Indonesian
J
our
nal
of
Electrical
Engineering
and
Computer
Science
V
ol.
24,
No.
2,
No
v
ember
2021,
pp.
904
∼
909
ISSN:
2502-4752,
DOI:
10.11591/ijeecs.v24.i2.pp904-909
❒
904
Exploiting
outage
perf
ormance
in
de
vice-to-de
vice
f
or
user
gr
ouping
Dinh-Thuan
Do,
Chi-Bao
Le
F
aculty
of
Electronics
T
echnology
,
Industrial
Uni
v
ersity
of
Ho
Chi
Minh
City
(IUH),
Ho
Chi
Minh
City
,
V
ietnam
Article
Inf
o
Article
history:
Recei
v
ed
Feb
22,
2021
Re
vised
Sep
7,
2021
Accepted
Sep
14,
2021
K
eyw
ords:
De
vice-to-de
vice
Non-orthogonal
multiple
access
Outage
probability
ABSTRA
CT
The
spectrum
ef
cienc
y
and
massi
v
e
connections
are
joint
designed
in
ne
w
form
of
de
vice-to-de
vice
for
user
grouping.
A
pair
of
users
is
implemented
with
non-
orthogonal
multiple
access
(NOMA)
systems.
Although
NOMA
benets
to
such
sys-
tem
in
term
of
the
serving
users,
de
vice
to
de
vice
(D2D)
f
aces
the
interference
from
normal
cellular
users
(CUE).
In
particular
,
we
deri
v
e
e
xact
formulas
of
outage
prob-
ability
to
sho
w
system
performance.
In
this
article,
we
compare
tw
o
schemes
to
nd
rele
v
ant
schem
e
to
implement
in
practice.
The
frame
structure
is
designed
with
tw
o
timeslot
related
to
uplink
and
do
wnlink
between
the
base
station
and
D2D
users.
W
e
conrm
the
better
scheme
in
numerical
result
by
considering
the
impacts
of
man
y
pa-
rameters
on
outage
performance.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Dinh-Thuan
Do
F
aculty
of
Electronics
T
echnology
Industrial
Uni
v
ersity
of
Ho
Chi
Minh
City
(IUH)
Ho
Chi
Minh
City
,
V
ietnam
Email:
dodinhthuan@iuh.edu.vn
1.
INTR
ODUCTION
T
o
implement
multiple
access
schemes
in
cellular
netw
orks
for
current
wireless
systems,
orthogonal
multiple
access
(OMA)
systems
is
deplo
yed
most
of
syst
ems,
e.g.,
frequenc
y
di
vision
multiple
access
(FDMA),
time
di
vision
multiple
access
(TDMA),
and
orthogonal
frequenc
y
di
vision
multiple
access
(OFDMA).
In
OMA,
e
xclusi
v
e
resources
are
allocated
to
users.
Although
OMA
has
adv
antages
such
as
lo
w
comple
xity
recei
v
ers
and
no
intracell
interference,
it
suf
fers
from
tw
o
main
disadv
antages
such
as
limited
number
of
users
and
lo
w
spectral
ef
cienc
y
.
In
the
perspecti
v
e
of
demand
of
massi
v
e
connections,
non-orthogonal
multiple
access
(NOMA)
is
promising
candidate
for
multiple
access
scheme.
In
the
principle
of
NOMA,
it
emplo
ys
dif
ferent
po
wer
le
v
els
to
multiple
x
multiple
users
at
the
same
frequenc
y
,
time
and
code
resources
[1]-[7].
The
w
ork
[8]
studied
do
wnlink
NOMA
by
e
xamining
joint
optimization
of
po
wer
f
actors
assigned
to
users
and
secure
performance
w
as
also
e
v
aluated.
The
current
communication
sys
tems
may
also
get
benets
by
enabling
NOMA
for
multiple
access.
The
NOMA
massi
v
e
MIMO
w
as
presented
in
[9],
[10]
to
e
xplore
antennas
di
v
ersity
.
The
w
ork
in
[11]
compared
NOMA
transmissions
between
multiple
antennas
case
and
single
antenna
case.
The
near
optimal
sum-r
ate
(SR)
performance
w
as
e
xplored
in
MIMO-NOMA
system
and
a
high-comple
xity
beamforming
w
as
recommended
in
such
multiple
antennas
NOMA
approach
[12].
It
is
further
necessary
to
study
de
vice-to-de
vice
(D2D)
communications
in
the
heterogeneous
nature
of
5G
cellular
NOMA
-aided
systems.
The
base
station
(BS)
normally
w
ants
to
e
xchange
their
controlling
signal
while
D2D
communications
enable
proximate
cellular
users
[
13
]
,
[14].
Especially
,
the
spectrum
band
is
reused
for
pair
of
D2D
users
in
the
cellular
systems
[15],
[16].
Ho
we
v
er
,
as
the
main
disadv
antage,
D2D
users
J
ournal
homepage:
http://ijeecs.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
905
meet
mutual
interference
among
D2D
and
normal
cellular
links.
The
authors
in
[17]
deplo
yed
D2D
for
the
applications
of
NOMA
netw
orks
by
allo
wing
one
D2D
transmitter
send
signals
to
multiple
D2D
recei
v
ers
with
assistance
of
NOMA.
The
other
promising
applications
of
D2D
can
be
seen
in
[18]-[24].
As
main
benet,
D2D
enables
users
to
communicate
ef
fecti
v
ely
at
close
distance,
especially
processing
multiple
access
with
NOMA
scheme.
Moti
v
ated
by
recent
studies
[18]-[24]
and
[25],
we
de
v
elop
tw
o
practical
schemes
of
D2D-NOMA
system
along
with
system
performance
analysis.
2.
SYSTEM
MODEL
Consider
uplink
and
do
wnlink
transmission
in
D2D-NOMA
system
which
consists
of
groups
of
paired
user
under
the
impacts
of
BS
and
con
v
entional
user
(CUE),
as
sho
wn
in
Figure
1
[25].
It
is
assumed
that
the
BS,
and
all
users
are
equipped
with
single
antenna.
In
each
group,
tw
o
users
need
tw
o
time
slots
for
signal
processing.
The
relay
is
assumed
to
decode
signal
perfectly
,
which
e
xhibit
tw
o
schemes.
R
e
l
a
y
U
E
C
U
E
D
1
U
E
D
2
B
S
F
i
r
s
t
t
i
m
e
s
l
o
t
,
d
e
s
i
r
e
d
s
i
g
n
a
l
S
e
c
o
n
d
t
i
m
e
s
l
o
t
,
d
e
s
i
r
e
d
s
i
g
n
a
l
F
i
r
s
t
t
i
m
e
s
l
o
t
,
i
n
t
e
r
f
e
r
e
n
c
e
s
i
g
n
a
l
S
e
c
o
n
d
t
i
m
e
s
l
o
t
,
i
n
t
e
r
f
e
r
e
n
c
e
s
i
g
n
a
l
Figure
1.
Enabling
D2D
in
NOMA
First,
P
iT
is
transmit
po
wer
at
the
source,
here
we
denote
(
i
=
1
,
2
,
c,
b,
r
)
.
W
e
characterize
h
ij
as
Raleigh
f
ading
channels
to
reect
g
ains
of
i
−
j
link
(
j
=
1
,
2
,
c,
b,
r
)
.
It
is
assumed
that
h
ij
=
h
j
i
.
The
additi
v
e
comple
x
Gaussian
noise
is
assumed
fro
noise
n
i
(
i
=
1
,
2
,
c,
b,
r
)
,
i.e.
n
i
∼
C
N
(0
,
N
0
)
:
P
ij
=
P
iT
d
−
α
ij
(1)
where
α
is
the
path-loss
e
xponent.
In
the
rst
phase,
tw
o
users
send
their
signals
(
s
1
and
s
2
)
to
the
relay
.
The
relay
needs
the
second
phase
to
send
back
its
signal
s
r
to
the
tw
o
destinations
(D1
and
D2).
W
e
treat
the
recei
v
ed
signal
as
collection
of
three
components
of
signals
as
belo
w:
y
D
F
r
=
p
a
1
P
1
r
h
1
r
s
1
+
p
a
2
P
2
r
h
2
r
s
2
+
p
P
cT
h
cr
s
c
+
n
r
(2)
In
the
second
phase,
the
relay
sends
signal
s
r
to
destinations.
By
treating
signal
s
b
from
the
base
station.
The
recei
v
ed
signal
at
user
D1
and
D2
are
gi
v
en
by
[25]:
y
D
F
r
1
=
√
P
r
T
h
r
1
s
r
+
√
P
bT
h
b
1
s
b
+
n
1
(3)
and
y
D
F
r
2
=
√
P
r
T
h
r
2
s
r
+
√
P
bT
h
b
2
s
b
+
n
2
(4)
In
Scheme
I,
it
is
assumed
that
to
decode
D1’
s
signal
the
rel
ay
can
eliminate
interference
from
D2
perfectly
.
F
or
the
rst
phase,
the
signal
to
interference
plus
noise
ratio
(SINR)
at
relay
to
detect
signal
s
1
is
gi
v
en
by:
γ
1
r
=
¯
P
1
r
|
h
1
r
|
2
P
cr
|
h
cr
|
2
+
N
0
(5)
Exploiting
outa
g
e
performance
in
de
vice-to-de
vice
for
user
gr
ouping
(Dinh-Thuan
Do)
Evaluation Warning : The document was created with Spire.PDF for Python.
906
❒
ISSN:
2502-4752
where
¯
P
1
r
=
a
1
P
1
r
.
Similarly
,
to
help
the
relay
decode
D2’
s
signal,
SINR
is
gi
v
en
by:
γ
2
r
=
¯
P
2
r
|
h
2
r
|
2
P
cr
|
h
cr
|
2
+
N
0
(6)
where
¯
P
2
r
=
a
2
P
2
r
.
In
the
second
phase
of
Scheme
I,
the
SINRs
are
computed
at
tw
o
destinations
D1,
D2
respecti
v
ely:
γ
r
1
=
P
r
1
|
h
r
1
|
2
P
cr
|
h
b
1
|
2
+
N
0
(7)
and
γ
r
2
=
P
r
2
|
h
r
2
|
2
P
cr
|
h
b
2
|
2
+
N
0
(8)
In
Scheme
II,
by
treating
interference
from
the
CUE,
SINR
in
the
rst
phase
is
gi
v
en
by
[25]:
γ
up
=
¯
P
1
r
|
h
1
r
|
2
+
¯
P
2
r
|
h
2
r
|
2
P
cr
|
h
cr
|
2
+
N
0
(9)
The
other
computations
of
SINRs
in
the
second
phase
at
Scheme
II
are
similar
as
one
in
Scheme
I.
3.
AN
AL
YSIS
OF
OUT
A
GE
PR
OB
ABILITY
The
main
system
performance
metric,
namely
outage
probability
,
which
is
dened
as
probability
to
SINR
less
than
the
required
thresholds
γ
th
.
Such
outage
probability
corresponding
SINR
γ
is
gi
v
en
by:
P
out
=
P
r
(
γ
≤
γ
th
)
(10)
3.1.
Scheme
I:
ideal
NOMA
Proposition
1:
The
outage
probability
at
relay
R
in
phase
I
or
at
de
vice
at
phase
II
to
detect
signal
from
each
de
vice
is
gi
v
en
by
[25]:
P
out,ij
=
1
−
Q
ij
P
k
j
γ
th
+
Q
ij
e
−
N
0
Q
ij
γ
th
,
Q
ij
=
¯
P
ij
,
i
∈
{
1
,
2
}
;
j
∈
{
r
}
P
ij
,
other
w
ise
(11)
Pr
oof:
W
e
denote
X
=
P
ij
|
h
ij
|
2
,
Y
=
P
k
j
|
h
k
j
|
2
+
N
0
and
Z
=
X
/
Y
.
The
PDFs
of
these
denotations
are
represented
as
f
X
(
x
)
=
1
/P
ij
e
−
x/P
ij
and
f
Y
(
x
)
=
1
/P
k
j
e
−
y
/P
k
j
e
N
0
/P
k
j
.
W
e
ha
v
e
PDF
f
Z
(
x
)
:
f
Z
(
x
)
=
Z
∞
N
0
y
f
(
z
y
,
y
)
dy
=
N
0
P
k
j
z
+
P
ij
e
−
N
0
P
ij
z
+
P
ij
P
k
j
(
P
k
j
z
+
P
ij
)
2
e
−
N
0
P
ij
z
(12)
In
particular
,
f
Z
(
γ
th
)
is
gi
v
en
by
[25]:
f
Z
(
γ
th
)
=
Z
γ
th
0
N
0
e
−
N
0
P
ij
z
(
P
k
j
z
+
P
ij
)
2
|
{z
}
F
Z
1
dz
+
Z
γ
th
0
N
0
e
−
N
0
P
ij
z
P
k
j
z
+
P
ij
|
{z
}
F
Z
2
dz
(13)
F
Z
1
=
1
−
P
ij
P
k
j
γ
th
+
P
ij
e
−
N
0
P
ij
γ
th
−
Z
γ
th
0
N
0
e
−
N
0
P
ij
z
P
k
j
z
+
P
ij
dz
+
Z
γ
th
0
N
0
e
−
N
0
P
ij
z
P
k
j
z
+
P
ij
dz
(14)
Then,
we
ha
v
e
outage
probability
for
uplink:
F
z
(
γ
th
)
=
1
−
P
ij
P
k
j
γ
th
+
P
ij
e
−
N
0
P
ij
γ
th
(15)
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
24,
No.
2,
No
v
ember
2021
:
904
–
909
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
907
Similarly
,
we
ha
v
e
outage
probability
for
do
wnlink,
then
we
achie
v
e
nal
P
out
.
This
completes
the
proof.
Therefore,
we
e
xamine
outage
performance
of
whole
system
D2D
which
is
formulated
by:
P
D
2
D
,out,I
=
1
−
(1
−
P
out,
1
r
)
(1
−
P
out,
2
r
)
(1
−
P
out,r
1
)
(1
−
P
out,r
2
)
(16)
3.2.
Scheme
II
Proposition
2:
In
Scheme
2,
considering
uplink
from
D2D
users
to
the
relay
,
the
outage
probability
at
relay
in
phase
I
is
gi
v
en
by:
P
out,up
=
F
(
γ
up
≤
γ
thm
)
=1
+
¯
P
2
1
r
¯
P
2
r
−
¯
P
1
r
P
cr
γ
thm
+
¯
P
1
r
e
−
N
0
¯
P
1
r
γ
thm
−
P
2
2
r
¯
P
2
r
−
¯
P
1
r
P
cr
γ
thm
+
¯
P
2
r
e
−
N
0
¯
P
2
r
γ
thm
(17)
Pr
oof:
W
e
denote
S
=
¯
P
1
r
|
h
1
r
|
2
+
¯
P
2
r
|
h
2
r
|
2
,
T
=
P
cr
|
h
cr
|
2
+
N
0
and
U
=
S
/T
.
W
e
ha
v
e
PDFs
ad
belo
w:
f
S
(
s
)
=
1
/
¯
P
2
r
−
¯
P
1
r
e
−
s/
¯
P
2
r
−
1
/
¯
P
2
r
−
¯
P
1
r
e
−
s/
¯
P
1
r
(18)
and
f
T
(
t
)
=
1
/P
C
T
e
−
t/P
cr
+
N
0
/P
cr
(19)
It
is
noted
that
f
asy
U
(
u
)
is
computed
by
[25]:
f
asy
U
(
u
)
=
Z
∞
N
0
tf
(
ut,
t
)
dt
=
e
N
0
P
cr
P
cr
¯
P
2
r
−
¯
P
1
r
¯
P
2
r
u
+
¯
P
2
r
P
cr
ne
−
u
¯
P
2
r
−
N
0
P
cr
+
e
N
0
P
cr
P
cr
¯
P
2
r
−
¯
P
1
r
¯
P
2
r
u
+
¯
P
2
r
P
cr
!
2
e
−
u
¯
P
2
r
−
N
0
P
cr
−
e
N
0
P
cr
P
cr
¯
P
2
r
−
¯
P
1
r
¯
P
1
r
u
+
¯
P
1
r
P
cr
N
0
e
−
u
¯
P
1
r
−
N
0
P
cr
−
e
N
0
P
cr
P
cr
¯
P
2
r
−
¯
P
1
r
¯
P
1
r
u
+
¯
P
1
r
P
cr
!
2
e
−
u
¯
P
1
r
−
N
0
P
cr
(20)
Then,
f
asy
U
(
u
)
is
re
written
by:
f
asy
U
(
u
)
=
¯
P
2
r
N
0
P
cr
¯
P
2
r
−
¯
P
1
r
1
u
+
¯
P
2
r
P
cr
!
e
−
N
0
¯
P
2
r
u
+
¯
P
2
2
r
P
cr
¯
P
2
r
−
¯
P
1
r
1
u
+
¯
P
2
r
P
cr
!
2
e
−
N
0
¯
P
2
r
u
−
¯
P
1
r
N
0
P
cr
¯
P
2
r
−
¯
P
1
r
1
u
+
¯
P
1
r
P
cr
!
e
−
N
0
¯
P
1
r
u
−
¯
P
2
1
r
P
cr
¯
P
2
r
−
¯
P
1
r
1
u
+
¯
P
1
r
P
cr
!
2
e
−
N
0
¯
P
1
r
u
(21)
F
or
uplink,
we
ha
v
e
P
out,up
as:
P
out,up
=
F
(
γ
up
≤
γ
thm
)
=
1
+
¯
P
2
1
r
¯
P
2
r
−
¯
P
1
r
P
cr
γ
thm
+
¯
P
1
r
e
−
N
0
¯
P
1
r
γ
thm
−
¯
P
2
2
r
¯
P
2
r
−
¯
P
1
r
P
cr
γ
thm
+
¯
P
2
r
e
−
N
0
¯
P
2
r
γ
thm
(22)
This
completes
the
proof.
By
combining
both
uplink
and
do
wnlink
between
the
relay
and
D2D
users,
we
can
achie
v
e
the
outage
probability
as
belo
w
for
Scheme
II:
P
D
2
D
,out,I
I
=
1
−
(1
−
P
out,up
)
2
(1
−
P
out,r
1
)
2
(1
−
P
out,r
2
)
2
(23)
Exploiting
outa
g
e
performance
in
de
vice-to-de
vice
for
user
gr
ouping
(Dinh-Thuan
Do)
Evaluation Warning : The document was created with Spire.PDF for Python.
908
❒
ISSN:
2502-4752
4.
NUMERICAL
RESUL
TS
W
e
conduct
10
6
iterations
for
realizing
independent
channels.
The
path
loss
e
xponent
setting
to
be
α
=
4
.
W
e
set
the
distances
d
12
=
1
,
d
1
r
=
0
.
7
and
d
2
r
=
0
.
3
,
γ
th
=
γ
thm
=
{
3
,
5
,
7
}
.
The
po
wer
allocation
coef
cients
for
NOMA
scheme
a
1
=
0
.
2
and
a
2
=
0
.
8
.
Figure
2
and
Figure
3
demonstrate
the
trends
of
outage
probability
of
Scheme
I
and
Scheme
II
v
ersus
transmit
SNR
respecti
v
ely
.
It
can
be
seen
clearly
that
better
outage
probability
occurs
at
high
SNR
re
gion.
The
lo
wer
required
threshold
γ
th
=
3
is
reported
as
the
better
case.
as
sho
wn
in
Figure
2.
Main
precise
result
is
recognized
when
Monte-Carlo
and
analytical
curv
es
are
matched
v
ery
well,
which
conrm
the
e
xactness
of
deri
v
ations.
Figure
4
and
Figure
5
compare
performance
of
tw
o
schemes
in
terms
of
outage
probability
and
throughput
respecti
v
ely
.
It
is
noted
that
throughput
at
the
x
ed
rate
R
is
computed
by
T
=
R
(1
−
P
out
)
.
0
5
10
15
20
25
30
35
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
th
= 3, 5, 7 (dB)
Figure
2.
Scheme
I:
D2D-NOMA
’
s
outage
performance
when
v
arying
transmit
SNR,
with
d
1
r
=
0
.
7
and
d
2
r
=
0
.
3
-5
0
5
10
15
20
25
10
-3
10
-2
10
-1
10
0
thm
= 3, 5, 7 (dB)
Figure
3.
Scheme
II:
D2D-NOMA
’
s
outage
performance
when
v
arying
transmit
SNR,
with
d
1
r
=
d
2
r
=
0
.
5
0
5
10
15
20
25
30
35
10
-1
10
0
th
=
thm
= 10 (dB)
th
=
thm
= 5 (dB)
th
=
thm
= 0 (dB)
Figure
4.
Comparison
of
outage
probability
between
Scheme
I
and
Scheme
II,
with
d
1
r
=
0
.
7
and
d
2
r
=
0
.
3
-5
0
5
10
15
20
25
10
-2
10
-1
10
0
SNR = 10 (dB)
SNR = 25 (dB)
Figure
5.
Comparison
of
throughput
between
Scheme
I
and
Scheme
II,
with
d
1
r
=
0
.
7
and
d
2
r
=
0
.
3
5.
CONCLUSION
In
this
paper
,
we
ha
v
e
studied
a
D2D
based
NOMA
transmission
scheme
in
the
e
xistence
of
traditi
onal
cellular
user
.
T
o
e
v
aluate
the
proposed
schemes,
we
computed
SINRs
and
then
e
xpressions
of
outage
proba-
bility
are
presented.
F
or
the
tw
o
scenarios,
we
pro
vided
comprehensi
v
e
analysis
of
the
system
performances
metrics,
and
deri
v
e
the
closed-form
e
xpressions
of
the
outage
probability
.
In
the
follo
wing,
we
concluded
that
system
performance
of
D2D-NOMA
system
relying
on
Scheme
I
is
better
than
that
using
Scheme
II.
More
paired
users
are
emplo
yed
in
D2D-NOMA
systems
in
the
future
w
ork.
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
24,
No.
2,
No
v
ember
2021
:
904
–
909
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
909
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Exploiting
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g
e
performance
in
de
vice-to-de
vice
for
user
gr
ouping
(Dinh-Thuan
Do)
Evaluation Warning : The document was created with Spire.PDF for Python.