T
E
L
K
O
M
N
I
K
A
T
elec
o
m
m
un
ica
t
io
n,
Co
m
pu
t
ing
,
E
lect
ro
nics
a
nd
Co
ntr
o
l
Vo
l.
1
8
,
No
.
5
,
Octo
b
e
r
2
0
2
0
,
p
p
.
27
80
~
2
7
8
6
I
SS
N:
1
6
9
3
-
6
9
3
0
,
ac
cr
ed
ited
First Gr
ad
e
b
y
Kem
en
r
is
tek
d
i
k
ti,
Dec
r
ee
No
: 2
1
/E/KPT
/2
0
1
8
DOI
: 1
0
.
1
2
9
2
8
/TE
L
KOM
NI
K
A.
v
1
8
i
5
.
1
4
4
7
0
2780
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//jo
u
r
n
a
l.u
a
d
.
a
c.
id
/in
d
ex
.
p
h
p
/TELK
OM
N
I
K
A
H
idden
Ma
rko
v
mo
del t
ech
nique
f
o
r dyna
mic spect
rum a
ccess
J
a
y
a
nt
P
.
P
a
wa
r
1
,
P
ra
s
ha
nt
V.
I
ng
o
le
2
1
R
esear
ch
Sch
o
lar
San
t
Gad
g
e
B
ab
a
Am
ar
av
ati
Un
iv
er
s
ity
,
I
n
d
ia
2
HOD,
Dep
ar
tm
en
t
o
f
I
T
,
PR
MI
T
&
R
,
I
n
d
ia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Oct
2
9
,
2
0
1
9
R
ev
is
ed
Ap
r
1
4
,
2
0
2
0
Acc
ep
ted
Ap
r
2
4
,
2
0
2
0
Dy
n
a
m
ic
sp
e
c
tru
m
a
c
c
e
ss
is
a
p
a
ra
d
ig
m
u
se
d
t
o
a
c
c
e
ss
th
e
sp
e
c
tru
m
d
y
n
a
m
ica
ll
y
.
A
h
i
d
d
e
n
M
a
rk
o
v
m
o
d
e
l
(HM
M
)
is
o
n
e
in
wh
ich
y
o
u
o
b
se
rv
e
a
se
q
u
e
n
c
e
o
f
e
m
issio
n
s,
b
u
t
d
o
n
o
t
k
n
o
w
th
e
se
q
u
e
n
c
e
o
f
sta
tes
th
e
m
o
d
e
l
we
n
t
t
h
r
o
u
g
h
to
g
e
n
e
ra
te
th
e
e
m
issio
n
s.
An
a
ly
sis
o
f
h
id
d
e
n
M
a
rk
o
v
m
o
d
e
ls
se
e
k
s
t
o
re
c
o
v
e
r
th
e
se
q
u
e
n
c
e
o
f
sta
tes
fro
m
th
e
o
b
se
rv
e
d
d
a
ta.
In
th
is
p
a
p
e
r,
we
e
stim
a
te
th
e
o
c
c
u
p
a
n
c
y
sta
te
o
f
c
h
a
n
n
e
ls
u
si
n
g
h
id
d
e
n
M
a
rk
o
v
p
ro
c
e
ss
.
Us
in
g
Viterb
i
a
lg
o
rit
h
m
,
we
g
e
n
e
ra
te
th
e
m
o
st
li
k
e
ly
sta
tes
a
n
d
c
o
m
p
a
re
it
w
it
h
th
e
c
h
a
n
n
e
l
sta
tes
.
We g
e
n
e
ra
ted
two
HMM
s,
o
n
e
slo
wl
y
c
h
a
n
g
i
n
g
a
n
d
a
n
o
t
h
e
r
m
o
re
d
y
n
a
m
ic
a
n
d
c
o
m
p
a
re
th
e
ir
p
e
rfo
rm
a
n
c
e
.
Us
in
g
th
e
Ba
u
m
-
Welc
h
a
lg
o
rit
h
m
a
n
d
m
a
x
imu
m
li
k
e
li
h
o
o
d
a
l
g
o
rit
h
m
we
c
a
lcu
late
d
th
e
e
stim
a
ted
tran
si
ti
o
n
a
n
d
e
m
issio
n
m
a
tri
x
,
a
n
d
t
h
e
n
we
c
o
m
p
a
re
th
e
e
stim
a
ted
sta
tes
p
re
d
icti
o
n
p
e
rfo
rm
a
n
c
e
o
f
b
o
th
t
h
e
m
e
th
o
d
s
u
si
n
g
sta
ti
o
n
a
ry
d
istri
b
u
ti
o
n
o
f
a
v
e
ra
g
e
e
stim
a
ted
tran
siti
o
n
m
a
tri
x
c
a
lcu
late
d
b
y
b
o
t
h
t
h
e
m
e
th
o
d
s.
K
ey
w
o
r
d
s
:
B
au
m
-
W
elch
alg
o
r
ith
m
C
o
g
n
itiv
e
r
ad
io
n
etwo
r
k
Dy
n
am
ic
s
p
ec
tr
u
m
ac
ce
s
s
Hid
d
en
Ma
r
k
o
v
p
r
o
ce
s
s
Ma
r
k
o
v
c
h
ain
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
:
J
ay
an
t P.
Pawar
,
R
esear
ch
Sch
o
lar
San
t
Gad
g
e
B
ab
a
Am
ar
av
ati
Un
iv
er
s
ity
,
Am
ar
av
ati
(
M.
S.)
,
I
n
d
ia
.
E
m
ail:
jay
an
tp
p
awa
r
@
y
ah
o
o
.
co
.
in
1.
I
NT
RO
D
UCT
I
O
N
Sp
ec
tr
u
m
s
en
s
in
g
is
u
s
u
ally
d
o
n
e
b
y
m
ea
s
u
r
in
g
th
e
p
o
wer
s
p
ec
tr
al
d
en
s
ity
o
f
th
e
ch
an
n
el
o
f
in
ter
est
in
co
g
n
itiv
e
r
ad
i
o
[
1
]
b
ased
s
y
s
tem
to
p
er
f
o
r
m
th
e
d
y
n
a
m
ic
s
p
ec
tr
u
m
ac
ce
s
s
[
2
]
o
p
e
r
atio
n
.
T
h
is
m
eth
o
d
d
o
esn
’
t
g
iv
e
esti
m
ated
v
alu
e
o
r
d
o
esn
’
t
h
elp
i
n
p
r
e
d
ictio
n
in
a
n
o
is
y
ch
a
n
n
el.
E
s
tim
atin
g
th
e
s
tatu
s
o
f
ch
an
n
el
as
b
ein
g
f
r
ee
o
r
b
u
s
y
is
im
p
o
r
t
an
t
asp
ec
t
o
f
co
g
n
itiv
e
r
ad
io
s
y
s
tem
.
A
h
id
d
en
Ma
r
k
o
v
p
r
o
c
ess
(
HM
P)
[
3
-
6
]
is
u
s
ef
u
l
in
th
is
p
r
ed
ictio
n
.
A
h
id
d
en
Ma
r
k
o
v
p
r
o
ce
s
s
(
HM
P)
is
a
d
is
cr
ete
-
tim
e
f
in
ite
s
tate
h
o
m
o
g
e
n
eo
u
s
Ma
r
k
o
v
ch
ain
(
MC)
[
7
]
o
b
s
er
v
ed
th
r
o
u
g
h
a
d
is
cr
ete
-
tim
e
m
em
o
r
y
less
in
v
ar
ian
t
ch
an
n
el.
HM
Ps
ar
e
m
o
r
e
co
m
m
o
n
l
y
r
ef
er
r
ed
to
as
h
id
d
en
Ma
r
k
o
v
m
o
d
els
[
3
]
.
T
h
e
p
ar
am
eter
o
f
HM
P
is
esti
m
ated
o
f
f
lin
e
f
r
o
m
r
ea
l
m
ea
s
u
r
em
en
ts
u
s
in
g
B
au
m
-
W
elch
(
B
-
W
)
a
lg
o
r
ith
m
[
8
,
9
]
an
d
m
ax
im
u
m
lik
elih
o
o
d
(
ML
)
alg
o
r
ith
m
[
1
0
]
.
Giv
en
th
is
p
ar
am
eter
s
th
e
s
tate
o
f
th
e
p
r
im
ar
y
u
s
er
at
a
g
iv
en
tim
e
an
d
f
r
eq
u
e
n
cy
b
a
n
d
is
d
eter
m
in
ed
.
Hid
d
e
n
Ma
r
k
o
v
m
o
d
el
(
HM
M
)
[
1
1
-
2
4
]
is
a
s
tatis
tical
Ma
r
k
o
v
m
o
d
el
in
wh
ich
th
e
s
y
s
tem
b
ein
g
m
o
d
eled
is
ass
u
m
e
d
t
o
b
e
a
Ma
r
k
o
v
p
r
o
ce
s
s
with
u
n
o
b
s
er
v
a
b
le
(
i.e
.
h
id
d
e
n
)
s
tates.
Her
e
we
av
o
id
ed
m
ath
e
m
atica
l
ex
p
r
ess
io
n
s
an
d
f
o
r
m
u
las an
d
p
r
o
v
id
ed
o
n
l
y
ex
p
er
im
e
n
tal
d
ata
an
d
r
esu
lt
s
.
T
h
e
r
est
o
f
th
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws.
I
n
s
ec
tio
n
2
,
s
y
s
tem
m
o
d
el
is
ex
p
lain
ed
.
I
n
s
ec
tio
n
3
,
we
f
in
d
th
e
m
o
s
t
lik
ely
s
tates
u
s
in
g
Viter
b
i
alg
o
r
ith
m
[
2
5
]
a
n
d
co
m
p
a
r
e
it
with
o
r
ig
in
al
s
tates
o
f
th
e
ch
an
n
el
.
I
n
s
ec
tio
n
4
,
we
co
m
p
a
r
e
th
e
B
au
m
-
W
elch
an
d
m
ax
im
u
m
l
ik
elih
o
o
d
al
g
o
r
ith
m
an
d
c
o
n
cl
u
d
ed
in
s
ec
tio
n
5
.
W
e
u
s
ed
@
MA
T
L
A
B
f
o
r
th
is
ex
p
e
r
im
en
tatio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
Hid
d
en
Ma
r
ko
v
mo
d
el
tec
h
n
iq
u
e
fo
r
d
yn
a
mic
s
p
ec
tr
u
m
a
cc
e
s
s
(
Ja
ya
n
t P
.
P
a
w
a
r
)
2781
2.
SYST
E
M
M
O
D
E
L
L
et
u
s
co
n
s
id
er
HM
Pθ
=
(
π,
A,
B
)
,
p
ar
am
eter
ized
b
y
th
e
i
n
itial
s
tate
m
atr
ix
π,
th
e
s
tat
e
tr
an
s
itio
n
m
atr
ix
A,
a
n
d
th
e
em
is
s
io
n
m
atr
ix
B
.
;
Her
e
we
ass
u
m
e
a
d
is
cr
ete
-
tim
e
m
o
d
el,
wh
er
e
th
e
tim
e
v
ar
iab
le
n
tak
es
v
alu
es
in
{1
,
2
,
…}.
T
h
e
in
p
u
t
to
th
e
s
y
s
tem
at
tim
e
n
co
n
s
i
s
ts
o
f
an
esti
m
ate
o
f
th
e
p
o
wer
s
p
ec
tr
al
d
en
s
ity
.
E
ac
h
ch
an
n
el
is
m
o
d
eled
as
a
two
-
s
tate
HM
P.
T
h
e
o
u
tp
u
t
o
f
th
e
s
y
s
tem
co
n
s
is
ts
o
f
an
esti
m
ated
tr
an
s
itio
n
an
d
em
is
s
io
n
p
r
o
b
ab
ilit
y
m
at
r
ices
o
f
ea
ch
ch
a
n
n
el
f
r
o
m
wh
ich
we
ca
n
p
r
ed
ict
th
e
cu
r
r
en
t
s
tates
as
well
as
th
e
f
u
tu
r
e
s
tates o
f
th
e
ch
an
n
el
u
s
in
g
p
r
e
d
icto
r
.
C
h
an
n
el
p
ar
am
eter
esti
m
atio
n
u
s
in
g
HM
P,
ass
o
ciate
wi
th
ea
ch
o
f
th
e
ch
a
n
n
els
is
b
ased
o
n
o
f
f
lin
e
tr
ain
in
g
d
ata.
HM
P
m
ay
b
e
v
iew
as
a
d
i
s
cr
ete
tim
e
b
iv
ar
iate
r
an
d
o
m
p
r
o
ce
s
s
{(
S
n
,Y
n
)
,
n
=1
,
2
,
…},
wh
er
e
{S
n
}
is
th
e
h
id
d
en
p
r
o
ce
s
s
i.e
.
s
tate
s
o
f
th
e
ch
an
n
el
an
d
{Y
n
}
is
t
h
e
o
b
s
er
v
ab
le
p
r
o
ce
s
s
i.e
.
s
eq
u
en
ce
s
.
T
h
e
h
id
d
en
p
r
o
ce
s
s
{S
n
}
is
a
d
is
cr
ete
ti
m
e
f
in
ite
s
tate
Ma
r
k
o
v
ch
ai
n
.
T
h
e
r
a
n
d
o
m
v
ar
ia
b
les
{Y
n}
ar
e
c
o
n
d
itio
n
a
lly
in
d
ep
en
d
en
t
g
iv
e
n
{S
n
}.
Fu
r
t
h
er
m
o
r
e
,
th
e
d
is
tr
ib
u
tio
n
o
f
Y
n
is
tim
e
in
v
ar
ian
t
an
d
d
ep
en
d
s
o
n
{S
n
}
o
n
ly
th
r
o
u
g
h
S
n
.
T
h
e
h
id
d
en
p
r
o
ce
s
s
{S
n
}
tak
e
s
v
alu
es
in
a
f
in
ite
s
et
S
=
{
0
,
1
,
…
M
-
1
}.
I
n
t
h
is
s
y
s
tem
we
h
av
e
f
o
cu
s
ed
o
n
th
e
ca
s
e
M=
2
,
s
u
ch
th
at
1
r
ep
r
e
s
en
ts
th
e
ch
an
n
e
l
is
f
r
ee
wh
er
ea
s
s
tate
2
r
ep
r
es
en
ts
a
p
r
im
ar
y
u
s
er
ex
is
ten
ce
o
n
th
e
c
h
an
n
el.
Fig
u
r
e
1
s
h
o
ws th
e
s
tate
-
tr
an
s
itio
n
d
iag
r
am
o
f
th
e
h
id
d
en
p
r
o
ce
s
s
.
Fig
u
r
e
1
.
T
h
e
s
tate
-
tr
an
s
itio
n
d
iag
r
am
o
f
a
h
i
d
d
en
p
r
o
ce
s
s
.
3.
F
I
NDING
M
O
ST
L
I
K
E
L
Y
ST
A
T
E
S
Usi
n
g
tr
an
s
itio
n
an
d
em
is
s
io
n
m
atr
ices
o
f
th
e
ch
an
n
el,
w
e
g
en
er
ated
th
e
s
eq
u
en
ce
s
an
d
s
tates
o
f
th
e
ch
an
n
el
u
s
in
g
@
MA
T
L
AB
.
Usi
n
g
Viter
b
i
alg
o
r
ith
m
,
we
g
en
er
ate
th
e
m
o
s
t
lik
ely
s
tates
an
d
co
m
p
ar
e
it
with
ch
an
n
el
s
tates.
Fig
u
r
e
2
s
h
o
ws
th
e
b
lo
ck
d
iag
r
am
we
u
s
ed
to
ch
ec
k
Viter
b
i
al
g
o
r
ith
m
.
W
e
cr
ea
te
th
e
Hid
d
en
Ma
r
k
o
v
Mo
d
el
(
HM
M)
u
s
in
g
tr
an
s
itio
n
p
r
o
b
ab
ilit
y
m
atr
ix
an
d
em
is
s
io
n
p
r
o
b
a
b
ilit
y
m
atr
ix
.
W
e
cr
ea
te
two
HM
M,
HM
M
1
an
d
HM
M2
h
a
v
in
g
s
am
e
e
m
is
s
io
n
p
r
o
b
ab
ilit
y
m
atr
i
x
co
n
s
id
er
in
g
th
e
s
am
e
co
m
m
u
n
icatio
n
s
y
s
tem
.
HM
M1
is
m
o
n
o
to
n
o
u
s
wh
ile
HM
M2
is
d
y
n
am
ic
wh
e
r
e
s
tates
ch
an
g
es
m
o
r
e
f
ast.
Her
e
T
r
an
s
1
an
d
T
r
a
n
s
2
ar
e
t
r
an
s
itio
n
m
atr
ices
f
o
r
HM
M1
an
d
HM
M2
r
esp
ec
tiv
ely
.
E
m
is
is
th
e
co
m
m
o
n
em
is
s
io
n
p
r
o
b
a
b
ilit
y
m
atr
ix
.
W
e
u
s
ed
,
T
r
an
s
1
=
[
0
.
9
5
,
0
.
0
5
;
0
.
1
0
,
0
.
9
0
]
,
T
r
a
n
s
2
=
[
0
.
0
5
,
0
.
9
5
; 0
.
9
0
,
0
.
1
0
]
an
d
E
m
is
=
[
0
.
2
5
,
0
.
2
0
,
0
.
1
0
,
0
.
2
0
,
0
.
2
5
;
0
.
0
5
,
0
.
2
,
0
.
5
,
0
.
2
,
0
.
0
5
]
.
H
er
e
Viter
b
i
alg
o
r
ith
m
is
u
s
ed
to
f
i
n
d
th
e
h
id
d
en
s
tates
f
r
o
m
th
e
g
iv
en
s
eq
u
en
ce
.
W
e
cr
ea
ted
ten
s
eq
u
en
ce
s
an
d
its
s
tate
s
f
r
o
m
s
am
e
HM
M
an
d
u
s
in
g
Viter
b
i
al
g
o
r
ith
m
f
o
u
n
d
o
u
t
esti
m
ated
s
tates.
On
a
n
av
er
ag
e
esti
m
ated
s
tate
s
eq
u
en
ce
s
ar
e
9
0
.
6
6
%
co
r
r
ec
t
f
o
r
HM
M1
an
d
8
4
.
8
%
co
r
r
ec
t
f
o
r
HM
M2
.
T
ab
le
1
s
h
o
ws
th
e
s
am
p
le
d
ata
f
o
r
est
im
atin
g
s
tates
u
s
in
g
Viter
b
i a
lg
o
r
ith
m
.
Fig
u
r
e
3
an
d
Fig
u
r
e
4
s
h
o
ws
th
e
eig
en
v
alu
es
o
f
tr
a
n
s
itio
n
p
r
o
b
ab
ilit
y
m
atr
ix
o
f
HM
M1
an
d
HM
M2
r
esp
ec
tiv
ely
.
An
eig
e
n
v
alu
e
p
lo
t
in
d
icate
s
wh
eth
er
th
e
Ma
r
k
o
v
c
h
ain
is
p
e
r
io
d
ic,
a
n
d
th
e
p
lo
t
r
e
v
ea
ls
th
e
p
er
io
d
o
f
th
e
c
h
ain
.
All
ei
g
en
v
alu
es
at
r
o
o
ts
o
f
u
n
ity
in
d
icate
th
e
p
er
io
d
icity
.
T
h
e
s
p
e
ctr
al
g
ap
is
th
e
ar
ea
b
etwe
en
th
e
cir
cu
m
f
er
en
ce
o
f
th
e
u
n
it
cir
cle
an
d
th
e
cir
cu
m
f
er
en
ce
o
f
th
e
cir
cle
with
a
r
a
d
iu
s
o
f
th
e
s
ec
o
n
d
lar
g
est
eig
en
v
alu
e
m
ag
n
itu
d
e
(
SLE
M)
.
T
h
e
s
ize
o
f
th
e
s
p
ec
tr
al
g
ap
d
eter
m
in
es
th
e
m
ix
in
g
r
ate
o
f
th
e
Ma
r
k
o
v
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1693
-
6
9
3
0
T
E
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m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
V
o
l.
1
8
,
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.
5
,
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b
e
r
2
0
2
0
:
2
7
8
0
-
2
7
8
6
2782
ch
ain
.
T
h
e
m
ix
in
g
tim
e
o
f
a
Ma
r
k
o
v
ch
ain
is
t
h
e
tim
e
u
n
til
th
e
Ma
r
k
o
v
ch
ain
is
"c
lo
s
e"
to
its
s
tead
y
s
tate
d
is
tr
ib
u
tio
n
.
I
n
g
en
er
a
l,
th
e
s
p
ec
tr
u
m
d
eter
m
in
es
s
tr
u
ctu
r
al
p
r
o
p
er
ties
o
f
th
e
ch
ain
.
Her
e
we
s
im
p
ly
ex
ch
an
g
e
t
h
e
o
cc
u
r
r
en
ce
p
r
o
b
ab
ilit
ies
o
f
b
o
th
s
tates
s
o
s
p
ec
tr
al
g
ap
f
o
r
b
o
th
th
e
H
MM
s
ar
e
s
am
e
b
u
t
eig
en
v
alu
es
ar
e
d
if
f
er
e
n
t.
A
s
tatio
n
ar
y
d
is
tr
ib
u
tio
n
o
f
a
MC
i
s
a
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
th
at
r
em
ain
s
u
n
ch
an
g
ed
in
a
MC
as
it
p
r
o
g
r
ess
es.
I
t
g
iv
e
u
s
th
e
im
p
o
r
tan
t
co
n
f
ir
m
atio
n
s
lik
e
tr
an
s
ien
t
s
tate
an
d
r
ec
u
r
r
en
t
s
tat.
I
t
r
ep
r
esen
ts
th
e
lim
itin
g
tim
e
-
in
d
ep
en
d
en
t
d
is
tr
ib
u
tio
n
o
f
th
e
s
tate
f
o
r
Ma
r
k
o
v
p
r
o
ce
s
s
as
th
e
n
u
m
b
er
o
f
s
tep
s
o
n
tr
an
s
itio
n
in
cr
ea
s
es.
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
t
o
ch
ec
k
Viter
b
i A
lg
o
r
ith
m
T
ab
le
1
.
Sam
p
le
d
ata
f
o
r
esti
m
atin
g
States
u
s
in
g
Viter
b
i a
lg
o
r
ith
m
.
S
e
q
u
e
n
c
e
4
4
4
5
5
5
4
4
4
1
1
4
3
4
2
3
3
1
3
3
1
3
2
2
1
S
t
a
t
e
s
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
1
Est
i
m
a
t
e
d
S
t
a
t
e
s
(
9
2
%
c
o
r
r
e
c
t
)
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
Fig
u
r
e
3
.
E
i
g
en
v
alu
es o
f
HM
M1
o
n
co
m
p
lex
p
lan
es
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
Hid
d
en
Ma
r
ko
v
mo
d
el
tec
h
n
iq
u
e
fo
r
d
yn
a
mic
s
p
ec
tr
u
m
a
cc
e
s
s
(
Ja
ya
n
t P
.
P
a
w
a
r
)
2783
Fig
u
r
e
4
.
E
i
g
en
v
alu
es o
f
HM
M2
o
n
c
o
m
p
lex
p
lan
es
4.
CO
M
P
ARI
SO
N
O
F
B
AU
M
-
WE
L
CH
AND
M
AXI
M
U
M
L
I
K
E
L
I
H
O
O
D
A
L
G
O
RI
T
H
M
Her
e
we
u
s
ed
th
e
f
o
llo
win
g
b
lo
ck
d
iag
r
am
(
Fig
u
r
e
5
)
t
o
co
n
d
u
ct
th
e
co
m
p
ar
is
o
n
.
Fo
r
B
a
u
m
-
W
elch
alg
o
r
ith
m
,
tr
an
s
itio
n
p
r
o
b
ab
ili
ty
m
atr
ix
an
d
em
is
s
io
n
p
r
o
b
a
b
ilit
y
m
atr
ix
a
lo
n
g
with
s
eq
u
en
ce
s
g
en
er
ate
d
by
th
em
h
av
e
b
ee
n
u
s
ed
to
f
in
d
o
u
t
th
e
esti
m
ated
m
atr
ice
s
.
W
h
ile
f
o
r
Ma
x
im
u
m
L
ik
elih
o
o
d
alg
o
r
ith
am
,
s
eq
u
en
ce
s
g
en
er
ated
an
d
s
tate
s
g
en
er
ated
b
y
th
ese
m
atr
ices
h
av
e
b
ee
n
u
s
ed
.
Fig
u
r
e
5
.
B
lo
ck
d
iag
r
am
t
o
f
in
d
co
m
p
a
r
is
o
n
o
f
two
alg
o
r
it
h
m
s
4
.
1
.
E
s
t
im
a
t
io
n us
ing
B
a
um
-
Welch
a
lg
o
rit
hm
Her
e
w
e
esti
m
ate
th
e
tr
an
s
iti
o
n
an
d
em
is
s
io
n
p
r
o
b
a
b
ilit
y
m
atr
ix
es
u
s
in
g
B
au
m
-
W
elch
alg
o
r
ith
m
.
Usi
n
g
MA
T
L
AB
,
we
esti
m
ated
th
e
m
atr
ix
es
u
s
in
g
th
e
s
eq
u
en
ce
s
an
d
tr
a
n
s
itio
n
p
r
o
b
ab
ilit
y
m
atr
ix
an
d
em
is
s
io
n
p
r
o
b
ab
ilit
y
m
at
r
ix
o
f
th
e
s
y
s
tem
.
B
y
r
u
n
n
in
g
th
e
ex
p
er
im
en
ts
s
ix
tim
es
we
f
o
u
n
d
th
at
av
e
r
ag
es
o
f
th
e
m
atr
ix
es
g
iv
es
b
etter
r
esu
lts
th
an
s
in
g
le
iter
atio
n
.
T
ab
l
e
2
s
h
o
ws
th
e
r
esu
lt
we
o
b
tain
f
o
r
HM
M1
.
Her
e
estTR
is
th
e
s
am
p
le
esti
m
ated
tr
an
s
itio
n
m
atr
ix
an
d
estEm
is
is
th
e
s
am
p
le
esti
m
ated
em
is
s
io
n
m
atr
ix
,
wh
ile
Av
E
s
ti
m
ated
T
r
an
is
th
e
av
er
ag
e
esti
m
ated
tr
an
s
itio
n
m
atr
ix
an
d
Av
E
s
tim
ated
E
m
is
is
th
e
av
er
ag
e
esti
m
ated
em
is
s
io
n
m
atr
ix
.
T
ab
le
3
s
h
o
ws th
e
r
esu
lt we
o
b
tain
f
o
r
H
MM
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
V
o
l.
1
8
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
2
7
8
0
-
2
7
8
6
2784
T
ab
le
2
.
Data
f
o
r
HM
M1
Tr
a
n
s
1
0
.
9
5
,
0
.
0
5
;
0
.
1
0
,
0
.
9
0
e
st
T
R
0
.
9
0
5
8
8
7
4
8
1
4
6
7
7
3
4
0
.
0
9
4
1
1
2
5
1
8
5
3
2
2
6
6
5
8
.
2
3
6
1
2
1
6
6
1
3
3
2
1
7
e
-
0
7
0
.
9
9
9
9
9
9
1
7
6
3
8
7
8
3
4
A
v
Est
i
ma
t
e
d
Tr
a
n
0
.
8
8
1
9
0
.
1
1
8
0
;
0
.
0
8
6
1
0
.
9
1
3
8
Emi
s
0
.
2
5
,
0
.
2
0
,
0
.
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T
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P
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2785
T
ab
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5
.
E
s
tim
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e
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CO
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SI
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Her
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ith
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ated
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ated
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ates
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ates
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u
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S
[1
]
M
it
o
la,
J
.
,
III;
M
a
g
u
ire,
G
.
Q.
Jr.,
“
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g
n
it
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v
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ra
d
i
o
:
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a
k
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n
g
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ftwa
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l
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l
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p
.
1
3
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8
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g
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st
1
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9
9
.
[2
]
Qin
g
Z
h
a
o
S
a
d
ler,
B.
M.,
“
A
S
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rv
e
y
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IEE
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7
9
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[3
]
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ra
im
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d
N.
M
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rh
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v
,
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Hid
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M
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6
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2
0
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2
.
[4
]
C.
G
h
o
sh
a
n
d
D.
P
.
Ag
ra
wa
l,
“
M
a
rk
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d
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n
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tru
m
se
n
sin
g
,
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Pro
c
.
IEE
E
Per
Co
m’0
9
,
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p
.
2
-
6
,
2
0
0
9
.
[5
]
Z.
Ch
e
n
a
n
d
R.
C.
Qi
u
,
“
P
re
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icti
o
n
o
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c
h
a
n
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sta
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p
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2
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6
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,
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rc
h
2
0
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0
[6
]
I.
Ak
b
a
r
a
n
d
W
.
Tran
ter,
“
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n
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m
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sp
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tru
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sin
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,
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in
Pro
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.
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E
S
o
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7
,
p
p
.
1
9
6
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2
0
1
,
2
0
0
7
.
[7
]
M
a
rk
o
v
,
A
.
A.
“
Th
e
o
ry
o
f
Al
g
o
rit
h
m
s
;
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a
n
sla
ted
b
y
Ja
c
q
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e
s
J
.
S
c
h
o
rr
-
Ko
n
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ff]
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Ac
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4
.
[8
]
Ra
b
in
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r
,
Law
re
n
c
e
,
“
F
irst
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n
d
:
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Hi
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d
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l
,”
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E
Glo
b
a
l
Histo
ry
Ne
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r
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,
Re
tri
e
v
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d
2
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to
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e
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2
0
1
3
.
[9
]
B
ak
er
,
Ja
m
e
s
K
,
“
Th
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DRA
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sy
ste
m
-
An
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v
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rv
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E
T
ra
n
sa
c
ti
o
n
s
o
n
Aco
u
st
ics
,
S
p
e
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c
h
,
a
n
d
S
ig
n
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l
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e
ss
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l
.
23
,
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p
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24
-
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,
1
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5
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0
]
Hen
d
r
y
,
Da
v
i
d
F
.
,
Nie
lse
n
,
“
Be
n
t
Ed
i
to
rs
Eco
n
o
m
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tri
c
M
o
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e
li
n
g
:
A
Li
k
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li
h
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d
Ap
p
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o
a
c
h
,
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Prin
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to
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:
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Pre
ss
,
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1
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o
,
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tak
a
,
“
Th
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o
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e
r
e
ffi
c
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c
y
imp
li
e
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fo
u
rt
h
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d
e
r
e
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n
c
y
,
”
J
o
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a
l
o
f
th
e
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a
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n
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5
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1
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2
]
S
.
Ya
rk
a
n
a
n
d
H.
Ars
lan
,
“
Bi
n
a
r
y
ti
m
e
se
ries
a
p
p
ro
a
c
h
to
sp
e
c
tru
m
p
re
d
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o
n
fo
r
c
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g
n
it
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v
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ra
d
io
,
”
in
Pro
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d
in
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s
o
f
2
0
0
7
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EE
6
6
t
h
Veh
ic
u
la
r
T
e
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h
n
o
lo
g
y
Co
n
fer
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n
c
e
(
VT
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-
2
0
0
7
Fa
ll
),
p
p
.
1
5
6
3
-
1
5
6
7
,
2
0
0
7
.
[1
3
]
C
.
Oliv
er
,
“
M
a
rk
o
v
P
ro
c
e
ss
e
sfo
rS
to
c
h
a
sticM
o
d
e
li
n
g
,
”
E
lse
v
ier
Aca
d
e
mic
Pre
ss
,
USA,
2
0
0
9
.
[1
4
]
D
.
T
r
ee
u
m
n
u
k
,
D
.
C
.
P
o
p
e
sc
u
,
“
Us
in
g
h
id
d
e
n
M
a
rk
o
v
m
o
d
e
ls
to
e
v
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l
u
a
te
p
e
rfo
rm
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n
c
e
of
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p
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ra
ti
v
e
sp
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c
tru
m
se
n
sin
g
,
”
IE
T
Co
mm
u
n
.
,
v
o
l.
7
,
n
o
.
17
,
p
p
.
1
9
6
9
-
1
9
7
3
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2
0
1
3
.
[1
5
]
E
.
C
h
atzia
n
to
n
io
u
,
B
.
Allen
,
V
.
Ve
li
sa
v
lj
e
v
ic,
“
An
HMM
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b
a
se
d
sp
e
c
tru
m
o
c
c
u
p
a
n
c
y
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re
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r
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r
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n
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rg
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e
fficie
n
t
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n
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ra
d
io
,
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so
n
a
l
I
n
d
o
o
r
a
n
d
M
o
b
il
e
R
a
d
io
Co
mm
u
n
ica
ti
o
n
s
(
PI
M
RC)
,
IEE
E
24
th
I
n
ter
n
a
ti
o
n
a
l
S
y
mp
o
si
u
m
,
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p
.
6
0
1
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6
0
5
,
8
-
11
S
e
p
t
e
m
b
e
r
2
0
1
3
.
[1
6
]
Law
r
e
n
c
e
,
R.
Ra
b
in
e
r,
F
e
ll
o
w
IE
EE
,
“
A
Tu
to
rial
o
n
Hi
d
d
e
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M
a
r
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o
v
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o
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e
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n
d
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e
lec
ted
Ap
p
li
c
a
ti
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p
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h
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o
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Re
a
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s in
sp
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re
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ti
o
n
,
IS
BN:
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-
5
5
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6
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4
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4
,
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p
.
2
6
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2
9
6
,
1
9
9
0
.
[1
7
]
Mo
h
am
ed
Lala
o
u
i,
Ab
d
e
ll
a
ti
f
E
l
Afia
,
Ra
d
d
o
u
a
n
e
Ch
i
h
e
b
,
“
A
S
e
lf
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n
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imu
late
d
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li
n
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m
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d
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n
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a
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v
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e
l
,
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In
ter
n
a
ti
o
n
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l
J
o
u
rn
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l
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E
lec
trica
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n
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Co
mp
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ter
En
g
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ry
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8
]
Hilm
an
F
.
P
a
rd
e
d
e
,
As
ri
R.
Y
u
li
a
n
i,
Ri
k
a
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u
stik
a
,
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n
v
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ti
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ra
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a
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d
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Tra
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ti
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t
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h
Re
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g
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it
i
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,
”
In
t
e
rn
a
ti
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n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
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d
C
o
mp
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ter
En
g
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)
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l.
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.
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5
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8
,
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c
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m
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8
.
[1
9
]
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Ny
e
in
M
o
n
,
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n
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a
,
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a
w
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u
,
“
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a
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,
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ter
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ti
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o
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)
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.
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p
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g
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[2
0
]
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.
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en
,
B
.
L
.
M
a
rk
,
Y
.
E
p
h
ra
im,
“
Hid
d
e
n
M
a
rk
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p
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c
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se
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d
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m
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c
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it
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ra
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,
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fo
rm
a
ti
o
n
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c
ien
c
e
s
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ms
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S
)
2
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1
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5
th
A
n
n
u
a
l
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o
n
.
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p
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1
-
6
,
8
-
11
S
e
p
t
e
m
b
e
r
2
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1
3
.
[2
1
]
Z
S
u
n
,
J
N
Lan
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m
a
n
,
“
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e
c
o
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d
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ry
a
c
c
e
ss
p
o
li
c
ies
wi
th
im
p
e
rfe
c
t
se
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sin
g
i
n
d
y
n
a
m
ic
sp
e
c
tru
m
a
c
c
e
ss
n
e
two
rk
s
”
,
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
fe
re
n
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C
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m
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s (IC
C)
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2
,
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p
.
1
7
5
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1
7
5
6
,
10
-
15
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n
e
2
0
1
2
.
[2
2
]
T
Yu
c
e
k
,
H
Ars
lan
,
“
A
su
rv
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y
o
f
sp
e
c
tr
u
m
se
n
sin
g
a
l
g
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m
s
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r
c
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n
it
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v
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ra
d
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o
a
p
p
li
c
a
ti
o
n
s
,
”
IEE
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mm
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n
.
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u
rv
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s
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u
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ri
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ls
,
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o
l.
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o
.
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p
p
.
1
1
6
-
1
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,
2
0
0
9
.
[2
3
]
C.
-
C.
Ch
a
o
a
n
d
Y.
-
L
.
Ya
o
,
“
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d
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n
M
a
rk
o
v
m
o
d
e
ls
f
o
r
th
e
b
u
rst
e
rro
r
sta
ti
stics
o
f
Viterb
i
d
e
c
o
d
i
n
g
,
”
IEE
E
T
r
a
n
s.
Co
mm
u
n
.
,
v
o
l.
4
4
,
p
p
.
1
6
2
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-
1
6
2
2
,
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c
e
m
b
e
r
1
9
9
6
.
[2
4
]
P
.
S
m
y
t
h
,
“
Hid
d
e
n
M
a
rk
o
v
m
o
d
e
ls
fo
r
fa
u
l
t
d
e
tec
ti
o
n
i
n
d
y
n
a
m
ic
sy
ste
m
s,”
P
a
tt
e
rn
Re
c
o
g
n
.
,
v
o
l.
2
7
,
n
o
.
1
,
p
p
.
1
4
9
-
1
6
4
,
1
9
9
4
.
[2
5
]
Qi
Wan
g
,
Lei
Wei
,
R
o
d
n
e
y
A.
K
e
n
n
e
d
y
,
“
Itera
ti
v
e
Vi
terb
i
De
c
o
d
i
n
g
,
Trelli
s
S
h
a
p
in
g
,
a
n
d
M
u
l
ti
lev
e
l
S
tru
c
t
u
re
fo
r
Hig
h
-
Ra
te
P
a
rit
y
-
Co
n
c
a
ten
a
ted
T
CM
,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
C
o
mm
u
n
ica
t
io
n
s
,
v
o
l.
50
,
p
p
.
4
8
-
55
,
2
0
0
2
.
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