TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3257 ~ 32
6
5
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.4944
3257
Re
cei
v
ed O
c
t
ober 1
5
, 201
3; Revi
se
d Novem
b
e
r
24, 2013; Accept
ed De
cem
b
e
r
12, 2013
Adaptive Two-Stage Sensing in Cognitive and Dynamic
Spectrum Access Networks
Yang Yu*, Yanli Ji, Weidong Wan
g
, Yinghai Zhan
g
Beiji
ng U
n
ivers
i
t
y
of Posts an
d T
e
lecommun
i
catio
n
s, Beiji
n
g
, 1008
76, Ch
i
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
y
u
ya
ng
19
86
@bu
p
t.edu.cn
A
b
st
r
a
ct
In this pap
er, we first investiga
t
e and co
ntrast t
he features of
energy d
e
tecti
on an
d cyclost
a
tion
ar
y
feature detecti
on for spectru
m
sens
in
g. Co
mb
ini
ng the a
d
v
antag
es of
bo
th, w
e
propose
an ada
ptive tw
o-
stage s
ensi
ng
sche
m
e w
h
ic
h
first perfor
m
s
spectru
m
se
ns
ing usin
g an e
nergy detector
in
c
ogn
itive a
n
d
dyna
mic sp
ec
trum
access
netw
o
rks. T
hen th
is sc
he
me
d
e
cid
e
s
w
hether or
n
o
t to i
m
ple
m
en
t
cyclostatio
nary
feature
detecti
on
base
d
o
n
th
e se
nsin
g re
s
u
l
t
s of the first st
age. On
the pr
emise of meeti
n
g
a giv
en c
onstr
aint o
n
the
pro
bab
ility of fa
lse
alar
m,
o
u
r pr
o
pose
d
sch
e
m
e
ai
m to
opti
m
i
z
e the
prob
ab
ilit
y of
detectio
n
. In o
r
der to obt
ain
the opti
m
al d
e
t
ection th
res
h
o
l
ds, the d
e
tection
mo
de
l is formulat
ed as
a
non
lin
ear
opti
m
i
z
at
io
n pr
obl
em. F
u
rth
e
r
m
o
r
e, the
perfo
rm
an
ce o
f
ou
r
sch
em
e i
n
sensi
n
g sp
ee
d i
s
a
l
so
ana
ly
z
e
d. T
he
simulati
on res
u
lts show
that the pro
pose
d
sche
m
e i
m
pr
ov
es the perfor
m
ance of spectr
um
sensi
ng c
o
mp
ared w
i
th th
e
ones w
h
ere
o
n
ly e
ner
gy
d
e
tection
or cycl
ostation
ary fea
t
ure det
ection
i
s
perform
ed.
Ke
y
w
ords
: c
ogn
itive ra
di
o
,
dyna
mic s
pectru
m
acc
e
ss, tw
o-stage sensi
ng, e
nergy
detecti
on,
cyclostationary
f
eature detection
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Future wi
rele
ss co
mmuni
cation
net
works env
isage
the ch
allen
g
e that the a
v
ailable
spe
c
tru
m
i
s
becoming
in
cre
a
si
ngly
scarce. Ho
wever, the
co
nventional
app
roach
of static
spectrum all
o
cation leads
to si
gnificant radi
o
spectrum underut
ilization;
e.g., at least 50%
of
broa
dcast tel
e
vision
ch
an
nels i
n
the
Wa
shin
gton
area
are u
n
u
s
ed,
co
nstitut
i
ng kno
w
n ‘
w
hite
s
p
ac
es
’ in the s
p
ec
trum [1].
Cog
n
itive ra
dio (CR) [2, 3] or
dynamic sp
ect
r
u
m
access (DSA)
tech
no
logy is a
promi
s
ing approach for
the more effective use
of existi
ng spectrum which can
intelligentl
y
identify unused lice
n
sed
band
s an
d al
low ad
aptive
ut
ilization of t
hem a
s
long
as not
cau
s
i
ng
una
cceptabl
e
interferen
ce
from unli
c
en
sed
or
se
c
o
nd
a
r
y us
er
s
(SU
s
)
to
lic
ens
e
d
o
r
pr
imar
y
use
r
s
(PUs).
In orde
r to de
termine
whet
her o
r
not the
licen
sed b
a
n
d
s a
r
e un
use
d
, the SUs ha
ve
to perfo
rm
sp
ectru
m
sen
s
i
ng. The
ne
ed
for fa
st
a
nd
effective (reli
able) spe
c
tru
m
sensi
ng
over
a
wide
ban
dwi
d
th is fu
nda
mentally imp
o
rtant to
DS
A. Meanwhil
e
, spe
c
trum
sen
s
in
g is
al
so a
chall
engin
g
task, becau
se
the receive
d
PU signal
at
SU receiver is possibl
e to be very we
ak
owin
g to path loss and fading [4], the perfe
ct de
tection of PU’s tra
n
smission is h
a
rd
to
impleme
n
t in pra
c
tice.
Variou
s
sp
ectrum
sen
s
in
g
sche
me
s h
a
v
e bee
n p
r
o
posed. M
any
of them
exp
l
oit two
typical featu
r
es, na
mely e
nergy [5] a
n
d
cyclo
s
ta
tion
a
r
y feature
s
[6
]. Energy det
ection i
s
one
of
the most po
p
u
lar te
chniq
u
e
s for
spe
c
trum se
nsin
g, whe
r
e a SU
make
s a d
e
ci
sion
with re
spect
to the presen
ce of PUs a
c
cording to th
e amount
of its received e
nergy [7]. This method i
s
e
a
sy
to implement,
and do
es
no
t need that th
e SU kno
w
s t
he inform
atio
n of the PU signal. Ho
wev
e
r,
it suffers fro
m
a relatively poo
r pe
rformance o
w
in
g
to the un
ce
rtainty of noise level in th
e
low
sign
al-to
-
noi
se ratio (S
NR) regime. A si
gnifica
nt
ly better perfo
rma
n
ce
can
be a
c
hieve
d
thro
u
gh
cyclo
s
tation
ary feature det
ection expl
oiting the pe
ri
o
d
ic
stru
cture of the
PU sig
nal, by ca
rryi
n
g
out cycli
c
spe
c
tral a
nalysi
s
[8]. Throug
h this me
th
od, n
o
ise
ca
n be
si
gnifica
ntly su
ppre
s
sed, thu
s
achi
eving mo
re robu
stne
ss than ene
rgy
detectio
n
. In addition, this
method d
e
tects only sig
nal
s
with the d
e
si
red feature an
d ther
efo
r
e i
s
able to di
stin
guish cert
ain types
from others.
Ho
wev
e
r,
the exact
cycl
ostation
ary fe
ature
of the P
U
si
gnal
may
not be
kn
own
to the SU an
d nee
ds a lo
n
g
observation t
o
be o
b
taine
d
. Also, the
downsi
de of
this metho
d
in gen
eral i
s
its increa
se
d
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3257 – 32
65
3258
comp
utationa
l com
p
lexity and m
e
mo
ry req
u
ire
m
ent
s, whi
c
h
m
a
kes thi
s
meth
od difficult f
o
r
pra
c
tical u
s
e,
espe
cially in
the envir
on
m
ents of high real
-time requi
reme
nts.
In a pra
c
tical
CR
system,
one commo
n
requi
reme
nt of sen
s
ing a
p
p
roa
c
h
e
s i
s
the fast
and
effective
(reli
able
)
d
e
tection
of idl
e
prima
r
y chan
nels by SUs
as
ch
ara
c
te
ri
zed
by the
m
ean
sen
s
in
g time.
The m
ean
sensi
ng time i
s
the
aver
a
g
e
time to
su
cce
ssfully
sen
s
e a
n
availa
ble
cha
nnel, whi
c
h de
pen
ds
on the se
arch algorith
m
.
The impo
rtan
ce of dete
c
to
r de
sign is fu
rther
enha
nced by the impact of
its operat
ing
cha
r
a
c
teri
stic which is r
eprese
n
ted by the prob
ability of
corre
c
t dete
c
tion,
P
d
, and the pro
bability
of false alarm,
P
f
, res
p
ec
t
i
vely.
As mention
e
d
above, cy
clo
s
tationa
ry feat
ure det
ection h
a
s
superi
o
rity in
sen
s
ing
effectivene
ss over en
erg
y
det
ection,
esp
e
ci
ally for low SNRs.
On the oth
e
r han
d, ene
rg
y
detectio
n
is a much q
u
icker a
nd ea
si
er sp
ect
r
um
sen
s
in
g meth
od, while it has not too m
u
ch
degradatio
n o
f
sen
s
in
g a
c
cura
cy comp
ared
with cy
clo
s
tationa
ry fea
t
ure d
e
tectio
n
for hi
gh S
N
Rs
[9], [10]. Thus, with the grai
n of nature, a
tr
adeoff bet
ween sen
s
ing
spe
ed an
d se
nsin
g accu
ra
cy
combi
n
ing the advantages of
these two
detection methods
will make the most sense.
In this
pap
er,
we
first
give
a b
r
ief int
r
o
ductio
n
to th
e me
cha
n
ism
s
of
ene
rgy d
e
tection
and
cyclo
s
ta
tionary featu
r
e d
e
tectio
n, and th
en prop
ose
a
n
adaptive
two
-
stag
e sen
s
i
ng
approa
ch b
a
s
ed
on en
ergy detection
and cy
clo
s
ta
tionary feat
ure d
e
tectio
n
to achieve
the
tradeoff me
ntioned
above.
By now, a lot
of pape
rs ha
ve investigat
ed two
-
stage
sen
s
in
g for
CR
system
s. Ho
wever, the
r
e
has b
een f
e
w
works
on
the com
b
in
ation of ene
rgy detection
and
cyclo
s
tation
ary detection, to the authors’ knowl
edg
e. In the first stage of the propo
sed sch
e
m
e
energy dete
c
t
i
on is pe
rformed. Th
e
n
, the p
r
op
ose
d
scheme
de
ci
des
wh
ethe
r
or n
o
t to pe
rform
cyclo
s
tation
ary detection a
c
cordi
ng to th
e sen
s
in
g re
sults of the first stage,
i.e., if the energy is
greate
r
th
an
a certai
n thre
shol
d, the
given
cha
nnel
is se
nsed to
b
e
a
c
tive, else
, cyclo
s
tation
ary
detectio
n
is p
e
rform
ed. In t
he
se
cond
st
age, th
roug
h comp
ari
ng
th
e
de
ci
sion m
e
tric with ano
ther
certai
n thre
shold, the given ch
ann
el is de
clare to be active or
idle. Aiming at optimizing
the
prob
ability of
detectio
n
u
n
d
e
r th
e
con
s
traint on
the
probability of fa
lse
ala
r
m, we
formul
ate th
e
detectio
n
mo
del a
s
a
nonli
near optimi
z
a
t
ion pr
oblem
and give th
e
method to
de
duce the a
b
o
v
e
two o
p
timal t
h
re
shol
ds. M
o
reove
r
,
we a
l
so
analyze t
he pe
rfo
r
man
c
e
of the p
r
o
posed
schem
e in
sen
s
in
g sp
ee
d by dedu
cin
g
the mean sensi
ng time.
The
remai
n
d
e
r of thi
s
p
a
per i
s
org
ani
zed
a
s
follo
ws. In S
e
ctio
n 2, we give
a b
r
ief
introdu
ction
to the p
r
op
ose
d
ad
apti
v
e two-
stag
e sen
s
ing
scheme. In
Section
3,
the
cha
r
a
c
teri
stics of en
ergy d
e
tection
and
cyclo
s
ta
tion
ary feature det
ection te
ch
ni
que
s are giv
en,
and the p
r
op
ose
d
schem
e
is describe
d
in more d
e
tail
. The optimal
threshold
s
fo
r the pro
p
o
s
e
d
two-stage se
nsin
g
sche
m
e
are also derived
i
n
this
se
ction. More
over, we analy
z
e the
perfo
rman
ce of
the
propo
sed scheme in
sen
s
i
ng
speed. Simula
tion results a
r
e prese
n
ted
in
Section 4, an
d con
c
lu
sio
n
s are drawn in Section 5.
2. The Propos
e
d
Algorithm
1
2
1
E
D
2
C
D
Figure 1. Adaptive Two-st
a
ge Spect
r
um
Sensin
g
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Adaptive T
w
o
-
Stage Sen
s
i
ng in Co
gnitive and Dyn
a
m
i
c Spect
r
um
Acce
ss Net
w
orks (Y
ang Y
u
)
3259
In
this secti
on,
we will briefly
introduc
e the
adaptive two-sta
ge spectrum
sensi
ng
scheme. T
h
e
flow cha
r
t of
the propo
sed
schem
e is
shown in Fi
gure 1. Fo
r sim
p
licity, we ign
o
r
e
the perio
d of data co
mmun
i
cation a
nd a
s
sume that
th
e spe
c
trum sensi
ng is
ca
rried out witho
u
t
interruption.
We furth
e
r a
s
sume that the
r
e is only a si
ngle chan
nel
to be sen
s
e
d
.
In the first
se
nsin
g sta
ge,
we u
s
e
ene
rgy detectio
n
. If the deci
s
i
on metri
c
E
D
is
gr
e
a
t
er
than a certai
n thre
shol
d
1
,
we de
cla
r
e t
he ch
ann
el is active and o
c
cupie
d
by a
PU. Else, the
se
con
d
stag
e is n
e
cessa
r
y an
d
we
re
analyze th
e
receive
d
sign
al by
cycl
ost
a
tionary
feat
ure
detectio
n
.
Similarly, we in
trodu
ce an
other con
s
titue
n
t detection
metric
C
D
and compa
r
e it with
anothe
r th
reshold
2
.
If
C
D
is
greater than
2
, we de
cla
r
e th
e chann
el i
s
occu
pied, el
se it i
s
decl
a
re
d to be idle.
3. Res
earc
h
Method
In this sectio
n, we first give the cha
r
a
c
te
risti
cs of en
ergy dete
c
tio
n
and cycl
ost
a
tionary
feature d
e
te
ction techniq
ues a
nd di
scu
ss the
m
in the co
nte
x
t of our ad
aptive two-st
age
s
p
ec
tr
um s
ens
in
g
.
3.1. First Sta
g
e: Energy
Detec
t
ion
In the first st
age, ene
rgy
detectio
n
is p
e
rform
ed. If SUs’ p
r
io
r kn
owle
dge i
s
li
mited, the
optimal dete
c
tor is
an e
n
e
r
gy detecto
r,
whe
r
e th
e re
ceived
sig
nal
over e
a
ch freque
ncy b
a
n
d
is
squ
a
re
d and i
n
tegrate
d
ove
r
the ob
servat
ion interval.
Acco
rdi
ng to
[11], spect
r
um
sen
s
ing
i
n
CR
networks can
be f
o
rmulate
d
a
s
a bin
a
ry
hypothe
sis-te
sting p
r
o
b
lem
,
whe
r
e hyp
o
t
hese
s
0
H
and
1
H
corre
s
p
ond
t
o
the ca
se
s of
absen
ce
and p
r
e
s
en
ce of PUs, re
spe
c
tively. Assuming
sen
s
ing at time
s
{
1
,
2
,
...
.,
}
nN
, the rec
e
ived
sign
al sam
p
le
s for the two
hypothe
se
s may be mode
led as:
0
1
:(
)
(
)
,
:(
)
(
)
(
)
,
yn
z
n
y
nh
s
n
z
n
H
H
(1)
Whe
r
e
()
y
n
,
h
,
()
s
n
, and
()
zn
denote th
e re
ceived
sign
al
sampl
e
s, the
cha
nnel g
a
in
, the
PU si
gnal
s, a
nd
zero-m
ea
n complex
ad
ditive white
G
aussia
n
noi
se (A
WG
N)
wi
th varian
ce
2
z
,
respe
c
tively. The
cha
nnel
gain
s
a
r
e
a
s
sumed
to b
e
consta
nt for the
du
rati
on of
spe
c
trum
sen
s
in
g. The
PU signal is
assume
d to be an inde
pe
ndent, identically distribute
d
(i.i.d.) rand
om
pro
c
e
ss
with
zero me
an a
nd varia
n
ce
2
s
.
The noi
se
sa
mples, the
chann
el gain
s
,
and the P
U
sign
als a
r
e a
s
sumed to b
e
mutually in
depe
ndent.
We furth
e
r a
s
sume that b
o
th the PU si
gnal
s
and the noi
se
sample
s a
r
e
temporally i.i.d..
The ene
rgy d
e
tector
use
s
t
he followi
ng d
e
ci
sion rule:
10
2
1
11
()
.
N
E
n
Dy
n
H
H
(2)
Ac
c
o
rding to [12], we model
the tes
t
s
t
atis
tic
for large
N
as
:
24
0
22
2
2
2
2
2
1
(,
2
)
~
((
)
,
2
(
)
)
.
zz
E
zs
z
s
NN
D
Nh
Nh
N
H
N
H
(3)
The p
r
ob
abili
ty of false al
arm a
nd the
prob
ability o
f
detection fo
r the given
chann
el
unde
r the en
ergy dete
c
tio
n
are given b
y
:
2
1
10
4
(|
)
2
E
z
fE
z
N
PP
D
Q
N
H
,
(4)
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ISSN: 23
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046
TELKOM
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KA
Vol. 12, No. 5, May 2014: 3257 – 32
65
3260
22
2
1
11
22
2
2
()
(|
)
2(
)
E
zs
dE
zs
Nh
PP
D
Q
Nh
H
,
(5)
Whe
r
e
()
Q
is the
stand
ard
G
a
ussian
compl
e
menta
r
y cu
mulative di
stribution fu
ncti
on,
i.e.:
2
2
1
d
2
t
x
Qx
e
t
.
3.2. Second Stage
:
C
y
closta
tionar
y
F
eatur
e De
te
c
t
ion
In
the se
co
n
d
sen
s
ing
stage, cyclo
s
ta
tionar
y
dete
c
tion is p
e
rfo
r
med.
Cyclo
s
t
a
tionary
pro
c
e
s
ses
are ran
dom p
r
oce
s
se
s for
whi
c
h t
he
statistical p
r
o
p
e
rties
su
ch a
s
the me
an
and
autocorrelatio
n
chan
ge pe
ri
odically as a functio
n
of time. This pape
r uses the
se
cond-order time
domain
cyclo
s
tationa
ry detector p
r
e
s
e
n
ted in [13].
A random p
r
oce
s
s
()
y
m
,
{
1
,
2
,
.
.
..,
}
mM
is wid
e
-sen
se seco
nd-o
r
d
e
r cy
cl
ostation
ary, if
there exist
s
a
K
>
0
s
u
c
h
that:
()
(
)
yy
mm
K
,
(6)
(,
)
(
,
)
,
yy
Rm
R
m
K
,
(7)
Whe
r
e
K
is t
he cy
clic p
e
ri
od,
()
[
(
)
]
y
mE
y
m
is the me
an value of t
he ra
ndom
proce
s
s
()
y
m
, and
*
(,
)
[
(
)
(
)
]
y
Rm
E
y
m
y
m
is the a
u
toco
rrelation
function.
(,
)
y
Rm
has a F
ouri
e
r-se
rie
s
re
presentation du
e to its perio
dicit
y
as follows [13]:
(,
)
(
)
j
m
yy
Rm
R
e
,
(8)
Whe
r
e the Fo
urie
r co
efficie
n
ts ca
n be ex
pre
s
sed a
s
:
1
0
1
()
l
i
m
(
,
)
M
j
m
yy
M
m
RR
m
e
M
,
With the cycl
e-fre
que
ncy
α
.
In prac
tic
e
, we c
o
ns
ider
the following estimator of
()
y
R
for a given
K
.
1
*
0
1
ˆ
()
(
)
(
)
()
()
M
jm
yy
y
m
Ry
m
y
m
e
R
M
,
(9)
Whe
r
e
()
y
denote
s
the e
s
timation erro
r whi
c
h equal
s to zero if
M
app
roache
s infinity.
Due to this
error, the est
i
mator
ˆ
()
y
R
hardly
ever equal
s to zero in p
r
acti
ce, whi
c
h leads a
difficult pro
b
l
e
m abo
ut det
ermini
ng whe
t
her o
r
not th
e
()
y
R
co
rrespon
d
i
ng to a give
n value of
ˆ
()
y
R
is
z
e
ro. To solve this
problem s
t
atis
tic
a
lly,
the decisio
n-ma
kin
g
app
roa
c
h in [13] is used.
We con
s
id
er a
vecto
r
of
ˆ
()
y
R
rather th
an a
singl
e value t
o
ch
eck fo
r the p
r
esen
ce
of
cy
cle
s
i
n
a
s
e
t
of
lag
s
at
the same tim
e
. Let
1
,
...,
K
be a
fixed set of lag
s
,
α
be
a c
and
id
a
t
e
cycle
-
fre
que
n
c
y, and:
11
ˆˆ
ˆ
ˆ
ˆ
R
e
()
,
.
.
.
,
R
e
(
)
,
I
m
()
,
.
.
.
,
I
m
(
)
yy
y
K
y
y
K
RR
R
R
R
,
(10)
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TELKOM
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ISSN:
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046
Adaptive T
w
o
-
Stage Sen
s
i
ng in Co
gnitive and Dyn
a
m
i
c Spect
r
um
Acce
ss Net
w
orks (Y
ang Y
u
)
3261
Be a
12
K
row vect
or co
nsi
s
ting
of second
-ord
er cy
cli
c
-cu
m
ulant estimat
o
rs from (9
). If
the asymptoti
c
value of
ˆ
y
R
is g
i
ven as:
11
R
e
()
,
.
.
.
,
R
e
(
)
,
I
m
()
,
.
.
.
,
I
m
(
)
yy
y
K
y
y
K
RR
R
R
R
,
(11)
Then u
s
ing
(9
), we can write
ˆ
yy
y
RR
ε
, where:
11
R
e
(
)
,
.
.
.
,R
e
(
)
,
I
m
(
)
,
.
.
.
,I
m
(
)
yy
y
K
y
y
K
ε
,
(12)
Is the estimat
i
on error ve
ctor.
Ac
c
o
rding to [3], the tes
t
s
t
atis
tic
related
to the detector in the
se
con
d
se
nsi
n
g
stage
can b
e
expre
s
sed a
s
follo
ws:
1
ˆ
ˆˆ
H
Cy
y
DM
R
Σ
R
,
(13)
Whe
r
e
ˆ
Σ
denote
s
the
covaria
n
ce
matrix
of
ˆ
y
R
. In [13], the authors show that the tes
t
statistic
follo
ws a central
chi
-
squa
red
distri
bution
unde
r the
hypothe
sis
0
H
, an
d it follows
a
Gau
ssi
an di
st
ribution
un
de
r the hyp
o
the
s
is
1
H
. The
r
efore, assumi
ng t
hat
M
is large
enou
gh, the
distrib
u
tion of
C
D
can b
e
expre
s
sed a
s
:
2
2
0
11
1
~
ˆˆ
ˆ
ˆ
ˆ
ˆ
(,
4)
.
K
C
HH
yy
y
y
D
MM
R
Σ
RR
Σ
R
XH
NH
(14)
If
2
C
D
we
can
dete
r
mine
α
i
s
a
cycle-frequ
en
cy and
the P
U
is p
r
e
s
e
n
t. Else, the
PU is
absent and th
e target chan
nel ca
n be u
s
ed for the SU.
The proba
bility of false alarm and dete
c
tion ca
n be giv
en as:
2
20
(2
,
)
(|
)
()
C
fC
K
PP
D
K
H
,
(15)
1
2
21
1
ˆ
ˆ
ˆ
(|
)
ˆˆ
ˆ
4
H
yy
C
dC
H
yy
M
PP
D
Q
M
R
Σ
R
R
Σ
R
H
,
(16)
Whe
r
e
()
is
the gamma func
tion and
1
(,
)
d
at
x
ax
t
e
t
is t
he incom
p
let
e
gamm
a
function.
3.3. Perform
a
nce Inde
xe
s of Our Pro
posed Sch
e
me
In this se
cti
on, we i
n
tro
duce the p
e
r
forma
n
ce in
dexes
of the
prop
osed
schem
e:
prob
ability of detectio
n
and
mean se
nsi
n
g time.
Based
on (4
), (5), (15
)
an
d (16
)
, the overall p
r
ob
abili
ty of false alarm and d
e
tection for
the adaptive two-stag
e se
n
s
ing
scheme
can b
e
formul
ated as:
(1
)
E
EC
ff
f
f
PP
P
P
,
(17)
(1
)
E
EC
dd
d
d
P
PP
P
.
(18)
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TELKOM
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Vol. 12, No. 5, May 2014: 3257 – 32
65
3262
In orde
r to m
easure th
e a
g
ility of our a
daptive two
-
stage sen
s
ing
scheme,
we
need to
comp
ute its
mean sen
s
in
g time which can b
e
expre
s
sed a
s
follo
ws:
E
C
TT
T
,
(19)
Whe
r
e
2
E
TN
W
is the mean sen
s
in
g time for the first sen
s
ing
stage (
W
is the cha
nnel
band
width
)
a
n
d
C
T
is
the
second sen
s
in
g stage mean sen
s
in
g
time,
whi
c
h can b
e
derive
d
a
s
follows
:
2
Cr
e
p
TP
M
W
,
(20)
Whe
r
e
rep
P
is the proba
bility that cyclo
s
tatio
nary
dete
c
tio
n
is perfo
rme
d
and is give
n as:
01
()
(
1
)
(
)
(
1
)
CC
rep
f
d
PP
P
P
P
HH
.
(21)
Hen
c
e, the to
tal mean se
n
s
ing time an
d
the sen
s
ing
spe
ed can be
expresse
d a
s
:
2
re
p
TN
P
M
W
,
(22)
1
vT
.
(23)
3.4. Optimal Thresh
olds Deriv
a
tion
In this
se
ction, our i
n
itial g
oal is to
de
si
gn the th
re
sh
olds
1
and
2
fo
r
op
timiz
i
n
g
s
ens
in
g
accuracy and sensing
speed under
a
given constrai
nt on the pro
bability of false alarm. Sinc
e
there
are two optimi
z
atio
n go
als, the
co
rr
espondi
ng n
online
a
r optimization
pro
b
lem
ca
n b
e
formulate
d
as:
12
11
2
2
0
(,
)
max
(
,
)
,
.
.
,
.
df
wP
w
v
s
t
P
v
v
,
(24)
Whe
r
e
1
w
and
2
w
are
the wei
ght
s,
0
v
is the
mi
nimum
sen
s
ing spee
d
requi
rem
ent.
Ho
wever, thi
s
pro
b
lem i
s
v
e
ry complex t
o
be
solved.
Additionally,
the value
of th
ese t
w
o
weig
hts
signifi
cantly impact
s
the p
e
rform
a
n
c
e o
f
the detector
and cann
ot be determi
ned
easily.
In
gen
eral, sensi
ng sp
eed
is mainly
li
mit
ed by
cycl
ostation
ary d
e
tection
which ne
ed
s
compl
e
x
calculation
s
a
nd
a lon
g
o
b
servation. To
th
e contrary, th
e sen
s
ing
a
c
curacy
is mai
n
ly
limited by the first sen
s
in
g stage. Thu
s
, the
prob
a
b
ility of impl
ementing the
second sen
s
ing
stage,
rep
P
determines th
e tra
deoff betwe
e
n
sen
s
in
g
sp
eed an
d se
nsing accu
ra
cy. Acco
rdin
g to
(21
)
-
(
23
), si
n
c
e
0
()
P
H
and
1
()
P
H
c
a
nn
ot b
e
kn
ow
n
by th
e
SU
, we fir
s
t foc
u
s
on
ma
ximize
th
e
prob
ability of detectio
n
, a
nd then
ch
eck whethe
r
th
e value of d
e
tection th
re
shol
ds m
eets the
requi
rem
ent
of sen
s
in
g sp
eed. If not, we fix the threshold
s
man
ual
ly. Thus, prob
lem (2
4)
can
be
simplified a
s
[14]
12
12
(,
)
ma
x
(
,
)
.
.
df
Ps
t
P
.
(25)
The ine
qualit
y con
s
traint i
n
the proble
m
(25
)
ma
ke
s this
pro
b
le
m hard to be
solved.
Fortun
ately, it can be red
u
ce
d to an equality co
nstraint becau
se the optima
l
value of the
prob
ability of detection i
s
attained by
f
P
. The rea
s
o
n
why su
ch a
simplificatio
n can b
e
applie
d is given as follo
ws.
Acco
rdi
ng to (5), (1
6) a
nd
(18
)
, we can
see that
P
d
is a differentia
ble and d
e
creasi
n
g
function
of th
e thre
sh
old
s
1
and
2
. Hen
c
e, i
t
is o
b
viou
s t
hat the
deriva
t
ive of
P
d
with res
p
ec
t t
o
1
or
2
is negative. Hence, we can obtain the maximum value of
P
d
if an
d only if
1
and
2
r
each
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TELKOM
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ISSN:
2302-4
046
Adaptive T
w
o
-
Stage Sen
s
i
ng in Co
gnitive and Dyn
a
m
i
c Spect
r
um
Acce
ss Net
w
orks (Y
ang Y
u
)
3263
their minimu
m possible v
a
lue.
Also, the derivative
of
P
f
with res
p
ec
t to
1
and
2
is also
negative. We
assu
me that
**
12
(,
)
repre
s
ent
s the optimal solution of (25
)
with the co
nstrai
nt
f
P
. We keep th
e thre
shol
d
*
1
to be
con
s
tan
t
and de
crea
se
*
2
until we
re
ach
f
P
. In this
ca
se, a highe
r prob
ability of detection is
attained for
*
22
.
Thus it is quit
e
obvious tha
t
**
12
(,
)
can
not b
e
the
optimal
solut
i
on of
proble
m
(2
5).
The
r
e
f
ore, the
opti
m
al
P
d
ca
n b
e
obtai
ned
when
f
P
.
Hen
c
e, the problem (25)
ca
n be re
written
as:
12
12
(,
)
ma
x
(
,
)
.
.
df
Ps
t
P
.
(26)
For a given
constraint
, we have the follo
wing relation
betwe
en
1
and
2
.
2
14
2
12
2
(2
,
)
()
()
2
(2
,
)
1
()
z
z
K
K
fQ
N
N
K
K
.
(27)
Therefore, th
e probl
em (2
6) ca
n be si
m
p
lified as:
2
22
ma
x
(
(
)
,
)
d
Pf
.
(2
8)
This proble
m
is uni
mo
dal in
2
and
can b
e
solve
d
by
un
con
s
train
e
d
opti
m
izatio
n
algorith
m
s, fo
r example, th
e steep
est d
e
scent al
g
o
rit
h
m. Due to the com
p
lex computation,
we
omit the solving pro
c
e
s
s of
1
and
2
.
After we obta
i
n the value of
1
and
2
, we can calculate the pr
obabilities of false alarm
and d
e
tectio
n
C
f
P
and
C
d
P
in the
se
con
d
sen
s
ing
stag
e. T
hus, u
s
in
g (2
1), we
can o
b
tain the
probability that cycl
ostationary detection
is performed,
rep
P
. Then, the total mean
s
e
ns
ing time
T
can b
e
obtai
n throug
h (2
2). Ho
weve
r, this total mean se
nsi
ng time may be longe
r than th
e
maximum se
nsin
g time which
we
can t
o
lerate. In
thi
s
case, we
should
return to pro
b
lem
(2
4),
and recon
s
id
er optimi
z
ing
the sen
s
in
g
spee
d. As
mentione
d a
bove, it is very com
p
lex to be
solved.
Ho
wever, on th
e
other
han
d, the physi
ca
l meanin
g
s
of
the overa
ll prob
ability of
detectio
n
d
P
and
the sen
s
ing
speed
v
are diffe
rent in pro
b
le
m (24), an
d the values of the weig
hts
1
w
and
2
w
are
subje
c
tive to a larg
e extent. Thu
s
, to solve p
r
oblem (24
)
wi
th inapp
rop
r
ia
te weight
s
1
w
and
2
w
is not ve
ry meanin
g
ful
and n
eed
s
hu
ge an
d exp
e
n
s
ive effort. Th
erefo
r
e, in
ge
neral,
we
apply pro
b
le
m (26). If the threshold
s
op
timization a
r
e
strictly su
bje
c
t to the overall prob
ability of
detectio
n
an
d
the sen
s
in
g spe
ed con
s
traint
s with
approp
riate
weig
hts
1
w
and
2
w
,
we turn to
probl
em (2
4).
4. Results a
nd Analy
s
is
.
In this
section, we present
sim
u
lation result
s to
illust
rate the performance of our
scheme. T
h
e
s
e expe
rime
n
t
al results a
r
e
used to
com
pare th
e pe
rforma
nce of the co
nventio
nal
one-stag
e (e
nergy dete
c
ti
on and
cyclo
s
tationa
ry
de
tection) and prop
osed
two-sta
ge sen
s
ing
scheme
s
. In t
he
simulatio
n
,
we e
m
ploy
a chann
el b
a
ndwi
d
th of 8
M
Hz an
d a
DVB OFDM
si
gnal
as PU
sign
al
whi
c
h con
s
ist
s
of 18 OF
DM sy
mbol
s. Denoting the
O
F
DM symbol length
by
T
s
, we
assume
the
con
s
id
ere
d
P
U
sign
al
exhi
bits cyclo
s
tati
onarity with
2
s
mT
,
mN
and
0
m
.
Furthe
r, we
s
e
t
1
m
. The simul
a
tion paramet
ers a
r
e
set in the followin
g
table.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3257 – 32
65
3264
Table 1. The
Simulation Param
e
ters
Parameter
Variable
Unit
band
w
i
dth
8
MHz
Number of
OFD
M
sy
m
bols
18
-
m
1 -
OFDM
s
y
mbol le
ngth
100
us
Figure 2. Probability of Detection
of the
Propose Scheme versus
2
Figure 2
p
r
e
s
ents th
e p
r
o
b
ability of dete
c
ti
on
of the
a
daptive two-stage
sen
s
in
g
scheme
with res
p
ec
t
to
2
for different
β
at
15
dB
SN
R
. From
the figure, it can b
e
se
e
n
that whe
n
f
P
, the maximum prob
ability of detection i
s
attained.
Then, we a
s
sume th
at
β
=0.1
, i.e. the same
probability of
false alarm
const
r
aint is
imposed on a
ll three se
nsi
ng schem
es.
Figure 3 pre
s
ent
s the det
ection p
e
rfo
r
manc
e versu
s
SNR fo
r the adaptive two-stag
e
sen
s
in
g sch
e
m
e, ene
rgy d
e
tection
and
cyclo
s
tati
on
ary detection.
As we
ca
n see, for an S
N
R
that is le
ss than
−
10
dB, the two
-
sta
g
e
se
nsi
ng
scheme
perfo
rms b
e
tter th
an both
ene
rgy
detectio
n
and
cyclo
s
tationa
ry detection.
-2
0
-1
8
-1
6
-1
4
-12
-10
-8
-6
-4
-2
0
20
40
60
80
100
120
140
160
180
200
220
S
NR (d
B
)
M
ean
s
ens
i
ng t
i
m
e
(
m
s
)
T
h
e p
r
op
os
ed
s
c
h
em
e
E
n
e
r
gy
de
t
e
c
t
i
o
n
C
y
c
l
o
s
t
a
t
i
onar
y
det
ec
t
i
on
0
()
0
.
7
P
0
()
0
.
3
P
Figure 3. Probability of Detection versus SNR
for Differe
nt Sensin
g Sch
e
me
Figure 4. Mean Sensi
ng Ti
me versus S
NR for
Different Sen
s
ing Schem
e
N
e
xt, w
e
p
r
es
e
n
t
the
mean
se
ns
in
g
time
ve
rs
us
SNR
fo
r d
i
ffe
r
ent s
e
ns
in
g sc
he
me
to
che
c
k
the se
nsin
g
spee
d for
the pro
p
o
s
ed
sc
he
me comp
ared wi
th
the
othe
r two
dete
c
tion
2
4
6
8
10
12
14
16
18
20
0.
7
0.
75
0.
8
0.
85
0.
9
0.
95
1
2
P
r
ob
abi
l
i
t
y
o
f
det
e
c
t
i
on
=0
.
2
=0
.
1
=0
.
0
5
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
SN
R
(
d
B)
P
r
o
b
a
b
ilit
y
o
f
d
e
t
e
c
t
i
o
n
T
he pr
o
pos
ed s
c
hem
e
E
nergy
det
ec
t
i
on
C
y
c
l
os
t
a
t
i
onary
det
ec
t
i
on
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TELKOM
NIKA
ISSN:
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046
Adaptive T
w
o
-
Stage Sen
s
i
ng in Co
gnitive and Dyn
a
m
i
c Spect
r
um
Acce
ss Net
w
orks (Y
ang Y
u
)
3265
scheme
s
in
Figure 4. As
the figure shows, when
0
()
0
.
3
P
H
, in the SNR ran
ge
whe
r
e the
prop
osed
sch
e
me pe
rform
s
better th
an
energy dete
c
tion, (SNR le
ss than
−
10
dB
), the pro
p
o
s
ed
scheme p
e
rf
orm
s
better t
han cy
clo
s
tationary dete
c
t
i
on in term
s of mean se
nsin
g time and
probability of detection.
However, when
0
()
0
.
7
P
H
, the prop
o
s
ed
schem
e doe
s not always
perfo
rm bette
r than cy
clost
a
tionary dete
c
tion in term
s of mean sen
s
ing time.
5. Conclusio
n
As the d
e
ma
nd of
spe
c
tru
m
re
sou
r
ce i
n
crea
se
s in
past fe
w yea
r
s
and li
ce
nsed ba
nd
s
are u
s
e
d
inefficiently, impro
v
ement in the
existi
ng sp
ectrum acce
ss
policy is exp
e
c
ted. DSA ca
n
resolve the
spectrum
sho
r
t
age by all
o
wi
ng SUs to
dy
namically utilize
spe
c
trum
hole
s
a
c
ro
ss
the
licen
se
d sp
e
c
trum
on no
n-inte
rferin
g
basi
s
.
In thi
s
pa
per, a
n
adaptive two-sta
ge
sen
s
ing
approa
ch wa
s presented.
Unde
r t
he consi
dered sy
stem mod
e
l, we
an
alyze
d
the feature
s
of
energy dete
c
tion an
d cy
clo
s
tationa
ry fea
t
ure det
ec
tion
and d
edu
ce
d
the pe
rform
a
nce i
ndexe
s
of
the pro
p
o
s
ed
scheme. M
o
st impo
rtant
ly, the opt
imal thre
shol
ds for the ada
ptive two-sta
ge
sen
s
in
g sche
me we
re de
signed in o
r
de
r to optimize
the proba
bili
ty of detection and se
nsi
n
g
spe
ed unde
r a
given co
nstraint
on
the prob
ability
of
false
ala
r
m.
Simulation
re
sults illu
strat
ed
that at low
SNR, whe
r
e
the ene
rgy d
e
tector i
s
n
o
t
reliable, th
e two-stag
e
sen
s
in
g sche
me
provide
s
imp
r
oved d
e
tecti
on. Additiona
lly, t
he mean sen
s
in
g time is mu
ch
lowe
r than
the
cyclo
s
taio
nari
t
y detection
schem
e fo
r m
o
st of th
e S
N
R ra
nge.
Ho
we
ver, the
sim
p
l
i
fied version
of
the formulate
d
origin
al opti
m
ization p
r
ob
lem (2
4
)
only
focuses o
n
optimizin
g se
nsin
g accu
ra
cy
but doe
s n
o
t optimizin
g se
nsin
g speed
due to the
hig
h
com
p
lexity of the origi
nal
probl
em, whi
c
h
may result in that the total mean
sen
s
in
g time
is long
er than the m
a
ximum se
nsing time we
can
tolerate. In the further wo
rk
,
we will
try to find
an
efficient
so
lution to j
o
in
tly optimize t
he
probability of detection
and sensing
speed.
Ackn
o
w
l
e
dg
ements
This work wa
s finan
cially suppo
rted by the
Re
se
arch
Fund for the
Do
ctoral Prog
ram of
High
er Edu
c
a
t
ion of China
(201
200
051
1
0001
).
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