Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
10,
No.
2,
April
2020,
pp.
2151
2163
ISSN:
2088-8708,
DOI:
10.11591/ijece.v10i2.pp2151-2163
r
2151
On
the
perf
ormance
of
non-orthogonal
multiple
access
(NOMA)
using
FPGA
Mohamad
A.
Ahmed,
Khalid
F
.
Mahmmod,
Mohammed
M.
Azeez
Colle
ge
of
Electronics
Engineering,
Nine
v
ah
Uni
v
ersity
,
P
.O.
41002,
Mosul,
Iraq
Article
Inf
o
Article
history:
Recei
v
ed
Jul
14,
2019
Re
vised
Oct
24,
2019
Accepted
No
v
1,
2019
K
eyw
ords:
Additi
v
e
white
g
aussian
noise
(A
WGN)
Field-programmable
g
ate
array
(FPGA)
Non-orthogonal
multiple
access
(NOMA)
Successi
v
e-interference
cancellation
(SIC)
ABSTRA
CT
In
this
paper
,
non-orthogonal
multiple
access
(NOMA)
is
designed
and
implemented
for
the
fifth
generation
(5G)
of
multi-user
wireless
communication.
Field-programmable
g
ate
array
(FPGA)
is
considered
for
the
implementation
of
this
technique
for
tw
o
users.
NOMA
is
applied
in
do
wnlink
phase
of
the
base-stati
on
(BS)
by
applying
po
wer
allocation
mechanism
for
f
ar
and
near
users,
in
which
one
signal
contains
the
superposition
of
tw
o
scaled
signals
dependi
ng
on
the
distance
of
each
user
from
the
BS.
W
e
assume
an
additi
v
e
white
Gaussian
noise
(A
WGN)
channel
for
each
user
in
the
presence
of
the
interference
due
to
the
non-orthogonality
between
the
tw
o
users’
signals.
Therefore,
successi
v
e-interference
cancel
lation
(SIC)
is
e
xploited
to
remo
v
e
the
undesired
signal
of
the
other
user
.
The
outage
probability
and
the
bit-
error
rate
performance
are
presented
o
v
er
dif
ferent
signal-to-interference-plus-noise
ratio
(SINR).
Furthermore,
Monte-Ca
rlo
simulations
via
Matlab
are
utilized
to
v
erify
the
results
obtained
by
FPGA,
which
sho
w
e
xact-close
match.
Copyright
c
2020
Insitute
of
Advanced
Engineeering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Mohamad
A.
Ahmed,
Colle
ge
of
Electronics
Engineering,
Nine
v
ah
Uni
v
ersity
,
P
.O.
41002,
Mosul,
Iraq.
Email:
mohamad.alhabbar@uonine
v
ah.edu.iq
1.
INTR
ODUCTION
The
ne
xt
generation
of
wireless
communication
(5G),
which
will
be
launched
be
yond
2020,
will
witness
high
demand
on
spectrum
ef
ficienc
y
and
capacity
[1,
2].
The
data
traf
fic
of
mobile
cellular
commu-
nication
systems
are
e
xpected
to
increase
e
xponentially
,
at
least
thousand
time
more
than
the
required
v
olume
of
the
last
decade
[3,
4].
In
the
pre
vious
generations
of
mobile
communication,
i.e.
3.9G
and
4G,
the
technique
of
orthogonal
multiple
access
(OMA)
has
been
wildly
e
xploited
to
achie
v
e
suitable
throughput
for
single-user
performance
[5].
Non-orthogonal
multiple
access
(NOMA)
is
considered
one
of
the
most
promising
multiple
access
(MA)
schemes
for
do
wnload
in
the
5G
[6].
This
MA
scheme
utilizes
the
po
wer
allocation
technique
in
the
po
wer
domain
instead
of
the
time
and
frequenc
y
multiple
access,
in
which
the
symbols
of
se
v
eral
users
are
scaled
on
the
base-station
(BS)
according
to
their
channels
conditions,
i.e.
the
attenuation
f
actor
caused
due
to
path
loss
of
each
user’
s
channel,
then
all
the
scaled
symbols
are
added
t
ogether
and
trans
mitted
as
one
symbol
called
NOMA
symbol
[7].
In
other
w
ords,
a
use
r
of
f
ar
distance
from
the
BS
will
be
gi
v
en
more
po
wer
than
a
user
with
near
distance.
At
the
f
ar
-user
(FU),
the
recei
v
er
will
deal
with
near
user
(NU)
signal
on
the
NOMA
symbol
as
a
noise,
while
at
the
NU,
success
i
v
e
interference
cancellation
(SIC)
is
required
to
remo
v
e
the
FU
po
wer
since
the
letter
is
bigger
than
the
intended
NU
po
wer
[8,
9].
Furthermore,
NOMA
with
SIC
can
of
fer
significant
user
-f
airness
and
better
connecti
vity
comparing
to
the
con
v
entional
OMA
[10].
In
the
conte
xt,
NOMA
technique
is
proposed
for
dif
ferent
applications
and
mechanism
in
communi
-
cations.
F
or
instant,
NOMA
is
suggested
to
be
a
part
of
the
cooperati
v
e
communications
via
relay
with
the
aid
of
b
uf
fering
technique
[11],
and
for
relays
selection
to
obtain
optimum
connecti
vity
[12].
Additionally
,
NOMA
J
ournal
homepage:
http://ijece
.iaescor
e
.com/inde
x.php/IJECE
Evaluation Warning : The document was created with Spire.PDF for Python.
2152
r
ISSN:
2088-8708
for
tw
o
w
ays
half-duple
x
relaying
netw
ork
is
modeled
and
analyzed
in
[13]
with
the
aid
of
decode-and-forw
ard
relay
.
Moreo
v
er
,
NOMA
is
proposed
with
massi
v
e
multiple-input
multiple-output
(MIMO)
relaying,
which
compared
with
con
v
entional
MIMO-OMA
sho
wing
significant
throughput
impro
v
ement
[14].
In
the
literature,
NOMA
based
on
dynamic
scheme
is
proposed
in
[15]
for
direct
comm
unications
with
the
users
near
to
a
BS
with
an
assistance
of
relay
for
f
ar
users
in
the
edge
of
cells.
In
[16],
NOMA
based
cooperati
v
e
netw
ork
is
e
xploited
to
serv
e
primary
and
secondary
users
by
a
BS,
in
which
spatial
di
v
er
-
sity
is
utilized
by
the
BS
and
among
the
secondary
user
to
cope
the
impairments
of
f
ading
in
the
channel.
The
authors
in
[17]
propose
NOMA
to
secure
transmissions
of
tw
o
transcei
v
ers
with
thei
r
relati
v
e
destinations
o
v
er
amplify-and-forw
ard
cooperati
v
e
relaying
technique.
In
the
other
hand,
cooperati
v
e
NOMA
via
relay
is
used
for
maximizing
the
po
wer
ef
ficienc
y
of
transmission
as
suggested
in
[18],
in
which
a
harv
ested
ener
gy
of
the
signals
is
e
xploited
for
sending
the
information
to
t
he
intended
destination.
Moreo
v
er
,
the
bit-error
rate
(BER)
in
e
xact-close
form
is
deri
v
ed
in
[19]
for
NOMA
o
v
er
Rayleigh
f
ading
channels,
considering
imperfect
SIC
in
the
uplink
and
do
wnlink.
Field-programmable
g
ate
array
(FPGA)
is
an
attracti
v
e
and
promising
technology
which
is
e
xploited
in
this
paper
to
implement
the
NOMA
system
in
the
real-time.
This
is
due
to
the
f
act
that
FPGAs
of
fer
more
fle
xibility
for
the
designer
for
modification
of
the
designed
systems
with
highest
a
v
ailable
throughput
[20].
Moreo
v
er
,
FPGAs
is
widely
used
practically
in
dif
ferent
applications
as
military
radios
and
the
cellular
netw
orks
infrastructure.
In
the
conte
xt,
to
reduce
the
latenc
y
and
comple
xity
,
real-time
FPGAs
is
used
to
implement
MIMO
long
with
orthogonal
frequenc
y
de
vision
multiple
xing
(OFDM)
in
[21],
in
which
iterati
v
e
recei
v
er
is
suggested.
In
[22],
real-time
FPGAs
is
utilized
to
design
massi
v
e
multi-user
MIMO-OFDM
with
approximate
minimum-mean-square
error
algorithm
for
detection.
Modern
and
ef
ficient
approach
is
proposed
in
[23]
to
e
v
aluate
performance
and
the
consumed
po
wer
for
wireless
communication
based-FPGAs.
Furthermore,
a
transcei
v
er
based
on
Spatio-T
emporal
array-recei
v
er
technique
for
most
NOMA
radio
types
is
proposed
in
[24].
This
approach
of
fers
lo
w
comple
x
adaptation
and
configuration.
This
mechanism
is
proposed
to
tackle
the
feas
ibility
of
hardw
are
and
for
concept
proofing
of
time-del
ay
estimator
based
on
this
technique
running
o
v
er
real-time
FPGA
and
MiniBee
softw
are
defined
radio
platforms.
Additionally
,
NOMA
is
mer
ged
with
massi
v
e-MIMO
and
millimeter
w
a
v
e
(mm-W
a
v
e)
in
[25]
to
enhance
the
capacity
of
the
ne
xt
generation
of
mobile
netw
orks.
The
analysis
of
capacity
is
deri
v
ed
in
this
research
paper
,
in
which
the
mm-W
a
v
e
is
modeled
by
using
the
angle
of
arri
ving
along
with
the
proposed
v
ersion
of
the
uniform-random
single
path
model.
moreo
v
er
,
the
performance
is
di
vided
into
tw
o
re
gions
depending
on
high
and
lo
w
SNRs.
In
[26],
NOMA
system
in
the
do
wnload
phase
along
with
code
w
ord
le
v
el
SIC
are
implemented
prac-
tically
via
emplo
ying
softw
are
defined
radio
mechanism
by
utilizing
Open-Air
-Interf
ace,
in
which
the
pro-
posed
system
follo
ws
the
long-term
e
v
olution
technique
in
the
basic
specifications
for
comparison
purposes.
Non-re
generati
v
e
relays
are
emplo
yed
in
[NonR-Relay]
to
secure
comm
u
ni
cations
with
massi
v
e-MIMO
base-
station.
The
proposed
system
utilizes
NOMA
at
the
transmitters
and
SIC
along
with
minimum-mean-square
error
equalization
at
each
recei
v
er
.
The
authors
deri
v
ed
e
xact
e
xpression
for
the
SINR,
which
is
used
then
to
e
v
aluate
the
capacity
of
the
proposed
system.
In
[27],
netw
ork
coded
multiple
access
is
in
v
estig
ated
as
a
ne
w
architecture
for
NOMA.
This
technique
emplo
ys
near
po
wer
balance
mechanism
NOMA
to
allo
w
se
v
eral
users
to
share
the
netw
ork
in
the
po
wer
domain.
This
approach
can
be
implemented
by
applying
ph
ysical
layer
netw
ork
coding
along
with
multi-user
decoding
to
enhance
the
system
capacities.
A
compromise
solution
between
bandwidth
and
po
wer
consumption
is
proposed
and
in
v
estig
ated
in
[28]
for
5G-Xhual
reconfigurable
netw
orks,
in
which
traditional
radio
base-stations
radio
remote
unit
are
used
to
handle
users’
generated
traf
fic,
the
reconfigurable
netw
orks
is
e
xploited
to
carry
the
sum
of
the
abo
v
e
traf
fic.
The
main
goal
of
this
research
paper
is
to
e
xperimentally
in
v
estig
ate
NOMA
technique
using
FPGA
o
v
er
A
WGN
channel,
in
which
NOMA
is
applied
for
tw
o
users
in
the
do
wnlink
phase
via
FPGA
simulation.
Furthermore,
po
wer
allocation
mechanism
is
emplo
yed
to
share
the
a
v
ailable
po
wer
between
tw
o
users
with
dif
ferent
distances
from
the
BS,
i.e.
f
ar
and
near
uses.
W
ithout
the
loss
of
generality
,
the
assumption
of
considering
only
tw
o
users
in
this
paper
,
is
due
to
the
f
act
that
re
g
ardless
of
the
number
of
users,
the
remote
user
al
w
ays
considers
other
users’
signals
as
just
additi
v
e
noise
as
defined
by
NOMA
theory
.
In
other
hand,
an
y
number
of
users
will
follo
w
the
same
procedure
in
processing
its
desired
signal
as
the
near
user
,
as
the
y
apply
SIC
to
remo
v
e
signals
of
other
users
with
higher
po
wer
allocation
f
actors.
Moreo
v
er
,
the
performance
Int
J
Elec
&
Comp
Eng,
V
ol.
10,
No.
2,
April
2020
:
2151
–
2163
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
2153
is
v
erified
by
utilizing
Monte-Carlo
simulation
via
Matlab
sho
wing
e
xact-closed
matching.
T
o
the
best
of
our
kno
wledge,
this
is
the
first
time
to
implement
NOMA
system
by
emplo
ying
FPGA
technique
via
a
code
of
VHDL
programming.
2.
SYSTEM
MODELING
AND
IMPLEMENT
A
TION
In
this
paper
,
a
wireless
com
munication
is
considered
for
a
BS
with
dif
ferent
distances
users
NU
and
FU.
W
e
assumed
that
each
terminal
is
equipped
with
single
antenna
as
sho
wn
in
Figure
1.
In
the
do
wnlink
phase,
the
BS
generates
tw
o
quadrature
phase
shift
k
e
ying
(QPSK)
signals
for
each
users.
QPSK
is
chosen
in
this
paper
since
all
the
symbols
in
this
modulation
scheme
ha
v
e
the
same
absolute
v
alue
in
both
the
real
and
imagery
parts,
which
means
that
the
y
ha
v
e
the
same
transmitted
po
wer
.
This
reduces
the
comple
xity
of
design
multi-le
v
el
amplifier
at
the
recei
v
er
and
mak
es
the
signal
processing
of
much
easier
.
The
signals
of
each
user
is
multiplied
by
a
f
actor
according
to
its
dis
tance
from
the
BS,
i.e.
N
and
F
for
the
near
and
f
ar
users,
respecti
v
ely
,
where
F
>
N
.
This
is
due
to
the
assumption
that
the
FU
needs
to
be
applied
with
more
po
wer
than
the
NU
in
order
to
satisfy
users
f
airness.
Moreo
v
er
,
the
relationship
between
the
tw
o
scaling
f
actors
can
be
e
xpressed
as
F
+
N
=
1
(1)
The
recei
v
ed
signal
at
the
K
th
node
can
be
e
xpressed
as
r
K
=
h
K
(
p
F
P
s
F
+
p
N
P
s
N
)
+
n
K
(2)
where
P
is
the
total
po
wer
allocated
for
the
tw
o
users,
s
K
with
K
2
(
F
;
N
)
represents
a
QPSK
signal
which
can
tak
e
four
possibl
e
comple
x
v
alues
defined
as
s
K
=
1
j
1
resulting
from
mapping
tw
o
bits.
Additionally
,
h
K
denotes
a
non-selecti
v
e
Rayleigh
flat
f
ading
channel
with
zero
mean
and
unity
v
ariance,
i.e.
h
K
C
N
(0
;
1)
,
in
which
the
po
wer
normalization
of
the
channel
between
the
BS
and
near
user
,
jj
h
N
jj
2
,
is
greater
than
the
normalized
po
wer
of
channel
between
the
BS
and
the
remote
user
,
jj
h
F
jj
2
,
i.e.
jj
h
N
jj
2
>
jj
h
F
jj
2
.
This
is
due
to
the
attenuation
accompanied
to
wireless
propag
ation
of
the
signals.
Figure
1.
NOMA
in
the
do
wnlink
phase
for
tw
o
users,
jj
h
N
jj
2
>
jj
h
F
jj
2
Furthermore,
n
C
N
(0
;
2
n
)
represents
a
comple
x
dis
trib
ution
of
the
additi
v
e
white
Gaussian
noise
(A
WGN)
with
zero
mean
and
a
v
ariance
of
2
n
which
is
added
at
each
node
independently
.
Furthermore,
the
signal-to-interference-plus-noise
ratio
(SINR)
at
the
K
th
user
,
which
is
denoted
as
K
can
be
e
xpressed
by
K
=
K
P
jj
h
K
s
K
jj
2
L
P
jj
h
K
s
L
jj
2
+
jj
n
K
jj
2
L
2
f
F
;
N
g
and
L
6
=
K
;
(3)
which
can
be
simplified
as
K
=
K
jj
h
K
jj
2
L
jj
h
K
jj
2
+
1
;
(4)
On
the
performance
of
non-ortho
gonal
multiple
...
(Mohamad
A.
Ahmed)
Evaluation Warning : The document was created with Spire.PDF for Python.
2154
r
ISSN:
2088-8708
where
K
=
K
P
2
n
and
L
=
L
P
2
n
represent
the
signal-to-noise
ratio
(SNR)
and
the
interference-to-noise
ratio
(INR)
at
the
user
of
interested.
Therefore,
the
Shannon
capacity
for
this
system
can
be
e
v
aluated
for
a
particular
K
th
user
as
C
K
=
1
2
log
2
(1
+
K
)
;
(5)
3.
NOMA
IMPLEMENT
A
TION
VIA
FPGA
The
implementation
is
achie
v
ed
by
utilizing
Spartan
3e,
which
has
a
slice
number
Xc3s500e.
The
starter
kit
board
of
Spartan
3e
f
amily
of
FPGA
has
an
embedded
con
v
enient
de
v
elopment
board,
for
v
arious
signal
processing
applications.
This
board
is
designed
to
meet
the
high
demand
on
lo
w
cost
and
high
v
olume
electronics
applications
[29].
Figure
2
sho
ws
the
impleme
nted
system,
in
which
the
transmitt
er
and
the
tw
o
recei
v
ers
will
be
discussed
in
more
details
in
this
paper
.
Furthermore,
Figure
7
and
Figure
8
represent
the
output
at
each
stages
of
the
designed
system
with
FU
and
NU
detections,
respecti
v
ely
.
Firstly
,
QPSK
symbols
are
generated
according
to
the
transmitted
bits
of
the
NU
and
FU,
respecti
v
ely
.
These
QPSK
symbols
for
each
users
are
then
scaled
by
p
N
and
p
F
.
The
tw
o
scaled
symbols
for
the
tw
o
users
are
then
added
together
to
create
NOMA
symbols,
which
transmitted
o
v
er
tw
o
independent
A
WGN
channels.
The
implementation
of
A
WGN
channel
is
discussed
in
the
ne
xt
subsection
in
more
details.
Moreo
v
er
,
in
our
FPGA
design,
N
and
F
can
tak
e
an
y
v
alues
depending
on
the
change
of
the
distances
of
NU
and
FU
from
the
base-station
by
applying
(1).
Ho
we
v
er
,
optimization
techniques
can
be
emplo
yed
to
find
the
best
v
alues
which
is
out
of
the
scope
of
this
paper
.
Figure
2
represents
the
entire
designed
NOMA
transmitter
along
with
the
FU
and
NU
recei
v
ers
by
using
FPGA.
All
the
defined
inputs/outputs
(I/O)s
with
the
block
diagram
for
each
stage
of
this
process
are
illustrated
clearly
.
Moreo
v
er
,
it
is
note
w
orth
y
that
tw
o
frequencies
are
used
in
our
design
which
are
50
MHz
and
12
:
5
MHz
for
the
purpose
of
synchronization.
The
tw
o
frequencies
are
generated
by
emplo
ying
frequenc
y
di
vider
technique
of
the
clock
generator
.
Figure
2.
The
entire
designed
of
NOMA
transmitter
along
with
the
FU
and
NU
recei
v
ers
via
FPGA,
the
signals
names,
abbre
viations
and
functions
are
illustrated
in
T
able
1
Int
J
Elec
&
Comp
Eng,
V
ol.
10,
No.
2,
April
2020
:
2151
–
2163
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
2155
T
able
1.
Signals
abbre
viations,
names
with
their
functions
as
used
in
Figure
2
Signal
Abbre
viation
Signal
Name
Function
of
the
signal
RST
Reset
Reset
system
Data-Stream
Data
Stream
Serial
data
stream
Input
V
al
id
i
V
alid
Input
When
this
signal
is
”1”
the
data
stream
input
will
be
read
b
ut
when
this
signal
is
”0”
the
data
stream
input
will
not
be
read,
it
just
ignored.
CLK
Clock
System
clock
(50MHz)
CLK-Di
v
Clock
di
vider
System
clock
(50MHz,
12.5MHz)
QPSK(1:0)
Quadrature
Phase
T
w
o
bits
of
QPSK
signal
for
output
symbol
block
Shift
K
e
ying
bits
QPSK-o
QPSK
output
QPSK
output
clock
for
synchronization
V
alid-o
V
alid
Output
V
alid
out
to
enable
recei
ving
data
input
stream
QPSK-F
A
QPSK
for
F
ar
user
Mapping
of
tw
o
bits
to
a
QPSK
Symbol
for
F
ar
user
QPSK-NR
QPSK
for
Near
user
Mapping
of
tw
o
bits
to
a
QPSK
Symbol
for
Near
user
F
A-Scale
F
ar
Scale
F
ar
user
symbol
Scaling
using
po
wer
allocation
technique
NE-Scale
Near
Scale
Near
user
symbol
Scaling
using
po
wer
allocation
technique
F
A-Scale
(39:0)
F
ar
Scale
for
40
bits
F
ar
Scale
Indication
NE-Scale
(39:0)
Near
Scale
for
40
bits
Near
Scale
Indication
NOMA-Channel
NOMA
channel
Add
F
ar
and
Near
symbols
along
with
adding
the
A
WGN
generated
by
Box
Muller
method
BO
X-Muller
-GN
Box
muller
Generation
Block
diagram
responsible
for
A
WGN
symbol
generation
NOMA-RX-F
A
Recei
v
ed
F
ar
The
recei
v
ed
NOMA
signal
for
the
F
ar
user
user
NOMA
NOMA-RX-NE
Recei
v
ed
Near
The
recei
v
ed
NOMA
signal
for
the
Near
user
user
NOMA
NOMA-Bit
NOMA
bit
The
bits
after
symbol
detection
of
the
F
ar
or
Near
user
corresponding
on
the
user’
s
recei
v
er
.
BER-F
A
Bit
error
rate
F
ar
Bit
error
rate
for
F
ar
signal
BER-NE
Bit
error
rate
Near
Bit
error
rate
for
Near
signal
Figure
3
sho
ws
the
percentage
v
alues
of
the
consumed
number
of
slices,
flip-flops,
4-input
lookup
tables
(LUT)s,
bounded
input/output
blocks
(IOB)s
and
GCLKs
in
the
utilized
Xc3s500e
Spartan-3e
kit.
In
this
figure,
a
v
ailable
and
the
utilization
number
of
each
of
the
abo
v
e
parameters
are
illustrated
after
applying
optimization
to
the
designed
system.
It
is
clear
that
all
utilization
percentages
are
lo
wer
than
the
max-
imum
a
v
ailable
capacity
of
the
kit,
e
xcept
the
number
of
the
bounded
IOBs
which
is
just
belo
w
the
maximu
number
.
This
issue
can
be
tackled
by
using
the
upgraded
v
ersion
Xc3s500e
Spartan-3e
kit
with
higher
g
ates.
Figure
3.
The
percentage
v
alues
of
the
consumed
number
of
components
in
Xc3s500e
Spartan-3e
FPGA
kit
On
the
performance
of
non-ortho
gonal
multiple
...
(Mohamad
A.
Ahmed)
Evaluation Warning : The document was created with Spire.PDF for Python.
2156
r
ISSN:
2088-8708
In
order
to
add
A
WGN
to
the
created
NOMA
symbols
in
FPGA,
we
follo
w
the
Box-Muller
technique
which
is
widely
e
xploited
in
dif
ferent
softw
are
for
this
purpose
as
in
[30,
31].
In
brief,
tw
o
random
v
ariables
x
1
and
x
2
,
which
ha
v
e
uniform
distrib
ution
between
0
and
1,
are
emplo
yed
to
create
random
Gaussian
noise
sample,
with
zero
mean
and
standard
di
vination
of
2
,
afterw
ards,
tw
o
functions
f
(
x
1
)
and
g
(
x
2
)
are
deri
v
ed
from
the
tw
o
v
ariables
as
f
(
x
1
)
=
p
ln
x
1
;
g
(
x
2
)
=
p
2
cos
(2
x
2
)
;
n
=
f
(
x
1
)
g
(
x
2
)
;
(6)
where
n
represents
the
A
WGN
symbol
created
from
the
tw
o
functions
f
(
x
1
)
and
g
(
x
2
)
according
to
the
tw
o
random
v
ariables
defined
abo
v
e
[30,
31],
respecti
v
ely
.
In
order
to
satisfy
small
v
ariation
of
x
1
,
non-uniform
quantization
can
be
used,
as
proposed
in
[32],
by
portioning
the
se
gment
[0
;
1]
recursi
v
ely
into
M
=
16
subse
gment
ha
ving
the
same
length.
Each
of
these
se
gments
are
then
di
vided
ag
ain
into
subse
gments.
This
process
is
implemented
L
times
using
1024
bytes
R
OM
to
store
f
(
x
1
)
which
has
the
quantized
v
alues
F
r
(
s
)
at
each
le
v
el
of
partitioning.
This
can
be
e
xpressed
as
F
r
(
s
)
=
R
2
m
f
s
+
16
r
(2
m
)
;
(7)
where
r
has
a
range
between
1
to
L
,
while
s
v
aries
between
1
to
M
1
.
Moreo
v
er
,
can
be
defined
as
a
real
number
within
the
range
[0
;
1]
to
indicate
the
position
of
each
sample.
It
is
note
w
orth
y
that
if
F
r
(
s
)
is
used
to
quantize
(
+
m
)
bits,
then
represents
the
inte
ger
v
alue
to
obtain
=
2
,
while
m
is
to
represents
the
fractional
part.
Furthermore,
b
R
c
is
the
maximum
inte
ger
belo
w
x
.
Additionally
,
for
s
=
0
in
(7)
F
r
(0)
=
0
.
No
w
,
the
v
ariable
x
1
can
be
obtained
by
using
L
random
generator
of
4
bits,
i.e.
r
g
r
with
r
=
1
to
L
.
The
quantization
function
of
the
second
v
ariable
g
(
x
2
)
can
be
simplified
by
e
xploiting
the
symmetrical
property
of
the
Cosine
function.
The
quantization
function
can
be
e
xpressed
as
G
(
s
0
)
=
R
2
m
0
p
2
cos
(
(
s
0
+
0
)
2
)
(2
m
0
)
;
(8)
where
m
0
and
0
are
as
defined
already
in
(7),
s
0
is
a
random
v
ariable
represented
by
8
bits.
Similarly
,
G
(
s
0
)
is
used
to
quantize
(1
+
m
0
)
bits,
where
1
and
m
0
are
to
represent
the
inte
ger
and
fraction
parts,
recepti
v
ely
.
After
obtaining
F
r
(
s
)
and
G
(
s
0
)
,
the
random
v
ariable
of
the
noise
can
be
created
using
half
Box
ed-Muller
with
b
bits
as
n
+
=
F
r
(
s
)
G
(
s
0
)
2
(
m
+
m
0
b
)
(2
b
)
;
(9)
which
can
be
used
to
create
the
complete
Box
ed-Muller
random
v
ariable
of
the
noise
by
applying
a
binary
random
v
ariable
sign
as
n
=
(1
2
sig
n
)
n
+
(10)
In
our
design,
we
e
xploit
Box-Muller
method
as
illustrated
in
Figure
4
to
generate
random
independent
A
WGN
for
each
user
with
dif
ferent
initial
seed.
In
thi
s
figure,
random
stream
of
bits
are
generated
to
feed
into
tw
o
8
bits
linear
feedback
shift
re
gisters
(LFSR).
The
designed
LFSR
is
sho
wn
Figure
5
which
follo
ws
the
polynomial
(
x
8
+
x
5
+
x
3
+
x
+
1
).
Moreo
v
er
,
a
logical
delay
,
denoted
by
D
,
is
applied
to
one
of
the
tw
o
branches
to
ensure
no
correlation
with
the
other
branch.
The
16
bits
LUT
is
used
to
e
v
aluate
the
equation
V
out
=
A
+
A
cos
(
w
t
)
where
A
=
2
:
5
v
olt
here
in
order
to
achie
v
e
V
out
=
5
v
olt
when
cos
(
w
t
)
=
1
,
and
V
out
=
0
v
olt
when
cos
(
w
t
)
=
1
.
Furthermore,
the
e
xploited
frequenc
y
is
12
:
5
MHz
and
for
10
bits
serial
peripheral
interf
ace
(SPI),
which
is
used
to
increase
the
resolution
and
reduce
the
processing
time
for
the
analogue
to
digital
con
v
erter
(ADC)
instead
of
using
the
con
v
entional
serial
to
parallel
technique.
The
output
of
each
LUT
is
multiplied
by
a
16
-bits
sign,
then
the
y
added
together
and
pass
the
output
to
a
re
gis
ter
with
a
length
of
11
bytes,
i.e.
(0
87)
bits.
This
output
represents
the
generated
A
WGN
comple
x
symbols
with
Int
J
Elec
&
Comp
Eng,
V
ol.
10,
No.
2,
April
2020
:
2151
–
2163
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
2157
zero
mean
and
v
ariance
equal
to
2
n
as
sho
wn
in
Figure
6
for
some
symbols
with
SNR=
15
dB.
It
is
w
orth
to
note
that
the
same
procedure
is
applied
at
the
other
user
with
dif
ferent
seed
to
ensure
independent
A
WGN.
Figure
4.
Box-Muller
method
used
to
generate
A
WGN
in
each
user’
s
recei
v
er
Figure
5.
The
schematic
diagram
of
the
8
bits
LFSR
with
a
polynomial
(
x
8
+
x
5
+
x
3
+
x
+
1
)
which
emplo
yed
in
Box-Muller
approach
to
generate
A
WGN
Figure
6.
Samples
of
the
generated
A
WGN
by
using
Box-Muller
technique
4.
DETECTION
OF
NOMA
In
the
detection
of
NOMA
signal,
which
contains
a
non-orthogonal
combination
of
the
multiple
us
ers,
dif
ferent
techniques
are
e
xploited
for
the
near
and
f
ar
users
depending
on
the
le
v
el
of
interference
caused
by
the
other
user
.
At
the
FU
terminal,
in
which
the
f
ar
signal
is
strong
while
the
near
signal
is
weak,
simple
and
ordinary
technique
can
be
used
for
dete
ction
by
considering
the
weak
NU
signal
as
a
noise.
In
contrast,
at
the
NU
terminal,
adv
anced
mechanism
should
be
used
to
detect
the
NU
weak
signal,
due
to
the
e
xistence
of
the
strong
FU
signal.
This
can
be
implemented
by
applyi
n
g
SIC.
In
brief,
SIC
is
simply
utilized
by
detecting
the
FU
signal
at
the
NU
terminal
and
subtract
it
from
the
o
v
erall
NOMA
signal
to
obtain
the
NU
signal.
5.
SIMULA
TIONS
RESUL
TS
AND
DISCUSSION
In
this
section,
the
simulat
ion
results
are
obtained
for
the
designed
NOMA
system
in
FP
GA
for
a
BS
communicating
with
tw
o
users,
NU
and
FU.
W
e
v
erify
the
results
by
utilizing
Monte-Carlo
simula-
tion
via
Matlab
for
the
same
system
o
v
er
A
WGN
channel
and
with
dif
ferent
SNR
and
po
wer
allocation
scales.
W
e
assume
that
the
attenuation
between
the
BS
and
NU
is
0
dB,
while
it
is
3
dB
between
the
BS
and
FU.
W
ithout
the
loss
of
genera
lity
,
do
wnlink
phase
is
considered
for
the
tw
o
users
in
this
paper
,
i.e.
for
the
f
ar
and
On
the
performance
of
non-ortho
gonal
multiple
...
(Mohamad
A.
Ahmed)
Evaluation Warning : The document was created with Spire.PDF for Python.
2158
r
ISSN:
2088-8708
near
distances
from
the
base-station,
in
which
the
FU
is
applied
with
lar
ger
portion
of
the
a
v
ailable
po
wer
of
NOMA
signal
than
the
NU.
This
is
due
to
the
f
act
that
the
signal
losses
par
t
of
its
po
wer
as
long
as
the
distance
is
increased,
this
what
is
called
attenuation
phenomena.
Figure
7
and
Figure
8
s
ho
w
the
FPGA
signaling
diagram
for
the
simulated
NOMA
BS
transmitter
with
FU
and
NU
recei
v
ers,
respecti
v
ely
,
in
the
do
wnlink
phase.
First
of
all,
a
series
of
bits
are
generated
to
represent
the
data
stream
for
each
user
.
Moreo
v
er
,
the
po
wer
allocation
f
actors
for
the
NU,
and
FU,
which
are
denoted
as
ne
scal
e
=
p
N
=
p
0
:
4
=
0
:
63
and
f
a
scal
e
=
p
F
=
p
0
:
6
=
0
:
77
,
respecti
v
el
y
,
are
chosen.
The
bits
are
con
v
erted
to
QPSK
symbols.
i.e.
e
v
ery
tw
o
bi
ts
are
con
v
erted
to
a
symbol
to
tak
e
one
of
the
four
possible
symbols
(
1
j
1
),
and
then
multiplied
by
the
assigned
scale
depending
on
the
channel
condition
of
each
user
.
The
scaled
symbols
of
NU
and
FU
are
added
together
to
create
the
NOMA
symbols.
The
latter
are
sent
to
w
ards
each
user
o
v
er
A
WGN
channel
with
dif
ferent
attenuation
f
actors.
Additionally
,
in
this
figure,
the
arri
v
ed
NOMA
symbols
at
the
FU
terminal
are
illustrated
and
the
de
tected
symbols
after
comparing
each
symbol
with
the
nearest
e
xpected
location
on
the
original
QPSK
constellation.
Finally
,
the
recei
v
ed
symbols
at
FU
recei
v
er
are
compared
with
the
transmitted
symbols,
and
an
y
dif
ference
leads
to
create
an
error
signal,
denoted
by
ber
which
are
summed
and
di
vided
by
the
total
number
of
bits
to
obtain
the
symbols
error
rate
(SER)
at
each
SNR.
Figure
7.
Base-station
NOMA
transmitter
timing
as
implemented
via
FPGA
and
the
FU
detection
Figure
8.
Base-station
NOMA
transmitter
timing
as
implemented
via
FPGA
and
the
NU
detection
by
applying
SIC
In
Figure
9,
the
ef
fect
of
the
A
WGN
on
a
symbol
is
clearly
illustrated
when
SNR=
15
dB.
This
figure
sho
ws
the
error
in
detection
a
symbol
transmitted
from
the
BS
as
tw
o
successi
v
e
logic
1,
i.e.
11
,
while
in
the
FU
recei
v
er
is
detected
it
wrongly
as
10
because
of
the
noise.
The
designed
system
detect
this
error
and
a
signal
ber
is
generated
for
the
purpose
counting
the
number
of
errors
as
mentioned
pre
viously
.
Figure
10
sho
ws
the
output
of
FPGA
simulation
similar
to
Figure
9,
b
ut
for
the
NU.
The
detection
at
this
user
be
gins
with
detection
of
the
FU
signal
at
the
near
terminal
as
e
xplained
pre
viously
,
follo
wed
by
subtracting
the
FU
from
the
entire
NOMA
signal
recei
v
ed
obtain
NU
symbols.
The
latter
are
mapped
ag
ain
to
their
nearest
positions
in
the
QPSK
constellation.
The
symbol
errors
which
are
tak
en
place
in
this
process
between
the
transmitted
and
recei
v
ed
Int
J
Elec
&
Comp
Eng,
V
ol.
10,
No.
2,
April
2020
:
2151
–
2163
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
2159
symbols
are
detected
by
creating
the
error
signal,
ber
,
which
is
summed
and
di
vided
by
the
total
number
of
bits
to
e
v
aluate
the
SER.
It
is
w
orth
to
mention
that
the
SER
is
di
vided
by
log
2
(4)
for
QPSK
scheme
to
obtain
bit
error
rate
(BER)
for
each
user
.
The
ef
fect
of
the
A
WGN
of
SNR=
15
dB
on
a
symbol
is
clearly
illustrated
in
Figure
10.
In
this
figure
the
error
in
detection
a
symbol
transmitted
as
00
by
the
BS
is
sho
wn
along
with
its
wrong
detection
as
11
because
of
the
noise.
Ag
ain,
the
designed
system
detect
this
error
by
creating
a
signal
ber
to
be
used
to
calculate
the
system
BER
vs.
SNR.
Figure
9.
The
detection
of
error
symbol
for
the
FU
recei
v
er
Figure
10.
The
detection
of
error
symbol
for
the
NU
recei
v
er
In
Fi
g
ur
e
11,
Monte-Carlo
simulations
via
Matlab
is
used
to
obtain
the
BER
o
v
er
dif
ferent
SNR
to
v
alidate
t
he
results
obtained
via
FPGA.
The
used
po
wer
allocation
f
actors
of
F
=
0
:
6
with
N
=
0
:
4
and
F
=
0
:
8
with
N
=
0
:
2
are
chosen
for
the
FU
and
NU,
respecti
v
ely
.
The
detection
of
the
FU
signal
is
implemented
by
calculating
the
minimum
Euclidean
distances
between
the
recei
v
ed
symbols
and
the
orig-
inal
symbols
in
the
QPSK
constellation.
Moreo
v
er
,
the
NU
signal
is
assumed
as
a
noise
at
the
FU
terminal.
In
contrast,
the
SIC
is
applied
at
the
NU
recei
v
er
to
remo
v
e
the
s
trong
FU
signal
and
detect
the
weak
NU
signal.
The
Euclidean
distance
of
each
detected
symbols
with
the
original
QPSK
constellation
points
are
e
v
aluated,
where
the
minimum
distance
refers
to
the
most
lik
ely
right
position.
In
this
simulation,
It
is
found
that
the
po
wer
allocation
f
actors
of
N
=
0
:
4
and
F
=
0
:
6
lead
to
obtain
the
same
BER-SNR
performance
especially
at
high
SNRs,
and
increasing
F
=
0
:
6
with
decreasing
N
=
0
:
4
lead
to
obtain
better
performance
in
the
F
ar
terminal.
This
is
in
order
to
satisfy
some
sort
of
user
-f
airness
in
this
performance
metric
by
applying
po
wer
allocation
technique
to
compensate
for
the
channel
weakness.
On
ot
her
w
ords,
for
dif
ferent
normalized
po
wer
of
the
near
and
f
ar
channels
as
defined
in
thi
s
paper
jj
h
N
jj
2
>
jj
h
F
jj
2
,
where
jj
h
N
jj
2
=
0
dB
and
jj
h
F
jj
2
=
3
dB,
we
found
that
when
N
=
0
:
4
and
F
=
0
:
6
,
the
tw
o
users
ha
v
e
the
same
BER-SNR
performance.
On
the
other
hand,
when
F
is
increased
and
N
is
decreased,
satisfying
F
+
N
=
1
,
this
will
lead
to
U
F
outperforming
U
N
.
Moreo
v
er
,
these
results
sho
w
e
xact-closed
matching
with
the
results
obtained
from
FPGA
simulations
after
using
the
same
parameters.
On
the
performance
of
non-ortho
gonal
multiple
...
(Mohamad
A.
Ahmed)
Evaluation Warning : The document was created with Spire.PDF for Python.
2160
r
ISSN:
2088-8708
Figure
12
sho
ws
the
performance
of
the
system
using
the
outage
probability
ag
ainst
the
SNR
for
a
threshold
BER
of
10
4
.
Three
sceneries
ha
v
e
been
tak
en
into
account,
which
are
F
=
0
:
6
with
N
=
0
:
4
,
F
=
0
:
7
with
N
=
0
:
3
and
F
=
0
:
8
with
N
=
0
:
2
.
The
channels
conditions
are
assumed
as
jj
h
N
jj
2
=
0
dB
and
jj
h
F
jj
2
=
3
dB.
It
can
be
noticed
that
the
performance
of
the
f
ar
user
outperforms
the
near
one
when
F
=
0
:
8
with
N
=
0
:
2
.
Some
sort
of
con
v
er
gence
in
the
outage
probability
can
be
seen
when
F
=
0
:
7
with
N
=
0
:
3
and
F
=
0
:
6
with
N
=
0
:
4
,
for
SNR
belo
w
23
dB
and
28
dB,
respecti
v
ely
.
While
after
these
tw
o
v
alues
of
SNRs
the
f
ar
user
performs
better
.
Figure
11.
BER
vs.
SNR
for
tw
o-user
NOMA-QPSK
in
the
do
wnlink
phase
with
F
=
0
:
6
with
N
=
0
:
4
and
F
=
0
:
8
with
N
=
0
:
2
,
for
jj
h
N
jj
2
=
0
dB
and
jj
h
F
jj
2
=
3
dB
SNR (dB)
15
20
25
30
Outage Probabilty
10
-3
10
-2
10
-1
10
0
Far
Near
β
N
=
0
.
2
,
β
F
=
0
.
8
β
N
=
0
.
3
,
β
F
=
0
.
7
β
N
=
0
.
4
,
β
F
=
0
.
6
Figure
12.
The
outage
probability
vs.
SNR
for
tw
o-user
NOMA-QPSK
in
the
do
wnlink
phase
with
F
=
0
:
6
with
N
=
0
:
4
,
F
=
0
:
7
with
N
=
0
:
3
and
F
=
0
:
8
with
N
=
0
:
2
,
for
jj
h
N
jj
2
=
0
dB
and
jj
h
F
jj
2
=
3
dB
and
for
a
BER
threshold
of
10
4
Moreo
v
er
,
the
constellation
of
the
recei
v
ed
NOMA
signal
at
both
users
is
sho
wn
in
Figure
13.
This
constellation
is
already
generated
in
the
base-station
by
adding
tw
o
QPSK
symbols
with
dif
ferent
po
wer
alloca-
tion
f
actors,
i.e.
N
and
F
for
the
near
and
f
ar
users,
respecti
v
ely
.
Furthermore,
Figure
14
sho
ws
the
symbols
after
applying
SIC
at
the
NU
recei
v
er
.
It
is
clear
that
the
16
-NOMA
symbols
in
Figure
13
ha
v
e
become
4
sym-
bols
in
Figure
14,
referring
to
the
QPSk
symbols,
after
applying
the
SIC,
in
which
the
symbols
of
the
remote
user
with
higher
po
wer
allocation
f
actor
is
detected
a
n
d
subtracted
from
the
entire
16
-NOMA
symbols
at
the
near
terminal
to
obtain
the
QPSK
symbols
of
the
near
user
only
.
Figure
13.
Do
wnlink
NOMA
constellation
created
from
adding
tw
o
QPSK
symbols
with
dif
ferent
po
wer
allocation
f
actors
i.e.
F
=
0
:
6
and
N
=
0
:
4
at
the
NU
front-end
before
applying
SIC,
the
blue
symbols
refer
to
the
original
16
-NOMA
constellation
at
the
BS
before
adding
the
noise
Figure
14.
Near
user
QPSK
constellation
at
the
NU
recei
v
er
after
applying
SIC
to
the
NOMA
signal
with
F
=
0
:
6
and
N
=
0
:
4
Int
J
Elec
&
Comp
Eng,
V
ol.
10,
No.
2,
April
2020
:
2151
–
2163
Evaluation Warning : The document was created with Spire.PDF for Python.