TELKOM
NIKA
, Vol. 11, No. 8, August 2013, pp. 43
3
5
~4
343
e-ISSN: 2087
-278X
4335
Re
cei
v
ed Fe
brua
ry 17, 20
13; Re
vised
Ma
y 11, 20
13
; Accepte
d
May 20, 20
13
Power Optimization between Sensing and Signaling for
Distributed Detection
X
i
a
n
gy
a
n
g
LI
U*
1
, Peisheng ZHU
2
, Do
nghong XIE
1
1
Departme
n
t of informatio
n
transmissio
n
, Xi’a
n Co
mmu
nicati
ons Institute, Xi’an S
haa
n
x
i, C
h
in
a
2
Chin
a Institute of Acoustics, Chin
es
e Aca
d
e
m
y
of Scie
nces
, Beijin
g,Chi
n
a
*Corres
p
onding author, e-mail: liux
i
an
gy
angdr@gmail.com
*
, zhups_ioa@126.com
A
b
st
r
a
ct
T
he p
o
w
e
r of
each s
ens
or n
ode
in w
i
re
less
sensor
netw
o
r
ks for sig
nal
d
e
tection
ap
plic
ations
i
s
scarce
an
d l
i
m
ite
d
. T
hus,
the
all
o
cati
on
of pow
er
re
sou
r
ce
o
f
a nod
e
sh
ou
l
d
m
a
ke
th
e de
te
ctio
n
perfor
m
a
n
ce o
f
the w
hole netw
o
rk maximu
m, w
h
ich is
compl
e
x due to
the detection
proba
bil
i
ty of
th
e
whole system
cannot be ex
pressed
ex
plicitly. The ant colony optim
i
z
a
tion algor
ithm
is good at solv
ing
m
u
ltidimens
ional optim
i
z
a
tion prob
lem
.
Consequently, continuous an
t colony system
(CACS) and ACO
R
prop
osed
i
n
l
i
terature
are
a
dopte
d
to
opti
m
i
z
e
th
e a
lloc
a
tion
of n
o
d
e
’
s pow
er
betw
een
sens
in
g a
n
d
communic
a
tio
n
s
. Simul
a
tio
n
show
that they can le
ad
to a g
ood p
o
w
e
r allo
cation. Mea
n
w
h
ile, the i
dentic
a
l
pow
er all
o
cati
o
n
sche
m
e (IPAS) that all se
ns
or no
des
h
a
ve
ide
n
tical
pow
er
assign
ment ca
n achi
eve
near
l
y
the sa
me d
e
te
ction
perfor
m
a
n
ce
as that
ach
i
eve
d
by
the
be
st sche
m
e
sear
ched
by
CACS
an
d ACO
R
. As
a
result, particularly for
a
lar
g
e num
ber
of identical sens
ors, IPAS can be
employed to
achiev
e near
ly t
h
e
best detecti
on
perfor
m
a
n
ce.
Ke
y
w
ords
: po
w
e
r allocati
on, sign
al det
ectio
n
, cross-
layer
opti
m
i
z
at
ion, w
i
reless s
ensor
netw
o
rk
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Distri
buted d
e
tection (D
D) system
s with
a set of ge
og
raphi
cally sep
a
rated se
nsors
have
been inve
stig
ated sin
c
e 1
980
s. In the detection
p
r
oblem, one
core obje
c
tive of the system
desi
gn i
s
to
disting
u
ish
betwe
en two
hypothe
se
s,
su
ch a
s
th
e ab
sen
c
e
(Hypothe
si
s 0
)
or
presence
(Hypothesi
s
1) of a
certai
n target. Such detection
ability is crucial for vari
ous
appli
c
ation
s
. As an exampl
e, in a battlefield su
rve
illan
c
e, the prese
n
ce o
r
ab
se
n
c
e of a targ
et is
usu
a
lly determined b
e
fore
its attribute
s
,
su
ch a
s
it
s
p
o
sition
or vel
o
city, are
esti
mated. With t
h
e
developm
ent
of wirele
ss sen
s
o
r
net
works
(WSNs), many a
u
thors have
analyse
d
the
perfo
rman
ce
of these DD systems in whi
c
h tran
sm
i
s
si
ons fro
m
sen
s
ors to the fusion
centre (F
C)
are subje
c
t to cha
nnel fa
ding and n
o
i
s
e [1-5], whi
c
h may re
nd
er the re
ceiv
ed de
cisio
n
s of
sen
s
o
r
s
at th
e fusio
n
centre unreliabl
e. One p
r
omi
n
e
n
t feature
of a ca
noni
cal
WSN, h
o
wev
e
r, is
its limited nod
e energy, whi
c
h po
se
s ma
ny challe
nge
s to network d
e
sig
n
and ma
nagem
ent.
The problem
of optimizin
g detectio
n
p
e
rfor
m
a
n
c
e
with su
ch im
perfe
ct com
m
unication
bring
s
a
ne
w chall
eng
e to
distrib
u
ted d
e
tection. Z
h
a
ng et al. [6]
con
s
id
ere
d
the pe
rform
a
n
c
e
optimizatio
n
with individ
u
a
l
and total tra
n
smitte
r po
wer con
s
trai
nts
on
the se
nsors.
T
he power
allocation sch
e
me obtai
ned
strikes
a tra
de-off bet
wee
n
the co
mmu
nicatio
n
ch
an
nel quality an
d
the local de
cision
quality. Con
s
id
erin
g the sce
n
a
r
io of
usin
g
di
stributed rada
r-l
ike sen
s
o
r
s
to
detect the prese
n
ce of an
object thro
u
gh active
sen
s
ing, Yang et
al. [7]
formul
ated the pro
b
l
em
of
ene
rgy-effi
cient routing
for
si
gnal det
ection
und
er the
Neym
an-Pearson
crite
r
ion. Mo
re
over,
they propo
se
d a distrib
u
te
d and en
ergy
-efficient fra
m
ewo
r
k that is scala
b
le wit
h
respe
c
t to the
netwo
rk
size, and is abl
e
to redu
ce g
r
eatly
the de
pend
en
ce on
the central fusion
centre
.
Masa
za
de et
al. [8] evaluated the
sen
s
or thre
sh
old
s
of di
stribut
ed si
gnal
det
ection
syste
m
by
formulatin
g a
nd solving a
multiobje
c
tive opt
imi
z
atio
n problem.
Unfortu
nately
,
although t
he
literature on
energy-effici
e
n
t comm
unication or
sign
al detectio
n
i
n
WSNs i
s
a
bund
ant, there is
much le
ss re
sea
r
ch on th
e power allo
cation betwe
e
n
sign
al dete
c
tion an
d co
mmuni
cation,
le
t
alone the
con
s
ide
r
ation of their joint opti
m
ization.
Obviou
sly, the energy co
nsum
ption of
the
whole system can b
e
lowe
red b
y
jointly
optimizin
g
th
e
si
gnal
dete
c
tion of sen
s
or nod
e
a
nd
t
he sign
aling
betwe
en se
n
s
or n
ode an
d
the
FC. In anoth
e
r wo
rd, for a
given node’
s powe
r
budg
et, we can fin
d
a powe
r
all
o
catio
n
sche
me
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Vol. 11, No
. 8, August 2013: 4335 –
4343
4336
that strike
s a
trade-off betwee
n
the co
mmuni
cation
cha
nnel qu
ali
t
y and the detection qualit
y o
f
local
sen
s
o
r
s with
the
obj
ective
of
the optim
um det
ection pe
rformance at the FC. In general,
there
are m
a
ny algo
rithm
s
to
solve th
e
power allo
cat
i
on p
r
obl
em.
Ho
weve
r, th
e difficulty i
s
t
hat
the p
r
ob
ability of dete
c
tio
n
of
a
DD sy
stem
ca
nnot
be exp
r
e
s
sed
explicitly, e
s
peci
a
lly with
the
probl
em in thi
s
pap
er.
In the 9
0
s
of 20th
ce
ntury
，
Italian schol
ar M
．
Dorigo
put fo
rward the
an
t colo
ny
optimizatio
n algorith
m
(ACO
) [9]. Thereafter,
ACO
algorithm
s h
a
ve been stu
d
ied and utili
zed
extensively. Artificial ants
move ran
d
o
m
ly instead
o
f
determini
stically. Therefo
r
e, it allows t
hem
to sea
r
ch
wid
e
variety of p
o
ssible
sol
u
tions
of a p
r
o
b
lem in
depe
n
dently and
in
parallel. In t
he
same
way, ACO
ba
sed
so
lutions are g
ood
at pr
odu
cing
a
good
sub
optimal
solution in
a v
e
ry
s
h
or
t p
e
r
i
o
d
.
T
h
es
e
c
h
ara
c
te
r
i
s
t
ics
ha
ve
in
sp
ir
ed u
s
to
d
e
s
i
gn
a
jo
in
t pow
e
r
as
s
i
gn
me
n
t
algorithm for distributed detection,
with the obj
ective of maximizing the overall probability
of
detectio
n
at the FC.
The
rem
a
ind
e
r
of this pa
per are o
r
g
a
n
ize
d
a
s
foll
ows. In Se
cti
on 2, t
he
problem
of
distrib
u
ted de
tection in pa
rallel fusio
n
n
e
tworks
with
noisy chan
ne
l, sensi
ng mo
del, link mo
d
e
l,
and fu
sio
n
ru
le are fo
rmul
ated, re
sp
ecti
vely. T
he po
wer allo
catio
n
proble
m
an
d its
optimiza
t
ion
by ACO
solut
i
ons are give
n in S
e
ction
3 an
d Se
ct
io
n
4, re
spe
c
tively.
The num
erical re
sults are
given in Secti
on 5. Finally, Section 6 con
c
lud
e
s the p
a
per.
2. Problem Formulation
2.1. Distribu
ted detection
Con
s
id
er a
scena
rio, wh
ere
N
sen
s
o
r
s are scattered over a
n
are
a
to
d
e
tect
the
p
r
es
e
n
c
e
(
t
he s
i
gn
a
l
p
l
us
no
is
e H
y
po
th
es
is
1
H
)
or ab
se
n
c
e
(the
noi
se
-only Hyp
o
the
s
is
0
H
) of
an
object, for ex
ample
people, vehicles, or military
targets, using
radar-lik
e sensors that em
anate
spe
c
ific el
ect
r
oma
gneti
c
si
gnal
s into th
e regi
on of intere
st. For t
he active
se
nsin
g appli
c
a
t
ion,
the monito
re
d sp
ace is ty
pically divid
e
d
into
ma
ny range
re
soluti
on cells. Ea
ch ra
nge
cell
could
be p
r
ob
ed
se
quentially in
turn to
dete
r
m
i
ne the
pres
e
n
ce
of a ta
rg
et by
u
s
ing
radar pul
se
s t
hat
are po
ssibly laun
che
d
by dire
ctional
a
n
tenna
s. Assume the po
sition of
k
-
t
h
s
e
ns
or
n
o
de is
(,
)
kk
x
y
. Each sen
s
o
r
gathe
rs info
rmation p
e
rt
a
i
ning to a target in the po
sition of
(,
)
tt
x
y
and
make
s a d
e
ci
sion
(for d
e
ci
ding the p
r
e
s
ence of t
he target a
nd oth
e
rwi
s
e
)
an
d send
s its bin
a
ry
deci
s
io
n to a fusion
cent
re
throug
h an u
n
relia
ble com
m
unication chann
el. In a word, the parallel
fusion mo
del
is ado
pted. The po
sition of
fusion centre
is assume
d to be
(,
)
fc
fc
x
y
.
2.2. Sensing Model
Acco
rdi
ng to the free-sp
ace rada
r equ
a
t
ion,
the power of the ech
oes fro
m
the target
with RCS
at rang
e
k
R
to the rada
r can be
expre
s
sed a
s
:
3
22
4
4
rt
k
PP
G
R
(
1
)
whe
r
e
t
P
is the radiate
d
transmitted p
o
w
er,
G
is the gain of rad
a
r anten
na,
is the
wavele
ngth, and
k
R
is the range bet
wee
n
the
k
-th ra
dar an
d the target. For
ra
dar with n
o
ise
figure
F
and ba
ndwi
d
th
B
, the
output sig
nal-to-noi
se ratio
()
o
SNR
of its receiver is:
3
22
4
4
te
k
o
SN
R
P
G
k
T
B
FL
R
(
2
)
Whe
r
e
k
is B
o
ltzman
n’s
co
nstant,
e
T
is the
effective noise temperature,
L
is the syst
em loss,
is
the pul
se duratio
n.
The
minimum de
tectable sig
n
a
l
min
S
an
d the
minimum
out
put sig
nal
-to-
noise ratio
()
min
o
SN
R
of a rada
r re
cei
v
er is rel
a
ted
by:
mi
n
mi
n
e
o
Sk
T
B
F
S
N
R
(
3
)
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TELKOM
NIKA
e-ISSN:
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-278X
Powe
r Optim
i
zation b
e
twe
en Sensi
ng a
nd Signalin
g
for Dis
t
ributed Detec
t
io
n (Xi
ang
yan
g
LIU)
4337
The sig
nal re
ceived by the
k
-th sen
s
or i
s
assu
med to
be:
1
0
rk
k
k
Pn
H
y
nH
(4)
Assu
me that
the
k
-t
h lo
cal
sen
s
o
r
ma
ke
s a bin
a
ry
de
cisi
on
{1
,
1
}
k
u
, with fals
e alarm
rate
0
[1
|
]
lfk
k
PP
u
H
and d
e
tection
proba
bility
1
[1
|
]
ldk
k
PP
u
H
, resp
ect
i
vely. Theref
ore, the
deci
s
io
n rule
of the
k
-th se
nso
r
is:
1,
1,
kk
k
kk
y
u
y
(5)
Whe
r
e
k
is decisi
on thre
sh
old determi
n
ed by the false ala
r
m rate
lfk
P
. When
k
n
is Gau
ssi
an
white n
o
ise
with ze
ro m
ean
and va
rian
ce
2
k
, the retu
rn f
r
om the S
w
e
r
li
ng 0 ta
rg
et is
con
s
tant. In
this
c
a
s
e
, the
ldk
P
and
lfk
P
can be
calcul
ated a
s
followin
g
,
2
22
11
2
e
rfc
,
e
rf
c
,
e
r
fc
(
)
22
22
kr
t
k
ld
k
l
f
k
x
kk
P
PP
x
e
d
t
(6)
2.3. Link Model
Let
co
m
tk
P
den
ote th
e ra
diated transmitted
po
wer of com
m
unication
si
gnal at the
k
-th
sen
s
o
r
. Con
s
iderin
g the
pa
th loss in
cu
rred du
rin
g
tra
n
smi
ssi
on, th
e po
we
r of
si
gnal
re
ceived
by
the FC and from the
k
-th sensor
is
()
k
fc
c
o
m
rk
tk
k
k
PP
d
(7)
Whe
r
e
k
is a consta
nt determined by
the antenn
a
ch
aracteri
stics,
k
is path loss exp
onent, an
d
k
d
is the rang
e
from the
k
-
t
h
s
e
ns
or
to
th
e F
C
. Ea
ch
loc
a
l de
c
i
s
i
o
n
k
u
is tran
smitted
throug
h a
fading Raylei
gh ch
ann
el a
nd the output
of the chann
el for the
k
-th
sen
s
o
r
is giv
en by Equati
o
n
(8).
fc
kr
k
k
k
k
rP
h
u
w
(8)
W
h
er
e
k
w
is zer
o
mea
n
Gau
ssi
an noi
se wit
h
v
a
ri
an
ce
2
k
w
, and
k
h
is
the
gain of
a re
al
value
d
Rayleig
h
fading ch
ann
el wi
th the PDF given by
2
()
2
,
0
k
h
kk
k
fh
h
e
h
.
2.4. Fusion Rule
Based
on the
kno
w
led
ge o
f
chann
el stat
istics and lo
cal detectio
n
p
e
rform
a
n
c
e i
ndexe
s
,
the LRT
-
CS (l
ikelih
ood ratio test based
on ch
ann
el st
atistics) [1] ca
n be refo
rmul
ated as:
12
1
12
2
0
2
22
21
e
r
f
e
x
p
1
2
(,
,
,
|
)
lo
g
l
o
g
(,
,
,
|
)
22
2e
r
f
e
x
p
1
2
1
2
2
fc
fc
fc
r
k
rk
rk
ldk
k
k
k
k
k
k
fc
fc
fc
rk
rk
rk
kk
k
k
k
N
tot
N
lf
k
k
PP
P
Pa
r
r
a
a
r
PP
P
a
fr
r
r
H
fr
r
r
rr
a
a
r
H
P
1
N
k
(9)
whe
r
e
22
1/
2
kk
fc
rw
k
kw
P
a
and
2
0
2
erf
x
t
x
ed
t
.
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TELKOM
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Vol. 11, No
. 8, August 2013: 4335 –
4343
4338
Whe
n
usi
ng
the fusion rul
e
above, the
global proba
bility of false alarm
ft
ot
P
and th
e
global p
r
ob
ab
ility of detection
dt
o
t
P
are dete
r
mined by Equ
a
tion (10
)
an
d (11
)
, re
spe
c
tively.
0
PH
ft
o
t
t
o
t
PT
(10)
1
PH
dt
ot
t
o
t
PT
(11)
In the equatio
ns ab
ove,
T
is the dete
c
tion thre
shol
d at the FC.
3. Optimizati
on of No
de’s
Po
w
e
r
Alloc
a
tion Schem
e
s
3.1. Po
w
e
r
Consumptio
n of Sensor
Node
In general, the powe
r
consumption of se
nso
r
nod
e ca
n be divided into two kind
s,
range
-
related p
o
we
r con
s
u
m
ptio
n and ra
nge
-free po
we
r
consumption.
Here, con
s
id
er two ki
nd
s o
f
rang
e-relate
d
powe
r
con
s
u
m
ption. One i
s
co
nsume
d
by target se
n
s
ing, de
noted
by
se
n
s
in
g
k
P
，
and
is relate
d to the drain ef
ficien
cy of powe
r
amplifie
r and ante
n
n
a
gain
s
. Assuming the to
tal
energy efficie
n
cy is
se
n
s
i
n
g
k
，
the con
s
um
ed p
o
we
r
se
n
s
in
g
kt
o
t
P
and the
radiated
sig
nal po
wer
se
n
s
in
g
k
P
has the follo
wing relatio
n
.
1
s
e
ns
i
n
g
s
e
n
si
ng
s
e
ns
i
n
g
kt
o
t
k
k
PP
(
1
2
)
For rada
r
se
nso
r
, the la
rger the
se
n
s
in
g
k
P
is
，
t
he strong
er t
he targ
et’s
return
s a
r
e a
n
d
corre
s
p
ondin
g
ly the high
er lo
cal sen
s
or’
s
det
ecti
on ca
pability
.
Therefo
r
e,
sen
s
o
r
’s ta
rget
detectio
n
perf
o
rma
n
ce ca
n be adju
s
ted b
y
adjusting
se
n
s
in
g
k
P
.
Another
kin
d
of range
-related p
o
wer co
nsumpt
ion is that
con
s
ume
d
by th
e
comm
uni
cati
on between
sen
s
o
r
no
de
and the FC.
Assumin
g
that the power of the sig
nal
radiate
d
into
wirele
ss
ch
annel
by sen
s
or
k
is de
not
ed by
co
m
k
P
and to
tal efficien
cy of po
wer
amplifier an
d
antenn
a i
s
d
e
noted
by
co
m
k
，
then the
po
we
r used fo
r
ra
diating
sign
al
co
m
kt
o
t
P
can
be
denote
d
by:
1
co
m
c
o
m
c
o
m
kt
o
t
k
k
PP
(
1
3
)
Except for the rang
e-relat
ed po
wer
co
nsum
ption, the other p
o
w
er
con
s
u
m
ption, for
example fro
m
low noi
se
amplifier, A/D co
nver
te
r, D/A convert
e
r and
so o
n
, is ran
ge-f
r
ee.
Furthe
rmo
r
e,
it can
be
con
s
ide
r
ed
fixed
or
ca
nnot be controlled
fre
e
ly.
Beside
s, for
mai
n
tainin
g
the normal f
unction of
sensor
network, sensor no
de will
consume some
energy, which
may
fluctuate. The
r
efore, the po
wer al
l
o
cation
of sensor n
o
de, con
s
id
ere
d
in this pap
e
r
, is a pro
b
le
m
about h
o
w to sh
are the
adju
s
table
power
bud
ge
t by the target se
nsi
ng
power
se
n
s
in
g
kt
ot
P
and
sign
aling po
wer
co
m
kt
o
t
P
. Assume t
hat the total powe
r
bud
get is
s
e
ns
ing+c
o
m
k
P
and then:
se
nsing
s
e
n
s
i
ng+c
o
m
ktot
k
co
m
kt
o
t
PP
P
(14)
For
optimum
syste
m
p
e
rf
orma
nce, the
match b
e
tween th
e
com
m
unication
capability
and the dete
c
tion pe
rform
ance index
of local se
nsor
node is n
eed
ed. That is to say, the target
sen
s
in
g power
se
n
s
in
g
kop
t
P
and the si
gnalin
g powe
r
co
m
kopt
P
maximize the detection
capability of the
whol
e system
. At
this time
，
there is:
se
nsing
c
om
se
nsing+c
o
m
kt
o
t
k
t
o
t
k
PP
P
(15)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Powe
r Optim
i
zation b
e
twe
en Sensi
ng a
nd Signalin
g
for Dis
t
ributed Detec
t
io
n (Xi
ang
yan
g
LIU)
4339
3.2. Objectiv
e Functio
n
For given ad
missi
ble maxi
mum
fal
s
e al
arm rate
，
the
obje
c
tive of
system
optim
ization
is equivale
nt to finding th
e sch
eme of
determinin
g
sensi
ng po
wer
s
en
si
n
g
kt
ot
P
and co
m
m
unication
power
s
e
n
s
ing+c
o
m
co
m
s
en
si
n
g
kk
t
tt
o
t
ko
PP
P
，
so
as to m
a
ximize the
gl
obal p
r
ob
abil
i
ty of detection
dt
ot
P
,
expre
s
sed a
s
the function
of the decisi
on thre
shol
d
k
of
k
-th sen
s
or, sen
s
in
g p
o
we
r
se
n
s
in
g
kt
o
t
P
,
comm
uni
cati
on po
wer
co
m
kt
o
t
P
, and the deci
s
io
n threshold
T
at the FC, as shown in:
s
e
ns
i
n
g
s
e
n
s
i
ng
se
nsi
n
g
11
1
1
Pr
H
,
,
,
,
,
,
,
,
co
m
c
om
c
o
m
d
t
o
t
to
t
D
to
t
t
o
t
k
k
to
t
k
to
t
N
to
t
k
to
t
PT
P
P
P
P
P
T
P
P
. (16)
The optimi
z
tion pro
b
lem
can be expressed a
s
:
se
nsing
s
e
n
sing
se
nsing
1
,,
,,
sens
i
n
g
s
ensi
ng+com
s
e
ns
i
n
g
.
.
0
,
0,
0,
,
ma
x
Nt
ot
tot
kt
o
t
dt
ot
PPP
co
m
c
o
m
k
k
to
t
k
to
t
fto
t
k
to
t
k
k
t
o
t
P
st
P
P
P
P
P
P
(17
)
Whe
r
e
ft
ot
P
is the global p
r
ob
ab
ility of
false al
arm.
4. Optim
i
zati
on Metho
d
4.1. The Iden
tical Po
w
e
r
Allocation S
c
heme (IPAS
)
In gene
ral, p
e
rform
a
n
c
e i
ndexe
s
(p
rob
abilitie
s of fa
lse ala
r
m a
n
d
dete
c
tion)
of local
sen
s
o
r
a
r
e n
o
t equal fo
r the sy
stem wi
th maximu
m detectio
n
pe
rforma
nce.
Ho
wever, whe
n
the
numbe
r of sensors app
ro
ach
e
s infi
nity, the system with identical local dete
c
tors will ha
ve
asymptotic
o
p
timum pe
rfo
r
man
c
e [1
0]. Therefor
e,
we a
s
sume
that every sensor n
ode
has
identical sen
s
ing
an
d co
mmuni
cation
perfo
rma
n
ce
an
d
thei
r power su
ppli
e
s have
i
d
e
n
tical
power. F
u
rth
e
rmo
r
e, a
s
su
me the
po
we
r bu
dget
th
at ca
n be
di
stri
buted b
e
twe
en
sen
s
ing
a
nd
comm
uni
cati
on is
s
e
ns
ing+c
o
m
k
P
.
A simple met
hod can be u
s
ed to find a
good all
o
cation method. A
c
cordi
ng to the total
power b
udg
e
t
s
e
ns
ing+c
o
m
k
P
，
determin
e
a suffici
ent small po
we
r i
n
crea
se
P
with the relation o
f
s
e
ns
ing+c
o
m
k
PL
P
. Let sensi
ng po
wer
s
en
si
n
g
kt
ot
P
be
P
,
2
P
,
,
L
P
s
u
ccess
ively and let
comm
uni
cati
on po
wer
s
e
ns
in
g+c
o
m
s
e
n
s
i
n
g
k
co
m
kt
ot
kt
o
t
PP
P
. Next, c
o
mpute
dt
ot
P
acco
rdin
g to Equation (16).
Record all the
dt
ot
P
s obtai
ned
and find the l
a
rge
s
t on
e a
m
ong them.
The sen
s
ing
powe
r
s
en
s
i
n
g
kt
o
t
P
with the larg
est
dt
ot
P
is the b
e
s
t one. In this metho
d
, all the node
s h
a
ve the ident
ical po
we
r
allocation scheme. So, the method can
be denoted by IPAS in abbreviation.
4.2. Ant Colon
y
Optimization
Although ACO wa
s propo
sed fo
r com
b
i
natorial p
r
o
b
l
e
ms, re
se
archers sta
r
ted t
o
adapt it
to continu
o
u
s
optimization
proble
m
s. T
he simp
l
e
st
approa
ch for applying ACO to continu
ous
probl
em
s wo
uld be
to di
screti
ze th
e re
al-value
d do
main of the
variable
s
. Thi
s
ap
proa
ch h
a
s
been
succe
s
sfully follo
we
d when
ap
pl
ying ACO
to
the
protei
n–
ligand
do
ckin
g p
r
obl
em [1
1].
Re
cently, Socha an
d Do
ri
go [12] has
pr
op
osed an
ACO algorit
hms, name
d
as ACO
R
, that
handl
e contin
uou
s pa
ram
e
ters natively, whe
r
e th
e pr
obability de
nsity functions that are impli
c
itly
built by the pheromo
ne
model a
r
e ex
plicitly re
p
r
e
s
ented by Ga
ussian
ke
rnel
function
s. T
heir
approa
ch ha
s also be
en ex
tended to mixed-va
riable p
r
oblem
s [13].
Ants ge
ne
rall
y start o
u
t m
o
ving at
ran
d
o
m. Ho
wev
e
r
,
whe
n
they
e
n
co
unter a
previously
laid trail, they can decide to follow it
, thus
rei
n
forcing th
e trail
with their
o
w
n p
heromo
ne
sub
s
tan
c
e. T
h
is colle
ctive behaviou
r
is a form of
au
tocatalytic p
r
oce
s
s. In this case, the more
ants follo
w a
trail; the mo
re attra
c
tive t
hat trail b
e
co
mes to
be fo
llowe
d by future
ants. T
h
i
s
pro
c
e
ss i
s
th
us exp
r
e
s
sed
as a po
sitive
feedba
ck lo
o
p
, whe
r
e the
prob
ability with whi
c
h an
a
n
t
sele
ct a path
incre
a
ses
wi
th the numb
e
r of ant
s th
at previou
s
ly sele
cted the
same path [
2
].
Hence, artificial ants probabilisti
cally develop
a sol
u
tion iteratively by considering pheromone
trails o
r
/and l
o
cal h
euri
s
tic
informatio
n a
s
well.
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 8, August 2013: 4335 –
4343
4340
Here, we a
d
o
p
t a model
,,
QS
f
o
f
continuo
us
optimizatio
n probl
em, wh
e
r
e
S
is a
sea
r
ch spa
c
e defined
o
v
er a finite set of co
ntinuou
s de
ci
si
on varia
b
le
s;
is the set o
f
con
s
trai
nts
a
m
ong th
e variable
s
;
:
fS
is
an
obje
c
tive fun
c
tion to
be m
i
nimize
d. Accordin
g
to the statem
ent above,
se
ns
i
n
g
c
om
se
ns
i
n
g
s
e
n
si
ng
11
1
2
2
sens
n
g
2
i
,,
,
,
,
,
,
,
,,
,
,
1
,
2
,
,
,
co
m
c
o
m
t
o
t
t
o
t
t
o
t
t
ot
Nt
ot
N
t
ot
co
m
kt
o
t
k
t
o
N
k
t
T
PP
P
P
PP
PT
N
Pk
Ss
(18
)
se
nsi
n
g
s
e
n
s
i
ng
se
ns
i
n
g
11
1
,,
,
,
,
,
,,
com
c
o
m
co
m
d
t
o
t
D
t
ot
t
o
t
k
k
t
ot
k
t
ot
Nt
ot
k
t
ot
fP
P
P
P
P
P
T
P
P
s
(19)
The
CACS
al
gorithm
was first
pro
p
o
s
ed
in
[14].
It
u
s
es a contin
uo
us phe
rom
o
n
e
mod
e
l
con
s
i
s
ting of
a Gau
s
sian
pdf ce
ntre
d
on the b
e
st
solutio
n
foun
d so fa
r. Th
e
best
solutio
n
at
pre
s
ent
is mo
dified a
c
cordi
ng to
a
wei
g
h
t
ed ave
r
age
of the
distan
ce bet
wee
n
e
a
ch i
ndividu
al i
n
the popul
atio
n and the be
st solution fou
nd so fa
r, as
sho
w
n in Equ
a
tion (20
)
.
1
2
11
mi
n
11
ant
ant
NN
jj
j
k
opt
kk
k
ko
p
t
s
s
ff
ff
(
2
0
)
W
h
er
e
an
t
N
is th
e nu
mbe
r
of
ants d
e
fine
d in
the
alg
o
rithm,
2
j
is th
e vari
an
ce
o
f
the
j
-th
dimen
s
ion,
opt
s
is the best sol
u
tion at pre
s
ent and the sup
e
rscript
j
denote the
j
-t
h dimen
s
ion
variable of th
e solutio
n
s
.
The mai
n
adv
antage
s of th
e CACS
are t
hat it
requi
re
s the setting
of just on
e pa
rameter
(the
numb
e
r
of ants in
the
pop
ulation
)
and
present
s a ve
ry
simpl
e
me
ch
ani
sm
to g
ene
rate
the
ants of the n
e
xt generatio
n. On t
he other han
d, a cl
ear d
r
a
w
ba
ck is that it only investigate
s
one
promi
s
in
g re
g
i
on of the pro
b
lem at a tim
e
, which
mea
n
s that the al
gorithm ten
d
s to con
c
ent
rat
e
the Gau
ssi
an
pdf aroun
d lo
cal optima ve
ry quick
ly, thus leadi
ng to a
prematu
r
e converg
e
n
c
e.
The A
C
O
R
al
gorithm
[12] consi
s
ts
of an archive
th
at h
o
lds the
k be
st
solution
s fo
und
so
far. In con
c
e
p
tual term
s,
each solution
co
rre
sp
ond
s to the
centre of a diffe
re
nt Gau
s
sian
pdf.
More
over, thi
s
a
r
chive i
s
u
s
ed
to calcul
ate the va
ria
n
ce
of ea
ch
distrib
u
tion,
so that the
wh
ole
pro
c
e
s
s can
be de
scrib
ed
as follo
ws. Initially, the
wh
ole archive
is stocha
st
icall
y
cre
a
ted (usi
ng
a unifo
rm di
st
ribution
)
, a
n
d
the g
ene
rate
d individu
als
are
so
rted
in
desce
nding
o
r
de
r of fitne
s
s.
Then, the m
a
in iteratio
n
start
s
by first
assigni
ng a
solutio
n
of
th
e archive to
each ant of t
h
e
probl
em, with
proba
bility proportio
nal to the wei
ght
k
of the
k
-th archiv
e
solutio
n
k
s
.
2
22
1(
1
)
exp
2
2
k
an
t
an
t
k
qN
qN
(21)
Whe
r
e
an
t
N
is the
numbe
r of a
n
ts,
k
i
s
the
rank
of the sol
u
tion on th
e a
r
chive, a
nd
q
is a vari
able
calle
d locality of the search p
r
o
c
e
ss a
nd used
to b
a
lan
c
e exploi
tation and e
x
ploration. T
h
e
mean
of ea
ch Ga
ussian
i
s
the
n
defin
e
d
a
s
bei
ng t
he
corre
s
po
n
dent a
r
chive
solutio
n
, and
its
varian
ce is gi
ven by:
di
m
1
,1
,
,
1
an
t
ii
N
kl
i
l
k
an
t
ss
iN
N
(22)
Whe
r
e
cont
rol
s
the spee
d
of conve
r
ge
n
c
e to dete
r
mi
ne ho
w fast t
he sol
u
tion
s
of the archive
will converge,
s
is a solutio
n
belongi
ng to
the archive, and
dim
N
is the di
mensi
on of th
e sea
r
ch
spa
c
e. Finally
,
this Gau
ssi
a
n
di
stributio
n with
m
ean
an
d varia
n
ce d
e
f
ined a
s
de
scribed
ab
ove i
s
use
d
to gene
rate a ne
w solution to the
proble
m
. After ea
ch ant h
a
s built a ca
ndidate
soluti
on,
these
candi
d
a
te solution
s
are
inserte
d
i
n
to the
archiv
e an
d a
r
e
sorted ag
ain. T
h
e alg
o
rithm
th
en
iteratively re
moves the worst
solution
s until t
he arch
ive return
s to its origin
al si
ze.
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ang
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4341
5. Numerical
Simulation
5.1. Simulation Condi
tions
In our simul
a
tions, we u
s
e
the WSN co
nfigur
atio
n d
e
scrib
ed in Section 2. Co
n
s
ide
r
a
WSN
with eig
h
t rada
r-li
k
e sensor no
de
s and a F
C
.
All units of coo
r
dinate are m
e
ters. Th
e F
C
is
with
coo
r
din
a
t
e (0,3
00).
Assume
that th
e
Y-axis co
o
r
di
nates of all
th
e sen
s
o
r
s are
ze
ro
an
d thei
r
X-axis coordi
nates a
r
e gi
ven in Table
1. Also
, assume the ta
rget to be d
e
tected i
s
wi
th
coo
r
din
a
te (2
0,-150
).
Table 1. X-ax
is Co
ordi
nate
s
of Sensor Node
s
Sensor’s No.
1
2
3
4
5
6
7
8
X-axis
coordinat
e -180
-120
-60
0 60 100
160 220
Assu
me the f
a
lse
alarm
rat
e
of the FC i
s
0.001. Each
sen
s
o
r
ha
s o
peratin
g freq
uen
cy
9375M
Hz, pu
lse
w
idth
10n
s, an
d
se
n
s
i
n
g
k
=0.18.
Assume
a
n
o
ise
figure F
= 8
dB, effective noise
temperature
0
290
TK
, antenn
a gai
n
28
d
B
G
and total
re
ceiver lo
ss
L
=
4 dB. Also,
a
s
sume
that, for targets following the Swerling I
I
fluctuat
ions with
average RCS
of
5 m2,
a probability o
f
detectio
n
0.5
and
rad
a
r return
s’
power o
f
-93
d
Bm
a
r
e
requi
re
d at
m
a
ximum
rang
e of 1
5
0
mete
rs
with false ala
r
m rate 0.01
or b
e
tter. Assume
that
co
mmuni
cation system ope
rates
at 2.4G
Hz
and ad
opts th
e followin
g
pa
th loss m
odel
given by Shellhamme
r [15].
10
10
40.
2
2
0
l
og
(
)
8
()
58.
5
3
3
l
o
g
8
8
dd
m
pl
d
d
dm
(23)
Assu
me that
the sig
nal-to
-
noise lo
ss
of t
he practi
cal
comm
uni
cati
on re
ceive
r
compa
r
ed
with the
ide
a
l
one
is 5dB.
Also, a
s
sume
that, fo
r bina
ry
symm
etric Rayleig
h
fadi
ng cha
nnel, a
bit
error rate
0.0
01 i
s
req
u
ire
d
at
re
ceiver
sen
s
it
ivity of -95dBm
at m
a
ximum
rang
e of 1
0
2
met
e
rs
with tran
smitted power 5
dBm. Let the drain e
fficie
n
cy of powe
r
amplifier of comm
uni
cati
on
module i
s
0.1
7
.
Monte
Ca
rlo
simulatio
n
i
s
use
d
to fin
d
t
he th
re
shold
s
k
(
1,
2
,
,
kN
) an
d
T
, as
sh
own
in the following. For positive
integer
n, generate I.I.D. sampl
e
s
1
x
,
2
x
,…,
n
x
, eac
h
with the same
distrib
u
tion a
s
the ra
ndom
variabl
e
X
. Sort
1
x
,
2
x
,…,
n
x
in asce
nding
order a
nd de
note th
em b
y
(1
)
(
2
)
(
)
n
x
xx
. Let
()
k
Tx
and then the co
rre
spondi
ng mea
n
1
m
and stan
dard d
e
viatio
n
1
of the fal
s
e
alarm rate
of the d
e
tect
or a
r
e
given
in Equ
a
tion
(24
)
and E
quation
(2
5),
r
e
spec
tively.
1(
)
1
EP
r
1
k
nk
mX
x
n
(24)
1(
)
1(
1
)
st
d
P
r
12
k
kn
k
Xx
nn
(
2
5
)
In the simul
a
tion of this pape
r, the param
et
ers to estimate de
tection thre
shold are
7
51
0
1
n
and
7
5
1
0
5
000
0
k
. Therefo
r
e,
1
0.001
m
and
4
2.0
1
0
. The probability
of
detectio
n
wa
s estimated by
5
31
0
experime
n
ts.
5.2 Simulation results
Whe
n
s
e
ns
ing+c
o
m
k
P
=6
0m
W a
nd
all th
e sen
s
ors ha
ve identi
c
al
sensi
ng
po
wer, the plot
of
probability of
detection
at FC
versus sensi
ng
power are
giv
en in Figure 1.
Obviously
sens
i
n
g
ktot
41
.9
P
mW will maximize the
dt
o
t
P
. T
he maximum
value obtain
ed is 0.87
8. A bad power
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4343
4342
allocation, fo
r exampl
e
sensi
n
g
ktot
5
P
m
W
an
d
co
m
kt
o
t
P
=55
mW, will m
a
ke the
system’s detection
perfo
rman
ce l
e
ss than 0.1. Ther
efore, a reasona
ble all
o
catio
n
of no
de’s p
o
wer is
necessa
ry.
Figure 1. Probability of Detection versus
Sensin
g Power und
er Po
wer Budg
et of 60mW
Figure 2. Local Optimum P
r
oba
bility Obtained
durin
g Iteratio
n
s
Table 2. Power Allocation
Schem
e Obta
ined by ACO
R
k
No. of iteration
1 2 3 4 5 6 7
8 9
10
11
12
se
n
s
in
g
kt
o
t
P
(m
w
)
1
48.71
13.72
8.64
32.41
33.69
26.55
35.70
42.98
41.95
41.95
47.28
36.70
2
53.22
37.40
43.22
56.07
44.51
46.65
42.05
45.00
44.38
44.38
45.30
45.61
3
38.20
44.22
37.73
41.77
43.56
41.52
43.92
43.61
46.27
46.27
43.86
44.91
4
28.94
39.51
33.73
35.25
34.62
36.71
37.93
37.42
37.73
37.73
37.90
37.65
5
35.46
44.89
36.13
39.95
39.45
40.92
42.1
1
41.01
40.73
40.73
40.34
40.51
6
46.21
49.
44.81
43.26
40.85
43.25
43.15
41.41
43.30
43.30
44.04
42.54
7
31.75
37.66
40.48
39.97
44.28
38.77
42.96
42.30
44.41
44.41
45.17
44.94
8
55.31
19.41
47.35
18.89
20.56
44.19
43.98
49.46
34.52
34.52
38.66
46.71
P
dtot
0.850
0.866
0.869
0.873
0.876
0.880
0.882
0.883
0.886
0.886
0.887
0.888
Whe
n
u
s
ing t
he ant
colony
optimizatio
n
algor
ith
m
, the
numbe
r of a
n
ts is
assum
ed 10
0.
The time
s of iteration
s
are
20. The lo
cal
best p
r
ob
abili
ty of detection of eac
h iteration is give
n
in
Figure 2. The
best
sen
s
ing
power of e
a
ch se
nsor
sea
r
che
d
by ACO
R
at ea
ch ite
r
ation are give
n
in Table 2. The re
sults ob
tained by CA
CS are given
in Table 3, whe
r
e
k
stan
ds for the No
. of
local sen
s
o
r
and
se
n
s
in
g
kt
o
t
P
is the se
nsin
g po
wer
of the
k
-th se
nso
r
.
Table 3. Power Allocation
Schem
e Obta
ined by CACS
k
No. of iteration
1 2 3 4 5 6 7
8 9
10
11
12
se
n
s
in
g
kt
o
t
P
(m
w
)
1
27.24
32.08
33.89
36.69
38.75
40.07
40.07
40.47
40.47
40.47
40.47
40.07
2
34.54
35.67
39.25
43.89
48.17
48.92
48.92
50.24
50.24
50.24
50.24
48.92
3
35.04
42.89
44.54
44.92
45.49
45.61
45.61
46.24
46.24
46.24
46.24
45.61
4
36.62
40.09
41.30
42.70
42.91
43.16
43.16
43.42
43.42
43.42
43.42
43.16
5
31.31
32.79
34.33
34.48
35.38
36.1
1
36.1
1
36.30
36.30
36.30
36.30
36.1
1
6
28.42
35.32
41.63
44.32
44.79
44.97
44.97
45.66
45.66
45.66
45.66
44.97
7
28.75
31.22
34.19
38.06
42.73
47.49
47.49
50.91
50.91
50.91
50.91
47.49
8
32.42
34.01
38.24
38.64
41.92
42.26
42.26
44.13
44.13
44.13
44.13
42.26
P
dtot
0.850
0.821
0.857
0.872
0.878
0.880
0.880
0.880
0.881
0.881
0.881
0.881
From
the
s
e
result
s a
bove,
we
can fin
d
that
the
CA
CS
conve
r
ge
s
rapidly to
t
he b
e
st
solutio
n
. Mo
reover, th
e b
e
st
solutio
n
s found
by A
C
O
R
outpe
rfo
r
m that
by
CACS sli
ghtly
and
there i
s
a
de
tection p
r
o
b
a
b
ility differen
c
e of
0.
008.
Comp
ared
wi
th the be
st
solution fou
n
d
by
IPAS, both A
C
O
R
a
nd
CACS ca
n obtai
n better
solu
tions. However, the dete
c
tion pro
babili
ty
differen
c
e b
e
t
ween the
m
i
s
sm
all and i
s
not mo
re t
han 0.01.
Co
nsid
erin
g the
simpli
city and
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
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e-ISSN:
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Powe
r Optim
i
zation b
e
twe
en Sensi
ng a
nd Signalin
g
for Dis
t
ributed Detec
t
io
n (Xi
ang
yan
g
LIU)
4343
robus
t
ness
of
the IPAS, the IPAS is
a f
eas
ible
s
u
boptimum
optimiz
ati
on
sc
heme for the WSN
with identi
c
al
node
s.
6. Conclusio
n
Con
s
id
erin
g the scen
ario
of using di
stri
but
ed ra
da
r-li
k
e sen
s
ors to
detect the prese
n
ce
of a target, we formul
ate the proble
m
o
f
powe
r
allo
cation bet
wee
n
se
nsi
ng an
d com
m
uni
ca
tion
for si
gnal
det
ection
und
er the Neyman
-Pearso
n
cr
it
erion. T
he
p
o
we
r allo
cati
on sch
e
me
h
a
s
been o
p
timized by mean
s of IPAS, CACS and ACO
R
, respe
c
tivel
y
. Results
sh
ow that they can
lead to a goo
d power allo
cation. Among
them, the ACO
R
can obt
ain the be
st solutio
n
and t
he
CACS has t
he second best perform
a
nce. Alt
hough the IPAS is the
worst
among them,
i
t
achi
eves
nea
rly the same
detectio
n
pe
rf
orma
nce
a
s
compa
r
ed
with
that achieve
d
by CA
CS a
nd
ACO
R
. The
r
ef
ore, fo
r the
WSN with
ide
n
tical
node
s, a
n
ide
n
tical
po
wer allo
catio
n
schem
e fo
r a
ll
sen
s
o
r
s
can
be employe
d
to achieve n
e
a
rly the best
power allo
cati
on schem
e.
Ackn
o
w
l
e
dg
ements
The
China
National Sci
e
n
c
e F
ound
atio
n und
er
Gra
n
t No
s. 611
0
2160
and
61
1790
02
and the proje
c
t for po
stgra
duate
s
of military
sci
ence (2010
JY04
23
-241)
sup
p
o
r
t this wo
rk.
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h
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n
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u
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