Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
5
,
No
. 3,
J
une
2
0
1
5
,
pp
. 42
9~
43
5
I
S
SN
: 208
8-8
7
0
8
4
29
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Automatic Modulation Recognition for MFSK Using Modified
Covari
ance Met
h
od
H
a
na
n M.
Hamee
*
, Ja
f
e
r
Wa
d
i
**
*Departem
e
nt
of
El
ectr
i
c
a
l
Engin
eering
,
B
a
s
r
a Un
ivers
i
t
y
,
Ir
aq
** Departement
of Electron
i
c En
gin
eer
ing, Bagh
dad University
, I
r
aq
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 19, 2015
Rev
i
sed
Mar
28
, 20
15
Accepted Apr 14, 2015
This paper
presents modulation
classi
fication method capab
l
e of
classif
y
in
g
MFSK digital signals without a priori
informatio
n using modified covarian
ce
method. This
method using for calcu
lation f
eatur
es for FSK modulation
should have a g
ood propert
ies o
f
sens
itiv
e with
FSK m
odulation index
and
insensitive with
signal to noise ratio SNR
varia
tion. Th
e
num
erica
l
sim
u
lations and
invest
igat
ion o
f
th
e performan
ce b
y
th
e supp
ort vectors
machine one against all (SVM
-OAA) as a classifier fo
r classify
ing 6 digitally
modulated signals which gi
ves p
r
obability
of cor
r
ect
ion classification up to
85.85 at SNR=-1
5dB.
Keyword:
AM
R
Aut
o
m
a
ti
c m
odul
at
i
o
n
FSK
m
odul
at
i
o
n
M
odi
fi
e
d
c
ova
ri
ance m
e
t
hod
SVM
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Hana
n M
.
Ha
m
ee,
Depa
rtem
ent of Electrical E
n
gine
ering
,
Basra Un
iv
ersity, Iraq
.
Em
a
il: saraen
g7
3@yahoo
.com
1.
INTRODUCTION
Aut
o
m
a
tic Modulation Recognition (A
MR) is a technique
that recognize
s the type of t
h
e receive
d
sig
n
a
l.
AMR
plays an
im
p
o
r
tan
t
ro
le in
v
a
ri
o
u
s
app
licatio
ns. Fo
r ex
am
p
l
e, in
m
ili
tary ap
p
licatio
n
s
, it can
b
e
e
m
p
l
o
y
ed
f
o
r
electr
o
n
i
c
sur
v
eillan
ce, interference recogn
ition and m
onitoring, while in
civilian applications
i
n
cl
udes spect
rum
m
a
nagem
e
nt
, net
w
or
k t
r
affi
c a
d
m
i
ni
st
rati
on, si
g
n
al
con
f
i
r
m
a
t
i
on,
soft
wa
re
radi
os,
in
tel
lig
en
t
m
o
d
e
m
s
, etc. [1
]. Au
to
m
a
t
i
c d
i
g
i
tal sig
n
a
l reco
g
n
itio
n
tech
n
i
qu
es u
s
u
a
lly are
categ
o
r
ized
in two
m
a
i
n
pri
n
ci
pl
es:
t
h
e deci
si
on t
h
eoret
i
c
(DT) t
echni
ques and t
h
e pat
t
e
rn
recogni
t
i
on (
P
R
)
t
echni
que
s. DT
tech
n
i
q
u
e
s u
s
e
p
r
ob
ab
ilistic an
d
h
ypo
th
esis te
stin
g
arg
u
m
en
t
s
to
fo
rm
u
l
ate
t
h
e recog
n
itio
n
p
r
ob
le
m
.
Th
e maj
o
r
draw
backs
of
DT t
echni
ques
are t
h
ei
r hi
g
h
com
put
at
i
onal
co
m
p
l
e
xi
ty
, l
ack of r
o
b
u
s
t
n
ess t
o
t
h
e m
odel
mis
m
a
t
ch as well as
the need for
a careful
analysis. W
h
ereas the
P
R
appr
oac
h
d
o
es
n
o
t
nee
d
s
u
ch c
a
ref
u
l
t
r
eatm
e
nt
s si
n
ce t
h
ey
are
e
a
si
l
y
im
pl
em
ent
e
d.
PR
t
e
c
h
ni
q
u
es ca
n
be
f
u
rt
he
r
di
vi
d
e
d i
n
t
o
t
w
o
m
a
i
n
subsystem
s
: th
e feature e
x
tra
c
tion and the c
l
assifier [2
]. T
h
e basic probl
e
m
in PR approach a
r
e how
can be
find the
features that be
s
u
itable for the si
gnal i
n
orde
r to
recog
a
n
i
ze th
is sign
al later. So
th
is
p
a
p
e
r g
i
v
e
s
apr
o
posal
m
e
tho
d
t
o
cl
assi
f
y
M
FSK
by
e
s
t
i
m
a
ti
on t
h
e
po
we
r s
p
ect
ral
de
nsi
t
y
usi
n
g
m
odi
fi
ed c
o
v
a
ri
ance
app
r
oach
whi
c
h i
t
consi
d
e
r
d
as a t
ool
t
o
cal
cul
a
t
e
feat
ure
vect
o
r
s w
h
ere
t
h
i
s
m
e
t
hod p
r
o
v
i
d
e feat
ures
t
h
at
have
a l
o
t
o
f
s
e
parat
i
o
n
bet
w
een si
gnal
s
t
o
be
reco
ga
ni
zed
as s
h
ow
l
a
t
e
r.
In the last years ago s
u
pport vect
or m
achine SVM was one the techni
que that used as classification
tools so, it used here as a classifi
er. (S
VM
s) base
d o
n
st
at
i
s
t
i
cal l
earni
ng t
h
e
o
ry
,
hav
e
been em
pl
oy
ed fo
r
application in the a
r
ea
of
patte
rn rec
o
gnition
because
of t
h
ei
r e
x
cellent ge
neralization ca
pabilities [3].
The pa
pe
r is orga
nized as fol
l
ows: In Section 2,
we will describe MFS
K
m
odulation signal m
odel.
The m
a
the
m
atical approac
h
es
for m
odified c
ova
riance m
e
tho
d
i
n
Sect
i
o
n
3 The cl
assi
fi
er ap
pr
oac
h
gi
ven
i
n
sect
i
on 4 t
h
e
dat
a
anal
y
s
i
s
sho
w
n i
n
sect
i
on
5, o
u
r
res
u
l
t
and di
scus
si
on i
s
o
ffe
red
i
n
Sect
i
on 6
f
i
nal
l
y
co
n
c
l
u
sion
and fu
tu
r
e
wor
k
in sectio
n 7.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
42
9 – 4
3
5
43
0
2.
MFSK MODULATION SIGNAL MODEL
The
si
gnal
m
o
del
t
h
at
has be
en use
d
i
n
t
h
e pape
r was de
fi
ned
as bel
o
w [
4
]
(1
)
wh
ere
n
(
t) is th
e ad
d
itiv
e
white Gau
ssian
no
ise,
x
(
t)
rep
r
esen
ts th
e m
o
du
latio
n
typ
e
. Th
e fo
llowing
m
o
d
e
ls
have
bee
n
use
d
f
o
r
x
t
.
x
FSK
∑
∆
(2
)
w
h
er
e
∆
∆
;
1
,
2
…
1
Fo
r ex
am
p
l
e, 2FSK fr
equ
e
n
c
y sh
if
t
k
e
ying
mo
du
latio
n princ
i
ple, the
carrier fre
quency
va
ries with
t
h
e cha
n
ge
of
t
h
e
di
gi
t
a
l
base
ban
d
si
g
n
al
.
2F
SK si
gnal
m
a
them
ati
cal
expr
essi
on
i
s
x
(t) = m
(t) c
o
s(w
1
t) +
̅
m(
t
)
c
o
s
(
w
2
t)
Whe
r
e t
h
e
w
1
i
s
the sym
bol 0
of a carrier
angular
fre
quency, w
2
is th
e sym
b
o
l
s
1
.
m
(
t) is no
rm
alized
with a
sym
bol
val
u
e b
e
t
w
een 0
a
n
d 1
,
̅
m
(
t) is th
e anti-co
d
e
. MFSK sign
al is 2FSK d
i
rect m
a
rk
etin
g [5
].
3.
MAT
H
EM
AT
ICAL
M
O
DE
LING
Spect
r
u
m
Est
i
m
a
t
i
on co
nsi
d
e
r
s t
h
e
pr
o
b
l
e
m
of
est
i
m
at
i
ng t
h
e
p
o
we
r s
p
ect
ral
de
nsi
t
y
o
f
a
wi
de se
nse
st
at
i
onary
ra
n
dom
pr
ocess
usi
n
g st
at
i
s
t
i
cal
descri
pt
ors
,
t
h
e ap
pr
oac
h
es fo
r s
p
ect
r
u
m
est
i
m
a
t
i
on m
a
y
b
e
gene
ral
l
y
cat
eg
ori
z
e
d
i
n
t
o
one
o
f
t
w
o cl
asses
.
T
h
e fi
rst
i
n
cl
ude
s t
h
e
cl
assi
cal
or
n
o
npa
ra
m
e
t
r
i
c
m
e
t
hod
s t
h
at
begi
n
by
est
i
m
at
i
ng t
h
e a
u
t
o
c
o
r
r
el
at
i
o
n
se
qu
ence
f
r
om
a
gi
ven
set
of
dat
a
. T
h
e
p
o
we
r s
p
ect
rum
i
s
t
h
e
n
esti
m
a
ted
b
y
F
o
urier tran
sfo
r
min
g
o
f
th
e esti
m
a
ted
au
to
correlatio
n
sequ
en
ce. Th
e s
econd class include
s
the
no
n
-
cl
assi
cal
or param
e
t
r
i
c
appr
oac
h
es, w
h
i
c
h are base
d
o
n
usi
n
g a
m
odel
fo
r t
h
e pr
ocess
i
n
orde
r t
o
est
i
m
at
e
the power spe
c
trum
. The
para
m
e
tric
approa
ch to spe
c
trum
estim
a
tion pr
oduces
a m
o
re accurate and
highe
r
reso
l
u
tio
n
sp
ectral esti
mate w
h
en
co
m
p
ared t
o
t
h
at
of n
o
n
-
param
e
t
r
i
c
approac
h
.
W
i
t
h
a param
e
t
r
i
c
approac
h
,
th
e first step
is to
select an
ap
pr
op
ri
at
e m
odel
fo
r t
h
e
p
r
oces
s. T
h
i
s
s
e
l
ect
i
on m
a
y
be ba
sed
o
n
a
pri
o
ri
kn
o
w
l
e
d
g
e a
b
out
h
o
w
t
h
e
pr
ocess i
s
ge
nerat
e
d,
or
,
p
e
rha
p
s,
o
n
e
x
peri
m
e
nt
al
resul
t
s
i
n
di
cat
i
n
g
t
h
at
a
part
i
c
ul
a
r
m
odel
“wor
ks
wel
l
”
. M
odel
s
t
h
at
are com
m
onl
y
use
d
i
n
cl
u
d
e a
u
t
o
reg
r
essi
ve
(
A
R
)
, m
ovi
n
g
a
v
era
g
e
(M
A)
, an
d aut
o
re
gre
ssi
ve m
ovi
ng a
v
era
g
e
(AR
M
A
)
. O
n
ce
a
m
odel has been selected, the ne
xt step is to
esti
m
a
te
th
e m
o
d
e
l p
a
ram
e
t
e
rs fro
m
th
e giv
e
n
d
a
ta. Th
e fin
a
l step
is t
o
estim
a
t
e th
e p
o
wer sp
ect
ru
m
b
y
in
corpo
r
ating th
e estim
ated
p
a
ram
e
ters in
to
th
e p
a
ram
e
tric form
fo
r t
h
e spectru
m
.
The
Param
e
t
r
i
c
m
e
t
hod
s
di
scu
ssed i
n
t
h
i
s
pa
p
e
r are
gi
ven
i
n
bri
e
f
bel
o
w:
3. 1 Au
tor
e
gre
ssi
ve
S
p
ectr
u
m
E
s
ti
m
a
ti
o
n
An
au
toreg
r
essiv
e
pro
cess,
x
(n), m
a
y b
e
rep
r
esen
te
d
as the o
u
t
p
u
t
o
f
an
all-p
o
l
e filter t
h
at is d
r
i
v
en
b
y
un
it v
a
rian
ce wh
ite
n
o
i
s
e.
The
p
o
we
r s
p
e
c
t
r
um
of t
h
e
pa
t
h
o
r
der a
u
t
o
re
gressi
ve
pr
oces
s i
s
|
0
|
|1
∑
|
(3
)
There
f
ore, if
b (0) a
n
d
can
be esti
m
a
ted
from
th
e d
a
ta, t
h
en
an
estim
ate of the
powe
r s
p
ectrum
m
a
y b
e
fo
rm
ed usin
g
|
0
|
|1
∑
|
(4
)
3.
2 Mo
vi
n
g
A
v
era
ge Spec
t
r
u
m
E
s
ti
m
a
ti
o
n
W
i
t
h
a m
oving avera
g
e m
odel, the
spectrum
m
a
y
be est
i
m
a
t
e
d i
n
on
e of t
w
o
way
s
. The
fi
rs
t
approach is t
o
take adva
ntage of t
h
e fact t
h
at th
e a
u
toc
o
rrelation seque
n
ce of a m
oving a
v
e
r
age
process is
fin
ite in
len
g
t
h
.
Sp
eci
fically, sin
ce
0
for
|
|
0
, th
en
a
n
a
tural esti
mate to
u
s
e is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Au
toma
tic Mod
u
l
a
tio
n Reco
gn
itio
n
f
o
r MFSK Using
Mod
ified
Co
va
rian
ce Metho
d
(Han
an
M. Ham
ee)
43
1
́
(5
)
Whe
r
e
́
(k) is
a su
itab
l
e estimate o
f
t
h
e auto
correlation
se
que
nce. T
h
e
second approa
ch is
to estim
a
t
e the
m
ovi
ng a
v
era
g
e pa
ram
e
t
e
rs,
fro
m
x
(n
), and th
en su
b
s
titu
te in
th
e fo
llowing
eq
u
a
tion
|
|
(6
)
The param
e
ters
can be e
s
t
i
m
at
ed usi
n
g t
h
e t
w
o-st
a
g
e
app
r
oach
de
ve
l
ope
d by
Du
r
b
i
n
.
Thi
s
pape
r
i
nvest
i
g
at
es t
h
e seco
nd a
p
p
r
oac
h
i
.
e.
ap
p
l
y
i
ng D
u
r
b
i
n
'
s
m
e
t
hod i
n
t
h
e real
i
zat
i
o
n
of M
A
s
p
ec
t
r
u
m
est
i
m
a
ti
on.
Var
i
ous AR
m
odel
i
ng t
echni
que
s used t
o
o
b
t
a
i
n
an est
i
m
a
t
e
of t
h
e AR
sp
ect
rum
.A
m
o
di
fi
e
d
cova
ri
ance
m
e
t
h
o
d
one
o
f
t
h
ese m
e
t
hods
whi
c
h
be
un
d
e
rst
a
n
d
i
n
g
be
l
o
w al
on
g
wi
t
h
t
h
e
m
a
t
h
em
at
i
c
al
anal
y
s
i
s
m
odi
fi
ed C
ova
ri
ance
m
e
t
hod i
n
t
h
i
s
sect
i
on
we s
h
o
w
t
h
e
[
6]
3. 3 M
o
di
fi
ed
Co
v
a
ri
ance
Met
h
o
d
s
T
h
e d
e
ri
vat
i
o
n o
f
t
h
i
s
m
e
t
hod can
be f
o
u
n
d
i
n
m
a
ny
refere
nc
es [6
-7]
.
A m
odi
fi
ed C
o
va
ri
ance
m
e
t
hod wa
s a basi
c t
ool
f
o
r
f
eat
ures o
f
M
F
SK. T
h
e m
odi
f
i
ed cov
a
ri
ance
m
e
t
hod i
s
si
m
i
l
a
r t
o
t
h
e cov
a
ri
ance
m
e
t
hod i
n
t
h
at
no
wi
n
d
o
w i
s
appl
i
e
d t
o
t
h
e
dat
a
. H
o
weve
r,
i
t
wor
k
t
o
est
i
m
a
t
e
t
h
e aut
o
r
e
gres
si
ve
para
m
e
t
e
rs
of or
de
r
p
(AR (p
))
can be
vi
ewe
d
as l
eas
t
squa
res-m
e
t
hod
base
o
n
t
h
e
m
i
nim
i
zat
i
on o
f
t
h
e
f
o
r
w
a
r
d a
n
d
back
wa
rd e
r
r
o
r
i
n
l
i
n
ear pre
d
i
c
t
o
r .i
f
we ha
v
e
i
nput
dat
a
x
(n
) f
o
r N sam
p
l
e
s .To
d
e
riv
e
th
e esti
m
a
to
r, let as
consider the
f
o
rwa
r
d
an
d
bac
k
wa
r
d
l
i
n
ear
p
r
edi
c
t
i
on
est
i
m
a
t
e
s of
o
r
der
p
g
i
ven a
s
(7
)
∗
(8
)
Wh
ere a
(k
)'s are AR
filter
param
e
ters. In
eith
er case
t
h
e
min
i
m
u
m
p
r
edictio
n
error
p
o
wer is
ju
st th
e wh
ite
noi
se
va
ri
ance
.the m
odified covaria
n
ce m
e
thod estim
ate
s
AR
pa
ram
e
t
e
rs
by
m
i
nim
i
zing
t
h
e
ave
r
age
o
f
t
h
e est
i
m
at
ed f
o
r
w
ar
d a
n
d
ba
ckwa
r
d
pre
d
i
c
t
i
on e
r
r
o
r
po
we
rs,
or
1
2
(9
)
1
|
|
(1
0)
1
|
∗
|
(1
1)
1,
1
2,1
….
,
1
2,
1
2,2
….
,
2
1,
⋮
2,
⋮⋯
,
⋮
⋮
0,1
0,2
0
,
⋮
(1
2)
W
h
er
e
,
∗
(1
3)
W
ith
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
42
9 – 4
3
5
43
2
,
∗
∗
(1
4)
So
lv
i
n
g equ
a
tio
n 12
will g
i
v
e
th
e v
a
l
u
e
o
f
a(k
)
k=1,2
,
…
,
p ,
t
h
en
th
e
po
wer sp
ectral d
e
nsity can
b
e
esti
mated
usi
n
g t
h
e
val
u
e
s
a(
k)
.th
e
esti
mate o
f
th
e
wh
ite no
ise
v
a
riance is
˰
0,0
˰
0,
(1
5)
Th
e
po
wer sp
ectral d
e
n
s
ity is calcu
late fro
m
eq
u
a
tion
(4
)
wh
ere
0
˰
In c
ont
rast
t
o
ot
he
r AR
spec
t
r
um
est
i
m
a
ti
on t
ech
ni
q
u
es, t
h
e m
odi
fi
ed c
ova
ri
ance m
e
tho
d
ap
pea
r
s t
o
gi
ve
st
at
i
s
t
i
call
y
stabl
e
spect
r
u
m
est
i
m
a
t
e
s wi
th hi
gh
res
o
l
u
t
i
on.
U
n
l
i
k
e t
h
e aut
o
c
o
r
r
el
at
i
on m
e
t
hod a
n
d t
h
e
cova
riance
m
e
thod t
h
e m
odifi
ed c
ova
riance
m
e
thod is
not s
u
bject to
s
p
ectral line splitting.
4.
SV
M CLAS
SI
FIER
Su
pp
ort
vect
o
r
m
achi
n
e (SV
M
) i
s
a st
ruct
ural
ri
s
k
base
d l
earni
ng m
achi
n
e,
w
h
i
c
h c
onst
r
uct
s
N-
di
m
e
nsi
onal
h
y
p
er
pl
ane t
o
opt
i
m
al
ly
separat
e
t
h
e i
n
p
u
t
dat
a
i
n
t
o
di
ff
erent
cat
eg
ori
e
s. A si
gm
oi
d ker
n
el
fu
nct
i
o
n m
ode
l
of
S
V
M
i
s
e
qui
val
e
nt
t
o
a
t
w
o
-
l
a
y
e
r,
fee
d
-
f
o
r
w
a
r
d
neu
r
al
net
w
or
k.
F
u
rt
herm
ore,
S
V
M
can
use
p
o
l
y
nom
i
a
l
fu
nct
i
o
n
or
r
a
di
al
basi
s
f
u
n
c
t
i
on
(R
B
F
)
i
n
w
h
i
c
h
t
h
e
we
i
ght
s
of
t
h
e
ne
t
w
o
r
k
are
f
o
u
n
d
b
y
so
lv
i
n
g
a
q
u
a
d
r
atic prog
ram
m
in
g
p
r
ob
lem with
lin
ear
co
n
s
t
r
ain
t
s [8
]. So
we
h
a
v
e
p
r
op
o
s
ed
a mu
lticlass
SVM
-
base
d cl
assifier (M
CS
VM
)
as
Figure
1 t
h
at has
a hi
erarc
h
ical st
ru
ct
ure.
SVM
s
w
e
re i
n
t
r
o
duce
d
on
t
h
e
fo
u
ndat
i
o
n o
f
st
at
i
s
t
i
cal l
earni
n
g
t
h
e
o
ry
. S
i
nce t
h
e m
i
ddl
e of
19
9
0
s, t
h
e al
gori
t
hm
s used f
o
r
SVM
s
st
art
e
d
e
m
erg
i
ng
with g
r
eater av
ailab
ility o
f
co
m
p
u
tin
g
p
o
wer,
pav
i
ng
th
e way for nu
m
e
ro
u
s
p
r
actical ap
p
l
i
catio
n
s
.
The
basi
c S
V
M
deal
s wi
t
h
t
w
o
-
cl
ass
pr
obl
em
s;
howe
v
e
r
,
i
t
can be
dev
e
l
ope
d f
o
r m
u
lt
i
c
l
a
ss cl
assi
ficat
i
o
n
.
The
fol
l
o
wi
n
g
sub
s
ect
i
o
n
s
bri
e
fl
y
desc
ri
be t
h
e
bi
na
ry
S
V
M
an
d M
C
SV
M
.
Fig
u
re
1
.
Th
e
p
r
op
o
s
ed
a m
u
lticlass SVM-based
classifier
(MCSVM)
Support Vector Machine (SVM) is
an empirical
m
odeling algorithm
a
nd is the state-
of
-the
-art f
o
r
th
e ex
istin
g
classificatio
n
m
e
th
od
s. Th
e SVM is basically
a two-class classi
fier base
d on the ideas of
“large
margin” and “map- ping dat
a
into
a highe
r dim
e
nsional s
p
ace”, and the
ke
rnel functions in the SVM
.
The
first obj
ectiv
e
o
f
the SVM cl
assificatio
n
is
th
e m
a
x
i
mi
zat
ion
of t
h
e m
a
rgi
n
bet
w
ee
n t
h
e t
w
o nea
r
est
dat
a
poi
nt
s bel
o
n
g
i
ng t
o
t
w
o se
pa
rat
e
cl
asses. T
h
e seco
n
d
o
b
j
e
c
tiv
e is to
co
nstrain
t
th
at all
d
a
ta po
in
ts b
e
l
o
ng
t
o
th
e rig
h
t
class. It is a
two
-
class so
lu
tion
wh
ich
can
u
s
e m
u
lti- d
i
m
e
n
s
io
n
featu
r
es. Th
e t
w
o
obj
ectiv
es
o
f
th
e
Su
pp
ort
Vect
o
r
C
l
assi
fi
er (S
VC
) p
r
obl
em
a
r
e then inc
o
rporated
into a
n
optim
i
zation problem
. SVC classifies
th
e p
o
i
n
t
s from two
lin
early sep
a
rab
l
e sets in
two
cl
asses b
y
so
lv
ing
a q
u
a
d
r
atic op
timizatio
n
p
r
ob
l
e
m
in
or
der t
o
fi
n
d
t
h
e o
p
t
i
m
a
l
separat
i
ng
hy
pe
r pl
ane bet
w
ee
n t
h
ese t
w
o cl
ass
e
s. Thi
s
hy
per
pl
ane m
a
xim
i
zes t
h
e
Class 1 Vs Classes
2,
3,
4,
5
Class 2 Vs Classes
3,
4,
5
Class 3 Vs Classes
4,5
Class 4 Vs Class 5
1
2
3
4
5
ɸ
(x
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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:
208
8-8
7
0
8
Au
toma
tic Mod
u
l
a
tio
n Reco
gn
itio
n
f
o
r MFSK Using
Mod
ified
Co
va
rian
ce Metho
d
(Han
an
M. Ham
ee)
43
3
distance
from
the convex
hulls of eac
h clas
s. The
s
e techniques ca
n
be e
x
tended to the
nonlinea
r cas
es by
e
m
beddi
ng t
h
e
data in a nonlinear s
p
ace using
ke
rnel fu
nc
tions.
T
h
e robustness of
SVC origi
n
ates from
the
st
ro
ng
f
u
ndam
e
nt
al
s o
f
st
a
tistical learn
i
ng
theo
ry.
SVC
ca
n be a
ppl
i
e
d t
o
se
pa
rabl
e a
nd
n
o
n
-
sepa
ra
bl
e dat
a
poi
nt
s. I
n
t
h
e no
n
-
sepa
ra
bl
e case, t
h
e
al
go
ri
t
h
m
adds
o
n
e m
o
re de
s
i
gn
pa
ram
e
t
e
r. Thi
s
param
e
ter is th
e wei
g
h
t
of th
e error cau
sed
b
y
th
e po
in
ts
prese
n
t in
t
h
e
wrong class re
gion.
In MC, t
h
is iss
u
e
occurs in
t
h
e low
SNR cases
.
Another
de
gree
of
free
dom
i
n
t
h
e m
e
t
hod
we us
ed i
n
t
h
i
s
pape
r t
o
cl
assi
fy
5 m
odul
at
i
o
n t
ech
ni
q
u
es,
f
i
rst
we cl
assi
fy
one cl
ass
fr
o
m
t
h
e
othe
rs and if the receive
d signal feat
ures (whic
h
be
- long
to one class of 5 classes
)
does not belong to the
si
ngl
e cl
ass
an
d
bel
o
ng
s t
o
t
h
e
ot
he
r cl
ass,
we
rem
ove
the single class
and take
one
class from
the ot
he
r
classes and
cl
assify it fro
m
th
e rest of
o
t
h
e
r
classes
and
so
o
n
un
til we co
rrectly classify th
e receiv
ed
si
gnal
[9]
.
5.
FEATU
R
E A
NAL
YSI
S
From
Fi
gure
2
t
h
at
sho
w
s t
h
e
fi
rst
t
e
n ha
rm
oni
cs of al
l
m
odul
at
i
on sc
hem
e
s un
der st
udy
i
ng
whe
r
e i
t
seem
s
n
o
t
in
terferen
ce b
e
t
w
een
th
em
esp
ecially at
th
e fi
rst h
a
rm
o
n
i
cs. So
th
ese features
will b
e
lead
s to
ease
of t
h
e SVM t
o
classify the
signal t
h
at have these
ha
r
m
oni
cs. Al
so
wi
t
h
a
deep
a
n
al
y
s
i
s
of
m
odi
fi
ed
cova
riance m
e
thod where t
h
e incr
easing o
f
th
e o
r
d
e
r p th
is lead
to
increase the re
cognition
rate but the
execut
i
o
n t
i
m
e bec
o
m
e
s l
ong
at
hi
g
h
val
u
e
o
f
p.
Fi
gu
re
2.
The
f
i
rst
t
e
n
harm
on
i
c
s of
al
l
m
odu
l
a
t
i
on sc
hem
e
s
Po
wer s
p
ect
ral
est
i
m
a
ti
on by
m
odi
fi
es co
v
a
ri
ance m
e
t
hod use
d
t
o
ge
n
e
rat
e
t
h
e feat
u
r
e vect
ors
,
whe
r
e dat
a
bas
e
of t
h
e si
g
n
at
ure m
odul
at
i
o
n si
gnal
are
ge
nerat
e
d. A
f
t
e
r
t
h
i
s
, t
h
e fi
rst
t
e
n ha
rm
oni
cs of eac
h
feature
observation and sa
ve
it. Then
use
d
these
features as
input for SVM classifier
i
n
or
der
to
t
r
ain
SV
M.
The reas
on tha
t
leads to ch
oose th
e first ten
h
a
rm
o
n
i
cs is th
at th
e in
terfe
rence betwee
n
classes increas
e as w
e
g
e
t toword
s the h
a
rm
o
n
i
cs that h
a
v
e
h
i
gh
o
r
d
e
r. So
t
h
e ch
oo
sing
o
f
h
a
rm
o
n
i
cs
will b
e
restricts o
n
th
e first ten
o
n
l
y. M
o
du
latio
n id
en
tificatio
n
in
cl
u
d
e
s in
ter-class classi
ficatio
n
for FSK with
5
class cl
assificatio
n
p
r
o
b
l
em
base
d o
n
SVM
.
Th
e st
r
u
ct
u
r
e
of
t
h
e
hi
era
r
c
h
ical classifier is as s
h
own in
Figure
3.
First
l
y, we e
x
tract
FSK2
fr
om
al
l
,
t
h
en
FSK
4
fr
om
t
h
e rest
a
n
d
s
o
on
.
Rate
of
Recog
nition
-1
5
-14
-13
-12
-1
1
-1
0
-9
-8
-7
-6
-5
75
80
85
90
95
10
0
F
SK2
F
SK4
F
SK8
F
SK1
6
F
SK6
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
42
9 – 4
3
5
43
4
Fi
gu
re
3.
The
s
t
ruct
u
r
e
of
the hierarc
h
ical
cla
ssifier
6.
RESULTS
A
N
D
DI
SC
US
S
I
ON
The p
r
op
ose
d
al
go
ri
t
h
m
was
veri
fi
e
d
an
d va
l
i
d
at
ed fo
r va
ri
ous
or
de
rs o
f
d
i
gi
t
a
l
l
y
m
odul
at
ed si
gnal
s
(B
FS
K,
QFS
K
, 8F
SK
, 1
6
F
S
K
an
d
6
4
FS
K
)
i
n
t
h
e
p
r
ese
n
ce o
f
noi
se
.
Here t
h
e w
o
rk
gi
ves a
hi
gh
rat
e
o
f
classification and
good results that sa
tisfies t
h
e goal of this
work, where
the recognition rate reaches to
highe
r
l
e
vel
an
d ca
n b
e
i
n
crease
d
at
m
o
re l
o
w
of
S
N
R
by
a
p
pl
y
i
ng t
h
e
o
p
t
i
m
i
zati
on t
e
c
hni
que
s
fo
r t
h
e
pa
ram
e
ters
of
SVM classifier .All th
e sim
u
latio
n
steps fo
r
th
e d
i
g
itally
modulated si
gnals, the
feat
ure ex
traction
,
trai
nin
g
o
f
th
e SV
M and
p
e
rf
or
m
a
n
ce ev
alu
a
tion
w
e
r
e
d
e
v
e
lop
e
d usin
g MA
TLA
B
. Th
e
pr
opo
sed classif
i
er
h
a
s
shown
an excellent pe
rform
a
nce in noise pres
ence
an
d
with
ou
t an
y
o
p
timizatio
n
fo
r SVM p
a
ram
e
ters. In
th
e train
i
n
g
pha
se,
5 m
odul
at
ed si
g
n
al
s
of
di
ffe
re
nt
o
r
de
r
s
are
fed
t
o
t
h
e
feat
u
r
e e
x
t
r
act
i
on
feat
u
r
e Sec
o
n
d
l
y
, cl
assi
fi
c
a
t
i
o
n
p
r
o
cess th
at can
b
e
u
s
ed
to
d
i
stin
gu
ish
b
e
tween
5
d
i
g
ital FSK
m
o
du
latio
ns. Fi
g
u
r
e
4
g
i
ves im
ag
in
atio
n
about
the
efficiency of
this feature to
reco
g
n
i
ze b
e
t
w
een
di
ffe
re
nt
i
nde
xes
of
FSK.
Where c
a
n that power
spectral
estim
a
tion by m
odified
cova
ri
ance m
e
thod a
strong tool in
m
odulation rec
o
gnition
world.
Figure 4.
Recognition rate
at
diffe
re
nt S
N
Rs
for
va
rious m
odulation
sc
hem
e
s whe
n
feat
ures extracte
d
from
the signal,
p=
30.
Si
gnal
t
o
noi
se
rat
i
o
(dB
)
Rate o
f
Recogn
itio
n
-1
5
-14
-13
-12
-1
1
-1
0
-9
-8
-7
-6
-5
75
80
85
90
95
10
0
F
SK2
F
SK4
F
SK8
F
SK1
6
F
SK6
4
Ma
gni
t
u
de
of
PSD
1
2
3
4
5
6
7
8
9
10
4
6
8
10
12
14
16
FSK2
FSK4
FSK8
FSK16
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Au
toma
tic Mod
u
l
a
tio
n Reco
gn
itio
n
f
o
r MFSK Using
Mod
ified
Co
va
rian
ce Metho
d
(Han
an
M. Ham
ee)
43
5
So
fro
m
co
m
p
arativ
e between
th
is
wo
rk
and
o
t
h
e
rs
wh
ere in
[10
]
, th
e
rate o
f
reco
gn
ition
at 0d
B
for
M
FSK reac
hes
t
o
94%
. I
n
[
1
1]
by
usi
n
g aut
o
re
gre
ssi
ve a
p
pr
oac
h
es t
h
at
g
i
ves a rat
e
of
r
ecog
n
i
t
i
on
9
5
%
aft
e
r
0dB
f
o
r FS
K2
,
FSK
4 o
n
l
y
. Tabl
e 1 sh
o
w
s t
h
e rat
e
o
f
m
odul
at
i
on rec
o
gni
t
i
on at
-5 dB
, Fi
gu
re 4 s
h
o
w
s t
h
e
perce
n
tage
of m
odulation rec
o
gnition
at di
fferent le
vel of
S
N
R
(-15, -10,
-5) dB
Table
1. MF
S
K
m
odulation
recognition at S
N
R=
-5dB
Trai
ning set
1000 s
a
m
p
les/class,
Testin
g
set 1000
sam
p
les/class, p
=
30
.
T
y
pe of
m
odulation
FSK2 FSK4
FSK8
FSK16
FSK64
FSK2 1000
FSK4
1000
FSK8
1000
FSK16
1000
FSK64
1000
7.
CO
NCL
USI
O
N
AN
D F
U
T
U
RE W
O
R
K
From
t
h
e a
b
o
v
e
resul
t
s
ca
n
be c
oncl
u
si
on
t
h
at
t
h
i
s
t
ool
s
ve
ry
wel
l
fo
r M
F
S
K
m
odul
at
i
o
n
recognition at l
o
w SNR. T
h
e
rate of rec
o
gni
tion reaches
to
97% at
SNR
=
-10dB. So
t
h
er are
m
a
ny think that
can be m
a
de in t
h
i
s
t
opi
c as
a fut
u
re w
o
r
k
one
of t
h
em
whi
c
h i
t
can b
e
im
prove
d t
h
e rat
e
of rec
o
g
n
i
t
i
on by
appl
y
i
n
g
of
o
p
t
im
i
zat
i
on t
echni
que
s f
o
r
t
h
e param
e
t
e
rs o
f
t
h
e
SVM
.
Al
so a
p
pl
i
e
d t
h
i
s
m
e
t
hod t
o
anot
her
t
y
pe of m
o
d
u
l
a
t
i
on s
u
ch as
PS
K an
d
QAM
o
r
any
t
y
pe
of
m
odul
at
i
on a
n
d m
a
ke a deci
si
on a
b
o
u
t
i
t
s
i
n
t
e
rest
s
and ot
her facts.
REFERE
NC
ES
[1]
Khandker Nad
y
a Haq, Ali Mansour, Sven Nordholm, “
Reco
gnition o
f
Digital Modulated S
i
gnals based o
n
Statisti
cal
Parame
te
rs
”, 4
t
h IEEE Intern
ational
Conference on
Di
gital Ecos
y
s
tems and
Technologies (IEEE DEST,
2010) .
[2]
Ataoll
ah Ebrah
i
m
zadeh Sherm
e
h, Rez
a
Ghaz
al
ian,
“
R
ecogn
itio
n of com
m
unication signa
l t
y
p
e
s using genet
i
c
algorithm and support vector machines ba
sed on
the higher ord
e
r statistics”,
Elsevier, Digita
l Sign
al Processing
,
20
(2010) 1748–17
57.
[3]
Li Cheng1 and
Jin Liu, “Automatic
Modulation Classifier Us
ing Artificial
Neural Network
Trained b
y
PSO
Algorithm”,
Jou
r
nal of Commun
i
cations
, 2013
, 8
(
5).
[4]
Lei Huo,
Tiand
ong Duan, Xian
gqian Fang, “
A
Novel M
e
thod o
f
Modulation C
l
assification
for Digital Signa
ls
”,
International Joint Conferen
ce
on Neural Networks
Sheraton Vancouver Wall Cen
t
re
Hotel, Vancouv
er,
BC,
Canada,
2006, 1
6
-21.
[5]
Qu Jun-suo, “A
Algorithm of Fast Digital Phase
Modulation
Sign
al Recogn
ition
”
,
TE
LKOMNIKA
, 2012, 10(8), pp
.
2330~2335
[6]
P.
Sasikiran, T. Gowri
Manoha
r, S. Koteswara
Rao, “Estimatin
g the power
spectrum of a wide sense Statio
n
a
r
y
random process
using parametr
ic
appro
aches (A
R, MA)”,
In
tern
ational Journal of
Recen
t Ad
van
ces in
Engin
eering
&
Technology (
I
JRAET)
. 2014, 2
(
2).
[7]
Lubna Badri
an
d Mujahid Al-Azzo, “Modelling
of long
wavelength detection
of obj
ects using
Elman network
m
odified covar
i
ance
com
b
inatio
n”,
The International Arab Journal of informatio
n technolog
y
, 20
08, 5(3), pp. 265
-
272.
[8]
Yu Wang, “Ultrasonic Flaw Signal Cl
assification using Wav
e
let Transf
orm and Support
Vector Machin
e”,
TE
LKOMNIKA
, 2013,
11(12)
.
[9]
Mohamed El-H
ad
y
Magd
y
Kes
hk1, El-S
ay
ed
Elrab
i
e, Fathi El-Say
ed A
bd
El-
S
amie, Mohammed Abd El-N
ab
y
,
“Blind Modulation Recognition
in Wire
less MC-CDMA
Sy
stems Using a Supp
or
t Vector Machine Classifier”,
Wire
le
ss
Eng
i
neering and Techn
o
logy
,2013
,4,14
5
-153, Published
on (
http://www.
scirp.
org/journal/wet
).
[10]
Sajjad Ahmed
Ghauri, I
j
az Mansoor
Qureshi, I
h
tesham Shah and Nasi
r Khan, “Modulation C
l
assification
using
C
y
clostationar
y
Features
on
Fading Channels”,
Research Journal
of Applied
Sc
ien
ces,
Engin
eering
and Techno
logy
2014, 7(24)
, pp
.
5331-5339.
[11]
He Ji-ai, Liu Huan, Li Ying-tan
g
,
Ding Li-qi,
Wang Jie, “Mod
ulation Rec
ognition Based on Fe
ature Extraction
b
y
AutoRegressive Model”,
TELK
OMNIKA Indon
esian Journal
o
f
Electrical
Eng
i
neering
2014, 12(3),
pp. 1911
~
1916.
Evaluation Warning : The document was created with Spire.PDF for Python.