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2
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In
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sc
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m
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m
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t
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h
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m
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lt
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-
F
DM
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a
s
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n
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m
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In
stit
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te o
f
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.
C
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s
p
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A
uth
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:
Ma
n
o
j
K.
Sh
u
k
l
a,
E
lectr
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n
ics E
n
g
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r
in
g
Dep
a
r
t
m
en
t,
H.
B
.
T
.
I
.
,
Kan
p
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I
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ia
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m
ail:
m
a
n
o
j
k
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s
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k
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@
g
m
ail
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co
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
t
h
e
li
ter
atu
r
e,
it
h
a
s
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ted
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DM
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ch
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m
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f
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th
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v
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tio
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”
(
L
T
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)
o
f
r
ad
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tr
an
s
m
is
s
io
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s
f
r
o
m
ce
ll
u
lar
p
h
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n
e
s
to
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ase
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ta
tio
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s
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n
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co
m
m
u
n
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n
.
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I
DM
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s
ch
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m
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m
m
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is
s
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m
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as
s
h
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u
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h
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A
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v
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ag
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w
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R
atio
)
.
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ir
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n
d
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m
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l
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i
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-
ca
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ter
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s
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p
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t
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D
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V
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2.
SC
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F
DM
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I
D
M
A
SCH
E
M
E
As
a
s
p
ec
ial
ca
s
e
o
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DM
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s
y
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te
m
,
I
DM
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r
elie
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ter
lea
v
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n
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a
s
th
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o
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l
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ea
n
s
to
d
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tin
g
u
is
h
th
e
s
i
g
n
als
f
r
o
m
d
if
f
er
en
t
u
s
er
s
.
T
h
e
I
DM
A
s
y
s
te
m
ad
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p
ts
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v
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s
i
m
p
le
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h
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p
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by
-
ch
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iter
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u
lti
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tio
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MU
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t
r
ateg
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f
o
r
ex
tr
ac
ti
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g
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s
er
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s
p
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if
ic
s
ig
n
al
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f
r
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m
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m
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ite
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m
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DM
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c
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m
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ig
n
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f
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v
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tio
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s
c
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m
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n
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ter
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s
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tr
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r
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eiv
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b
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[1
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,
[
2
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
SC
-
F
DM
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DMA
S
ch
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C
H
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R
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s
p
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s
t
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o
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m
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DM
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k
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k
n
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w
n
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DM
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s
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u
ltip
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r
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o
f
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-
FD
MA
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n
d
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DM
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s
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m
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s
.
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n
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[
3
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Nu
m
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r
e
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l
ts
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SC
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p
in
g
o
p
er
atio
n
s
.
Fu
r
t
h
er
d
ata
is
p
ass
ed
th
r
o
u
g
h
I
DFT
b
lo
ck
b
ef
o
r
e
its
tr
an
s
f
er
to
ch
an
n
el
w
it
h
A
W
GN
d
is
tu
r
b
an
ce
s
.
O
n
t
h
e
r
ec
ei
v
er
s
id
e,
r
ec
eiv
ed
co
m
b
in
ed
d
ata
is
r
ec
o
n
v
er
ted
to
t
h
e
co
m
p
atib
le
d
ata
s
u
itab
le
f
o
r
E
SE
B
lo
ck
[
4
]
.
Her
e,
lo
w
co
m
p
lex
i
t
y
E
SE
alg
o
r
it
h
m
is
u
s
ed
f
o
r
s
ig
n
al
d
etec
tio
n
.
T
h
is
a
lg
o
r
ith
m
i
s
d
er
iv
ed
th
r
o
u
g
h
Ga
u
s
s
ian
ap
p
r
o
x
i
m
at
io
n
b
ased
o
n
t
h
e
a
s
s
u
m
p
t
io
n
th
at
th
e
in
ter
f
er
i
n
g
s
y
m
b
o
l
s
a
r
e
in
d
ep
en
d
en
t
o
f
ea
ch
o
t
h
er
.
T
h
is
a
s
s
u
m
p
tio
n
is
r
ea
s
o
n
ab
le
w
h
e
n
t
h
e
co
d
ed
b
lo
ck
is
lo
n
g
e
n
o
u
g
h
d
u
e
to
u
s
er
-
s
p
ec
i
f
ic
in
ter
lea
v
er
s
.
Si
n
ce
I
SI
is
o
n
l
y
p
r
esen
t
i
n
t
h
e
f
ir
s
t
L
g
s
a
m
p
le
s
o
f
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ei
v
ed
s
eq
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e
n
ce
R
(
n
)
,
n
=
L
g
,
…
,
N
−1
,
th
ese
L
g
s
a
m
p
les
ar
e
r
e
m
o
v
e
d
b
ef
o
r
e
FF
T
o
p
er
atio
n
.
Fu
r
th
er
,
o
n
r
ec
eiv
ed
co
m
b
i
n
ed
d
at
a
FF
T
o
p
er
atio
n
if
p
er
f
o
r
m
ed
[5
-
1
0
]
.
Fig
u
r
e1
.
SC
-
FDM
-
I
DM
A
S
y
s
te
m
Af
ter
FF
T
o
p
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atio
n
̅
∑
w
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v
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……
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N
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1
T
h
en
,
it
im
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le
m
e
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ts
s
u
b
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r
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ier
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e
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ield
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ata
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ic
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f
ter
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e
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atio
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r
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r
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k
c
User
-
1
DE
C
П
1
П
1
-
1
I
DF
T
User
-
k
DE
C
П
k
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1
c
y
1
y
k
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se
(
A
W
G
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)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8708
I
J
E
C
E
Vo
l.
7
,
No
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2
,
A
p
r
il 2
0
1
7
:
9
9
2
–
9
9
8
994
I
n
th
e
p
r
o
ce
s
s
o
f
I
DM
A
d
etec
t
io
n
,
w
e
r
e
f
o
r
m
u
late
t
h
e
alg
o
r
it
h
m
f
o
r
QP
SK si
g
n
all
in
g
as
f
o
l
lo
w
i
n
g
.
r
(
j)
=∑
k
h
k
x
k
(
j
)
+n
(
j
)
r
(
j)
=h
k
x
k
(
j
)
+ζ
k
(
j
)
(
)
(
)
(
)
T
h
e
r
ec
eiv
ed
co
m
p
lex
s
i
g
n
al
c
an
b
e
ex
p
r
ess
ed
b
y
:
(
)
∑
(
(
)
(
)
)
∑
(
(
)
(
)
)
(
)
Fu
r
t
h
er
r
ea
l a
n
d
i
m
a
g
i
n
ar
y
p
ar
ts
o
f
x
ar
e
o
b
tain
ed
in
a
s
i
m
ila
r
m
a
n
n
er
w
ith
t
h
e
h
elp
o
f
f
u
r
t
h
er
an
al
y
s
i
s
.
Step
I
: E
ST
I
MA
T
I
ON
OF I
N
T
E
R
FERENCE
ME
A
N
A
ND
VARI
A
N
C
E
(
)
∑
(
(
)
(
)
)
∑
(
(
)
(
)
)
(
)
(
(
)
)
∑
(
(
(
)
(
(
)
)
)
(
(
)
)
∑
(
)
(
(
)
)
∑
(
)
(
(
)
)
(
)
∑
(
(
(
)
)
(
(
)
)
)
(
(
̅
̅
̅
̅
̅
(
)
)
)
(
)
(
(
)
)
(
)
(
(
)
)
(
)
(
(
)
)
Step
I
I
: L
L
R
GE
NE
R
A
T
I
ON
&
C
O
MB
I
NI
NG
T
h
e
o
u
tp
u
t o
f
ele
m
e
n
tar
y
s
i
g
n
al
esti
m
ato
r
b
lo
ck
is
as f
o
llo
ws,
(
(
)
)
(
̅
̅
̅
(
)
)
(
(
̅
̅
̅
(
)
)
)
(
(
̅
̅
̅
(
)
)
)
w
h
er
e
Ψ
(
j
)
is
th
e
co
v
ar
ian
ce
o
f
i
m
ag
in
ar
y
a
n
d
r
ea
l
p
ar
ts
o
f
r
ec
eiv
ed
s
ig
n
al
f
o
r
j
ch
ip
.
T
h
e
esti
m
ates
E
(
.
)
an
d
Var
(
.
)
d
en
o
te
th
e
ex
p
ec
tatio
n
an
d
v
ar
ia
n
ce
.
T
h
e
DE
C
ca
r
r
i
es
o
u
t
A
P
P
alg
o
r
ith
m
.
T
h
e
ex
t
r
in
s
ic
L
L
R
s
w
i
ll
b
e
u
s
ed
in
t
h
e
E
SE
to
u
p
d
ate
th
e
in
ter
f
er
e
n
ce
m
ea
n
a
n
d
v
ar
ian
c
e
in
th
e
n
ex
t iter
a
tio
n
[
1
1
]
.
(
(
(
)
)
(
(
(
)
)
)
(
(
)
)
(
(
(
)
)
)
3.
B
CH
CO
DE
T
h
e
B
C
H
co
d
es
f
o
r
m
a
clas
s
o
f
c
y
cl
ic
er
r
o
r
-
co
r
r
ec
tin
g
co
d
es
th
a
t
ar
e
co
n
s
tr
u
cted
e
m
p
lo
y
in
g
f
i
n
ite
f
ield
s
.
O
n
e
o
f
t
h
e
k
e
y
f
ea
t
u
r
es
o
f
B
C
H
co
d
es
is
a
p
r
ec
is
e
co
n
tr
o
l
o
v
er
th
e
n
u
m
b
er
o
f
s
y
m
b
o
l
er
r
o
r
s
co
r
r
ec
tab
le
b
y
t
h
e
co
d
e
d
u
r
in
g
its
co
d
e
d
esig
n
in
g
p
r
o
ce
s
s
.
I
n
ad
d
itio
n
to
it,
B
C
H
ca
n
ea
s
il
y
b
e
d
ec
o
d
ed
u
s
in
g
an
al
g
eb
r
aic
m
et
h
o
d
k
n
o
w
n
a
s
s
y
n
d
r
o
m
e
d
ec
o
d
in
g
.
B
C
H
c
o
d
es
o
p
er
ate
o
v
er
f
in
i
te
f
ield
s
o
r
Galo
is
f
ield
s
.
B
C
H
co
d
es
ca
n
b
e
d
ef
i
n
ed
b
y
t
w
o
p
ar
a
m
eter
s
th
at
ar
e:
co
d
e
w
o
r
d
len
g
th
(
n
)
an
d
t
h
e
n
u
m
b
er
o
f
er
r
o
r
s
to
b
e
co
r
r
ec
ted
,
[1
2
-
1
4
]
.
T
h
e
B
C
H
co
d
es
ar
e
a
class
o
f
c
y
cle
c
o
d
es
w
h
o
s
e
g
en
er
ato
r
p
o
l
y
n
o
m
ial
i
s
p
r
o
d
u
ct
o
f
d
is
tin
ct
m
in
i
m
u
m
p
o
l
y
n
o
m
ia
ls
co
r
r
esp
o
n
d
in
g
to
α
,
α
2
,....
α
2t
,
w
h
er
e
α
ε
GF(
2
m
)
i
s
a
r
o
o
t
o
f
t
h
e
p
r
i
m
iti
v
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
SC
-
F
DM
-
I
DMA
S
ch
eme
E
mp
lo
yin
g
B
C
H
C
o
d
in
g
(
R
o
o
p
a
li A
g
a
r
w
a
l)
995
p
o
ly
n
o
m
ia
l
g
(
x
)
.
An
ir
r
ed
u
ci
b
le
p
o
ly
n
o
m
ial
g
(
x
)
o
f
d
eg
r
e
e
m
is
s
a
id
to
b
e
p
r
im
iti
v
e
i
f
o
n
l
y
i
f
it
d
iv
id
es
p
o
ly
n
o
m
ia
l
f
o
r
m
o
f
d
eg
r
ee
n
,
x
n
+
1
f
o
r
n
o
n
less
th
a
n
2
m
-
1
.
I
n
f
ac
t,
e
v
er
y
b
in
ar
y
p
r
i
m
iti
v
e
p
o
ly
n
o
m
ia
l
g
(
x
)
o
f
d
eg
r
ee
m
is
a
f
ac
to
r
o
f
x
2
m
1
+1
.
L
et
m
i
(
x
)
b
e
th
e
m
i
n
i
m
al
p
o
ly
n
o
m
ial
o
f
α
i
.
L
et
p
(
x
)
=
p
0
+
p
1
x
+
p
2
x
2
+ ....
..+
p
n
-
1
x
n
-
1
(
1
)
be
a
co
d
e
p
o
ly
n
o
m
ial
w
it
h
co
ef
f
icien
ts
f
r
o
m
GF(
2
)
.
I
f
p
(
x
)
h
as
α
,
α
2
…
α
2t
as
it
s
r
o
o
ts
,
p
(
x)
is
d
iv
is
ib
le
b
y
t
h
e
m
i
n
i
m
al
p
o
l
y
n
o
m
ial
s
m
1
(
x
)
,
m
2
(
x
)
…
m
2t
-
1
(
x
)
.
T
h
e
g
en
er
ato
r
p
o
ly
n
o
m
ia
l
g
(
x
)
o
f
t
h
e
t
-
er
r
o
r
co
r
r
ec
tin
g
B
C
H
o
f
len
g
th
co
d
e
w
o
r
d
s
n
=
2
m
-
1
an
d
r
ate
co
d
es
k
/n
is
th
e
lo
west
d
eg
r
ee
p
o
ly
n
o
m
ia
l
o
v
er
GF(
2
)
[
1
5
-
1
8
]
.
T
h
u
s
,
th
e
g
e
n
er
ato
r
p
o
ly
n
o
m
ial
o
f
th
e
co
d
e
m
u
s
t
b
e
th
e
leas
t
co
m
m
o
n
m
u
lt
ip
le
(
L
C
M)
o
f
th
e
s
e
m
i
n
i
m
a
l
p
o
ly
n
o
m
ia
ls
:
g
(
x
)
=L
C
M{
m
1
(
x
)
,
m
2
(
x
)
,
.
.
.
.
.
.
,
m
2t
(
x
)
(
2
)
I
n
g
en
er
al,
f
o
r
an
y
p
o
s
iti
v
e
in
te
g
e
r
m
≥
3
an
d
t
<n
/
2
,
th
er
e
is
a
b
in
ar
y
B
C
H
co
d
e
w
i
th
p
ar
a
m
eter
s
o
f
co
d
e
w
o
r
d
s
l
en
g
t
h
n
=
2
m
-
1
,
n
u
m
b
er
o
f
p
ar
it
y
c
h
ec
k
b
it
s
n
-
k
≤
m
t
,
an
d
m
i
n
i
m
u
m
d
is
tan
ce
d
0
=2
t
+1
≤
d
m
in
.
T
h
e
d
esig
n
ed
d
is
tan
ce
o
f
t
h
e
co
d
e
is
d
0
=
2
t +
1
.
T
h
e
m
i
n
i
m
u
m
d
is
tan
ce
d
m
in
co
u
ld
b
e
lar
g
er
th
an
d
0
[1
6
]
.
A
lg
o
r
ith
m
f
o
r
d
es
ig
n
in
g
B
C
H
co
d
es is
:
1
.
C
h
o
o
s
e
a
p
r
i
m
it
iv
e
p
o
l
y
n
o
m
ia
l o
f
d
eg
r
ee
m
,
an
d
co
n
s
tr
u
ct
G
F (
2
m
).
2
.
Fin
d
t
h
e
m
i
n
i
m
al
p
o
l
y
n
o
m
ia
l m
i
(
x
)
o
f
α
i
f
o
r
i =
1
,
2
…
2
t.
3
.
Ob
tain
g
(
x
)
.
4
.
Dete
r
m
i
n
e
k
f
r
o
m
n
-
k
,
w
h
ic
h
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o
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g
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x
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5
.
Fin
d
t
h
e
m
i
n
i
m
u
m
d
i
s
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ce
d
min
≥
2
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f
all,
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er
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o
r
m
a
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SI
M
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r
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F
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u
r
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u
r
e
4
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as
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DM
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1
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10
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t
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1
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5
3
3
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5
4
4
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5
5
5
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6
10
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10
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10
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10
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10
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E
b
/
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t
E
r
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t
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1
6
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k
=
1
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
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2
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8
8
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u
r
e
5
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er
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r
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n
ce
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o
m
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ar
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M
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g
(W
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,
23
-
2
5
S
e
p
t.
,
pp
.
1
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5
,
2
0
1
1
.
[2
]
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.
P
i
n
g
,
e
t
a
l
.
,
“
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terle
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v
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-
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isio
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M
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c
c
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s
s
,
”
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ra
n
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ti
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n
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n
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mm
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l
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4
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p
p
.
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,
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0
0
6
.
[3
]
F
.
M
o
a
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a
m
i,
“
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u
c
c
e
siv
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Co
-
Ch
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n
n
e
l
In
terf
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re
n
c
e
Ca
n
c
e
ll
a
ti
o
n
,”
In
d
o
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e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
In
f
o
rm
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ti
c
s (
IJ
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/i
ss
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e
:
3
(1
)
,
2
0
1
5
.
[4
]
M
.
K
.
S
h
u
k
la,
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o
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a
n
c
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Ev
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lu
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f
IDMA
S
c
h
e
m
e
in
W
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ss
Co
m
m
u
n
ica
ti
o
n
,
”
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h
.
D.
t
h
e
sis,
2
0
1
0
.
[5
]
I
.
F
ra
n
k
,
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a
l
.
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“
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u
lt
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-
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c
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f
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In
3
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P
P
L
T
E
,
”
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d
o
n
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sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
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rin
g
a
n
d
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n
fo
rm
a
ti
c
s (
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I)
,
v
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l
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ss
u
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:
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(
3
),
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0
1
3
.
[6
]
L
.
P
in
g
,
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t
a
l.
,
“
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h
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OFDM
-
IDMA
A
p
p
ro
a
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to
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ss
Co
m
m
u
n
ica
ti
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n
S
y
ste
m
s
,
”
IEE
E
W
ire
les
s
Co
mm
u
n
ica
ti
o
n
s
,
pp
.
18
-
24
,
2
0
0
7
.
[7
]
H
.
G
.
M
y
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g
a
n
d
D
.
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o
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m
a
n
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in
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rrier
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DM
A
A
Ne
w
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ir
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terfa
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f
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g
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m
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lu
ti
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n
,
”
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il
e
y
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ries
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n
W
irele
ss
Co
m
m
u
n
ica
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s an
d
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o
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il
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C
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g
.
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]
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S
C
-
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DMA
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DMA
in
LT
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”
915
-
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7
2
5
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0
1
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0
9
.
[9
]
J.
G
.
P
ro
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k
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“
Dig
it
a
l
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m
m
u
n
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ti
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n
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M
c
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rk
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8
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.
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0
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;
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o
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A
.
;
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u
rtaz
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M
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rib
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sity
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ter
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p
.
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2
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8
.
[1
1
]
K
.
Ku
su
m
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t
a
l.
,
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s C
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p
p
.
1
-
8
,
2
0
0
9
.
[1
2
]
L
.
P
i
n
g
,
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t
a
l.
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“
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u
n
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p
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lt
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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3
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4
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rm
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5
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ter
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6
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.
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n
g
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a
l.
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terle
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v
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Co
d
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s,
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o
u
rn
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l
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ted
Are
a
s in
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n
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p
.
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7
7
,
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0
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6
.
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7
]
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.
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b
ro
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a
n
d
M
.
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o
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so
n
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h
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tec
ti
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n
,
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t
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p
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2
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8
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h
tt
p
:
//
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n
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m
m
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on.
Evaluation Warning : The document was created with Spire.PDF for Python.