Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 2
,
A
p
r
il
201
5, p
p
.
29
7
~
30
3
I
S
SN
: 208
8-8
7
0
8
2
97
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
Discr
e
te Markov Chain Based
Spectrum Sensing for
Cognitive
Radio
Mohammadre
z
a
Amini
1
, As
ra Mirz
avandi
2
,
Mo
s
r
afa
R
eza
e
i
3
1,3
Departem
ent
o
f
El
ectr
i
c
a
l
and
Com
puter Engin
eering
,
Co
lleg
e
of Engin
eerin
g,
I
s
lam
i
c Azad
Uni
v
ers
i
t
y
,
Boruj
e
rd
Branch,
Boruj
e
r
d
, Ir
an
2
Departem
ent
of
El
ectr
i
c
a
l
and C
o
m
puter Engin
e
ering,
Coll
ege
of
Engin
eering
,
Is
lam
i
c Az
ad Univ
ers
i
t
y
,
Yazd
Bra
n
ch,
Yazd,
Iran
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 13, 2014
Rev
i
sed
D
ec 28
, 20
14
Accepte
d
Ja
n 16, 2015
Spectrum
sensing is one of the f
unction
a
lit
ies of
cognitiv
e rad
i
o
s
to exploit
spectrum holes
without in
terrup
ting pr
imar
y
us
ers transmission. Th
e more
efficient of th
e
spectrum sensin
g, th
e high
est the throughput o
f
secondar
y
and primar
y
network. This paper pres
ents spectr
u
m sensing met
hod based o
n
phase t
y
p
e
m
o
d
e
lling
th
at
is si
m
p
le to do
for
secondar
y
us
ers to
conclud
e
about the
chan
nel stat
e (idl
e or busy
)
under
collision cons
traint
. Th
e
parameters of phase ty
p
e
m
odel
can be adjus
t
ed
based on desired operatin
g
point of the rec
e
iver s
e
ns
or in its
ROC curve. The pres
ent
e
d a
pproach can
run a tr
ade off b
e
tween sensing
time and th
e two
error probab
ilities of sensor
fals
e al
arm
and m
i
s
s
-
detection
.
Keyword:
Spectrum
Sens
ing
Co
gn
itiv
e Rad
i
o
Mar
k
o
v
Ch
ai
n
False Alarm
Miss-Detection
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
:
Mohamm
adreza Am
ini,
Depa
rtem
ent of Electrical a
nd Co
m
p
u
t
er
Engin
eer
ing
,
Islamic Azad
Uni
v
ersity, B
o
rujerd B
r
anc
h
,
Ira
n.
Em
a
il: m
oha
mmadreza.am
ini
@
ec.iut.ac
.ir
1.
INTRODUCTION
Sin
ce sp
ectrum
in
wireless co
mm
u
n
i
catio
n
s
h
a
s b
e
co
m
e
v
a
lu
ab
le, co
gnitiv
e rad
i
o
s
are d
e
v
e
lop
e
d to
expl
oi
t
t
h
e spe
c
t
r
um
hol
es i
n
l
i
censed
ban
d
s
un
de
r p
r
ot
ect
i
v
e co
nst
r
ai
nt
s
fo
r i
n
c
u
m
b
ent
users
[
1
,
2]
. S
o
t
h
e
co
gn
itiv
e users (second
ary
u
s
ers) sho
u
l
d
act in
tellig
en
tly i
n
ord
e
r to
u
s
e
th
e sp
ectru
m
fo
r
d
a
ta transmission
an
d
no
t to
in
terfere with
the p
r
im
ary u
s
ers (PU) sim
u
ltan
e
ou
sly [3
,
4, 5
]
. In
su
ch
a case, op
por
tu
n
i
stic
spectrum
acce
ss (OSA) named Interwea
ve
m
odel has been
evolve
d to enable the users dynam
i
cally
access
the spect
rum
[6,
7]. OSA
ha
s two m
a
in steps, s
p
ectru
m
sensing a
nd
spe
c
trum
access [8,
9]. In the
se
nsing
step, a seconda
ry user (SU) evaluates the spectrum
bands to
find
id
le ch
an
n
e
ls and
in
the second step,
the SU
shoul
d
deci
de on
its
access for data
transm
ission [10, 11
,
12].
At the e
n
d of se
nsing
phase the SU concludes
abo
u
t
t
h
e st
at
e
o
f
c
h
a
nnel
oc
cupa
ncy
a
n
d t
h
ere
i
s
a
l
e
v
e
l
of
u
n
c
ertain
ty in
its
d
ecision
.
So
m
e
of spectru
m
sen
s
ing
m
e
th
od
s su
ch
as
featu
r
e
d
e
tectio
n, cyclo
-
sta
tio
n
a
ry d
e
tection
an
d m
a
tch
e
d
filter h
a
v
e
co
nsid
ered
phy
si
cal
cha
r
a
c
t
e
ri
st
i
c
s of P
U
si
g
n
al
[1
3,
1
4
,
15]
w
h
i
l
e
t
h
e ot
hers e
x
pl
oi
t
som
e
general
param
e
t
e
rs of
si
gnal
su
ch
as en
erg
y
lev
e
l along
wi
th
statistical analysis to
co
ncl
ude
a
b
o
u
t
t
h
e
chan
nel
occ
u
p
a
ncy
[
1
6, 1
7
]
.
In
t
h
i
s
pape
r we p
r
o
p
o
se spect
r
u
m
sensi
n
g m
e
t
hod
based o
n
p
h
as
e type
m
odelling for channel
state detection. The
p
r
esen
ted
app
r
o
ach
can
run
a trad
e off
b
e
tween
sensin
g
time an
d
th
e two
error prob
abilit
ies o
f
sensor false
alarm
and m
i
ss
-detection
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Di
scret
e
M
a
rk
ov C
hai
n B
a
se
d
Spect
r
u
m
Se
nsi
n
g f
o
r C
o
g
n
i
t
i
ve Radi
o
(
M
oh
a
m
m
a
drez
a Ami
n
i
)
29
8
2.
SYSTE
M
MODEL AND PROBLEM FORMUL
ATION
In
ou
r p
r
o
p
o
se
d m
odel
,
at
t
h
e begi
n
n
i
ng
of t
h
e sensi
ng
pr
o
cess t
h
e SU i
s
i
n
t
h
e zer
o st
at
e of M
a
r
k
o
v
ch
ain
sh
own
in fig
u
re1
an
d
st
arts to
tran
sit between
states based
on
th
e prob
ab
ilities d
e
p
e
n
d
i
n
g
u
pon
receiv
ed
sig
n
a
l
v
a
lu
es sa
m
p
led
in each
tim
e step
. Th
e
p
r
o
cess contin
u
e
s till th
e
Marko
v
ch
ain
en
ters th
e ab
sorb state
o
f
A. Dep
e
nd
in
g on
wh
ich
path
was trav
ersed
to en
ter th
e
abs
o
rb state, t
h
e cha
nnel
state is deci
ded.
W
i
th the
m
e
nt
i
oned
des
c
ri
pt
i
o
n,
t
h
e
M
a
rk
o
v
c
h
ai
n
i
s
a di
sc
ret
e
p
h
as
e t
y
pe
m
odel
PH
τ
,
[1
8]
. The
di
scr
e
t
e
p
h
ase
-
typ
e
d
i
stribu
tio
n is d
e
n
s
e in th
e fiel
d
of al
l d
i
screte
p
o
sitiv
e-v
a
lu
ed
d
i
stribu
tio
n
s
, th
at
is, it can
b
e
used
t
o
ap
pro
x
i
m
a
te a
n
y d
i
screte po
sitiv
e-v
a
lu
ed
d
i
strib
u
tion
[1
9,
2
0
]
.
1
,
0
P
1
,
0
P
0
,
1
P
0
,
1
P
1
1
N
1
2
N
Fi
gu
re 1.
P
h
as
e t
y
pe re
pre
s
en
t
a
t
i
on o
f
se
nsi
n
g
pr
oce
d
u
r
e
Su
pp
ose at
t
h
e
t
i
m
e
s
t
e
p
(
sa
m
p
le) th
e SU is in
th
e
state (
1
1
).
Hav
i
n
g
sam
p
led
t
h
e si
g
n
al r(t
)
, t
h
e
SU in the ch
ai
n
t
r
an
sits to state n
+
1 with
pro
b
a
b
ility
and
to
s
t
a
t
e
n
-
1 with
p
r
o
b
a
b
ility (
1
), in
wh
ich
is
th
e o
b
s
erv
a
tio
n v
a
riab
le,
see Figu
re 2
t
h
e ob
serv
ation
vari
a
b
l
e
i
s
t
h
e
o
n
e t
h
at
a
de
ci
si
on a
b
out
c
h
an
nel
st
at
e c
oul
d
be m
a
de base
d
on
s
u
c
h
as e
n
e
r
gy
l
e
vel
o
f
sam
p
les. In this p
a
p
e
r
we
defin
e
≜
|
|
. Th
ese tran
sitio
n
p
r
o
b
a
b
ilities are equ
a
l to lik
elihoo
d
v
a
lu
e of
si
gnal
sam
p
l
e
due
t
o
H
and
H
hy
pot
heses:
,
Z
k
,
h
k
∗S
k
Z
k
(1
)
in
wh
ich
is th
e
sam
p
l
e
of si
gnal
,
Z
k
i
s
t
h
e Ga
ussi
an
ra
nd
om
va
ria
b
le
with mean
zero a
nd
som
e
variance
σ
and
h
k
an
d
S
k
are
the c
h
a
nnel
coe
fficient a
n
d
PU tr
ansm
i
tted
sig
n
a
l
resp
ectiv
ely. If
we
negl
ect
t
h
e
va
ri
at
i
on
of c
h
an
nel
coe
ffi
ci
ent
du
ri
n
g
t
h
e se
nsi
n
g t
i
m
e (be
cause t
h
e se
ns
i
ng
phas
e
i
s
a sho
r
t
peri
od
of t
i
m
e) an
d i
f
t
h
e
sam
p
l
e
s are consi
d
ere
d
as i
.
i
.
d ra
n
dom
vari
abl
e
s, i
t
can be s
h
ow
n t
h
at
t
h
e
d
i
str
i
bu
tio
n
a
n
d
are c
h
i-s
q
uare
whic
h are
s
h
own in
equ
a
tio
n (2
) and
(3
)
[
2
1
,
22
].
|
σ
σ
0
(2
)
|
σ
σ
σ
/
(3
)
in
wh
ich th
e
fun
c
tio
n
is :
0
0
0
1
0
and
I
is th
e m
o
dified
Bessel
fun
c
tio
n of t
h
e
first k
i
n
d
and
g
i
s
th
e ch
an
n
e
l
gain
.
Because si
gnal
sam
p
les are
random
variabl
e
s due t
o
st
oc
hastic be
ha
viour of c
h
a
nnel,
the Markov chain is
no
n
-
h
o
m
ogene
ous
a
n
d
de
pe
n
d
s
on
sam
p
le
at
tim
e
step.
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
. 2, A
p
ri
l
20
15
:
29
7 – 3
0
3
2
99
)
(
0
k
y
f
)
(
1
0
k
y
f
Fi
gu
re
2.
Tra
n
s
i
t
i
on bet
w
ee
n s
t
at
es fo
r sec
o
n
d
ary
use
r
So t
h
e eq
ui
val
e
nt
phase t
y
pe
m
odel
(t
hat
descri
bes t
h
e di
st
ri
but
i
o
n o
f
t
o
t
a
l
num
ber o
f
sam
p
l
e
s needed t
o
d
ecid
e
abou
t ch
ann
e
l
o
c
cup
a
n
c
y) h
a
s th
e i
n
itial p
r
ob
ab
ilit
y m
a
trix
τ
and
th
e tran
sition
prob
ab
ility
m
a
trix
(at
t
i
m
e
st
ep) descri
bed
bel
o
w:
(4)
1,
0
0,
o
.
w
(5
)
,
(6
)
Th
e p
r
ob
ab
ilities
P
,
fo
r
i
N
1
,…,N
1
can be d
e
scri
be
d
as
bel
o
w:
P
,
f
y
P
y
|
H
P
,
1
f
y
P
y
|
H
P
,
0
fo
r
j
i
1
and
j
i
1
No
w
we
ha
ve t
o
a
n
sw
er t
w
o
q
u
estio
ns.
1-
Ho
w t
o
c
o
m
pute
N
and
N
for t
h
e
chain
?
2-
How to
i
n
tro
d
u
ce th
e co
llision
pro
b
a
b
ility c
o
n
s
t
r
ain
t
s in
t
o
th
e sensing
sch
e
m
e
to
p
r
o
t
ect PU sign
al from
interfe
rence
?
It is obv
iou
s
that th
e m
o
re th
e v
a
lu
e of
N
, th
e
m
o
re sa
m
p
les n
eed
ed
t
o
d
ecid
e
ab
ou
t
b
e
ing id
le and
also the m
o
re
the value of
N
, t
h
e m
o
re sam
p
l
e
s nee
d
e
d
t
o
deci
de a
b
out
bei
n
g b
u
sy
.
If
bot
h
N
and
N
in
cr
ease t
h
e
f
i
nal d
ecision
h
a
s h
i
gh
lev
e
l of
cer
t
ain
t
y bu
t th
e ti
m
e
to
d
ecisio
n
abou
t ch
annel o
ccup
a
n
c
y
gr
ow
s
rapi
dl
y
.
I
n
ot
h
e
r
wo
r
d
s,
t
h
e
v
a
l
u
es
of
N
and
N
d
i
rectly im
p
act
on
t
h
e
prob
abilit
y o
f
false-alarm
an
d
m
i
ss-
d
e
tectio
n. Th
erefore if th
ese
p
r
ob
ab
ilitie
s are k
nown
p
r
ev
i
o
u
s
ly, th
e
v
a
lues for
N
and
N
can be calc
u
lated
accordingly. To m
eet
the collision c
onst
r
aint, the operating poi
nt of sensor
in its ROC curve m
u
st be adj
u
sted
so
t
h
at:
(7
)
th
en
t
h
e
p
r
ob
lem
o
f
find
ing
N
and
N
tu
rn
s to calcu
l
atin
g
t
h
ese
p
r
ob
ab
ilities. So
we
h
a
v
e
:
P
H
|
H
P
H
and
n
N
|
H
∞
P
H
|
H
P
H
and
n
N
|
H
∞
whe
r
e
n
is th
e to
tal nu
m
b
er
o
f
sam
p
les n
e
ed
ed
for d
ecisi
o
n
.
Co
nd
itio
n
e
d on
sam
p
les
v
a
lue th
e prob
ab
ility of
m
i
ss-det
ect
i
on can be deri
ved
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Di
scret
e
M
a
rk
ov C
hai
n B
a
se
d
Spect
r
u
m
Se
nsi
n
g f
o
r C
o
g
n
i
t
i
ve Radi
o
(
M
oh
a
m
m
a
drez
a Ami
n
i
)
30
0
…
P
H
and
n
N
|
H
,Y
y
∞
f
dy
Assu
m
i
n
g
signal sam
p
les are i.i.
d a
n
d
co
nsi
d
eri
n
g t
h
e
co
n
d
i
t
i
on
H
it can
b
e
written
as:
f
f
y
We have
al
so:
PH
and
n
N
|
H
,Y
y
P
SUgoesfr
o
mstat
e0t
o
N
1
i
n
N
1
st
eps
|
H
,Y
y
PSUgoes
f
r
omstat
e
N
1
t
oAattheinal
st
e
p
|
H
,Y
y
Proceedi
n
g to
com
pute we
ha
ve:
P
SUgo
e
sfr
o
m
s
tat
e
0t
o
N
1
i
n
N
1
st
eps
|
H
,Y
y
T
,…T
,
P
SUgo
e
sfr
o
m
s
tat
e
N
1
to
s
t
at
eAat
t
heinals
t
e
p
|
H
,Y
y
f
y
whe
r
e
T
is th
e
prob
ab
ility
m
a
trix
of
p
h
ase type co
m
p
u
t
ed
fo
r
i
sam
p
l
e
and
P
,
mean
s t
h
e en
try
o
f
m
a
trix
P
in
row i an
d colu
m
n
j
.
…
T
,
f
y
f
y
∞
d
y
N
(8
)
in
wh
ich
f
y
is th
e prob
ab
ility d
e
n
s
ity fun
c
tion
o
f
ob
serv
ation
v
a
riab
le und
er
H
h
ypo
th
esis.
Th
e sam
e
p
r
o
c
ed
ure can
b
e
ap
p
lied fo
r th
e false-alarm
p
r
ob
ab
ility to
d
e
ri
v
e
:
P
H
|
H
P
H
and
n
N
|
H
∞
P
…
,
1
y
f
y
∞
d
y
(9
)
C
onsi
d
eri
n
g
t
h
e eq
uat
i
o
ns
(7
)
,
(
8
)
a
n
d
(
9
)
ca
n
be s
o
l
v
e
d
n
u
m
eri
cal
l
y
for t
h
e m
i
nim
u
m
val
u
es
of
N
and
N
to
h
a
v
e
t
h
e mi
n
i
mu
m s
e
n
s
i
n
g
t
i
me
.
R
e
me
mb
e
r
t
h
a
t
and
ar
e
no
n-in
cr
easing fu
nctio
n
of
co
m
p
u
t
atio
n of
N
and
N
respecti
v
ely s
o
t
h
e i
n
tegrals
go to ze
ro
quic
k
ly as
N
and
N
inc
r
ease. In gene
ral
th
e two
d
e
riv
e
d
p
r
o
b
a
b
ilities are no
t so
tract
ab
le to
work
with
, th
at is
b
e
cau
s
e
o
f
no
n-h
o
m
o
g
e
n
e
ou
s
p
r
o
p
e
rty
o
f
a Marko
v
ch
ain
.
C
h
ang
i
ng
th
e tran
sitio
n law b
e
tween
th
e states resu
lt
s in
m
o
re tractab
le equ
a
tio
ns wh
ich
i
s
i
n
ou
r next
s
t
udy
.
3.
N
U
M
E
RICAL R
E
SU
LT
In
t
h
is section
p
r
ob
ab
ility o
f
false-alar
m
an
d
m
i
ss-d
e
tectio
n
are p
l
o
tted
versu
s
N
and
N
. It
shoul
d
b
e
n
o
t
ed
t
h
at
p
r
ob
ab
ility o
f
miss-d
e
tectio
n and
false-alarm
are d
e
p
e
n
d
e
n
t
on
bo
th
N
and
N
bu
t it can be
easily in
ferred
th
at th
eir
d
e
pen
d
e
n
c
ies are insig
n
i
fican
t
t
o
N
and
N
resp
ectiv
ely.
Sim
u
latio
n
p
a
ram
e
ter
and
th
eir v
a
l
u
es are sh
own
in
th
e Tab
l
e1. Figu
re3
and
4
show th
e two
p
r
ob
ab
ilities v
e
rsu
s
N
and
N
. To
ha
ve
a
certain
prob
ab
i
lity o
f
false-alarm
an
d
co
llisio
n
,
su
ch
curv
es
can
b
e
d
r
awn
to
calcu
late th
e
n
u
m
b
e
r
o
f
stat
es or
equat
i
o
ns
(
8
)
a
n
d
(
9
)
can
be
s
o
l
v
e
d
num
eri
cal
l
y
for
N
and
N
.
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. 2, A
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7 – 3
0
3
3
01
Tabl
e 1. Si
m
u
lat
i
on param
e
t
e
rs
Value
Para
m
e
ter
1
σ
1
g
Fi
gu
re
3.
Fal
s
e
al
arm
pro
b
abi
l
i
t
y
versu
s
N1
a
n
d
N
2
Fig
u
re 4
.
Miss-Detectio
n
probab
ility
v
e
rsu
s
N1
and
N2
In t
h
i
s
pa
rt
, w
e
com
p
are our
prese
n
t
e
d m
e
t
hod
wi
t
h
t
h
e
m
o
st
com
m
on spect
r
u
m
sensi
ng al
go
ri
t
h
m
,
i.e., en
erg
y
d
e
t
ecto
r
. En
erg
y
d
e
tecto
r
e are
kn
own
b
eca
u
s
e th
ey are si
m
p
l
e
to
d
o
for cogn
itiv
e rad
i
o
s
an
d
d
o
not
nee
d
p
r
i
o
r i
n
f
o
rm
at
i
on of PU si
g
n
al
. Ot
h
e
r sensi
n
g ap
p
r
oache
s
are co
m
p
l
e
x and hav
e
t
o
kno
w som
e
pri
o
r
k
nowledg
e abo
u
t
PU sign
al
. Th
e relation b
e
tween
t
h
e two pro
b
a
b
ilities in
su
ch
a d
e
tector
u
n
d
e
r th
e
assum
p
t
i
on of
i
nde
pen
d
e
n
cy
of p
r
i
m
ary
si
g
n
al
and n
o
i
s
e a
nd t
h
e ass
u
m
p
t
i
on o
f
Ga
ussi
a
n
zero m
ean fo
r noi
se
is as fo
llows
[23
]
.
2
1
(1
0)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Di
scret
e
M
a
rk
ov C
hai
n B
a
se
d
Spect
r
u
m
Se
nsi
n
g f
o
r C
o
g
n
i
t
i
ve Radi
o
(
M
oh
a
m
m
a
drez
a Ami
n
i
)
30
2
In
whic
h
τ
,
γ
,
f
a
r
e t
h
e
sensi
n
g
t
i
m
e, si
gnal
t
o
noi
se rat
i
o a
n
d
sa
m
p
li
ng
f
r
eq
ue
ncy
resp
ect
i
v
el
y
.
P
is
th
e pro
b
a
b
ility o
f
d
e
ted
c
tio
n
wh
ich
is t
h
e com
p
le
men
t
o
f
P
.
Equ
i
v
a
len
tly,
based
on
th
e num
b
e
r o
f
sen
s
i
n
g
sam
p
les (N)
eq
u
a
tion
(1
0)
will b
e
ch
ang
e
d
to
:
2
1
(1
1)
If we assu
m
e
t
h
at th
e n
o
i
se po
wer (v
arian
ce) is u
n
ity
(to com
p
are with the achieve
d curves in the numerical
results) and
unde
r the
sam
e
sim
u
lati
on environm
ent, the
expected
num
be
r of sam
p
les nee
d
ed to
reach a
decision a
b
out
the
channel sta
t
e with
P
0
.
1
and
P
0
.
0
5
i
s
p
l
o
tted
in Figu
re 5.
As it can b
e
seen,
t
h
e num
ber o
f
sam
p
l
e
s
t
o
dec
i
de abo
u
t
t
h
e c
h
an
nel
st
at
e i
s
con
s
i
d
era
b
l
y
l
o
we
r i
n
t
h
e p
r
esent
e
d m
e
t
hod t
h
an
to
th
e en
erg
y
detecto
r
; h
e
n
ce t
h
e sen
s
ing
time b
e
co
m
e
s less.
Fi
gu
re
5.
A
de
ci
si
on a
b
out
t
h
e cha
nnel
st
at
e wi
t
h
P
0
.
1
and
P
0
.
0
5
4.
CO
NCL
USI
O
N
In t
h
i
s
pa
pe
r
spect
r
u
m
sensi
n
g
base
d
o
n
di
scer
ete Markov c
h
ain
wa
s presente
d. T
h
e
prese
n
te
d
ap
pro
ach
is so si
m
p
le
to
d
o
to
for
seco
n
d
ar
y
users t
o
deci
de o
n
cha
nnel
occu
pa
ncy
.
Th
e param
e
t
e
rs of t
h
e
p
r
op
o
s
ed
m
o
d
e
l are ad
ju
sted
so
th
at th
e co
llisio
n
probab
ility
i
m
p
o
s
ed
b
y
th
e p
r
im
ary n
e
two
r
k
on
the
seco
nda
ry
net
w
o
r
k i
s
m
e
t
.
Furt
herm
ore t
h
e
prese
n
t
e
d ap
p
r
oac
h
gi
ves us
t
o
adapt
t
h
e s
e
nsi
n
g t
i
m
e
. It
m
eans
whe
n
the
received si
gnal
power of prim
ary user is high,
the
sensing tim
e
takes m
u
ch
less than that of for low
si
gnal
p
o
w
er,
whi
l
e
m
a
i
n
t
a
i
n
i
ng t
h
e o
p
e
r
at
i
ng
poi
nt
of t
h
e
sens
or co
nst
a
n
t
(t
he fal
s
e al
arm
and
m
i
ss-det
ect
i
o
n
p
r
ob
ab
ilities remain
u
n
c
h
a
n
g
e
d
)
.
W
e
v
a
lidate ou
r an
alysis
b
y
sim
u
latio
n
an
d co
m
p
ared
th
e propo
sed
meth
o
d
wi
t
h
e
n
er
gy
de
t
ect
or, t
h
e m
o
st
com
m
on spec
t
r
um
sensi
n
g al
go
ri
t
h
m
.
ACKNOWLE
DGE
M
ENTS
Th
is St
u
d
y
w
a
s supp
or
ted b
y
I
s
lam
i
c A
zad
U
n
i
v
er
sity
, B
o
ru
jer
d
B
r
anc
h
,
Ira
n.
T
h
e a
u
tho
r
s
w
oul
d
lik
e to
ackn
owled
g
e
staffs of
u
n
i
v
e
rsity.
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BIOGRAP
HI
ES OF
AUTH
ORS
M
oham
m
a
drez Am
ini, is
an
a
c
a
dem
i
c m
e
m
b
er
of Is
lam
i
c
Aza
d
Univers
i
t
y
,
B
o
rujerd Br
anch
,
Iran. He was born in 1981 and is a telecommunica
tion research
er. He won so
me n
a
tion
a
l awards
in his
r
e
s
ear
ch
ar
ea.
Asra Mirzavand
i
is now an M.sc
student of
el
ectr
onic eng
i
neering
.
She was born in 1887 and is
a
student member
of IEEE.
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