−
1
=
0
−
1
=
0
(
1
)
wh
er
e
k
=
0
,
1,
2
,
-
-
-
M
-
1
,
d
=
I
n
p
u
t
b
in
ar
y
s
eq
u
en
ce
.
W
ith
th
e
h
elp
o
f
P
n,
m
[
k
]
h
a
v
in
g
m
atr
ix
s
iz
e
1
x
N
SC
M
an
d
P
C
h
av
in
g
m
atr
ix
s
ize
N
SC
M
x
1
,
th
e
GFDM
m
atr
ix
A
f
o
r
m
ed
a
n
d
i
t c
an
b
e
wr
itten
as
,
x
=A
d
(
2)
wh
er
e
A
is
ca
lled
as GFDM
m
o
d
u
latio
n
m
atr
ix
with
s
ize
N
SC
Mx
N
SC
M.
T
o
an
aly
s
e
p
e
r
f
o
r
m
an
ce
in
te
r
m
s
o
f
s
y
m
b
o
l
er
r
o
r
r
ate
(
SER)
an
d
s
ig
n
al
to
n
o
is
e
r
atio
(
SNR
)
b
y
ass
u
m
in
g
AW
GN
c
h
an
n
el
an
d
it c
an
b
e
wr
itten
as
,
P
AW
G
N
=
2
(
−
1
)
(
√
)
−
(
−
1
)
2
2
(
√
)
(
3
)
W
h
er
e
=
3
2
(
2
−
1
)
.
(
4
)
---
SNR
in
d
B
an
d
=
.
.
+
+
(
5
)
is
th
e
n
u
m
b
er
o
f
b
its
p
er
b
in
ar
y
p
h
ase
s
h
if
t
k
e
y
in
g
(
B
PS
K
)
/
q
u
ad
r
at
u
r
e
p
h
ase
s
h
if
t
k
ey
in
g
(
QPSK
)
/QAM
s
y
m
b
o
l,
=
√
2
,
N
CP
a
n
d
N
CS
ar
e
th
e
len
g
th
o
f
CP
an
d
C
y
clic
Su
f
f
i
x
r
esp
ec
tiv
ely
,
is
av
e
r
ag
e
en
e
r
g
y
p
er
s
y
m
b
o
l,
is
No
is
e
p
o
wer
d
en
s
ity
.
No
w
th
e
r
ec
eiv
ed
s
ig
n
al
y
is
f
o
r
m
ed
b
y
ad
d
in
g
t
r
an
s
m
itted
s
ig
n
al
with
n
o
is
e
.
y
=
x
+
P
AWG
N
(
6
)
T
h
is
s
ig
n
al
h
as
to
b
e
d
em
o
d
u
l
ated
u
s
in
g
tr
an
s
p
o
s
e
o
f
GFDM
tr
an
s
m
itter
m
atr
ix
(
A)
with
th
e
r
ec
eiv
ed
s
ig
n
al
af
ter
ch
an
n
el
.
R
X
=
(
A
T
)
*
y
(
7
)
Af
ter
d
em
o
d
u
latio
n
,
th
e
an
aly
s
is
i
s
co
n
d
u
cted
o
n
th
e
r
ec
eiv
ed
s
ig
n
al
to
co
m
p
ar
e
SER
ag
ain
s
t
SN
R
.
I
n
itially
,
SNR
i
s
as
s
u
m
ed
to
b
e
ze
r
o
,
with
th
e
s
ize
o
f
th
e
m
atr
ix
eq
u
al
to
SNR
in
d
ec
ib
els.
SER
f
o
r
ea
ch
SNR
is
co
m
p
u
ted
b
y
m
ea
s
u
r
in
g
th
e
d
if
f
er
en
ce
in
e
r
r
o
r
s
b
etwe
e
n
t
h
e
r
ec
eiv
ed
an
d
tr
an
s
m
itted
s
ig
n
als
[
2
2
]
.
T
h
is
ca
n
b
e
ex
p
r
ess
ed
as
(
8
)
.
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
:
153
-
1
6
3
156
[
,
]
=
(
,
)
(
8
)
T
h
e
ab
o
v
e
will c
o
m
p
ar
e
th
e
el
em
en
ts
in
two
m
atr
ices
.
T
h
e
n
u
m
b
er
o
f
d
i
f
f
er
en
ce
s
is
o
u
tp
u
t
in
.
T
h
e
r
atio
o
f
to
th
e
n
u
m
b
e
r
o
f
elem
e
n
ts
is
o
u
tp
u
t o
f
.
No
w
th
e
SER will b
e
ca
lcu
lated
u
s
in
g
.
∑
(
)
=
(
)
+
_
=
0
(
9
)
I
n
th
is
p
ap
er
,
th
e
s
n
r
_
d
b
is
tak
en
f
r
o
m
0
to
2
0
d
b
with
2
d
b
i
n
ter
v
al.
3.
ANALY
SI
S O
F
E
XIS
T
I
NG
P
UL
S
E
SH
AP
I
NG
F
I
L
T
E
R
T
h
ese
f
ilter
s
ar
e
in
teg
r
al
to
t
h
e
g
en
er
atio
n
o
f
GFDM
s
ig
n
al
s
,
as
th
ey
m
o
d
if
y
th
e
c
h
ar
ac
-
t
er
is
tics
o
f
th
e
tr
an
s
m
itted
s
ig
n
al.
T
h
e
p
r
i
m
ar
y
o
b
jectiv
e
o
f
em
p
lo
y
in
g
PS
Fs
is
to
o
p
tim
ize
th
e
tr
an
s
m
itted
s
ig
n
al
f
o
r
th
e
ch
an
n
el
co
n
d
itio
n
s
.
T
r
an
s
-
m
it
tin
g
h
ig
h
l
y
m
o
d
u
lated
s
ig
n
als
in
n
ar
r
o
w
b
a
n
d
wid
th
c
o
m
m
u
n
icatio
n
ch
a
n
n
els
o
f
ten
r
esu
lts
in
I
SI.
PS
Fs
ar
e
u
tili
ze
d
to
m
itig
ate
I
SI
b
y
n
ar
r
o
win
g
th
e
b
a
n
d
wid
th
o
f
t
h
e
m
o
d
u
lated
s
ig
n
al
in
ac
co
r
d
an
ce
with
th
e
c
h
an
n
el
ch
ar
ac
ter
is
tics
,
th
er
eb
y
in
f
lu
en
cin
g
th
e
o
v
e
r
all
p
r
o
p
e
r
ties
o
f
th
e
GFDM
s
ig
n
al
[
2
3
]
.
-
R
aised
co
s
in
e
f
ilter
Un
lik
e
th
e
co
n
s
tr
ain
ts
ass
o
ciate
d
with
u
s
in
g
r
ec
ta
n
g
u
lar
p
u
ls
es
in
OFDM,
th
e
R
C
F
ad
o
p
ts
th
e
f
o
u
r
ier
tr
an
s
f
o
r
m
o
f
a
r
ec
tan
g
u
lar
p
u
ls
e,
n
am
ely
th
e
s
in
c
p
u
ls
e.
T
h
is
ch
o
ice
is
p
ar
ticu
lar
ly
ad
v
a
n
tag
eo
u
s
f
o
r
b
an
d
-
lim
ited
d
ata
tr
an
s
m
is
s
io
n
,
as it o
f
f
er
s
s
u
p
e
r
io
r
s
u
itab
ili
ty
an
d
p
er
f
o
r
m
an
ce
[
2
4
]
.
L
et
P
rcf
(
ω
)
b
e
th
e
s
p
ec
tr
u
m
o
f
R
C
F
an
d
γ
will
b
e
r
o
llin
g
f
ac
to
r
th
en
s
p
ec
tr
u
m
f
o
r
R
C
F
is
e
x
is
ted
in
b
etwe
en
.
P
rcf
(
ω
)
=
τ
f
o
r
0
≤
ω
≤
π
(
1
−
γ
)
τ
(
1
0
)
P
rcf
(
ω
)
=
τ
2
(
1
−
s
in
(
(
τ
2γ
)
(
ω
−
π
τ
)
)
)
f
o
r
π
(
1
−
γ
)
τ
≤
ω
≤
π
(
1
+
γ
)
τ
(
1
1
)
P
rcf
(
ω
)
=
0
f
o
r
ω
≥
π
(
1
−
γ
)
τ
(
1
2
)
P
rcf
(
ω
)
f
o
r
m
s
a
s
in
c
p
u
ls
e
wh
ich
is
ex
is
ted
in
b
etwe
en
π
(
1
−
γ
)
τ
≤
ω
≤
π
(
1
+
γ
)
τ
an
d
n
o
p
u
ls
e
is
ex
is
ted
af
ter
ω
≥
π
(
1
−
γ
)
τ
,
d
u
e
to
th
is
n
atu
r
e
I
SI
ca
n
b
e
r
ed
u
ce
d
.
T
h
e
tim
e
r
esp
o
n
s
e
o
f
P
rcf
(
t)
is
o
b
tain
ed
b
y
ap
p
ly
in
g
in
v
er
s
e
f
o
u
r
ier
tr
an
s
f
o
r
m
to
P
rcf
(
ω
)
.
T
h
e
r
esp
o
n
s
e
s
ig
n
al
o
f
R
C
F
is
tak
en
b
y
co
m
b
in
in
g
two
s
ig
n
als
wh
ich
ar
e
9
0
°
p
h
ases
to
ea
ch
o
th
er
.
T
h
o
s
e
s
ig
n
als ar
e
:
P
rcf1
(
t)
=
s
in
(
πτ
T
(
1
−
γ
)
)
an
d
P
rcf2
(
t)
=
co
s
(
πτ
T
(
1
+
γ
)
)
th
en
P
rcf
(
t)
=
P
r
c
f
1
(
t
)
+
4
γ
t
T
P
r
c
f
2
(
t
)
π
t
T
(
1
−
(
4
γ
t
T
)
2
)
(
1
3
)
w
h
er
e
γ
is
r
o
ll
o
f
f
f
ac
to
r
,
th
e
r
e
s
p
o
n
s
e
o
f
GFDM
s
ig
n
al
is
v
ar
ied
b
y
v
ar
y
in
g
γ
in
b
etwe
en
0
t
o
1
a
n
d
T
is
th
e
s
y
m
b
o
l p
er
i
o
d
[
2
5
]
.
4.
ANALY
SI
S
O
F
P
RO
P
O
SE
D
P
UL
S
E
SH
AP
I
NG
F
I
L
T
E
RS
T
h
e
ex
is
tin
g
f
ilter
co
n
s
is
ts
o
f
o
n
ly
o
n
e
v
ar
iab
le
p
ar
am
ete
r
s
u
ch
as
r
o
ll
o
f
f
f
ac
to
r
(
γ
)
.
Alo
n
g
with
γ
,
th
e
p
r
o
p
o
s
ed
f
ilter
s
co
n
s
is
t
o
f
s
en
s
itiv
ity
v
ar
iab
le
an
d
win
d
o
win
g
v
a
r
iab
le.
Du
e
to
th
ese
ad
d
itio
n
al
v
a
r
iab
le
p
ar
am
eter
s
,
th
e
s
h
ap
e
o
f
th
e
p
u
ls
e
is
v
ar
ied
s
u
ch
th
at
in
ter
f
e
r
en
ce
d
ec
r
ea
s
es.
4
.
1
.
B
et
t
er
t
ha
n r
a
is
ed
co
s
in
e
f
ilte
r
T
h
is
f
ilter
g
iv
es
b
etter
p
u
ls
e
s
h
ap
in
g
co
m
p
a
r
ed
t
o
R
C
F
b
y
i
n
tr
o
d
u
ci
n
g
s
en
s
itiv
ity
v
a
r
iab
le
n
am
ed
as
β [
26
]
.
T
h
e
r
esp
o
n
s
e
o
f
th
is
f
il
ter
is
g
iv
en
b
y
(
1
4
)
.
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
E
n
h
a
n
ce
d
p
u
ls
e
s
h
a
p
in
g
filt
ers
fo
r
min
imiz
in
g
in
terf
e
r
en
ce
in
GF
DM
…
(
S
a
ir
a
m
V
a
msi
Ta
d
ika
ma
lla
)
157
P
brcf1
(
t)
=
s
in
(
πγτ
T
)
an
d
P
brcf2
(
t)
=
co
s
(
πγτ
T
)
P
brcf
(
t)
=
s
in
c
(
τ
T
)
2
βτ
T
P
b
r
c
f
1
(
t
)
+
2
P
b
r
c
f
2
(
t
)
−
1
⁄
1
+
(
βτ
T
⁄
)
2
(
1
4
)
w
h
er
e
T
is
th
e
tr
an
s
m
is
s
io
n
p
e
r
io
d
an
d
β
=
ln
(
2
)
/
γ
T
.
4
.
2
.
M
o
dified
ba
rt
let
t
ha
nn
ing
f
ilte
r
T
h
is
f
ilter
in
tr
o
d
u
ce
s
a
win
d
o
w
s
h
ap
in
g
p
ar
am
eter
d
en
o
ted
as
α
,
ty
p
ically
r
an
g
in
g
b
etw
ee
n
0
.
5
to
1
.
8
8
.
R
em
ar
k
a
b
ly
,
th
is
p
ar
am
eter
izatio
n
y
ield
s
s
u
p
er
io
r
s
h
ap
in
g
c
o
m
p
a
r
ed
to
o
th
er
f
ilter
s
[
27
]
.
T
h
e
r
esp
o
n
s
e
o
f
th
is
f
ilter
is
ch
ar
ac
ter
ized
b
y
(
1
5
)
.
P
mbhf1
(
t)
=
s
in
(
π
ατ
T
)
an
d
P
mbhf2
(
t)
=
co
s
(
π
ατ
T
)
P
mbhf
(
t)
=
s
in
c
(
τ
T
)
[
(
2
(
1
−
α
)
P
m
b
h
f
1
(
t
)
1
−
(
2
γτ
T
)
2
)
−
(
(
1
−
2
α
)
P
m
b
h
f
1
(
t
)
(
γ
π
τ
T
)
)
]
(
1
5
)
T
h
er
e
ar
e
d
if
f
e
r
en
t p
u
ls
e
s
h
ap
es
ar
e
f
o
r
m
ed
b
y
v
ar
y
i
n
g
α
an
d
γ
p
ar
am
eter
s
.
T
h
e
T
ab
le
1
s
h
o
ws
th
o
s
e
ty
p
es o
f
f
ilter
s
.
T
ab
le
1
.
Dif
f
e
r
en
t
PSFs
b
ased
o
n
α
a
n
d
p
ar
am
eter
s
Α
Ty
p
e
o
f
f
i
l
t
e
r
0
.
5
t
o
1
.
8
8
0
R
e
c
t
a
n
g
u
l
a
r
p
u
l
s
e
s
h
a
p
e
f
i
l
t
e
r
0
.
5
0
t
o
1
R
a
i
s
e
d
c
o
si
n
e
p
u
l
se
sh
a
p
e
f
i
l
t
e
r
1
0
t
o
1
B
a
r
t
l
e
t
t
h
a
n
n
i
n
g
f
i
l
t
e
r
1
1
F
r
a
n
k
p
u
l
se
s
h
a
p
i
n
g
f
i
l
t
e
r
Fro
m
th
e
T
ab
le
1
,
wh
en
win
d
o
win
g
p
ar
a
m
eter
is
0
,
th
en
ty
p
e
o
f
f
ilter
is
r
ec
tan
g
u
lar
p
u
ls
e
s
h
ap
e
f
ilter
wh
ich
is
g
en
er
ally
u
s
ed
f
o
r
OFDM
m
o
d
u
latio
n
tech
n
iq
u
es
[
2
8
]
.
5.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
I
n
th
is
s
ec
tio
n
,
a
co
m
p
ar
is
o
n
i
s
co
n
d
u
cted
am
o
n
g
all
th
r
ee
P
SF
s
b
y
v
ar
y
in
g
th
e
r
o
ll
-
o
f
f
f
ac
to
r
as
0
.
1
,
0
.
5
,
an
d
0
.
9
.
T
h
e
c
h
o
s
en
m
o
d
u
latio
n
tech
n
iq
u
e
is
QAM
,
as
it
co
n
s
is
ten
tly
y
ield
s
s
u
p
e
r
io
r
r
esu
lts
co
m
p
ar
ed
to
th
e
o
th
er
m
o
d
u
latio
n
tech
n
i
q
u
es.
T
h
e
s
im
u
latio
n
en
v
i
r
o
n
m
e
n
t f
o
r
t
h
is
an
aly
s
is
is
o
u
tlin
ed
in
T
ab
le
2
.
T
h
r
o
u
g
h
o
u
t
th
e
en
tire
a
n
aly
s
is
,
th
e
r
o
ll
-
o
f
f
f
ac
t
o
r
is
v
ar
ied
as
0
.
1
,
0
.
5
,
a
n
d
0
.
9
.
T
y
p
ically
,
t
h
e
r
o
ll
-
o
f
f
f
ac
to
r
r
an
g
es
f
r
o
m
0
to
1
,
an
d
as
it
in
cr
ea
s
es
f
r
o
m
0
to
1
,
in
ter
f
er
en
ce
also
in
cr
ea
s
es,
co
n
s
eq
u
en
tly
lead
in
g
t
o
h
ig
h
er
SER
v
alu
es.
T
h
er
e
f
o
r
e,
to
f
ac
ilit
ate
a
clea
r
u
n
d
e
r
s
tan
d
in
g
,
v
al
u
es
ar
e
ch
o
s
en
at
th
e
in
itial
(
0
.
1
)
,
m
i
d
d
le
(
0
.
5
)
,
an
d
e
n
d
(
0
.
9
)
o
f
th
is
r
an
g
e.
T
ab
le
2
.
Simu
latio
n
e
n
v
ir
o
n
m
en
t c
o
n
s
id
er
ed
f
o
r
an
aly
s
is
P
a
r
a
me
t
e
r
P
r
e
f
e
r
r
e
d
v
a
l
u
e
N
o
.
o
f
s
u
b
c
a
r
r
i
e
r
s
64
S
u
b
s
y
m
b
o
l
s
p
e
r
b
l
o
c
k
6
C
y
c
l
i
c
p
r
e
f
i
x
l
e
n
g
t
h
16
N
o
o
f
b
i
t
s
p
e
r
s
y
mb
o
l
3
M
o
d
u
l
a
t
i
o
n
t
e
c
h
n
i
q
u
e
B
P
S
K
,
Q
P
S
K
,
Q
A
M
PSF
R
C
F
,
B
R
C
F
,
M
B
H
F
S
N
R
(
i
n
d
B
)
0,
2,
4
_
_
_
2
0
R
o
l
l
o
f
f
f
a
c
t
o
r
0
.
1
,
0
.
5
,
a
n
d
0
.
9
W
i
n
d
o
w
sh
a
p
i
n
g
p
a
r
a
me
t
e
r
(
u
se
d
o
n
l
y
f
o
r
M
B
H
F
)
0
.
5
t
o
1
.
8
8
Up
o
n
ex
am
i
n
atio
n
o
f
Fig
u
r
es
2
-
4
,
alo
n
g
with
T
ab
le
3
,
it
b
ec
o
m
es
ap
p
ar
en
t
th
at
t
h
e
SER
is
im
p
ac
ted
b
y
an
i
n
cr
ea
s
e
in
th
e
r
o
ll
-
o
f
f
f
ac
to
r
.
Sp
ec
if
ically
,
as
th
e
r
o
ll
-
o
f
f
f
ac
to
r
in
c
r
ea
s
es,
it
tak
es
a
lo
n
g
er
tim
e
to
ac
h
iev
e
s
ig
n
if
ican
tly
lo
w
S
E
R
v
alu
es
r
elativ
e
to
SNR
.
Fu
r
th
er
m
o
r
e
,
it
is
o
b
s
er
v
e
d
th
at
th
e
MBHF
co
n
s
is
ten
tly
y
ield
s
v
er
y
lo
w
SER
v
alu
es
in
co
m
p
ar
is
o
n
to
th
e
o
th
er
two
PSFs
.
Ad
d
itio
n
ally
,
MBHF
d
em
o
n
s
tr
ates su
p
er
io
r
lin
ea
r
ity
ch
ar
ac
ter
is
tics
wh
en
co
m
p
ar
ed
to
th
e
r
e
m
ain
in
g
f
ilter
s
.
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
:
153
-
1
6
3
158
Fig
u
r
e
2
.
SER v
s
SNR
p
lo
t w
ith
r
o
ll o
f
f
f
ac
to
r
0
.
1
Fig
u
r
e
3
.
SER v
s
SNR
p
lo
t w
ith
r
o
ll o
f
f
f
ac
to
r
0
.
5
Fig
u
r
e
4
.
SER v
s
SNR
p
lo
t w
ith
r
o
ll o
f
f
f
ac
to
r
0
.
9
T
ab
le
3
.
C
o
m
p
a
r
ativ
e
an
aly
s
is
o
f
ex
is
tin
g
a
n
d
p
r
o
p
o
s
ed
f
ilter
s
0
2
4
6
8
10
12
14
16
18
20
M
o
d
u
l
a
t
i
o
n
R
o
l
l
o
f
f
PSF
0
.
7
4
0
.
7
0
.
6
4
0
.
5
8
0
.
4
9
0
.
3
9
0
.
2
8
0
.
1
6
0
.
0
8
0
.
0
3
0
QAM
0
.
1
RCF
0
.
5
9
0
.
5
0
.
4
0
.
2
9
0
.
1
8
0
.
0
8
0
.
0
3
0
.
0
1
0
0
0
B
R
C
F
0
.
4
9
0
.
4
0
.
3
4
0
.
2
9
0
.
1
8
0
.
0
8
0
.
0
3
0
0
0
0
M
B
H
F
0
.
8
4
0
.
8
0
.
7
4
0
.
6
8
0
.
5
9
0
.
4
9
0
.
3
8
0
.
2
6
0
.
1
8
0
.
0
8
0
0
.
5
RCF
0
.
7
4
0
.
7
0
.
6
4
0
.
5
8
0
.
4
9
0
.
3
9
0
.
2
8
0
.
1
6
0
.
0
8
0
.
0
3
0
B
R
C
F
0
.
5
9
0
.
5
0
.
4
0
.
2
9
0
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1
8
0
.
0
8
0
.
0
3
0
.
0
1
0
0
0
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B
H
F
0
.
9
4
0
.
9
0
.
8
4
0
.
7
8
0
.
6
9
0
.
5
9
0
.
4
8
0
.
3
6
0
.
1
8
0
.
0
8
0
.
0
1
0
.
9
RCF
0
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8
4
0
.
8
0
.
7
4
0
.
6
8
0
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5
9
0
.
4
9
0
.
3
8
0
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2
6
0
.
1
8
0
.
0
8
0
B
R
C
F
0
.
7
4
0
.
6
9
0
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6
4
0
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5
8
0
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4
9
0
.
3
8
0
.
2
7
0
.
1
6
0
.
0
8
0
.
0
2
0
M
B
H
F
5
.1
.
M
o
dified
ba
rt
let
t
ha
nn
ing
f
ilte
r
I
n
th
is
s
ec
tio
n
th
e
an
aly
s
is
i
s
d
o
n
e
b
y
ta
k
in
g
in
d
i
v
id
u
al
f
ilt
er
with
all
th
r
ee
m
o
d
u
latio
n
t
ec
h
n
iq
u
es
an
d
r
o
ll
o
f
f
f
ac
to
r
s
.
Fig
u
r
e
5
s
p
ec
if
ies
d
if
f
er
en
t
ty
p
es
o
f
p
u
ls
e
-
s
h
ap
in
g
f
ilter
s
,
alo
n
g
with
m
o
d
u
latio
n
tech
n
iq
u
es,
b
y
v
ar
y
in
g
t
h
e
r
o
ll
-
o
f
f
f
a
cto
r
s
f
o
r
d
if
f
e
r
en
t f
ilter
s
u
s
ed
in
th
e
a
n
aly
s
is
p
r
esen
ted
in
th
is
p
ap
er
.
5
.
1
.
1
.
Ra
is
ed
co
s
ine f
ilte
r
T
h
is
s
ec
tio
n
in
tr
o
d
u
ce
s
th
e
f
u
n
d
am
e
n
tal
PSF
u
til
ized
f
o
r
g
en
er
atin
g
GFDM
s
i
g
n
als.
T
h
e
ch
ar
ac
ter
is
tics
o
f
th
e
SER
v
s
SNR
p
lo
t
ar
e
o
b
s
er
v
ed
to
v
a
r
y
b
y
alter
in
g
th
e
r
o
ll
-
o
f
f
f
ac
to
r
with
in
th
e
r
an
g
e
o
f
0
to
1
.
Sp
ec
if
ically
,
r
o
ll
-
o
f
f
f
ac
to
r
s
o
f
0
.
1
,
0
.
5
,
a
n
d
0
.
9
ar
e
s
elec
ted
,
alo
n
g
s
id
e
v
a
r
y
in
g
ty
p
es
o
f
m
o
d
u
latio
n
tech
n
iq
u
es.
B
ased
o
n
Fig
u
r
es
6
-
8
,
as
well
as
T
ab
le
4
,
th
e
SER
v
s
SNR
p
lo
ts
f
o
r
GFDM
u
s
in
g
th
r
e
e
d
if
f
er
e
n
t
m
o
d
u
latio
n
s
a
n
d
v
ar
y
in
g
r
o
ll
-
o
f
f
f
ac
to
r
s
o
f
0
.
1
,
0
.
5
,
a
n
d
0
.
9
a
r
e
p
r
e
-
s
en
ted
,
e
m
p
lo
y
i
n
g
th
e
R
C
F
f
ilter
.
Fro
m
th
e
p
lo
ts
,
it
is
ev
id
en
t
t
h
at
B
PS
K
m
o
d
u
latio
n
y
ield
s
s
u
p
er
io
r
SER
v
alu
es,
with
th
e
SER
r
ea
ch
in
g
its
m
in
im
u
m
with
in
a
1
0
d
B
SNR
r
an
g
e.
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
E
n
h
a
n
ce
d
p
u
ls
e
s
h
a
p
in
g
filt
ers
fo
r
min
imiz
in
g
in
terf
e
r
en
ce
in
GF
DM
…
(
S
a
ir
a
m
V
a
msi
Ta
d
ika
ma
lla
)
159
Fig
u
r
e
5
.
T
y
p
es o
f
P
S
F
s
Fig
u
r
e
6.
SER v
s
SNR
p
lo
t o
f
R
C
F with
B
P
SK
Fig
u
r
e
7.
SER v
s
SNR
p
lo
t o
f
R
C
F with
QPSK
Fig
u
r
e
8.
SER v
s
SNR
p
lo
t o
f
R
C
F with
8
-
QAM
T
ab
le
4
.
C
o
m
p
a
r
ativ
e
an
aly
s
is
o
f
R
C
F with
th
r
ee
m
o
d
u
latio
n
s
0
2
4
6
8
10
12
14
16
18
20
M
o
d
u
l
a
t
i
o
n
R
o
l
l
o
f
f
0
.
0
8
0
.
0
4
0
.
0
1
0
0
0
0
0
0
0
0
B
P
S
K
0
.
1
0
.
1
2
0
.
0
7
0
.
0
3
0
.
0
1
0
0
0
0
0
0
0
B
P
S
K
0
.
5
0
.
1
7
0
.
1
1
0
.
0
6
0
.
0
3
0
.
0
1
0
0
0
0
0
0
B
P
S
K
0
.
9
0
.
3
0
.
2
0
.
1
1
0
.
0
5
0
.
0
1
0
0
0
0
0
0
Q
P
S
K
0
.
1
0
.
3
7
0
.
2
8
0
.
1
8
0
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1
0
.
0
4
0
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0
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5
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2
6
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0
8
0
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0
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P
S
K
0
.
9
0
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5
9
0
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5
1
0
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4
1
0
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2
9
0
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1
8
0
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0
9
0
.
0
3
0
.
0
1
0
0
0
QAM
0
.
1
0
.
6
4
0
.
5
7
0
.
4
9
0
.
3
8
0
.
2
7
0
.
1
6
0
.
0
7
0
.
0
2
0
0
0
QAM
0
.
5
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
:
153
-
1
6
3
160
5
.
1
.
2
.
B
et
t
er
t
ha
n r
a
is
ed
co
s
ine f
ilte
r
T
h
e
s
en
s
itiv
ity
v
ar
iab
le
h
as b
ee
n
in
tr
o
d
u
ce
d
in
B
R
C
F to
p
r
o
d
u
ce
b
etter
SER v
s
SNR
p
lo
ts
co
m
p
ar
ed
to
R
C
F.
Her
e
also
B
R
C
F is
ap
p
lied
b
y
c
h
an
g
i
n
g
ty
p
e
o
f
m
o
d
u
latio
n
s
.
B
ased
o
n
Fig
u
r
es
9
-
1
1
,
as
well
as
T
ab
le
5
,
th
e
an
aly
s
is
o
f
th
e
B
R
C
F
f
ilter
wi
th
th
r
ee
d
if
f
er
en
t
m
o
d
u
latio
n
s
is
p
r
esen
ted
.
Up
o
n
o
b
s
er
v
atio
n
,
it
is
n
o
ted
th
at
B
PS
K
m
o
d
u
latio
n
ex
h
ib
its
s
u
p
er
io
r
ch
ar
ac
ter
is
tic
cu
r
v
es
co
m
p
ar
e
d
to
QAM
an
d
QPSK,
as
it
y
ield
s
s
ig
n
if
ican
tly
lo
wer
SER
v
alu
es
an
d
r
ea
ch
es
th
e
m
in
im
u
m
with
in
a
1
0
d
B
SN
R
r
an
g
e.
F
u
r
th
er
m
o
r
e,
in
co
m
p
a
r
is
o
n
to
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
R
C
F
f
ilter
,
th
e
cu
r
v
es
p
r
o
d
u
ce
d
b
y
th
e
B
R
C
F f
ilter
d
em
o
n
s
tr
ate
b
etter
lin
ea
r
ity
i
n
t
er
m
s
o
f
SER v
alu
es.
Fig
u
r
e
9
.
SER v
s
SNR
p
lo
t o
f
B
R
C
F with
B
PS
K
Fig
u
r
e
10
.
SER v
s
SNR
p
lo
t o
f
B
R
C
F with
QPS
K
Fig
u
r
e
11
.
SER v
s
SNR
p
lo
t o
f
B
R
C
F with
8
-
QAM
T
ab
le
5
.
C
o
m
p
a
r
ativ
e
an
aly
s
is
o
f
B
R
C
F wi
th
th
r
ee
m
o
d
u
latio
n
s
0
2
4
6
8
10
12
14
16
18
20
M
o
d
u
l
a
t
i
o
n
R
o
l
l
o
f
f
0
.
0
8
0
.
0
4
0
.
0
1
0
0
0
0
0
0
0
0
B
P
S
K
0
.
1
0
.
2
0
.
1
4
0
.
0
9
0
.
0
4
0
.
0
2
0
0
0
0
0
0
B
P
S
K
0
.
5
0
.
2
3
0
.
1
8
0
.
1
3
0
.
0
8
0
.
0
3
0
.
0
1
0
0
0
0
0
B
P
S
K
0
.
9
0
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1
9
0
.
1
4
0
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1
0
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0
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P
S
K
0
.
1
0
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2
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0
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2
0
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1
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P
S
K
0
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5
0
.
3
8
0
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3
3
0
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2
7
0
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2
0
.
1
0
.
0
6
0
.
0
2
0
0
0
0
Q
P
S
K
0
.
9
0
.
5
9
0
.
5
0
.
4
0
.
2
9
0
.
1
8
0
.
0
8
0
.
0
3
0
0
0
0
QAM
0
.
1
0
.
6
9
0
.
6
4
0
.
5
7
0
.
4
9
0
.
3
8
0
.
2
7
0
.
1
6
0
.
0
8
0
.
0
3
0
.
0
1
0
QAM
0
.
5
5
.
1
.
3
.
M
o
dified
ba
rt
let
t
ha
nn
ing
f
ilte
r
T
h
is
MBHF
in
tr
o
d
u
ce
s
W
in
d
o
win
g
p
ar
am
eter
(
α
)
to
in
cr
ea
s
e
ch
ar
ac
ter
is
tics
o
f
GFDM
S
E
R
v
s
SNR
p
er
f
o
r
m
an
ce
.
I
n
g
en
er
al,
th
e
W
in
d
o
win
g
p
ar
am
eter
is
co
n
s
id
er
ed
as
1
f
o
r
all
th
r
ee
m
o
d
u
latio
n
s
.
Fro
m
Fig
u
r
es 1
2
-
1
4
,
alo
n
g
with
T
ab
l
e
6
,
th
e
an
aly
s
is
o
f
MB
HF
wi
th
th
r
ee
d
if
f
er
en
t
m
o
d
u
latio
n
s
is
p
r
esen
ted
.
Up
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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f
&
C
o
m
m
u
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T
ec
h
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o
l
I
SS
N:
2252
-
8
7
7
6
E
n
h
a
n
ce
d
p
u
ls
e
s
h
a
p
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g
filt
ers
fo
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min
imiz
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in
terf
e
r
en
ce
in
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DM
…
(
S
a
ir
a
m
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a
msi
Ta
d
ika
ma
lla
)
161
o
b
s
er
v
atio
n
,
it
is
ev
id
en
t
t
h
a
t
QAM
m
o
d
u
latio
n
ex
h
ib
its
s
ig
n
if
ican
tly
lo
wer
SER
v
alu
es,
with
its
v
alu
e
d
ec
r
ea
s
in
g
to
v
er
y
lo
w
le
v
els with
in
a
1
0
d
B
SNR
r
an
g
e.
Up
o
n
co
m
p
ar
in
g
all
th
r
ee
PSFs
w
ith
th
r
ee
m
o
d
u
latio
n
tech
n
iq
u
es,
it
is
ev
id
en
t
t
h
at
QAM
m
o
d
u
latio
n
with
th
e
MBHF
y
ield
s
f
av
o
u
r
ab
le
SER
v
s
SNR
p
lo
ts
f
o
r
GFDM
s
ig
n
als.
T
h
is
p
ap
er
co
m
p
r
eh
e
n
s
iv
ely
ex
am
in
es a
ll
cu
r
v
es wh
ile
em
p
lo
y
in
g
8
-
Q
AM
m
o
d
u
latio
n
,
a
n
d
it is
n
o
ted
th
at
in
cr
ea
s
in
g
th
e
s
ize
o
f
QAM
m
ay
lead
to
e
v
en
b
etter
p
er
f
o
r
m
a
n
ce
r
esu
lts
.
Fig
u
r
e
1
2
.
SER v
s
SNR
p
lo
t o
f
MBHF with
B
PS
K
Fig
u
r
e
1
3
.
SER v
s
SNR
p
lo
t o
f
MBHF with
QP
SK
Fig
u
r
e
1
4
.
SER v
s
SNR
p
lo
t o
f
MBHF with
8
-
QAM
T
ab
le
6
.
C
o
m
p
a
r
ativ
e
an
aly
s
is
o
f
MBHF with
th
r
ee
m
o
d
u
latio
n
s
0
2
4
6
8
10
12
14
16
18
20
M
o
d
u
l
a
t
i
o
n
R
o
l
l
o
f
f
0
.
0
8
0
.
0
4
0
.
0
1
0
0
0
0
0
0
0
0
B
P
S
K
0
.
1
0
.
2
0
.
1
4
0
.
0
9
0
.
0
4
0
.
0
2
0
0
0
0
0
0
B
P
S
K
0
.
5
0
.
2
3
0
.
1
8
0
.
1
3
0
.
0
8
0
.
0
3
0
.
0
1
0
0
0
0
0
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P
S
K
0
.
9
0
.
1
9
0
.
1
4
0
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1
0
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0
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0
1
0
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0
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K
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1
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2
7
0
.
2
0
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1
5
0
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0
9
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0
6
0
.
0
2
0
0
0
0
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P
S
K
0
.
5
0
.
3
8
0
.
3
3
0
.
2
7
0
.
2
0
.
1
0
.
0
6
0
.
0
2
0
0
0
0
Q
P
S
K
0
.
9
0
.
5
9
0
.
5
0
.
4
0
.
2
9
0
.
1
8
0
.
0
8
0
.
0
3
0
0
0
0
QAM
0
.
1
0
.
6
9
0
.
6
4
0
.
5
7
0
.
4
9
0
.
3
8
0
.
2
7
0
.
1
6
0
.
0
8
0
.
0
3
0
.
0
1
0
QAM
0
.
5
6.
CO
NCLU
SI
O
N
T
h
e
SER
h
as
b
ee
n
a
n
aly
s
ed
as
a
f
u
n
ctio
n
o
f
SNR
f
o
r
v
ar
io
u
s
PSFs
u
s
in
g
m
o
d
u
latio
n
s
ch
em
es
B
PS
K,
Q
PS
K,
an
d
QAM
.
T
h
e
r
esu
lts
clea
r
ly
d
em
o
n
s
tr
ate
th
at
th
e
p
r
o
p
o
s
ed
f
ilter
s
,
B
R
C
F
an
d
MBHF,
co
u
p
led
with
QAM
m
o
d
u
latio
n
,
ex
h
ib
it
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
in
ter
m
s
o
f
SER
ag
ain
s
t
S
NR
co
m
p
ar
ed
to
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
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8
7
7
6
I
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&
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,
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4
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No
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1
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A
p
r
il
20
2
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:
153
-
1
6
3
162
ex
is
tin
g
R
C
F
f
ilter
.
Ad
d
itio
n
a
lly
,
th
e
r
o
ll
-
o
f
f
f
ac
to
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is
ex
a
m
in
ed
f
o
r
all
m
o
d
u
latio
n
s
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ac
r
o
s
s
th
e
t
h
r
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f
ilter
s
,
r
ev
ea
lin
g
th
at
th
e
am
p
l
itu
d
e
o
f
th
e
s
ig
n
al
g
en
e
r
ate
d
with
th
e
GFDM
s
ch
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e
d
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r
ea
s
es
wh
ile
th
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SE
R
in
cr
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an
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e
r
o
ll
-
o
f
f
f
ac
to
r
.
RE
F
E
R
E
NC
E
S
[
1
]
S
.
P
.
B
e
n
d
a
l
e
a
n
d
J.
R
a
j
e
s
h
P
r
a
sa
d
,
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S
e
c
u
r
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t
y
t
h
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c
h
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m
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b
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w
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t
w
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k
s,
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n
Pr
o
c
e
e
d
i
n
g
s
-
2
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1
8
I
EEE
G
l
o
b
a
l
C
o
n
f
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r
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n
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e
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W
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p
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t
w
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N
o
v
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p
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C
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N
.
2
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6
6
8
6
3
5
.
[
2
]
A
.
K
h
a
l
i
d
,
“
T
h
e
c
o
n
c
e
p
t
o
f
f
i
f
t
h
g
e
n
e
r
a
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(
5
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mo
b
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h
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y
,
”
C
o
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m
u
n
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c
a
t
i
o
n
s
o
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A
p
p
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l
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v
o
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.
2
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p
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p
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o
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5
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2
0
/
c
a
e
2
0
1
5
6
5
1
8
5
3
.
[
3
]
Z.
W
e
i
e
t
a
l
.
,
“
O
r
t
h
o
g
o
n
a
l
t
i
me
-
f
r
e
q
u
e
n
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y
s
p
a
c
e
m
o
d
u
l
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t
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o
n
:
a
p
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m
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v
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,
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EEE
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m
m
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c
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t
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2
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.
[
4
]
S
.
P
.
S
o
t
i
r
o
u
d
i
s
,
G
.
A
t
h
a
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d
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.
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d
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S
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o
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m
b
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p
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f
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4
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a
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5
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w
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EEE
T
ra
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An
t
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Pr
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p
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/
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3
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[
5
]
M
.
H
u
,
J.
W
a
n
g
,
W
.
C
h
e
n
g
,
a
n
d
H
.
Z
h
a
n
g
,
“
N
e
a
r
-
o
p
t
i
ma
l
p
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w
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se
l
i
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p
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sf
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A
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n
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f
O
F
D
M
s
y
st
e
ms,
”
I
EE
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r
a
n
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Br
o
a
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a
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0
9
/
t
b
c
.
2
0
2
4
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3
4
4
3
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6
.
[
6
]
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