Indonesian
Journal
of
Electrical
Engineering
and
Computer
Science
V
ol.
7,
No
.
3,
September
2017,
pp
.
802
808
DOI:
10.11591/ijeecs
.v7.i3.pp802-808
802
Optimal
Ener
gy
Har
vesting
Sc
heme
f
or
P
o
wer
Beacon-Assisted
Wireless-P
o
wered
Netw
orks
Dinh-Thuan
Do
F
aculty
of
Electronics
T
echnology
,
Industr
ial
Univ
ersity
of
Ho
Chi
Minh
City
12
Nguy
en
V
an
Bao
,
Go
V
ap
Dist.,
Ho
Chi
Minh
City
,
Vietnam
e-mail:
dodinhthuan@gmail.com
Abstract
In
this
paper
,
w
e
consid
er
one-w
a
y
rela
y
with
energy
har
v
esting
system
based
on
po
w
er
beacon
(PB),
in
which
the
rela
y
node
har
v
ests
tr
ansmitted
po
w
er
from
the
PB
station
to
f
orw
ard
signals
to
destination.
W
e
also
analyse
the
rela
y
netw
or
k
model
with
amplify-and-f
orw
ard
(AF)
protocol
f
or
inf
or
mation
cooper
ation
and
P
o
w
er
Splitting-based
Rela
ying
(PSR)
protocol
f
or
po
w
er
tr
a
nsf
er
.
In
par
ticular
,
t
he
outage
probability
and
optimal
energy
har
v
esting
(EH)
po
w
er
splitting
fr
action
of
no
v
el
scheme
in
are
p
resented.
W
e
obtain
analytical
closed-f
or
m
e
xpression
of
optimal
energy
har
v
esting
(EH)
po
w
er
splitting
fr
action
to
minimiz
e
the
outage
probability
of
system.
Using
n
umer
ical
and
analytical
sim
ulations
,
the
perf
or
mances
of
diff
erent
cases
are
presented
and
discussed.
K
e
yw
or
ds:
po
w
er
beacon,
Energy
Har
v
esting,
po
w
er
splitting-based
rela
ying,
Amplify
and
F
orw
ard
Cop
yright
c
2017
Institute
of
Ad
v
anced
Engineering
and
Science
.
All
rights
reser
v
ed.
1.
INTR
ODUCTION
Recently
,
wireless
access
will
be
a
reality
in
fifth
gener
ation
(5G)
wireless
systems
,
with
a
ser
ies
of
emerging
technology
,
such
as
massiv
e
m
ultiple-input
and
m
ultiple-output
(MIMO),
de
vice-to-de
vice
comm
unication
and
small
cell
architectures
,
which
ha
v
e
launched
a
huge
data
v
olume
in
wireless
ser
vices
,
such
as
mobile
gaming
,
mobile
TV
and
mobile
Inter
net.
Fur
ther
more
,
with
f
ast
increasing
n
umber
of
users
o
wning
smar
tphones
and
tab
lets
,
and
hence
one
of
the
most
cr
itical
prob
lem
is
that
limited
oper
ation
lif
e
time
of
mobile
de
vices
due
to
finite
energy
ability
.
T
o
address
this
hard
issue
,
r
adio-frequency
(RF)
based
energy
har
v
esting
model
has
receiv
ed
a
consider
ab
le
research
interest
[1].
A
promising
technology
of
RF-assisted
energy
signals
enab
les
wireless
energy
tr
ansf
er
(WET)
to
pro
vide
contin
uous
and
con
v
enient
po
w
er
supply
to
energy-
a
w
are
wire
less
ter
minals
.
As
a
result,
wireless
po
w
ered
comm
unication
(WPC)
system
together
with
wireless
de
vices
(WDs)
is
designed
to
tr
ansf
er
data
to
the
inf
or
mation
receiv
ers
(IRs),
e
.g.,
sensor
nodes
.
Such
ter
minals
is
po
w
ered
up
b
y
the
means
of
wireless
po
w
ered
equipment
as
a
dedicated
energy
tr
ansmitters
(ETs).
In
f
act,
wireless
recharging
is
one
of
the
most
desir
ab
le
ne
w
f
eatures
f
or
mobile
de
vices
to
eliminate
the
need
of
po
w
er
cords
and
po
w
er
charge
rs
.
T
o
realiz
e
this
wireless
po
w
er
tr
ansf
er
,
a
no
v
el
netw
or
k
architecture
where
stations
called
po
w
er
beacons
(PBs)
are
installed
in
tr
aditional
cellular
netw
or
k
f
or
boosting
oper
ation
efficiency
of
mobiles
and
sensors
via
micro
w
a
v
e
r
adiation
kno
wn
as
micro
w
a
v
e
po
w
er
tr
ansf
er
(MPT)
In
[2][9],
the
w
or
ks
ha
v
e
lately
adopted
some
tr
ansmission
policies
f
or
EH
cooper
ativ
e
netw
or
ks
.
EH
rela
ys
w
ere
first
imp
lemented
in
cooper
ativ
e
comm
unication
[2]
.
In
[3][5],
assuming
a
perf
ect
EH
model
under
which
the
energy
arr
iv
al
time
and
the
amount
of
har
v
ested
energy
are
calculated
pr
ior
to
tr
ansmit
such
energy
,
regarding
EH
rela
y
systems
,
there
w
ere
some
po
w
er
allocation
policies
giv
en.
Ne
v
er
theless
,
due
to
the
r
andom
energy
arr
iv
al
time
and
the
amount
of
har
v
ested
energy
,
the
dete
r
ministic
EH
model
seems
to
be
abstr
act.
Thus
,
under
gener
al
energy
har
v
esting
profiles
,
the
authors
in
[6][9]
proposed
a
n
umber
of
tr
ansmission
policies
.
P
ar
ticular
ly
,
there
w
ere
se
v
er
al
joint
rela
y
selection
and
po
w
er
allocation
schemes
giv
en
due
to
th
e
stationar
ity
and
erodicity
of
the
energy
har
v
esting
process
[6].
Lik
e
wise
,
in
[7],
[8],
since
dur
ing
an
y
time
of
data
tr
ansmission,
energy
can
be
sca
v
enged,
se
v
er
al
po
w
er
allocation
schemes
f
or
cooper
ativ
e
EH
netw
or
ks
w
ere
put
f
orw
ard.
The
study
in
[9]
based
on
what
ha
v
e
been
accomplished
in
[7]
Receiv
ed
Apr
il
22,
2017;
Re
vised
A
ugust
12,
2017;
Accepted
A
ugust
27,
2017
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4752
803
and
[8]
to
e
xpand
the
b
uff
er-aided
link
adaptiv
e
EH
rela
y
system,
in
which
the
change
of
EH
r
ates
can
be
positiv
ely
assisted.
In
[10],
the
authors
planned
the
no
v
el
impression
of
de
plo
ying
dedicated
po
w
er
nodes
to
enab
le
wireless
po
w
er
tr
ansf
er
in
an
e
xisting
cellular
netw
or
k,
named
po
w
er
beacons
(PBs).
The
densities
and
tr
ansmit
po
w
er
of
PBs
are
in
v
estigated.
By
using
tool
of
the
stochastic
ge-
ometr
y
theor
y
under
data
links’
outage
constr
aint.
With
this
PB
based
energy
tr
ansf
er
,
w
e
thus
could
consider
a
ne
w
netw
or
k
,
so-called
PB-assisted
wireless
netw
or
ks
.
In
such
netw
or
ks
,
each
user
can
har
v
est
wireless
energy
from
the
dedicated
PB
.
F
or
th
is
ne
w
model,
the
optimization
prob
lem
need
be
solv
ed
to
optimally
allocate
the
resources
of
po
w
ered
netw
or
k
including
po
w
er
and
time
fr
action
f
or
wireless
po
w
er
processing
and
inf
or
mation
tr
ansmission.
T
o
the
best
of
our
kno
wledge
,
this
is
still
an
open
question,
which
motiv
ates
this
paper
.
In
this
paper
,
w
e
consider
a
PB
rela
ying
netw
or
k
consisting
of
one
PB
and
rela
y-destination
pair
.
W
e
assume
that
the
PB
are
connected
to
constant
po
w
er
supplies
.
Each
AP
(access
point)
station
aims
to
collect
the
inf
or
mation
from
its
associated
source
.
It
is
assumed
that
each
source
has
no
embedded
energy
supply
b
ut
has
the
ability
to
har
v
est
and
store
the
energy
from
RF
signals
broadcast
b
y
its
AP
.
The
PB
is
installed
to
assist
APs
dur
ing
the
energy
har
v
esting
phase
.
Specifically
,
w
e
f
or
m
ulate
a
closed-f
or
m
e
xpression
of
the
optimal
resource
po
w
er
allocation
of
energy
har
v
esting
protocol
to
obtain
optimal
outage
perf
or
mance
.
The
rest
of
the
paper
is
organiz
ed
as
f
ollo
ws
.
Section
II
descr
ibes
the
signal
and
channel
models
of
the
EH
enab
led
rela
ying
netw
or
k.
In
Section
III,
the
outage
probability
and
throughput
are
f
or
m
ulated
and
solv
ed
in
order
to
maximiz
e
perf
or
mance
.
Numer
ical
result
s
and
compar
isons
are
presented
in
section
IV
.
Finally
,
summar
izing
remar
ks
are
giv
en
in
section
V
.
2.
SYSTEM
MODEL
Figure
1.
The
system
model
In
this
paper
,
w
e
consider
a
PB-assisted
rela
ying
netw
or
k
consisting
of
one
m
ulti-antenna
PB
and
rela
y-destination
pairs
.
In
vie
w
of
the
state
of
ar
t
and
trend
of
RF
energy
tr
ansf
er
,
the
considered
netw
or
k
setup
is
v
er
y
lik
ely
to
find
its
applications
in
the
pr
actical
scenar
io
of
small
cells
,
such
as
picocells
(r
ange
from
10
to
100
meters)
and
f
emtocells
(WiFi
lik
e
r
ange),
which
has
been
regarde
d
as
one
of
the
k
e
y
e
nab
ling
technologies
of
the
upcoming
5G
cellular
netw
or
ks
.
It
is
also
w
or
th
mentioning
that
although
introducing
the
PB
ma
y
result
in
some
e
xtr
a
cost
and
comple
xity
to
the
system,
this
could
be
beneficial
as
a
whole
based
on
the
f
ollo
wing
consider
ations:
(i)
The
PB
could
be
dedicated
designed
f
or
po
w
er
tr
ansf
er
only
and
thus
can
achie
v
e
a
higher
energy
har
v
esting
efficiency
b
y
e
xploiting
the
benefits
of
energy
beamf
or
ming
enab
led
b
y
m
ultiple
antennas
.
(ii)
The
PB
design
is
adapted
to
applications
required
lo
w
po
w
er
such
as
in
small
cell
netw
or
ks
.
Optimal
Energy
Har
v
esting
Scheme
f
or
P
o
w
er
Beacon-Assisted
...
(Dinh-Thuan
Do)
Evaluation Warning : The document was created with Spire.PDF for Python.
804
ISSN:
2502-4752
(iii)
It
can
be
f
ound
optimal
energy
le
v
el
f
or
energy
har
v
esting
phase
and
calculated
at
PB
.
As
a
result,
model
of
PB
can
pro
vide
wireless
charging
ser
vices
in
real
lif
e
.
The
entire
comm
unication
consists
of
tw
o
diff
erent
phases
,
namely
,
energy
har
v
esting
and
inf
or
mation
tr
ansmission.
Assuming
a
po
w
er
fr
action
of
tr
ansmitted
po
w
er
of
PB
dur
ing
the
first
phase
is
assigned
to
energy
tr
ansf
er
,
in
which
the
AP
station
har
v
est
energy
from
the
PB
to
f
orw
ard
signal
to
destination
D
.
Dur
ing
the
energy
har
v
esting
processing
stage
,
t
he
receiv
ed
signal
at
the
AP
can
be
e
xpressed
as
y
r
=
p
P
S
h
T
1
x
+
n
r
;
(1)
where
n
r
is
the
additiv
e
white
Gaussian
noise
(A
WGN)
with
with
the
v
ar
iance
as
N
0
.
It
is
noted
that
the
PB
is
equipped
with
m
ultiple
antennas
,
energy
beamf
or
ming
is
de-
plo
y
ed
to
prog
ress
the
perf
or
mance
of
energy
tr
ansf
er
,
i.e
.,
x
=
ws
;
(2)
where
w
is
the
beamf
or
ming
v
ector
with
w
=
1
and
s
is
the
energy
symbol
with
unit
po
w
er
.
There-
f
ore
,
the
optimal
beamf
or
ming
v
ector
is
giv
en
b
y
w
=
h
H
k
h
k
2
;
(3)
in
which
(
:
)
H
denotes
the
Her
mitian
tr
anspose
matr
ix.
F
ollo
wing
the
pr
inciple
of
po
w
er
splitting
-based
rela
y
prototcol,
the
first
par
t
in
the
re-
ceiv
ed
RF
signal
is
allocated
f
or
energy
gather
ing
with
po
w
er
fr
action
2
[0
;
1]
.
Applying
no
v
el
energy
har
v
esting
pr
inciple
,
the
total
e
xpected
energy
at
the
end
of
the
first
phase
at
the
AP
can
be
calculated
as
E
h
=
P
S
k
h
k
2
+
N
0
T
;
(4)
where
(0
<
1)
is
the
energy
con
v
ersion
efficiency
of
the
EH
circuit,
T
is
b
loc
k
time
of
signal
processing
per
iod,
P
S
is
tr
ansmit
po
w
er
of
the
PB
.
The
har
v
ested
po
w
er
at
the
AP
use
to
f
orw
ard
inf
or
mation
to
the
destination
node
,
e
.g.
mobile
users
,
this
procedure
is
deplo
y
ed
in
the
second
stage
.
Ne
xt,
the
tr
ansmitted
po
w
er
at
the
AP
is
e
xpressed
as
P
r
=
E
h
T
=
P
S
k
h
k
2
+
N
0
(5)
In
pr
actical
applications
,
P
r
is
g
reater
than
0,
which
results
in
0
<
1
.
At
the
same
time
of
the
first
stage
,
the
RF
signal
perf
or
m
an
allocation
as
p
1
y
r
f
or
inf
or
mation
processing.
The
receiv
ed
signal
in
the
inf
or
mation
processing
stage
is
giv
en
b
y
~
y
r
=
p
1
p
P
S
hx
+
n
r
+
n
p
;
(6)
in
which
n
p
denotes
is
the
additional
baseband
Gaussian
noise
with
z
ero
mean
and
v
ar
iance
N
0
.
In
this
scenar
io
,
the
po
w
er
splitting
fr
action
is
s
e
lected
appropr
iately
f
or
obtaining
the
optimal
outage
perf
or
mance
.
In
this
model,
AF
scheme
is
applied
in
rela
y
node
,
after
that
the
tr
ansmitted
signal
at
rela
y
in
the
second
hop
is
e
xpressed
as
x
r
=
p
P
r
G
(
)
~
y
r
:
(7)
In
this
proposed
architecture
,
the
AP
is
assumed
that
it
equipped
b
y
amplify
circuit
to
broaden
har
v
ested
po
w
er
and
then
using
such
po
w
er
f
or
the
ne
xt
processing
stage
.
The
rela
y
amplifies
the
receiv
ed
signal
and
the
tr
ansmitted
signal
from
the
rela
y
b
y
the
f
actor
as
belo
w
G
(
)
=
v
u
u
t
1
(1
)
P
S
k
h
k
2
+
N
0
+
N
0
(8)
IJEECS
V
ol.
7,
No
.
3,
September
2017
:
802
808
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4752
805
In
the
second
phase
,
AP
tr
ansmits
inf
or
mation
to
mobile
user
via
channel
link
using
the
energy
har
v
ested
in
the
first
phase
.
Hence
,
the
receiv
ed
signal
As
a
result,
receiv
ed
signal
at
mobile
user
is
f
or
m
ulated
b
y
y
d
=
g
x
r
+
n
d
=
r
(1
)
P
S
P
r
(1
)
(
P
S
k
h
k
2
+
N
0
)
+
N
0
h
g
x
S
+
g
q
P
r
(1
)
(
P
S
k
h
k
2
+
N
0
)
+
N
0
p
1
pn
r
+
n
p
+
n
d
(9)
where
n
d
is
additiv
e
Gaussian
noise
with
z
ero
mean
and
v
ar
iance
N
0
and
then,
the
signal-to-noise
r
atio
(SNR)
at
the
end-user
can
be
calculated
as
.
S
N
R
=
P
S
k
h
k
2
j
g
j
2
j
g
j
2
N
0
+
j
g
j
2
N
0
1
+
N
0
P
r
G
(
)
2
(1
)
(10)
3.
OPTIMAL
OUT
A
GE
PERFORMANCE
In
this
section,
to
address
optimal
tr
ansmission
mode
,
a
R
TS
(requestto-send)/CTS
(clear-
to-send)
scheme
is
deplo
y
ed
with
assumption
of
f
aultless
channel
assessment.
Bef
ore
star
ting
the
inf
or
mation
tr
ansmission,
the
PB
node
sends
a
R
TS
pac
k
et
to
the
the
AP
node
.
The
AP
node
analyse
receiv
ed
pilot-dr
iv
en
data
and
can
estimate
the
channel
gain
h.
After
receiving
the
R
TS
,
the
AP
node
retur
ns
a
CTS
pac
k
et
to
the
source
PB
.
As
a
result,
the
AP
node
can
obtain
full
CSI,
i.e
.,
h
bef
ore
the
entire
tr
ansmission.
T
o
obtain
the
v
alues
of
g
at
the
PB
,
w
e
assume
to
use
similar
scheme
.
Similar
ly
,
the
AP
can
also
estimate
g
b
y
itself
and
send
f
e
edbac
k
to
the
PB
node
.
It
is
w
or
th
noting
that
the
eff
ect
of
channel
estimation
error
is
out
of
the
scope
of
our
paper
.
Through
the
R
TS/CTS
mechanism,
which
is
compatib
le
with
IEEE
802.11
ser
ies
standards
,
the
AP
and
PB
node
ca
n
obtain
the
full
CSI
bef
ore
the
entire
tr
ansmission
po
w
er
and
data
signal.
S
urely
,
e
xtr
a
o
v
erhead
and
energy
consumption
are
added
to
the
R
TS/CTS
processing
mechanism
in
ter
m
of
channel
estimation.
But,
this
hard
prob
lem
is
out
of
topic
of
this
paper
In
this
in
v
estigation,
the
prob
lem
here
is
that
using
the
kno
wledge
of
h
and
g,
w
e
aim
to
minimiz
e
the
outage
probability
which
corresponding
to
maximiz
e
the
instantaneous
SNR
at
the
mobile
user
.
It
is
w
or
th
noting
that
the
outage
e
v
ent
can
be
e
xpressed
as
O
P
=
Pr
(
S
N
R
<
0
)
;
(11)
in
which
0
is
the
threshold
SNR.
Theref
ore
,
the
optimization
prob
lem
of
outage
probability
can
be
wr
itten
as
maximize
S
N
R
(
)
s:t:
0
<
<
1
(12)
T
o
der
iv
e
optimal
v
alue
of
po
w
er
splitting
fr
action
of
EH,
it
is
noted
that
S
N
R
(
)
is
a
nonnegativ
e
contin
uous
function
.
In
f
act,
S
N
R
(
)
is
a
c
o
nca
v
e
function
on
0
<
<
1
.
Here
,
the
first
order
der
iv
ativ
e
of
S
N
R
(
)
with
respect
to
optimal
po
w
er
splitting
fr
action
is
der
iv
ed
as
result
of
belo
w
equation
@
S
N
R
(
)
@
=
0
;
0
<
<
1
(13)
Replacing
e
xpression
of
P
r
and
G
,
w
e
obt
ain
ne
w
e
xpression
of
the
end-to-end
SNR
a
s
belo
w
S
N
R
=
P
S
k
h
k
2
j
g
j
2
(1
)
j
g
j
2
N
0
2
+
2
N
0
j
g
j
2
N
0
+
N
0
+
N
2
0
k
h
k
2
P
S
+
N
0
(14)
F
or
simplicity
,
it
can
be
e
xpressed
SNR
as
S
N
R
=
ax
(1
)
b
2
+
c
+
d
(15)
Optimal
Energy
Har
v
esting
Scheme
f
or
P
o
w
er
Beacon-Assisted
...
(Dinh-Thuan
Do)
Evaluation Warning : The document was created with Spire.PDF for Python.
806
ISSN:
2502-4752
in
which,
w
e
denote
a
=
P
S
k
h
k
2
j
g
j
2
;
(16)
b
=
j
g
j
2
N
0
;
(17)
c
=
2
N
0
j
g
j
2
N
0
;
(18)
d
=
N
0
+
N
2
0
=
k
h
k
2
P
S
+
N
0
(19)
It
is
w
or
th
noting
that
the
der
iv
ation
of
SNR
is
too
complicated
as
belo
w
@
(
S
N
R
)
@
=
a
d
2
d
+
(
b
c
)
2
(
d
+
(
c
b
))
2
(20)
T
o
obtain
e
xtreme
v
alues
,
w
e
need
to
solv
e
the
equation
@
(
)
@
=
0
.
w
e
can
see
the
sign
of
@
(
)
@
corresponds
with
the
n
umer
ator
ter
m,
f
(
)
=
d
2
dx
+
(
b
c
)
x
2
Hence
w
e
just
need
to
solv
e
f
(
)
=
0
.
In
this
proposed
model,
is
f
ound
and
then
it
can
achie
v
e
the
maxim
um
SNR
=
(
1
2
;
if
b
c
=
0
d
p
bd
+
cd
+
d
2
b
c
;
if
b
c
6
=
0
(21)
4.
NUMERICAL
RESUL
TS
In
this
section,
the
analytical
e
xpressions
are
der
iv
ed
to
v
alidate
in
the
pre
vious
sections
b
y
deplo
ying
Monte
Car
lo
sim
ulation
results
.
All
the
sim
ulation
results
are
acquired
b
y
a
v
er
aging
o
v
er
10
6
independent
e
xper
iments
.
W
e
set
the
fix
ed
tr
ansmission
r
ate
R
=
3
bps=H
z
,
hence
the
outage
SNR
threshold
is
giv
en
b
y
=
2
R
1
=
7
.
The
energy
har
v
esting
efficiency
is
set
to
be
=
0
:
9
.
Also
,
w
e
set
a
v
er
age
channel
gain
as
h
=
g
=
1
:
5
.
W
e
obser
v
ed
that
the
outage
probability
achie
v
ed
b
y
the
proposed
po
w
er
splitting
policies
as
sho
wn
in
Fig.
2.
As
can
be
seen
clear
ly
,
the
a
v
er
age
outage
probability
decreases
when
the
tr
ansmit
po
w
er
increases
.
It
can
be
confir
med
that
the
proposed
po
w
er
splitting
policies
attain
better
perf
or
mances
than
all
the
other
patter
ns
with
fix
ed
.
That
is
to
sa
y
the
policy
with
par
tial
CSI,
which
incurs
less
o
v
erhead,
approaches
the
policy
with
full
CSI
closely
.
If
the
R
TS/CTS
mechanism
is
not
a
v
ailab
le
,
policy
with
par
tial
CSI
is
suggested
In
Fig.
3,
it
can
be
freely
obser
v
ed
that
dr
iving
more
antennas
at
the
PB
can
significantly
increase
the
achie
v
ab
le
outage
probability
.
This
occurrence
is
quite
intuitiv
e
,
since
increasing
the
n
umber
of
antennas
can
pro
vide
higher
energy
beamf
or
ming
gain,
hence
,
the
amount
of
the
har
v
ested
energy
at
the
source
impro
v
es
,
which
in
tur
n
reduces
the
outage
probability
of
the
system.
This
confir
ms
the
role
of
PB
in
f
eeding
energy
to
wireless
node
.
5.
CONCLUSION
This
paper
considered
a
point-to-point
wireless
po
w
ered
comm
unication
system,
which
ma
y
find
potential
applications
in
future
netw
or
ks
such
as
medical,
sensor
,
and
underw
ater
com-
m
unications
systems
.
A
detailed
in
v
estigation
on
the
a
v
er
age
outage
perf
or
mance
of
such
sys-
tems
w
as
presented
with
optimal
po
w
er
splitting
fr
action
of
nergy
har
v
esting
protocol.
F
or
po
w
er
beacon
equippe
d
m
ulti
an
tenna
f
or
energy
tr
ansf
er
tr
ansmission
modes
,
the
n
umber
of
antenna
contr
ib
ute
to
better
the
a
v
er
age
outage
perf
or
mance
as
seen
in
n
umer
ical
result.
In
addition,
a
solution
of
the
optimal
splitting
fr
action
to
minimiz
e
the
a
v
er
age
ouatge
w
as
e
xamined,
and
sim-
ulation
w
ere
obtained,
which
w
ere
sho
wn
to
be
v
er
y
accur
ate
.
Since
the
optimal
split
depend
on
the
instantaneous
channel
state
in
f
or
mation,
it
is
a
lo
w
comple
xity
solution
to
enhance
the
system
perf
or
mance
.
IJEECS
V
ol.
7,
No
.
3,
September
2017
:
802
808
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4752
807
0
5
10
15
20
25
30
35
40
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
P
S
(dBm)
P
o
u
t
optimal
ρ
fixed
ρ
=0.4
fixed
ρ
=0.6
Figure
2.
Outage
probability
at
destination
node
with
respect
to
energy
har
v
esting
po
w
er
splitting
fr
actions
0
5
10
15
20
25
30
35
40
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
P
S
(dBm)
P
o
u
t
number of antenna = 2
number of antenna = 4
number of antenna = 6
Figure
3.
Outage
probability
destination
node
with
respect
to
n
umber
of
antenna
at
PB
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808
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808
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