T
E
L
KO
M
NIK
A
, V
ol
.
17
,
No.
6,
Dec
em
be
r
20
1
9,
p
p.
2
98
3
~
2
99
1
IS
S
N: 1
69
3
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6
93
0
,
accr
ed
ited
F
irst
Gr
ad
e b
y K
em
en
r
istekdikti,
Decr
ee
No: 2
1/E/
K
P
T
/20
18
DOI:
10.12928/TE
LK
OM
N
IK
A
.v
1
7
i
6
.
11511
◼
29
83
Rec
ei
v
ed
O
c
tob
er
20
,
20
1
8
; Rev
i
s
ed
J
an
u
ary
2
3
,
20
1
9
; A
c
c
ep
te
d
Ma
r
c
h 1
2
,
20
1
9
P
A
PR
anal
y
s
is
of
O
FDM
s
y
st
e
m u
si
ng
A
I
bas
e
d
mu
lt
iple
si
gn
a
l repre
sen
tat
i
on
met
ho
d
s
J
y
o
t
i S
h
u
k
la
1
,
A
l
o
k J
o
shi
2
, Raj
e
sh T
y
agi
3
1
M
e
w
a
r Un
i
v
e
rs
i
ty
,
G
h
a
z
i
a
b
a
d
,
In
d
i
a
2
J
a
y
p
e
e
In
s
ti
tu
te
o
f
I
n
fo
rm
a
t
i
o
n
T
e
c
h
n
o
l
o
g
y
,
Noi
d
a
,
In
d
i
a
3
SRM
Un
i
v
e
rs
i
ty
,
G
h
a
z
i
b
a
d
,
In
d
ia
*C
o
rre
s
p
o
n
d
i
n
g
a
u
th
o
r
e
-
m
a
i
l
:
j
y
o
ti
.s
h
u
k
l
a
2
@g
m
a
i
l
.
c
o
m
1
,
2
0
.
a
l
o
k
@
g
m
a
i
l
.
c
o
m
2
,
p
ro
fra
j
e
s
h
k
u
m
a
rty
a
g
i
@gm
a
i
l
.
c
o
m
3
Ab
strac
t
O
FD
M
(o
rth
o
g
o
n
a
l
fr
e
q
u
e
n
c
y
d
i
v
i
s
i
o
n
m
u
l
t
i
p
l
e
x
i
n
g
)
i
s
wi
d
e
l
y
u
s
e
d
i
n
4
th
g
e
n
e
ra
t
i
o
n
a
p
p
l
i
c
a
ti
o
n
s
o
win
g
to
i
ts
r
o
b
u
s
tn
e
s
s
i
n
f
a
d
i
n
g
e
n
v
i
ro
n
m
e
n
ts
.
Th
e
m
a
j
o
r
i
s
s
u
e
s
wit
h
O
FDM
s
y
s
te
m
s
i
s
th
e
h
i
g
h
PAPR
(p
e
a
k
-
to
-
a
v
e
ra
g
e
p
o
wer
ra
ti
o
)
o
f
th
e
tra
n
s
m
i
tt
e
d
s
i
g
n
a
l
s
,
i
t
l
e
a
d
s
t
o
i
n
a
n
d
o
u
t
o
f
b
a
n
d
d
i
s
to
r
ti
o
n
.
SL
M
(s
e
l
e
c
ti
v
e
m
a
p
p
i
n
g
)
a
n
d
PT
S
(p
a
rti
a
l
tra
n
s
m
i
t
s
e
q
u
e
n
c
e
)
a
r
e
two
k
e
y
m
e
th
o
d
s
fo
r
PAPR
re
d
u
c
ti
o
n
.
Bo
th
th
e
m
e
t
h
o
d
s
r
e
q
u
i
r
e
e
x
h
a
u
s
ti
v
e
s
e
a
rc
h
i
n
g
o
f
p
h
a
s
e
fa
c
to
rs
t
o
o
p
ti
m
i
z
e
th
e
PAPR
,
th
e
s
e
s
e
a
rc
h
e
s
l
e
a
d
t
o
h
i
g
h
c
o
m
p
u
ta
ti
o
n
a
l
c
o
m
p
l
e
x
i
t
y
.
Th
i
s
p
a
p
e
r
d
i
s
c
u
s
s
e
s
u
s
i
n
g
o
p
ti
m
i
z
a
ti
o
n
b
a
s
e
d
PAPR
r
e
d
u
c
ti
o
n
m
e
t
h
o
d
s
whi
c
h
a
n
b
e
u
s
e
d
wi
th
PTS
fo
r
th
e
re
d
u
c
ti
o
n
o
f
c
o
m
p
u
ta
ti
o
n
a
l
c
o
m
p
l
e
x
i
t
y
a
n
d
s
e
a
r
c
h
s
p
a
c
e
.
In
th
i
s
p
a
p
e
r
we
h
a
v
e
a
n
a
l
y
z
e
d
PTS
a
n
d
SL
M
wit
h
p
a
rti
c
l
e
s
warm
o
p
ti
m
i
z
a
ti
o
n
(PSO
),
Arti
fi
c
i
a
l
Be
e
Co
l
o
n
y
(ABC)
a
n
d
d
i
ff
e
r
e
n
ti
a
l
e
v
o
l
u
ti
o
n
(DE).
PA
PR a
n
d
BER (b
i
t
e
rr
o
r ra
te
)
c
o
m
p
a
ri
s
o
n
i
s
d
o
n
e
f
o
r
b
o
t
h
t
h
e
c
a
s
e
s
.
Key
w
ords
:
ABC, DE
,
PAPR
,
PTS,
PSO
Copy
righ
t
©
2
0
1
9
Uni
v
e
rsi
t
a
s
Ahm
a
d
D
a
hl
a
n.
All
rig
ht
s
r
e
s
e
rve
d
.
1.
Int
r
o
d
u
ctio
n
O
r
tho
go
na
l
f
r
eq
ue
nc
y
d
i
v
i
s
i
on
m
ul
ti
pl
ex
i
n
g
(
O
F
DM)
[1,
2]
i
s
a
m
ul
ti
c
arr
i
er
tr
an
s
m
i
s
s
i
on
m
eth
od
w
h
i
c
h
pl
a
y
s
an
i
m
po
r
tan
t
r
ol
e
i
n
ac
h
i
e
v
i
ng
h
i
g
h
d
ata
r
ate
i
n
4
th
g
en
erat
i
o
n
a
pp
l
i
c
at
i
on
s
.
In
O
F
DM
a
v
a
i
l
ab
l
e
b
an
d
wi
dth
i
s
d
i
v
i
de
d
i
n
t
o
na
r
r
o
w
ba
nd
c
h
an
ne
l
s
a
nd
ea
c
h
o
f
the
c
ha
nn
el
s
c
arr
y
a
s
ub
c
arr
i
er
l
ea
di
n
g
t
o
a
m
ul
ti
c
arr
i
er
s
y
s
tem
.
O
F
DM
ha
s
ga
i
ne
d
i
ts
p
op
ul
ar
i
t
y
o
wi
ng
to
i
ts
s
up
erla
t
i
v
e
pe
r
f
orm
an
c
e
i
n
the
f
ad
i
ng
e
nv
i
r
on
m
en
ts
.
Us
e
of
gu
ard
ba
nd
an
d
c
y
c
l
i
c
pref
i
x
i
n
O
F
DM
w
ork
s
w
el
l
ag
ai
n
s
t
m
en
ac
e
of
i
nte
r
s
y
m
bo
l
i
nt
erf
erenc
e
(
IS
I)
a
n
d
i
nt
er
-
c
arr
i
er
i
nte
r
f
erenc
e
(
ICI)
[
3].
Ho
wev
er
O
F
DM
i
s
l
arg
el
y
af
f
e
c
ted
b
y
prob
l
em
of
hi
gh
p
ea
k
to
a
v
era
ge
po
w
er
r
ati
o
(
P
A
P
R)
[
4].
W
h
e
n
O
F
DM
s
i
gn
a
l
i
s
tr
a
ns
m
i
tte
d
where
e
ac
h
of
the
s
u
bc
arr
i
er
i
s
di
f
f
erent m
od
ul
ate
d b
y
d
i
f
f
erent s
y
m
bo
l
s
i
t
m
i
gh
t l
ea
d
t
o h
i
gh
pe
ak
s
i
n
do
m
ai
n
w
h
en
a
nu
m
be
r
of
s
ub
c
ar
r
i
ers
a
l
i
gn
i
n
s
am
e p
ha
s
e.
T
he
s
e
h
i
gh
p
ea
k
s
l
ea
d t
o
h
i
g
h
po
w
er,
w
h
en
s
uc
h
O
F
DM
s
i
gn
al
are
f
ed
to
h
i
gh
p
o
w
er
a
m
pl
i
f
i
ers
(
HP
A
)
whi
c
h
are
em
pl
o
y
e
d
f
or
do
wnl
i
nk
p
urpos
e,
c
au
s
es
ha
r
m
on
i
c
di
s
tort
i
on
a
nd
i
nte
r
m
od
ul
at
i
on
.
T
hi
s
i
s
d
ue
t
o
no
n
l
i
ne
ar
c
ha
r
ac
ter
i
s
ti
c
s
o
f
H
P
A
.
T
o
m
a
k
e
s
ure
tha
t
HP
A
wor
k
s
i
n
the
l
i
ne
ar
r
eg
i
o
n
l
arge
b
ac
k
-
o
ff
i
s
r
eq
ui
r
ed
,
thi
s
r
ed
uc
es
ef
f
i
c
i
en
c
y
of
HP
A
.
T
he
r
e
are
nu
m
erous
m
eth
od
s
de
ta
i
l
ed
i
n
l
i
terat
ure
[
4]
f
or
P
A
P
R
r
ed
uc
ti
on
,
s
u
c
h
as
c
l
i
pp
i
n
g
w
h
ere
s
i
g
na
l
i
s
c
l
i
p
pe
d
of
f
be
y
on
d
a
c
ert
a
i
n
s
i
gn
a
l
l
ev
el
[
5],
us
i
ng
f
orw
ard
err
or
c
orr
ec
ti
on
c
od
es
[6,
7]
f
or
ge
ne
r
ati
ng
c
om
bi
na
ti
on
wi
t
h
l
o
wer
P
A
P
R,
t
on
e
i
nj
ec
ti
on
(
T
I)
[8,
9],
ton
e
r
es
erv
ati
on
(
T
R)
[10
,
11
]
where
ad
di
t
i
o
na
l
d
ata
bl
oc
k
an
d
po
wer
r
e
du
c
ti
o
n
c
arr
i
ers
are
us
ed
f
or
P
A
P
R
r
e
du
c
ti
on
,
c
om
pa
nd
i
n
g
r
ed
uc
es
P
A
P
R
b
y
c
om
pres
s
i
ng
the
h
i
gh
er
pe
ak
s
at
the
tr
an
s
m
i
tte
r
[12
,
1
3],
p
r
e
-
di
s
torti
on
an
d
DF
T
-
s
preadi
ng
are
s
o
m
e
of
th
e
pre
-
c
od
i
n
g
[
14
]
m
eth
od
f
or
P
A
P
R
r
e
du
c
ti
o
n,
ac
t
i
v
e
c
on
s
te
l
l
ati
on
ex
te
ns
i
on
[15
,
1
6]
us
es
ex
ten
s
i
on
of
ex
i
s
ti
ng
c
on
s
tel
l
at
i
on
wi
th
ou
t
af
f
ec
ti
ng
ac
tua
l
d
ata
.
A
l
l
of
the
a
bo
v
e
m
en
ti
on
m
eth
od
s
are
ei
th
er
r
es
ul
t
i
n
to
d
i
s
tort
i
on
or
r
eq
u
i
r
es
hi
g
h
p
o
w
er
tr
an
s
m
i
s
s
i
on
.
Mu
l
ti
pl
e
s
i
g
na
l
r
e
pres
en
t
ati
on
m
eth
o
d
s
uc
h
as
s
el
ec
ted
m
ap
pi
ng
(
S
L
M)
[1
7
,
18
]
an
d
p
arti
a
l
tr
a
ns
m
i
t
s
eq
ue
nc
es
(
P
T
S
)
[19
-
2
1]
ar
e
m
os
t
s
ou
gh
t
c
ho
i
c
es
f
or
P
A
P
R
r
ed
uc
t
i
o
n
as
th
e
r
es
u
l
ta
nt
s
i
g
na
l
d
o
es
no
t
ha
v
e
an
y
d
i
s
torti
on
.
S
LM
pe
r
f
orms
be
tte
r
i
n
t
erm
s
of
P
A
P
R
r
ed
uc
ti
on
b
ut
P
T
S
i
s
pref
err
ed
ov
er
i
t
o
wi
ng
to
l
es
s
c
o
m
pu
tat
i
on
a
l
c
o
m
pl
ex
i
t
y
.
I
n
c
o
nv
en
t
i
on
al
P
T
S
i
np
ut
d
ata
s
et
i
s
s
ub
d
i
v
i
de
d
i
n
to
un
c
orr
e
l
ate
d
s
u
b
-
bl
oc
k
s
,
af
ter
proc
es
s
i
ng
th
es
es
s
ub
-
bl
o
c
k
s
throug
h
Inv
ers
e
F
as
t
F
o
urie
r
T
r
an
s
f
or
m
s
(
IFF
T
)
e
ac
h
of
the
m
i
s
m
ul
ti
pl
i
ed
b
y
a
p
ha
s
e
f
ac
t
or
an
d
f
i
n
al
l
y
th
e
y
are
s
u
m
m
ed
up
t
o
ge
n
erate
O
F
DM
c
an
di
da
t
e,
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
be
r
20
19
:
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8
3
-
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e
v
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t
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a
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th
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s
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s
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o
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i
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um
ph
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e
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c
es
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v
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c
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s
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eq
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r
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e
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o
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g
h c
om
pu
t
ati
o
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om
p
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i
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In
th
i
s
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w
e
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i
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T
S
[2
2].
S
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on
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be
r
of
s
ea
r
c
he
s
w
i
l
l
l
ea
d
to
l
o
wer
c
om
pu
tat
i
o
na
l
c
om
pl
e
x
i
t
y
[23
]
.
B
y
us
i
ng
op
t
i
m
i
z
a
ti
on
tec
h
ni
qu
es
nu
m
be
r
of
r
eq
ui
r
ed
s
ea
r
c
he
s
c
an
be
r
ed
uc
ed
.
S
om
e
o
f
the
ex
c
es
s
i
v
el
y
us
ed
m
eth
od
s
are
G
en
et
i
c
A
l
go
r
i
t
hm
(
G
A
)
[24
,
25
],
P
art
i
c
l
e
S
war
m
O
pti
m
i
z
at
i
o
n
(
P
S
O
)
[26
],
A
r
t
i
f
i
c
i
al
B
ee
C
ol
o
n
y
(
A
B
C)
[2
7
,
2
8],
B
i
og
eo
gra
ph
y
B
as
e
d
O
pti
m
i
z
ati
on
(
B
B
O
)
[29
]
a
nd
di
f
f
erenti
a
l
ev
o
l
ut
i
o
n
(
DE
)
[
30
]
.
2.
P
ea
k to
A
v
e
r
age
P
o
w
er
Ratio
in
O
F
DM
S
ys
t
ems
A
n OF
DM
s
i
gn
al
wi
t
h
N
-
s
u
bc
arr
i
er i
s
r
ep
r
es
en
te
d a
s
(
)
=
1
√
∑
−
1
=
0
.
e
xp
(
.
2
.
.
.
)
(
1)
w
he
r
e
N
i
s
the
n
um
be
r
of
s
ub
c
arr
i
ers
i
.
e
(
k
=
0
,1…
.N
-
1
)
an
d
X
k
i
s
th
e
s
y
m
b
ol
m
od
ul
ati
ng
the
k
th
s
ub
c
arr
i
er.
IFF
T
s
um
i
n
O
F
DM
m
a
y
r
es
u
l
ts
i
n
to
l
arg
e
en
v
el
o
pe
p
ea
k
s
i
n
ti
m
e
do
m
ai
n.
T
hi
s
r
es
ul
ts
i
n
to
hi
gh
pe
a
k
to
av
erage
p
o
w
er
r
ati
o.
P
ea
k
to
a
v
erag
e
po
w
er
r
at
i
o
i
s
t
he
r
ati
on
pe
ak
po
wer
of
th
e
O
F
D
M
s
i
gn
al
to
th
e
a
v
er
ag
e
p
o
w
er
of
the
c
arr
i
er.
P
A
P
R
f
or
a
n
O
F
DM
s
i
g
na
l
x
i
s
gi
v
e
n a
s
:
(
)
=
m
ax
0
≤
≤
−
1
|
|
2
/
{
|
|
2
}
(
2)
w
he
r
e
|
|
the
m
ag
ni
t
ud
e
a
nd
E
i
s
r
ep
r
es
e
nti
ng
th
e
ex
pe
c
tat
i
on
op
erator.
T
o
ev
a
l
u
ate
P
A
P
R
r
ed
uc
ti
o
n
pe
r
f
or
m
an
c
e
of
a
m
eth
od
c
om
pl
em
en
tar
y
c
um
ul
ati
v
e
f
un
c
ti
on
i
s
us
ed
as
a
pe
r
f
or
m
an
c
e
i
nd
ex
.
CC
DF
r
ep
r
es
en
ts
the
proba
b
i
l
i
t
y
t
ha
t
s
i
gn
a
l
l
ev
el
wi
l
l
r
em
ai
n
ab
ov
e
a p
art
i
c
ul
ar l
e
v
e
l
, p
o
w
er
l
e
v
el
i
n c
as
e
of
P
A
P
R. C
DF
c
an
b
e repres
e
nte
d
as
=
Pr
(
>
0
)
(
3)
3.
M
u
lt
iple S
ign
al
Rep
r
es
ent
atio
n
M
eth
o
d
s
In
s
uc
h
m
eth
od
s
am
e
s
et
of
da
ta
i
s
r
ep
r
es
e
nte
d
b
y
a
s
et
of
O
F
DM
c
an
di
da
te
s
i
gn
a
l
s
whi
c
h
ar
e
ge
ne
r
at
ed
wi
th
t
he
he
l
p
of
di
f
f
erent
ph
as
e
s
ets
.
T
he
c
an
di
d
ate
wi
th
l
ea
s
t
P
A
P
R
i
s
tr
an
s
m
i
tte
d.
T
he
t
w
o
wi
d
el
y
us
ed
m
eth
od
s
are
S
L
M a
n
d P
T
S
.
3.1
.
S
L
M
S
el
ec
ted
m
ap
pi
n
g
[19
-
2
2]
s
c
he
m
e
i
s
s
ho
w
n
i
n
F
i
g
ure
1.
T
he
i
np
ut
s
y
m
bo
l
s
are
m
ul
ti
pl
i
ed
wi
th
a
s
et
of
ph
as
e
v
ec
tors
an
d
af
ter
IFF
T
bl
oc
k
m
ul
ti
pl
e
O
F
D
M
s
i
gn
a
l
c
an
di
d
ate
s
r
ep
r
es
en
t
i
ng
th
e
s
am
e
d
at
a
s
et
are
pro
du
c
ed
t
he
n
o
ne
wi
t
h
t
he
l
ea
s
t
P
A
P
R
i
s
c
ho
s
en
f
or
f
i
n
al
tr
an
s
m
i
s
s
i
on
.
T
hi
s
al
s
o
r
e
q
ui
r
es
tr
an
s
m
i
s
s
i
on
of
s
i
d
e
i
nf
or
m
ati
on
f
or
err
or
f
r
ee
r
ec
o
v
er
y
of
O
F
DM s
y
m
bo
l
s
.
F
i
gu
r
e
1.
O
F
DM
s
y
s
tem
w
i
t
h S
L
M t
ec
hn
i
qu
e
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
P
A
P
R a
na
l
y
s
i
s
of
O
F
D
M
s
y
s
tem
us
i
ng
A
I b
as
ed
mu
l
ti
pl
e s
i
gn
al
.
.. (
J
y
oti
S
hu
k
l
a
)
2985
E
v
er
y
da
ta
b
l
oc
k
i
s
m
ul
ti
p
l
i
ed
b
y
U
ph
as
e
s
eq
ue
nc
es
,
wi
th
ea
c
h
bl
oc
k
of
eq
ua
l
s
i
z
e
N
,
the
ph
as
e
f
ac
tor
(
)
=
[
,
0
,
,
1
,
…
,
,
−
1
]
,
w
h
er
e
u
=
1,2
…U,
an
d
,
=
,
an
d
,
∈
[
0
,
2
)
f
or
v
=
0,
1…
.
N
-
1.
T
hi
s
r
es
ul
ta
nt
s
i
gn
a
l
i
s
:
=
,
(
4)
af
ter
tak
i
ng
i
ts
IFF
T
the
v
ario
us
O
F
DM
s
eq
u
en
c
e
g
et
ge
n
erate
d
am
on
g
w
h
i
c
h
̃
=
̃
,
wi
th
l
o
w
es
t
P
A
P
R
i
s
s
el
ec
ted
f
o
r
trans
m
i
s
s
i
on
.
̃
=
arg
m
i
n
=
1
,
2
,
…
,
(
m
ax
|
[
]
|
)
(
5
)
3.2
.
P
T
S
F
i
gu
r
e
2
s
h
o
w
s
t
y
p
i
c
a
l
P
T
S
s
c
he
m
e.
T
he
da
ta
s
eq
ue
nc
e
i
s
s
pl
i
t
i
n
t
o
s
ub
bl
oc
k
s
of
eq
ua
l
l
en
gt
h
.
T
he
n
s
ub
bl
oc
k
s
are
m
ul
ti
pl
i
ed
wi
th
u
ni
q
ue
ph
as
e
v
ec
tor
.
Res
u
l
ti
ng
i
n
to
m
ul
ti
pl
e OF
D
M c
an
di
d
ate
s
f
or di
f
f
erent p
ha
s
e c
om
bi
na
ti
on
, e
ac
h
of
th
em
i
s
gi
v
en
b
y
(
6
)
:
=
∑
.
−
1
=
0
(
6
)
w
he
r
e
=
[
]
,
wi
th
J
z
ph
as
e
wei
g
hts
tot
a
l
nu
m
be
r
of
ph
as
e
wei
g
hts
w
hi
c
h
ne
e
d
to
b
e
an
a
l
y
z
e
d a
r
e
J
V
-
1
, a
s
f
or the
f
i
r
s
t s
ub
bl
oc
k
th
e
p
ha
s
e f
a
c
tor i
s
us
ua
l
l
y
c
h
os
en
as
1.
T
he
op
ti
m
u
m
ph
as
e f
ac
tor i
s
t
he
on
e
whi
c
h p
r
od
uc
es
m
i
ni
m
u
m
P
A
P
R of
c
an
di
da
te
s
i
gn
al
x
’
as
gi
v
en
b
y
(
7)
:
[
1
̃
,
…
,
̃
]
=
a
r
g
min
[
1
,
…
…
…
.
]
(
ma
x
=
0
,
1
…
−
1
|
∑
[
]
=
1
|
)
(
7
)
F
i
gu
r
e
2.
O
F
DM
s
y
s
tem
s
us
i
ng
P
T
S
3.
3
. Com
p
l
ex
C
o
mp
u
t
atio
n
s i
n
P
T
S
F
or
V
s
u
b
-
bl
oc
k
s
an
d
J
-
ph
a
s
e
w
ei
gh
ts
,
J
V
-
1
po
s
s
i
bl
e
ph
as
e c
om
bi
na
ti
on
is
s
ea
r
c
he
d a
n
d
an
a
l
y
s
e
d
w
h
i
c
h
r
es
u
l
ts
i
n
t
o
s
am
e
nu
m
be
r
of
P
T
S
c
an
di
da
tes
are
g
en
er
ate
d
.
F
o
r
N
-
po
i
nt
IFF
T
op
erat
i
o
ns
(
N
-
s
ub
c
arr
i
er O
F
DM)
:
Com
pl
ex
ad
d
i
ti
on
:
l
og
2
an
d
m
ul
ti
p
l
i
c
at
i
on
s
(
/
2
)
.
l
og
2
(
8
)
f
or
an
ov
ers
a
mp
l
i
n
g
f
a
c
tor
of
R,
F
ac
tor
of
N
w
i
l
l
be
r
ep
l
ac
ed
b
y
N.R.
In
ge
ne
r
ati
on
of
P
T
S
c
an
di
da
tes
ad
d
i
ti
on
al
×
−
1
×
(
−
1
)
m
ul
ti
pl
i
c
a
ti
o
ns
an
d a
d
di
ti
o
ns
w
i
l
l
be
r
eq
ui
r
e
d.
S
o,
Ove
r
a
l
l
c
omp
l
e
x
a
ddit
ion
s
=
.
.
l
og
2
+
.
×
−
1
×
(
−
1
)
Ove
r
a
l
l
c
omp
l
e
x
mul
itp
l
ic
a
tion
s
=
.
.
(
/
2
)
l
og
2
+
.
×
−
1
×
(
−
1
)
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
be
r
20
19
:
29
8
3
-
2991
2986
If
we
c
an
r
ed
uc
e
the
nu
m
be
r
of
s
e
arc
he
s
fr
om
J
V
-
1
,
the
n
um
b
er
of
c
o
mp
u
tat
i
on
s
r
eq
ui
r
e
d
wi
l
l
al
s
o red
uc
e.
O
pt
i
m
i
z
at
i
on
me
th
od
s
c
an
be
us
ed
t
o s
e
r
v
e t
he
p
urpos
e.
4.
M
u
lt
iple
O
p
t
imiz
atio
n
M
et
h
o
d
s
b
as
ed P
T
S
Us
i
ng
op
t
i
m
i
z
ati
on
m
eth
od
s
,
we
c
an
pu
t
a
c
ap
on
t
he
s
ea
r
c
h
es
r
eq
u
i
r
ed
an
d
thu
s
ov
era
l
l
c
om
pu
tat
i
on
al
c
om
pl
ex
i
t
y
of
P
T
S
s
y
s
t
em
s
.
In
thi
s
pa
p
er
we
us
ed
A
B
C,
P
S
O
,
DE
an
d
G
A
m
eth
od
f
or r
ed
uc
ti
on
of
nu
m
be
r
of
s
ea
r
c
he
s
.
4.1
.
P
a
r
t
icl
e
S
w
ar
m O
p
t
i
miz
atio
n
A
lgo
r
it
h
m
(
P
S
O
)
-
P
T
S
T
he
m
eth
od
l
a
be
l
s
the
p
o
pu
l
ati
on
as
s
w
arm
an
d
ea
c
h
i
nd
i
v
i
d
ua
l
i
s
c
al
l
ed
a
p
arti
c
l
e.
T
he
t
y
p
i
c
al
f
l
o
w
c
ha
r
t
f
or
th
e
a
l
go
r
i
thm
i
s
s
ho
w
n
i
n
F
i
g
ure
3.
P
S
O
-
P
T
S
tec
h
ni
q
ue
i
s
i
m
pl
em
en
ted
b
y
c
ha
n
gi
ng
ph
as
e
f
ac
tor
c
om
bi
na
ti
o
n
b
v
whi
c
h
us
e
d
as
po
s
i
ti
on
v
ec
tor.
E
ac
h
P
T
S
c
an
di
da
t
e
x
i
s
c
on
s
i
de
r
e
d
as
a
pa
r
ti
c
l
e
wi
th
p
os
i
ti
on
v
ec
tor,
b
v
(
v
=
0,1
….
V
-
1)
al
on
g
wi
th
th
e
v
el
oc
i
t
y
v
ec
tor
i
s
c
ha
ng
e
d
i
s
c
ha
ng
ed
to
g
et
a
ne
w
s
ol
ut
i
o
n
or
P
T
S
c
an
di
da
te
.
A
tr
ue
s
ol
uti
on
i
s
the
on
e
whi
c
h
us
i
ng
b
v
ac
hi
ev
es
de
s
i
r
ed
r
el
at
i
o
n b
et
w
e
en
an
d
l
oc
al
a
nd
g
l
o
ba
l
o
bj
ec
t
i
v
e o
f
th
e a
l
go
r
i
thm
. p
be
s
t
an
d
g
be
s
t
are
P
A
P
R
v
a
l
ue
s
f
or
a
s
et
of
b
v
.
T
he
i
terati
on
s
en
d
when
bo
t
h
the
v
ar
i
ab
l
e
ac
h
i
e
v
es
the
pre
-
de
c
i
d
ed
P
A
P
R
thre
s
ho
l
d.
T
he
ne
w
v
e
l
oc
i
t
y
f
or
i
th
pa
r
ti
c
l
e
i
s
gi
v
e
n
b
y
:
(
+
1
)
=
.
(
)
+
1
.
1
.
(
(
)
−
(
)
)
+
2
.
2
(
(
)
−
(
)
)
(
10
)
w
he
r
e
a
1
an
d
a
2
are
ac
c
el
e
r
ati
on
f
ac
tors
an
d
c
1
, c
2
ar
e
un
i
f
orm
l
y
di
s
tr
i
bu
t
ed
r
.v
i
n [
0,1
]
an
d
z
i
s
r
ep
r
es
en
t
i
ng
the
v
e
l
oc
i
t
y
.
N
e
w
po
s
i
ti
on
wi
l
l
b
e:
,
(
+
1
)
=
,
(
)
+
(
+
1
)
(1
1
)
F
i
gu
r
e
3.
F
l
o
w
c
ha
r
t f
or P
S
O
al
g
orit
hm
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
P
A
P
R a
na
l
y
s
i
s
of
O
F
D
M
s
y
s
tem
us
i
ng
A
I b
as
ed
mu
l
ti
pl
e s
i
gn
al
.
.. (
J
y
oti
S
hu
k
l
a
)
2987
4.
2
.
P
a
r
t
icl
e
A
r
t
if
ici
al
B
ee
Co
lon
y (
A
BC)
-
P
T
S
T
he
al
go
r
i
thm
c
on
tai
ns
thr
ee
d
i
s
s
i
m
i
l
ar
groups
of
b
ee
s
:
“
em
pl
o
y
e
d
be
es
”
,
“
on
l
o
ok
er
be
es
”
an
d
“
s
c
ou
t
b
ee
s
”
.
T
he
di
f
f
erent
s
ou
r
c
es
he
r
e
are
m
e
m
be
r
o
f
s
ol
uti
on
s
p
ac
e
an
d
ne
c
tar
r
ep
r
es
en
ts
f
i
tne
s
s
.
A
c
c
ordi
ng
t
o
th
i
s
a
l
go
r
i
thm
i
ni
t
i
a
l
l
y
a
r
a
nd
om
l
y
d
i
s
tr
i
b
ute
d
po
pu
l
at
i
o
n
i
s
ge
ne
r
ate
d
w
h
i
c
h
r
ep
r
es
e
nt
the
em
pl
o
y
ed
be
es
.
T
he
e
m
pl
o
y
ed
be
es
ex
ec
ute
v
ar
i
ou
s
op
erati
on
s
wi
th
the
n
ei
g
hb
orhoo
d
v
a
l
u
es
i
n
s
ee
k
i
ng
the
be
s
t
v
al
u
e.
If
th
e
s
o
l
ut
i
on
i
n
th
e
v
i
c
i
ni
t
y
i
s
he
al
t
hi
er
tha
n
the
i
n
i
ti
al
l
y
r
ec
ei
v
e
d
on
e,
the
ne
w
s
ol
u
ti
o
n
i
s
a
l
l
oc
a
ted
i
n
pl
ac
e
of
the
f
i
r
s
t
on
e.
W
he
n
the
en
t
i
r
e
s
ea
r
c
h
proc
es
s
o
f
the
em
pl
o
y
e
d
be
e
i
s
c
on
c
l
ud
ed
,
t
he
y
di
s
tr
i
bu
te
t
hi
s
i
nf
orm
ati
on
wi
th
the
ne
x
t
s
et
of
be
es
i
.
e.
“
on
l
oo
k
er
be
es
.
T
he
em
pl
oy
e
d
be
e
t
urns
to
war
ds
t
he
f
oo
d
s
ou
r
c
e.
T
he
go
a
l
i
s
to
d
i
s
c
ov
er
a
ph
as
e
v
ec
tor
w
i
t
h
ex
tr
e
m
e
f
i
tne
s
s
v
al
ue
;
the
f
i
tn
es
s
f
un
c
ti
on
i
s
gi
v
en
b
y
:
(
)
=
1
1
+
(
)
⁄
(
10
)
w
he
r
e
x
j
i
s
the
s
ol
ut
i
o
n
pri
m
ed
i
n
c
on
ti
nu
o
us
s
pa
c
e
an
d
th
en
tr
an
s
f
orm
ed
i
nto
di
s
c
r
ete
ph
as
e
v
ec
tor
s
pa
c
e.
A
l
s
o,
f
(
x
j
)
r
ep
r
es
en
ts
the
P
A
P
R
v
al
u
e.
W
h
en
ev
er
f
i
tne
s
s
i
s
hi
gh
,
P
A
P
R
ha
s
a
l
o
w
v
a
l
ue
.
A
c
orr
es
po
nd
i
n
g f
i
tn
es
s
v
al
ue
of
th
e
ph
as
e
v
ec
t
ors
are c
al
c
u
l
at
ed
,
i
f
th
e
ol
d
v
a
l
ue
i
s
l
o
wer
tha
n
th
e
ne
w
v
a
l
ue
,
t
he
n
t
he
be
e
m
e
m
ori
z
es
the
n
e
w
p
ha
s
e
v
al
u
e.
T
he
ne
w
p
ha
s
e
v
ec
t
or
i
s
c
ho
s
en
b
y
:
=
+
(
−
)
(1
1
)
w
he
r
e
α
j
i
s
a
r
an
d
om
nu
m
be
r
ge
ne
r
ate
d
i
n
th
e
r
a
ng
e
[
-
1,
1],
a
nd
x
p
i
s
the
s
ol
ut
i
on
wi
th
i
n
the
n
ei
gh
b
orho
od
of
x
j
th
e
f
i
tne
s
s
v
a
l
ue
i
s
t
he
n
po
ol
e
d
b
y
th
e
o
nl
oo
k
er
be
es
,
wh
en
th
e
wor
k
o
f
em
pl
o
y
ed
b
ee
s
i
s
f
i
ni
s
he
d.
O
nl
o
ok
er
be
es
m
ov
e
to
w
ards
ne
w
f
oo
d
s
ou
r
c
es
,
ba
s
ed
on
the
k
no
w
l
e
dg
e
pro
v
i
de
d
to
t
he
m
b
y
em
pl
o
y
e
d b
ee
s
, th
r
ou
gh
a
f
orm
ul
a:
=
(
)
∑
(
)
=
1
⁄
(1
2
)
t
he
o
nl
oo
k
er
be
e
d
em
ea
no
r
s
a
s
ea
r
c
h
i
n
the
ne
i
gh
bo
r
h
oo
d
of
the
f
oo
d
s
ou
r
c
e
c
h
o
s
en
b
y
(
12
)
t
i
l
l
the
t
hres
ho
l
d
v
a
l
ue
.
A
B
C
-
P
T
S
i
m
pl
e
m
en
tat
i
o
n
i
s
s
h
o
wn i
n
Fig
ure
4.
F
i
na
l
l
y
,
when
t
he
on
l
oo
k
er
be
es
ac
c
om
pl
i
s
h
th
ei
r
tas
k
,
the
em
pl
o
y
ed
be
es
tr
a
ns
form
to
s
c
ou
t b
ee
s
,
i
n
order
t
o s
ee
k
ne
w
f
oo
d s
o
urc
es
r
an
do
m
l
y
, b
y
t
he
f
ol
l
o
wi
ng
f
or
m
ul
a:
=
min
(
)
+
(
0
,
1
)
∗
(
ma
x
(
)
−
min
(
)
)
(1
6
)
where, ra
nd
(
0
,1) i
s
t
he
r
a
n
do
m
nu
m
be
r
wi
th
a u
ni
f
orm
di
s
tr
i
b
uti
on
.
4.
3.
D
if
f
er
ent
ial
E
v
o
lut
ion
(
DE
)
-
P
T
S
T
he
DE
tec
hn
i
q
ue
t
w
i
tc
he
s
wi
th
a
n
i
n
i
ti
al
s
ol
uti
on
s
et.
T
he
DE
proc
es
s
us
ua
l
l
y
t
hree
c
hi
ef
proc
es
s
es
:
i
ni
ti
a
l
i
z
a
ti
o
n,
m
uta
ti
on
o
pe
r
at
i
o
n,
c
r
os
s
ov
er
op
erat
i
on
,
an
d
s
e
l
ec
t
i
on
op
erat
i
o
n.
DE
i
s
i
m
pl
em
ented as
per
f
ol
l
o
w
i
ng
bl
oc
k
dia
gr
am
s
hown
i
n F
i
g
ur
e 5
.
5
.
S
i
mu
latio
n
s a
n
d
Result
s
T
he
s
i
m
ul
ati
on
s
ha
s
be
en
c
arr
i
ed
ou
t
i
n
MA
T
LA
B
f
or
N=
12
8
f
or
V
=
8
s
u
b
b
l
oc
k
s
an
d
4
ph
as
e
wei
g
hts
{
1
,
,
−
1
,
−
}
.
Ma
pp
i
ng
s
c
he
m
e
us
ed
i
s
B
P
S
K
,
10
00
O
F
DM
s
y
m
bo
l
s
ha
v
e
be
en
us
ed
f
or
s
i
m
ul
ati
on
s
.
R
a
y
l
i
gh
f
ad
i
ng
c
ha
nn
e
l
i
s
u
s
ed
wi
th
4
ta
ps
f
or
B
E
R
c
al
c
ul
at
i
o
ns
.
F
i
gu
r
e
6
(
a)
s
ho
w
s
P
A
P
R
r
ed
uc
ti
on
c
a
pa
b
i
l
i
t
i
es
of
P
T
S
,
A
B
C
-
P
T
S
a
nd
P
S
O
-
P
T
S
i
n
ter
m
s
of
CCDF
.
It
c
l
ea
r
l
y
s
ho
w
s
tha
t
A
B
C
a
nd
P
S
O
-
P
T
S
pe
r
f
or
m
s
be
tte
r
tha
n
c
on
v
en
ti
o
na
l
o
ne
.
T
he
P
A
P
R
v
al
ue
s
f
or
A
B
C
-
P
T
S
are
i
n
t
he
r
an
g
e
of
4
-
7
dB
wher
e
as
f
or
P
S
O
-
P
T
S
v
al
u
e
m
a
y
go
up
to
9
d
B
as
c
om
pa
r
ed
to
>
1
0
dB
f
or
P
T
S
.
F
i
gu
r
e
6
(
b)
c
o
m
pa
r
es
the
P
A
P
R
r
e
du
c
ti
on
pe
r
f
or
m
an
c
e
of
S
LM
,
A
B
C
-
S
LM
an
d
P
S
O
-
S
L
M.
A
ga
i
n,
th
e
CCDF
c
ur
v
es
are
pl
ott
ed
i
t
i
m
pl
i
es
tha
t,
th
e
P
A
P
R
v
al
ue
s
f
or
A
B
C
-
S
LM
ar
e
i
n
th
e
r
a
ng
e
of
4
-
6
.8
d
B
where
as
f
or
P
S
O
-
S
L
M
v
a
l
ue
m
ay
go
up
t
o 7
.
8 d
B
as
c
o
m
pa
r
ed
to
9.
4
dB
f
or S
LM
.
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
be
r
20
19
:
29
8
3
-
2991
2988
F
i
gu
r
e
4.
Im
pl
em
en
ti
ng
A
B
C
-
P
T
S
al
g
o
r
i
t
hm
F
i
gu
r
e
5.
Im
pl
em
en
ti
ng
DE
al
g
orit
hm
F
i
gu
r
e
s
7
(
a)
an
d
(
b)
s
ho
w
s
B
E
R
pe
r
f
orm
an
c
e
of
A
B
C
a
nd
P
S
O
i
n
S
LM
a
n
d
P
T
S
O
F
DM
s
y
s
t
em
s
B
E
R
c
urv
e
s
s
ho
w
s
i
m
i
l
ar
pe
r
f
or
m
an
c
e
an
d
tr
e
nd
S
LM
an
d
P
T
S
ho
w
e
v
er
A
B
C
r
es
ul
ts
i
n
to
be
tt
er
B
E
R
v
al
u
e
th
an
P
S
O
.
O
v
era
l
l
,
we
c
an
s
a
y
t
ha
t
P
A
P
R
p
erf
or
m
an
c
es
o
f
the
op
t
i
m
i
z
ati
on
-
ba
s
e
d
m
eth
od
s
ar
e
g
oo
d
e
no
u
gh
i
n
prac
ti
c
al
s
c
en
ari
os
.
T
ab
l
e
1
s
um
m
ariz
es
the
r
es
ul
t
of
a
bo
v
e
s
tud
y
f
or
P
T
S
i
t
c
l
e
arl
y
s
h
o
w
s
th
at
f
or
l
o
w
er
nu
m
be
r
of
i
ter
ati
o
ns
s
i
m
i
l
ar
P
A
P
R p
erf
or
m
an
c
e c
an
be
ac
hi
e
v
e
d.
T
h
i
s
w
i
l
l
l
e
ad
t
o r
ed
uc
ti
on
i
n c
om
pl
ex
i
t
y
.
Redu
c
t
i
on
i
n
i
tera
ti
o
ns
wi
l
l
r
ed
uc
e
th
e
nu
m
be
r
of
c
o
m
pl
ex
ad
d
i
t
i
o
ns
an
d
m
ul
ti
pl
i
c
a
ti
o
ns
e.g
.:
F
or
4
s
ub
-
bl
oc
k
s
an
d
4
p
ha
s
e
w
ei
g
hts
nu
m
be
r
of
c
o
m
pl
ex
m
ul
ti
pl
i
c
a
ti
o
ns
wi
l
l
be
=
4
(4
-
1)
×
3
=
1
92
.
S
i
m
i
l
arl
y
,
nu
m
be
r
of
c
om
pl
ex
m
ul
ti
pl
i
c
ati
on
s
wi
l
l
be
=
19
2
.
H
o
w
e
v
er,
the
s
es
v
a
l
u
es
wi
l
l
r
ed
uc
e
to
18
a
nd
9
9
f
or
A
B
C
a
nd
DE
ba
s
e
d
P
T
S
m
eth
od
s
.
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Ref
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[1
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Evaluation Warning : The document was created with Spire.PDF for Python.