TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4500 ~ 4
5
0
4
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.548
9
4500
Re
cei
v
ed
De
cem
ber 2
4
, 2013; Re
vi
sed
Febr
uary 21,
2014; Accept
ed March 6, 2
014
Highly Effective Algorithm of the Threshold Detection
in the Cognitive Radio
Qing Long Xu*
1
, Zhan Ga
o
1,2
1
Institute of Communicati
on a
nd Eng
i
n
eeri
n
g
,
PLA Un
iversit
y
of Scie
nce a
nd T
e
chnol
og
y (ICE, PLAUST
)
2
Nation
al Eng
i
neer
ing R
e
se
a
r
ch Center for
Short W
a
ve Co
mmunicati
on
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 1585
06
208
5
0
@1
63.com
A
b
st
r
a
ct
Opportun
i
stic spectru
m
acces
s
(OSA) is a ke
y
techniq
ue en
abli
ng the sec
o
ndary us
ers (SUs) in
a
cogn
itive ra
di
o
(CR) netw
o
rk to trans
mit ov
er
the “s
pectru
m
hol
es
”
un
occu
p
i
ed by
the
pri
m
ary users (PUs
).
In contrast to OSA,
with spectrum
shar
in
g (SS) is allow
ed
to transmit
re
g
a
rdl
e
ss of the PU
’
s
on/off status,
provi
ded that the resu
lting
i
n
terferenc
e to PU is kept belo
w
a predef
ine
d
threshol
d. In this pa
per, w
e
foc
u
s
on the thr
e
sh
ol
d detecti
on
alg
o
rith
m study fo
r spectru
m
sh
a
r
ing, w
h
ich
ai
ms to get
the SI
R of the PUs
a
s
quickly a
nd pr
ecisely as p
o
s
s
ible. W
e
prop
ose a dich
oto
m
y al
gorith
m
w
i
th low
e
r comp
lexity an
d mor
e
quickly
in c
ont
rast to the tra
d
itio
nal f
u
ll s
e
arch a
l
gor
ith
m
. Nu
mer
ous si
mu
lati
on res
u
lt
s are pr
ovi
ded
t
o
valid
ate the pr
opos
ed a
l
gor
ithm.
Ke
y
w
ord:
op
portun
i
stic sp
ectrum
acces
s
, cognitiv
e
radi
o, spectru
m
sh
arin
g, thresho
l
d d
e
tectio
n
,
dich
oto
m
y alg
o
r
ithm
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
By enablin
g
the second
ary use
r
s (S
Us) to a
c
cess to the
occu
pied
ch
annel
of the
prima
r
y u
s
ers (P
Us) i
n
a
cog
n
itive ra
di
o (CR) [1
-2], spe
c
trum
sh
aring
(SS) [3] is
rega
rd
ed
as
one
pro
m
isin
g solution to
re
solving
th
e spe
c
trum
scarcity
versus sp
ectrum
und
erutili
zat
i
on
para
dox in
wirel
e
ss
com
m
unication
s
[4-6]. In [7], the authors prop
osed a
hidden
po
wer-
feedba
ck loo
p
for th
e
CR.
If PU is
rea
c
ti
ve and
re
act
s
upo
n receiving SU’
s
i
n
terf
eren
ce, S
U
will
rea
c
tive a po
wer-b
o
o
s
ted
PU sig
nal
s th
at is ea
sie
r
to dete
c
t. In [8], it investigates the e
n
e
r
gy
efficien
cy ma
ximization
problem
of
co
gnitive
radio
syste
m
s an
d p
r
op
oses to stu
d
y e
nergy
efficien
cy of
cog
n
itive rel
a
y tran
smissi
on sc
h
e
me
based o
n
co
operative sp
ectru
m
sen
s
i
ng.
Paper [9] propo
se
s an i
m
prove
d
co
g
n
itive radio
spectrum sen
s
ing al
gorith
m
, which ai
ms to
improve the
SU’s d
e
tectio
n perfo
rma
n
ce and redu
ce
s the interfe
r
ence of the SUs to the P
U
s.
But it doe
sn
’t solve th
e
spe
c
tru
m
sh
aring
bet
wee
n
PUs
and
SUs.To
de
si
gn o
p
timal
SS
strategi
es, t
w
o go
als are a
ddre
s
sed
at t
he
same
time
: the maximu
m sig
nal to
in
terfere
n
ce ra
dio
(SIR) of the
PUs
sho
u
ld b
e
detecte
d q
u
ickly and p
r
eci
s
ely. Therefore
we ne
e
d
to find a ki
nd of
threshold d
e
tection al
gorit
hm, which ca
n detect the
SIR quickly and pre
c
i
s
ely.
The re
st of the pape
r is organi
zed a
s
follows
: Sectio
n II present
s the system m
odel for
PUs and SUs in a
CR
network.
Section III describes
the threshold detection algorithm
and
simulate
s the
propo
se
d al
gorithm. Se
ction IV analyses the si
mula
tion results a
nd com
p
a
r
e
s
the
prop
osed
alg
o
rithm
with
the tradition
al full
se
a
r
ch a
l
gorithm. Fin
a
lly,
Section
V
co
ncl
ude
s the
pape
r.
2. Sy
stem Model
We con
s
ide
r
a CR net
wo
rk con
s
isting of
two SUs an
d
two PUs. Fig
u
re 1 sho
w
s t
hat the
PUs have dif
f
erent sp
ect
r
um acce
ss
st
rategie
s
,
whi
c
h mea
n
s th
e PUs
can switch to an
other
comm
uni
cati
on fre
que
ncy
whe
n
the
current comm
unication fre
quen
cy is inf
l
uen
ced. In t
h
is
pape
r, we a
s
sume that the two PUs are in com
m
unication with each oth
e
r at F
0
in the
begin
n
ing. Th
e block dia
g
ram is a
s
sho
w
n in Figu
re
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Highl
y Effective Algo
rithm
of the Thre
sh
old De
te
ction
in the Cog
n
itive Radio (Qin
g Long Xu
)
4501
As sho
w
n in Figure 2, the
two SUs a
r
e within
the po
wer
coverage
of
the PU1. If the two
SUs also wan
t
to
comm
uni
cate at
F
0
, there
are
two
competing
go
a
l
s
shoul
d b
e
addresse
d at
the
same time: the quality of commu
nicati
on for SUs
should be g
u
a
rante
ed a
s
far as po
ssib
le,
whe
r
ea
s the i
n
terferen
ce from
SUs can
not affect the
norm
a
l co
m
m
unication b
e
twee
n the P
U
1
and PU2. In other
words,
we ne
ed to control the
tra
n
smit po
we
r
of the SUs a
nd ke
ep it bel
ow a
pred
efined
th
reshold
of the
PU2. T
herefore
we
shoul
d get th
e ma
ximum SIR of
the PU2. In t
h
is
pape
r, we
put
forward
a m
e
thod that S
U
1
sen
d
s
a t
entative interf
eren
ce
po
we
r to PU2, then
we
can
dete
r
min
e
whethe
r th
e PU2’
com
m
unication
is
interfe
r
ed
th
roug
h th
e fee
dba
ck chan
n
e
l. If
the PU2’
co
mmuni
cation
is influen
ce
d, we shoul
d
redu
ce the tra
n
smit po
we
r
of the SU1
with a
unit of
△
P as soo
n
a
s
po
ssible. Oth
e
rwi
s
e, we shoul
d increa
se th
e tran
smit po
wer
with a
un
it of
△
P as soo
n
a
s
po
ssi
ble.
△
P is variable.
After several i
t
eration
s
, we
can eve
n
tuall
y
get the PU2’s
anti-inte
rfere
n
ce threshold
-
SIR.
3. Algorithm Design
The thou
ght
of the algo
rith
m desi
gn
co
mes from
the
detectio
n
alg
o
rithm of the
relatively
cog
n
itive sig
nal, whi
c
h
send
s the int
e
rferen
ce
p
o
w
er t
o
the o
b
jective
cog
n
i
tive system
at a
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4500 – 4
504
4502
workin
g fre
q
uen
cy F
0
. Each tim
e
the
value of int
e
rferen
ce p
o
w
er is
different. After se
veral
iteration
s
,
we
ca
n
get the
critical
po
wer
of
inte
rference
whe
n
PUs are fo
rced to
switch
the
workin
g freq
u
ency.
The tra
d
ition
a
l full sea
r
ch
algorith
m
(FS
A
) [10] is de
scrib
ed a
s
foll
ows: First, it
need to
determi
ne a
f
i
xed
po
we
r step size
△
P. Then
SU ran
domly
send
s a
tentative int
e
rferen
ce
po
we
r
P
0
towa
rds t
he P
U
2. If th
e PU2
swit
ch
es th
e frequ
e
n
cy, the
po
wer P
0
is la
rg
er
th
an
th
e a
n
ti-
interferen
ce thre
shol
d of PU2 and the
interfer
e
n
ce
powe
r
that will be se
nt next time should
subt
r
a
ct
s
△
P
.
Otherwi
se
we shoul
d ad
d a
△
P. After several itera
t
ions, the SIR of PU2
will
be
acq
u
ire
d
. Its accuracy of converg
e
n
c
e i
s
relate
d to
△
P, which me
a
n
s the le
ss
△
P is, the high
er
the a
c
cura
cy
of co
nverg
e
n
c
e i
s
.
Ho
wev
e
r the
hig
her
accuracy
of converg
e
n
c
e i
s
at th
e
co
st
of
highe
r
compl
e
xity, which
cannot m
eet t
he go
al of
fa
st an
d efficie
n
t dete
c
tion.
In this p
ape
r
we
prop
ose a
al
gorithm
ba
se
d on
di
choto
m
y [11], whi
c
h is a
fast
se
arch
algo
rith
m. The
ba
se
d-o
n
dich
otomy al
gorithm
is
b
e
tter than
F
SA in t
he
te
rms
of
the speed of
the accuracy of the
conve
r
ge
nce. In this pa
per we p
u
t forwa
r
d a
th
re
shol
d dete
c
tion al
gorithm
ba
se
d on di
ch
oto
m
y,
whi
c
h are de
scribe
d as foll
owin
g:
Firstly, like th
e FSA, we
sh
ould
set a mi
nimum p
o
wer re
solution
△
(dBm) a
nd 2
N
optiona
l
interferen
ce power p
i
=i*
△
,
i=1,2,3,……,
2
N
. Secondly, defining events
E
p
and
E
p
. The
E
p
mean
s the PU ca
nnot
sta
nd the interfe
r
en
ce
, sto
p
communi
catin
g
or switch to
anothe
r
freque
ncy when interfe
r
e
n
ce p
o
we
r switch to p. Similarly,
E
p
repre
s
e
n
ts th
at when
interferen
ce
power
swit
ch
to p, it means th
e
inte
rferen
ce p
o
wer i
s
belo
w
the interfe
r
e
n
ce
threshold of
PU. Therefo
r
e, to acquire
the critic
al i
n
terferen
ce p
o
we
r,
the interferen
ce po
wer
sho
u
ld meet the followi
ng condition
s: (1
)
E
p
; (2)
E
p
; (3)
p
p
=
△
.
To achi
eve the above g
o
a
l, firstly, we use
exp
one
ntial algorith
m
to roughly se
arch for
the threshold
.
Secondly, whe
n
app
roa
c
hin
g
the
thresh
old, we a
d
just the po
wer by dicho
t
omy
algorithm to tes
t
the PU.
After N ti
me
s’ it
eration
s
, th
e
critical
po
wer
of interfe
r
en
ce can
be
foun
d.
The algo
rithm
is as follo
win
g
:
a) Initializin
g para
m
eters: k=1
，
p
2
*
∆
，
p
=f
(
p
,
r
).
b) k++, if the event of
E
p
happ
en
s,
p
p
2
∗∆
, else the even
t o
f
E
p
must happe
n,
p
p
2
∗∆
. Depe
ndi
ng on the interferen
ce po
wer, we can
get
p
f
p
,r
.
c) If k<N, go
back to
, else e
nd an
d
get the criti
c
al
power of i
n
terferen
ce, whi
c
h is
divided into three
con
d
itio
ns:
¡
If
p
2
∗∆
and
both
of
E
p
and E
p
happ
en
, it is beyo
nd the rang
e of
estimation
p
thres
h
old>
2
∗∆
, it mean
s the method do
es n
o
t work.
(¡¡
)
If
p
∆
and
E
p
,
p
threshold
=
∆
/2+
p
.
(
¡¡¡
)
p
thres
h
old=
（
p
p
）
/2+
p
.
4. The Anal
y
s
is of Simulation Results
We u
s
e the
conve
r
ge
nce of the ste
ady-sta
te val
ue to judge
the accuracy of the
estimation of
the critical po
wer of inte
rfe
r
en
ce.
We u
s
e the numbe
r of iterations
to measu
r
e t
h
e
conve
r
ge
nce
spee
d of the algo
rith
m
.
Figure 3
sho
w
s that different
△
P
have different
conve
r
ge
nce
results i
n
the
FSA. Whe
n
the
△
P i
s
la
rge en
oug
h, the FSA
can
also
achieve
the
same
sp
eed
of the conve
r
gen
ce
as th
e dich
otom
y
algorith
m
. Howeve
r, the
accuracy of t
h
e
convergence will
de
clines as
the
△
P in
crea
se
s. In Fig
u
re
4 we can
see
wh
en u
s
i
ng expo
nenti
a
l
algorith
m
to roug
hly se
arch for th
e an
ti-interfe
ren
c
e
threshold of
PU, the cho
i
ce of the b
a
s
e
numbe
r i
s
ve
ry importa
nt. If the b
a
se n
u
m
ber is t
oo l
a
rge, the
nu
m
ber
of PU’
s
switchi
ng
wo
rkin
g
freque
ncy will
incre
a
se, whi
c
h may affect
the PU
’s co
mmuni
cation.
However, if the ba
se num
ber
is too little, th
e numbe
r of the iteration
s
to appr
oa
ch the anti-interfe
r
ence thre
shol
d of the PU will
also i
n
crea
se
. Therefo
r
e, a
prop
er
ba
se
numbe
r
i
s
very important.
Figure 5
sho
w
s th
at different
simulatio
n
on
condition th
at the SIR of t
he PU is 4dB and the SNR is 20
dB
, 10dB and 0dB.
Dep
endin
g
o
n
the re
sults
of the simula
tion, we
can
see
whe
n
the SNR i
s
20
dB as sho
w
n
in
Figure 5
(
a), t
he nu
mbe
r
of
the it
erations of the FSA i
s
30
whe
n
the
dich
otomy al
gorithm’
s
i
s
1
5
.
Whe
n
the S
NR
de
cline
s
to 10dB an
d
0dB as
s
h
o
w
n in Fi
gure
5(b
)
, (c), th
e numb
e
r of
th
e
iteration
s
of
FSA keep
s th
e sam
e
a
s
th
e re
sult
of wh
en the SNR i
s
20
dB. But the convergen
ce
of the steady-state value
has a mino
r fluctuat
ion
s
. Ho
wever the
dichotomy a
l
gorithm alm
o
st
remai
n
s the
same a
s
th
e
result
of when
the
SNR i
s
2
0dB. Wh
en t
he SNR
co
ntinue
s to
de
cline
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Highl
y Effective Algo
rithm
of the Thre
sh
old De
te
ction
in the Cog
n
itive Radio (Qin
g Long Xu
)
4503
to -20
d
B as
sho
w
n i
n
Fig
.
5.(d), the
co
nverge
nce speed
of FSA is rather sl
o
w
, whi
c
h
alm
o
st
can
not
conv
erge. B
u
t at
the
same
time t
he
co
nverge
nce
speed
and
the a
c
curacy
of
conve
r
ge
nce
of the dichotomy algo
rithm ar
e al
most still u
n
ch
ang
eable.
Therefore,
the
dich
otomy al
gorithm i
s
a f
a
st and
highl
y effective
algorithm, which is very fit for the thresh
old
detectio
n
of the PU.
Figure 3. The
Results of Simulation of
Different
p for FSA
Figure 4. The
Results of Simulation of di
fferent
Base nu
mbe
r
for Dichotom
y Algorithm
(a)
(b)
(c
)
(d)
Figure 5. The
Results of for Differe
nt SNR
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
S
I
R=
4d
B
S
N
R
=
1
0dB
num
be
r
of
i
t
erat
i
o
ns
i
n
t
e
rf
ere
n
c
e
po
w
e
r
△
p=
1
△
p=
5
△
p=
10
10
20
30
40
50
60
70
80
90
10
0
0
10
20
30
40
50
60
70
80
90
100
n
u
m
b
er
of
i
t
er
a
t
i
ons
i
n
t
e
r
f
e
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4500 – 4
504
4504
5. Conclusio
n
The FSA sa
crifice
s
its con
v
ergen
ce
spe
ed to
get the accura
cy of
conve
r
ge
nce, which
can
not be a
daptive to the terminal e
quipme
n
ts
wi
th cognitive functio
n
. It does not have
the
quick reaction capability. In contra
st, the dichotomy
algorithm is v
e
ry
fast and
effective, whi
c
h i
s
widely used i
n
math sea
r
ch. In this paper we ma
ke f
u
ll use of the
advantage o
f
the dichoto
m
y
algorith
m
to
detect th
e SIR of the
PU. We
al
so
compa
r
e the
two
algo
rithm
s
by
com
put
er
simulatio
n
. From the re
sult
s, we can see
the
dichotom
y algorithm is better than the FSA.
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