Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
8,
No.
6,
December
2018,
pp.
5215
5226
ISSN:
2088-8708,
DOI:
10.11591/ijece.v8i6.pp5215-5226
5215
New
T
echnique
Combining
the
T
one
Reser
v
ation
Method
with
Clipping
T
echnique
to
Reduce
the
P
eak-to-A
v
erage
P
o
wer
Ratio
Hajar
Abdelali
1
,
Smail
Bachir
2
,
and
Mohamed
Oumsis
3
1
Lims
Laboratory
,
F
aculty
of
Sciences
Dhar
Mahraz,
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
of
Fez,
Morocco
2
Xlim
Laboratory
,
UMR
CNRS
7252,
Uni
v
ersity
of
Poitiers,
France
3
Lrit
Laboratory
,
Unit
Associated
W
ith
CNRST
,
URA
C
29,
Uni
v
ersity
Mohamed
V
,
Rabat,
Maroc
Article
Inf
o
Article
history:
Recei
v
ed
Dec
26,
2017
Re
vised
Jul
3,
2018
Accepted
Jul
29,
2018
K
eyw
ord:
OFDM
System
P
APR
Reduction
W
iMAX
IEEE
802.16e
T
one
Reserv
ation
Clipping
Conjug
ate
Gradient
ABSTRA
CT
Nonlinear
di
stortions
and
impairment
s
appear
in
multicarrier
signal
with
high
fluctu-
ations
when
amplified
by
a
Radio
Frequenc
y
Po
wer
Amplifier
(RF
P
A).
This
article
is
a
contrib
ution
to
impro
ving
the
T
one
Reserv
ation
(TR)
method
dedica
ted
to
reduc-
ing
fluctuations
in
the
Orthogonal
Frequenc
y
Di
vision
Multiple
xing
(OFDM)
mod-
ulation.
This
method
e
xploits
the
null
sub-carriers
in
communications
standards
in
order
to
generate
a
correction
signal
used
to
reduce
the
Peak-to-A
v
erage
Po
wer
Ratio
(P
APR)
with
ne
v
ertheless
limited
performances
due
to
the
reduced
number
of
these
sub-carriers.
F
or
this
purpose,
our
contrib
ution
is
to
combine
the
TR
method
with
the
Clipping
(CL)
method
to
im
pro
v
e
the
P
APR
reduction
without
significantly
impacting
the
quality
of
transmissions.
W
e
also
sho
w
the
g
ain
pro
vided
by
this
strate
gy
compared
to
the
use
of
classical
methods.
Experiments
using
a
simulated
e
xample
on
a
complete
W
iMax
802
:
16
e
transmitter
ha
v
e
been
made
in
order
to
in
v
estig
ate
the
P
APR
reduc-
tion
performances
on
presence
of
the
non-linear
Po
wer
Amplifier
model
based
on
g
ain
compression
response
and
phase
distortion.
Copyright
c
2018
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Hajar
Abdelali,
LIMS
Laboratory
,
F
aculty
of
Sciences
Dhar
Mahraz,
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
of
Fez,
Morocco.
abdelali.hajar@usmba.ac.ma
1.
Intr
oduction
OFDM
technique
[1]
is
a
v
ery
popular
modulation
method
and
tends
to
become
the
most
widespread
multicarrier
modulation
in
recent
radio
communication
systems,
such
as
W
ireless
Local
Area
Netw
ork
(WLAN),
W
orldwide
Interoperability
for
Micro
w
a
v
e
Access
(W
iMax)
and
D
VB.
T
oday
,
it
w
as
chosen
for
the
fourth
Generation
(
4
G)
mobile
communication
systems,
where
the
Long
T
erm
Ev
olution
Adv
anced
(L
TE-A)
stan-
dard
allo
ws
broadband
services
with
a
theore
tical
transmission
rate
up
to
100
Mbps.
The
adv
antages
of
OFDM
modulation
are:
its
optimal
spectral
congestion,
its
fle
xibility
in
the
allocation
of
the
sub-carriers
and
its
sim-
plicity
of
implementation
using
F
ourier
transforms
at
the
transcei
v
er
.
Ho
we
v
er
,
it
presents
some
disadv
antages
and
dra
wbacks
such
as;
OFDM
system
generates
high
po
wer
peaks
in
t
ime-domain
signal,
termed
as
Peak
to
A
v
erage
Po
wer
Ratio
(P
APR)
[2]
results
in
nonlinear
distortions
when
amplified
by
the
Radio
Frequenc
y
Po
wer
Amplifier
(RF
P
A)
[3],[4].
These
distortions
lead
to
a
in-
band
spectral
re
gro
wth
and
out-of-band
spectral
re
gro
wth
that
result
in
de
graded
communication
metrics
lik
e
J
ournal
Homepage:
http://iaescor
e
.com/journals/inde
x.php/IJECE
Evaluation Warning : The document was created with Spire.PDF for Python.
5216
ISSN:
2088-8708
Adjacent
Channel
Po
wer
Ratio
(A
CPR),
Error
V
ector
Magnitude
(EVM)
and
Bit
Error
Rate
(BER).
In
literature,
there
are
se
v
eral
approaches
for
P
APR
reduction
lik
e
CL
[5],[6],
Clipping-Filtering
(CF)
[7],[8],[9],
Selecti
v
e
Mapping
(SLM)
[9],[10],[11],
P
artial
T
ransmit
Sequence
(PTS)
[9],[10],[12],
Block
Cod-
ing
[13],
T
one
Injection
[14]
and
TR
[15],[16].
These
methods
dif
fer
in
their
principle
and
impl
ementation,
b
ut
also
in
their
dra
wbacks:
some
of
them
add
side
information
decreasing
data
rate
and/or
bandwidth
lik
e
PTS,
others
sacrifice
BER
performances
for
the
benefit
of
P
A
ef
ficienc
y
such
as
CL
and
CF
while
some
others
are
ef
ficient
b
ut
too
dif
ficult
to
implement
lik
e
SLM.
In
this
paper
,
our
contrib
ution
called
(TRCL)
is
a
ne
w
method
based
on
the
combination
of
tw
o
meth-
ods
to
reduce
P
APR,
TR
[15],[16]
with
Conjug
ate
Gradient
Optimization
algorithm
[17],[18]
and
CL
[5],[6].
These
tw
o
methods
present
a
certain
complementarity:
the
TR
method
based
on
the
addition
of
signal
i
s
one
of
the
methods
ha
ving
the
property
of
do
wnw
ard
compatibility
and
impro
ving
the
performance
of
EVM
and
BER
due
to
their
lo
w
de
gradation
and
their
lo
w
intak
e
of
supplementary
computational
comple
xity
,
b
ut
its
perfor
-
mance
remains
limited
because
of
the
reduced
number
of
free
subcarriers,
while
the
CL
is
v
ery
simple
of
those
kno
wn
this
day
and
theoretically
allo
ws
an
unlimited
clipping
of
the
signal
b
ut
unfortunately
with
a
de
gradation
of
all
the
communication
criteria
and
a
decrease
in
performance
caused
by
a
loss
of
some
information.
Despite
its
limitations,
this
is
the
TR
method
that
is
preferred
in
practice
because
it
requires
no
mod-
ification
the
recei
v
er
.
In
[19],
the
author
proposed
the
use
of
the
TR
method
based
on
the
conjug
ate
gradient
algorithm
in
order
to
reduce
the
v
alue
of
P
APR
and
impro
v
e
the
speed
of
con
v
er
gence.
In
this
paper
,
we
are
going
to
describe
and
study
our
TRCL
method
and
compare
it
with
other
e
xisting
methods
TR
and
CL.
W
e
will
see
belo
w
ho
w
our
ne
w
method
impro
v
es
the
performance
in
terms
of
P
APR
reduction
and
the
communication
criteria
EVM
and
BER.
The
study
of
the
performances
in
terms
of
reduction
of
the
P
APR
is
carried
out
on
the
standard
W
iMax
-
IEEE
802.16e
[20].
T
o
study
the
impact
of
this
association,
simulations
in
the
presence
of
a
Solid
State
Po
wer
Amplifiers
(SSP
A)
modeled
by
a
nonlinearity
of
the
g
ain
and
phase,
are
carried
out
in
order
to
e
v
aluate
the
quality
of
the
transmissions.
The
paper
will
be
or
g
anized
as
follo
ws:
section
2
will
present
the
Problem
position,
while
section
3
,
will
discuss
tw
o
methods
of
P
APR
reduction:
Clipping
and
T
one
Reserv
ation
based
on
the
Conjug
ate
Gradient
Optimization
Algorithm,
and
present
the
proposed
technique
based
on
the
conjunction
of
CL
and
TR
(TRCL).
In
section
4
,
we
present
the
simulation
results
of
our
ne
w
method
TRCL
compared
to
the
TR
and
the
CL.
Finally
,
we
conclude,
in
section
5
.
2.
Pr
oblem
P
osition
T
o
transmit
a
signal,
the
OFDM
signal
model
(figure
1)
di
vides
at
first
a
frequenc
y
range
into
se
v
eral
independent
orthogonal
sub-carriers
which
ha
v
e
the
same
width
of
frequenc
y
band.
The
representation
of
an
OFDM
signal
can
then
be
written:
c
(
k
)
=
1
p
N
N
1
X
k
=0
C
k
e
j
(
2
nk
N
)
;
1
n
N
(1)
where
C
k
is
the
data
symbols
with
k
=
0
;
;
N
1
is
the
inde
x
of
the
sub-carrier
,
C
=
[
C
0
;
C
1
;
;
C
N
1
]
indicate
the
carrier
v
ector
data
and
N
is
the
number
of
sub-carriers.
Subsequently
,
it
applies
the
algorithm
of
the
in
v
erse
F
ourier
T
ransform
(IFFT)
on
this
OFDM
signal
by
the
F
ollo
wing
equation:
x
=
Q
X
(2)
where
Q
is
the
matrix
of
transformation
IFFT
of
size
N.
From
equation
1,
when
all
the
sub-carriers
are
weighted
at
high
le
v
el,
the
constructi
v
e
sum
needs
to
appear
peaks
in
the
temporal
domain.
This
establi
shes
the
major
incon
v
enience
of
the
OFDM
systems
[1].
T
o
measure
these
fluctuations,
the
P
APR,
defined
as
a
highest
peak
po
wer
to
a
v
erage
po
wer
of
one
OFDM
symbol,
such
as:
P
AP
R
(
x
)
dB
=
10
l
og
10
max
0
t
T
j
x
(
t
)
j
2
E
(
j
x
(
t
)
j
2
)
(3)
IJECE
V
ol.
8,
No.
6,
December
2018
:
5215
–
5226
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
5217
Channel
co
ding
Sym
b
ol
map
Serial
to
P
arallel
IFFT
to
Serial
P
arallel
Cyclic
extension
D
A
C
RF
tx
ADC
Timing
and
sync
h
Remo
v
e
extension
freq
Cyclic
Serial
to
P
arallel
FFT
to
Serial
P
arallel
Sym
b
ol
demap
Deco
ding
Bits
F
requency
corrected
signal
Bits
OFDM
T
ransmitter
RF
rx
OFDM
Receiv
er
Figure
1.
Model
of
OFDM
transmitter
and
recei
v
er
for
WIMAX
In
literature,
we
can
find
se
v
eral
techniques
for
P
APR
reduction
[2]
which
present
some
i
mpro
v
em
ents
b
ut
at
the
cost
of
man
y
incon
v
eniences.
F
or
e
xample,
the
CL
method
has
in
theoretical
unlimited
performances
in
term
of
P
APR
reduction
b
ut
its
application
induces
systematically
errors
of
transmission
(lik
e
increasing
BER
and/or
Out-Of-Band
distortion,
etc.).
These
dra
wbacks
can
be
a
v
oided
using
the
TR
method,
b
ut
the
use
of
only
nul
subcarriers
allo
ws
about
2
to
4
dB
of
i
mpro
v
ement
.
Here,
we
propose
ne
w
technique
combining
TR
and
CL
methods
to
impro
v
e
performances
by
a
v
oiding
the
disadv
antages
of
each
one.
As
we
pre
viously
noted,
we
will
cite
the
adv
antages
and
the
incon
v
eniences
of
the
tw
o
techniques
TR
and
CL:
TR
:
this
technique
is
one
of
the
methods
ha
ving
the
property
of
do
wnw
ard
compatibility
and
impro
v
es
the
performance
of
”EVM”
and
”BER”
due
to
their
lo
w
de
gradation
and
their
lo
w
intak
e
of
supplemen-
tary
computational
comple
xity
b
ut
it
is
limited
by
a
restricted
number
of
free
subcarriers
in
the
standard,
comple
xity
of
implementation,
etc.
CL
:
this
technique
is
v
ery
simple
and
has
an
unlimited
performances
in
term
of
P
APR
reduction
b
ut
its
application
induces
systematically
de
gradation
of
all
transmission
criteria
(BER
and/or
Out-of-Band
distortion)
3.
Pr
oposed
T
echnique
Unuse
d
sub
c
arriers
Data
sub
c
arriers
t
t
iFFT
P
APR
Reducer
x
x
+
c
c
De
dic
ate
d
sub
c
arrie
rs
for
c
orr
e
ctive
signal
(PR
T)
+
A
−
A
A
t
t
Figure
2.
The
combination
of
both
techniques
TR
and
CL
(TRCL).
Here,
we
will
in
v
estig
ate
the
possibilities
of
combining
both
techniques
TR
and
CL
(figure
2).
These
tw
o
techniques
can
be
complementary
because
the
TR
allo
ws
to
reduce
the
majority
of
peaks
in
an
OFDM
symbol.
Still
a
fe
w
samples
of
the
s
y
m
bol
that
cannot
be
reduced
by
this
method
and
which
will
be
af
fected
by
the
non-linearities
of
the
circuits
such
as
the
po
wer
amplifier
.
In
this
case,
we
propose
to
apply
the
CL
method
to
a
v
oid
an
y
e
xceeding
the
clipping
v
alue.
Ne
w
T
ec
hnique
Combining
the
T
one
Reservation
Method...
(Hajar
Abdelali)
Evaluation Warning : The document was created with Spire.PDF for Python.
5218
ISSN:
2088-8708
3.1.
Clipping
CL
[5],[6]
is
the
simplest
method
of
those
kno
wn
this
day
which
allo
ws
reducing
the
v
alue
of
P
APR.
The
objecti
v
e
of
this
method
is
to
clip
all
points
whose
amplitude
e
xceeds
a
predetermined
threshold
A
to
reduce
the
po
wer
v
ariation.
This
procedure
is
repeated
until
no
point
e
xceeds
this
threshold.
Equation
4
sho
ws
the
principle
of
clipping.
The
simplicity
of
this
method
has
an
impact
on
the
signal
reception
performance
will
be
reduced
because
the
information
remo
v
ed
by
clipping
are
lost.
f
(
x
)
=
A:sig
n
(
x
(
t
))
if
j
x
(
t
)
j
>
A
x
(
t
)
otherwise
(4)
3.2.
T
one
Reser
v
ation
TR
[15],[16]
is
the
most
recent
method
based
on
the
addition
of
a
signal
to
the
original
signal
to
reduce
the
P
APR.
The
Useful
sub-carriers
are
reserv
ed
for
the
broadcast
of
the
original
signal
and
the
sub-carriers
not
used
are
e
xploited
to
generate
the
signal
of
cancellation
of
peak
without
loss
of
flo
w
of
data
and
Reduced
the
P
APR.
The
generation
of
the
temporal
signal
for
the
reduction
of
the
P
APR
by
process
TR
w
as
formulated
as
problem
of
con
v
e
x
optimization
which
requires
a
high
computational
cost
of
the
order
of
O
(
N
r
N
2
L
)
,
where
N
r
is
the
number
of
reserv
ed
carriers,
N
the
number
of
carriers
of
the
OFDM
and
L
is
the
o
v
er
-sampling
f
actor
.
T
o
solv
e
this
problem,
there
are
four
iterati
v
e
optimization
algorithms,
b
ut
in
this
paper
we
are
going
to
concentrate
on
one
optimization
algorithm:
Conjug
ate
Gradient.
It
is
an
iterati
v
e
method
just
lik
e
the
method
of
the
gradient,
b
ut
it
uses
an
algorithm
so
that
the
direction
of
research
is
optimal.
This
direction
is
determined
by
the
gradient
at
the
point
X
n
and
the
gradient
of
the
pre
vious
point
X
n
1
[17].
F
or
the
first
iteration,
the
chosen
direction
is
the
ne
g
ati
v
e
gradient:
d
0
=
g
0
(5)
At
the
k
+
1
th
iteration,
the
point
X
n
+1
is
chosen
by
finding
the
minimum
of
the
function
in
the
direction
pre
viously
determined
to
reduce
the
number
of
iterations.
X
k
+1
=
X
k
+
k
:d
k
(6)
k
is
the
conjug
ate
gradient
step,
and
d
k
represents
the
direction
of
conjug
ate
gradient.
The
ne
xt
direction
is
determined
by
the
pre
vious
direction.
This
method
in
v
olv
es
combining
the
pre
vious
direction
d
k
1
with
the
gradient
at
the
point
X
k
to
calculate
the
ne
w
direction:
d
k
=
g
k
+
k
:d
k
1
(7)
There
are
se
v
eral
v
ersions
of
the
method
of
the
combined
gradient,
the
y
v
ary
by
the
w
ay
the
constant
k
is
calculated.
Here
is
the
method
of
calculation
of
Fletcher
-Ree
v
es
[21]:
k
=
g
T
k
:g
k
g
T
k
1
:g
k
1
(8)
k
represents
then
the
report
between
the
standard
to
the
square
of
the
current
gradient
and
the
standard
to
the
square
of
the
pre
vious
gradient.
Here
is
the
method
of
calculation
of
Polak-Ribire
[22]:
k
=
(
g
k
g
k
1
)
T
:g
k
g
T
k
1
:g
k
1
=
g
T
k
1
:g
k
g
T
k
1
:g
k
1
(9)
IJECE
V
ol.
8,
No.
6,
December
2018
:
5215
–
5226
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
5219
3.3.
New
TRCL
Method
The
number
of
null
subcarriers
in
a
gi
v
en
standard
is
limited,
the
TR
method
reduces
the
maj
ority
of
peaks
in
an
OFDM
symbol,
b
ut
al
w
ays
remains
some
samples
whose
amplitude
is
high
and
which
will
consequently
be
af
fected
by
the
non-linearities
of
the
circuits
lik
e
the
po
wer
amplifier
.
In
this
case,
we
propose
to
apply
,
after
the
TR,
the
CL
method
in
order
to
a
v
oid
an
y
e
xceeding
of
the
A
threshold.
Therefore,
the
first
phase
is
to
reduce
the
P
APR,
using
the
TR
method
which
calculates
the
correcti
on
signal
c,
from
the
null
subcarriers,
according
to
the
Conjug
ate
Gradient
algorithm
which
is
used
to
reduce
the
con
v
er
gence
time
of
the
optimization
algorithm.
The
second
phase
consists
in
applying
a
clipping
to
the
same
threshold
A
as
the
pre
vious
phase
in
order
to
eliminate
the
remaining
peaks
4.
Simulation
Results
In
this
section,
we
present
the
e
xperimental
e
v
aluation
results
of
our
ne
w
method
TRCL
with
the
standard
IEEE
802
:
16
e
or
“W
iMAX”
[20].
The
follo
wing
table
1
represents
the
W
iMAX
param
eters
used
in
simulations
to
impro
v
e
the
P
APR
reduction
of
OFDM
signals.
T
able
1.
The
IEEE
802.16
parameters
used
in
simulation
Name
of
the
parameter
v
alue
System
OFDM
Modulation
64QAM
Num
of
Sub-carriers
512
Sub-carriers
Datas
384
Sub-carriers
Pilots
42
Sub-carriers
GI
86
P
AP
R
tar
g
et
2
:
17
This
standard
is
a
broadband
wireless
technology
of
the
fourth
generation
allo
wing
data
transmis
sion
on
long
distances
(dozens
of
kilometers
until
50km)
at
high
speed
70
Mbits/s
and
with
an
optimal
security
.
The
systems
based
on
the
802
:
16
e
standard
is
called
“Mobile
W
imax”.
The
communication
by
this
standard
can
be
realized
on
Line
Of
Sight
(LOS)
or
Not
Line
Of
Sight
(NLOS).
The
number
of
carriers
for
WIMAX
802.16e
can
v
ary
between
2048
,
1024
,
512
and
128
,
and
there
are
three
types
of
subcarriers
for
OFDM:
Subcarrier
data,
Pilot
subcarriers
and
Subcarriers
care
(or
subcarriers
zeros).
The
distrib
ution
of
these
sub-carriers
v
aries
accordi
ng
to
the
mode
of
allocation
FUSC
(Fully
Used
Sub
Channel
ization)
and
PUSC
(P
artially
Used
Sub
Channelization)
and
the
nature
of
the
link
DL
(Do
wnlink)
or
UL
(Uplink):
these
tw
o
modes
dif
fer
by
the
f
act
of
total
or
partial
use
of
channels
and
depend
on
the
need
for
the
users.
In
this
paper
,
the
simulation
is
car
ried
out
for
512
subcarriers
and
we
consider
the
Mode
sub-channel
FUSC
in
the
do
wnlink
DL
by
using
a
F
ast
F
ourier
T
ransform
(FFT)
(figure
3).
4.1.
P
APR
r
eduction
T
o
mak
e
an
e
v
aluation
on
the
mo
v
ement
of
a
signal,
there
are
se
v
eral
criteria
to
mak
e
it,
among
t
hese
criteria
we
find
the
P
APR
and
the
CCDF
.
As
we
ha
v
e
already
seen
pre
viously
that
the
P
APR
is
the
report
between
the
maximum
po
wer
and
the
a
v
erages
po
wer
of
a
temporal
signal.
Ho
we
v
er
,
for
a
better
mo
v
ement
e
v
aluation
of
a
signal
,
we
use
the
second
parameter
CCDF
which
is
a
Complementary
Cumulati
v
e
Distrib
ution
Function
of
the
mo
v
ement
on
an
interv
al
of
fix
ed
time.
Thus
CCDF
is
the
probability
that
the
v
alue
of
P
APR
is
superior
to
a
fix
ed
v
alue.
C
C
D
F
=
P
r
(
P
AP
R
P
AP
R
0
)
(10)
Ne
w
T
ec
hnique
Combining
the
T
one
Reservation
Method...
(Hajar
Abdelali)
Evaluation Warning : The document was created with Spire.PDF for Python.
5220
ISSN:
2088-8708
Sym
b
ol
mapping
Input
data
X
1
×
384
X
1
×
426
C
1
×
86
X
512
×
1
X
512
×
1
x
576
×
1
x
1
×
576
P
APR
reduction
Serial
to
parallel
S/P
Flexible
OFDM
system
P/S
BER
EVM
Ev
aluation
blo
c
k
Output
data
Q
512
×
512
512pt.
iFFT
t
P
APR
Reducer
c
De
dic
ate
d
sub
c
arrie
rs
for
c
orr
e
ctive
signal
(PR
T)
+E
-E
Pilot
insertion
S/P
,
Remo
v
e
GI
,
FFT
,
Equalizing
and
Demapping
OFDM
demo
dulation
Add
guard
in
terv
al
White
noise
P
A
Figure
3.
OFDM
data
symbol
generation
and
TRCL
scheme
for
802.16e
standard
F
or
that
purpose,
for
an
y
signal,
the
dynamics
of
this
signal
will
al
w
ays
be
superior
or
equal
to
0
dB
thus
the
v
alue
of
P
APR
will
also
ha
v
e
a
probability
superior
or
equal
to
0
dB.
The
more
the
CCDF
parameter
has
a
lo
w
v
alue,
the
more
the
probability
of
ha
ving
a
high
P
APR
v
alue
tends
to
0
.
0
2
4
6
8
10
12
10
−3
10
−2
10
−1
10
0
PAPR, PR0 dB
Probabilite, PR > PR0
CCDF of PAPR with transmission IEEE 802.16e
Original
with TR
with CL
with TRCL
Figure
4.
CCDF
of
P
APR
with
dif
ferent
method
to
reduce
the
P
APR
in
IEEE
802.16e
In
this
part,
the
impact
of
the
studied
methods
on
CCDF
will
be
discussed.
The
figure
4,
sho
ws
the
CCDF
curv
es
in
function
of
P
AP
R
0
obtained
by
the
dif
ferent
methods
allo
wing
the
P
APR
v
alue
reduction
(TR,
CL,
TRCL)
and
the
CCDF
of
a
OFDM
classic
signal
(i.e.
without
reduction
technique
of
the
P
APR
”Original”).
W
e
can
notice
that
the
combinaison
TRCL
reduce
the
P
APR
from
10
:
6
dB
to
4
:
8
dB
with
a
probability
of
approximately
10
2
.
It
represents
a
reduction
f
actor
of
about
5
:
8
dB,
while
CL
of
fers
a
reduction
f
actor
of
approximately
5
:
5
dB
and
TR
of
fers
approximately
3
dB.
From
that,
we
can
conclude
that
the
CCDF
of
the
TRCL
and
CL
methods
are
comparable
and
decrease
rapidly
compared
to
the
others
methods
(TR
and
Original).
The
second
results
sho
wn
in
figure
5,
represents
the
temporal
e
v
olution
of
the
OFDM
signal’
s
en
v
elope
for
the
dif
ferent
P
APR
reduction
methods.
These
results
are
obtained
from
a
unit
mean
po
wer
signal
with
a
clipping
of
normalized
amplitude
A
=
1
:
65
to
ha
v
e
a
v
alue
of
P
AP
R
tar
g
et
equal
to
2
:
17
(see
equation
11).
A
=
10
P
AP
R
tar
g
et
10
:E
(
j
x
(
t
)
j
2
)
(11)
It
can
be
noted
that
the
TR
(figure
5.a)
method
lea
v
es
a
fe
w
peaks
that
e
xceed
the
A
,
the
CL
method
IJECE
V
ol.
8,
No.
6,
December
2018
:
5215
–
5226
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
5221
0
0.5
1
1.5
2
2.5
T
×
10
4
0
0.5
1
1.5
2
2.5
3
3.5
|x|
Original
Avec TR
Avec CL
Avec TRCL
(a).
W
ith
the
dif
ferent
methods
of
the
P
APR
reduction.
0
0.5
1
1.5
2
2.5
T
×
10
4
0
0.5
1
1.5
2
2.5
3
3.5
|x|
Original
Avec TR
Avec CL
Avec TRCL
(b).
W
ithout
TRCL.
Figure
5.
“The
temporal
e
v
olution
of
the
en
v
elope
for
OFDM
signal.
”
(figure
5.b)
clipped
all
the
peaks
that
are
higher
than
A
,
and
for
TRCL
(figure
5.a)
we
can
sho
w
that
the
results
obtained
are
identical
to
those
of
CL,
b
ut
with
an
impro
v
ement
in
BER
and
EVM
transmission
errors
(as
we
will
see
later
on).
In
the
ne
xt
section,
a
nonlinear
amplifier
and
a
channel
model
will
be
introduced
to
observ
e
the
de
gradation
of
the
CL
method
and
the
performance
of
our
TRCL
method
in
terms
of
BER
and
EVM.
4.2.
P
erf
ormances
in
pr
esence
of
nonlinear
P
A
model
The
emission
information
in
wireless
netw
orks
o
v
er
a
great
distance
such
as
WIMAX
requires
the
use
of
po
wer
amplifiers
P
A
[3],
to
ensure
a
complete
transmission.
The
role
of
P
A
is
to
increase
the
po
wer
of
the
RF
signal
without
distorting
the
signal
at
its
input
and
without
ener
gy
dissipation
when
issued
to
its
output.
The
follo
wing
equation
12
represents
the
relationship
non-linear
between
the
input
signal
to
a
P
A
and
its
output:
P
out
=
G
(
P
in
)
:P
in
(12)
where
P
in
and
P
out
are
the
P
A
po
wer
of
the
input
and
the
output
signal,
respecti
v
ely
,
and
G
is
the
g
ain
of
the
P
A
depending
on
the
amplifier’
s
input
po
we
r
.
The
g
ain
v
alue
remains
constant
for
the
weak
po
wers
i
n
the
linear
zone,
it
will
be
called
also
linear
g
ain,
then
it
decreases
when
the
po
wer
increased
in
the
other
areas.
P
A
is
characterized
by
tw
o
inputs-outputs
relationships
also
called
transfer
characteristics
of
con
v
er
-
sions
AM/AM
(Amplitude
Modulation)
and
AM/PM
(Phase
Modulation).
The
AM/AM
represents
the
v
aria-
tion
of
the
output
signal
po
wer
depending
on
the
input
signal
po
wer
(as
sho
w
in
figure
6),
while
the
AM/PM
represents
the
phase
dif
ference
between
the
P
A
output
and
input
signals
depending
on
the
input
signal
po
wer
.
Ne
w
T
ec
hnique
Combining
the
T
one
Reservation
Method...
(Hajar
Abdelali)
Evaluation Warning : The document was created with Spire.PDF for Python.
5222
ISSN:
2088-8708
−20
−15
−10
−5
0
5
10
15
−10
−5
0
5
10
P
in
P
out
P
out,sat
P
in,sat
1 dB compression point
Saturation point
Linear zone
Compression
zone
Saturation
zone
P
in,1dB
IBO (dB)
OBO
(dB)
P
out,1dB
P
out
mean
P
in
mean
Figure
6.
AM/AM
characteristics
The
mathematical
model
of
the
amplifier
P
A
is
based
on
the
most
wides
pread
models,
namely
,
the
Rapp
model
descri
bed
by
the
e
xpression
of
con
v
ersion
AM/AM
(equation
13)
and
the
Saleh
model
which
is
described
by
AM/PM
(as
sho
w
in
equation
14)
[23]:
F
AM
AM
(
j
x
(
t
)
j
)
=
j
x
j
1
+
j
x
j
A
sat
2
p
1
2
p
(13)
where
j
x
(
t
)
j
is
the
instantaneous
modulated
en
v
elope
of
the
input
signal.
W
ith
A
sat
=
2
:
1
and
p
=
3
F
AM
P
M
(
j
x
(
t
)
j
)
=
p
:
j
x
j
2
1
+
p
:
j
x
j
2
(14)
with
p
=
pi=
3
and
p
=
1
.
The
parameters
p
and
p
are
used
to
describe
the
beha
vior
of
the
amplifier
.
The
AM
/
AM
curv
e
of
the
P
A
is
di
vided
into
three
functioning
zones
(According
to
figure
6),
the
linear
zone
of
the
amplifier
where
the
output
po
wer
is
proportional
to
the
input
po
wer
according
to
a
g
ain
of
the
amplifier
which
remains
constant.
After
a
certain
po
wer
input
,
the
g
ain
starts
to
decrease
slo
wly
,
this
zone
is
called
compression
zone.
And
finally
,
the
saturation
zone
where
the
amplifier
reaches
its
maximum
output
po
wer
.
The
point
to
1
dB
compression
of
g
ain
represents
the
po
wer
output
where
the
dif
ference
between
the
g
ain
calculated
in
the
linear
zone
and
the
real
g
ain
of
the
P
A
is
w
orth
than
1
dB.
The
saturation
point
is
a
point
where
the
amplifier
reaches
the
maximum
v
alue
to
issue
an
output
signal
and
its
po
wer
appointed
po
wer
of
saturation.
Most
used
amplifiers
are
non-linear
,
since
the
linear
amplifiers
are
v
ery
e
xpensi
v
e.
Ho
we
v
er
,
the
non-linearities
of
a
P
A
has
to
impact
the
e
xistence
of
distortions
temporal
and
frequenc
y
signals
to
transmit
which
are
reflected
by
a
distortion
of
the
signal.
T
o
a
v
oid
such
distortions,
we
must
tak
e
a
step
back
in
po
wer
,
compared
to
the
point
of
compression
to
1
dB
steps.
This
decline
allo
ws
to
w
ork
in
the
linear
zone
as
well
as
the
signal
is
closest
to
the
non-l
inear
zone
of
the
P
A.
It
is
defined
by
the
IBO
(Input
Back-of
f)
and
the
OBO
(Ouput
Back-of
f)
which
represents
the
decline
in
a
v
erage
po
wer
input
and
output,
respecti
v
ely
,
compared
to
the
point
of
compression
to
1
dB
(figure
6).
In
our
simulations,
we
ha
v
e
added
noise
to
simulate
a
Additi
v
e
White
Gaussian
Noise
channel
(A
WGN).
This
is
a
fundamental
characteristic
of
the
transmission
channel.
This
channel
noise
is
modeled
by
a
random
signal
n
(
t
)
,
whose
probability
distrib
ution
follo
ws
the
Gaussian
la
w
.
The
recei
v
ed
signal:
r
(
t
)
=
s
(
t
)
+
n
(
t
)
(15)
IJECE
V
ol.
8,
No.
6,
December
2018
:
5215
–
5226
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
5223
2
3
4
5
6
7
8
9
10
11
10
−4
10
−3
10
−2
10
−1
10
0
EbNo (dB)
BER
a. BER as a function of SNR with IBO=5
Original
with TR
with CL
with TRCL
2
3
4
5
6
7
8
9
10
11
10
15
20
25
30
35
EbNo (dB)
EVM (%)
b. EVM as a function of SNR with IBO=5
Original
with TR
with CL
with TRCL
Figure
7.
EVM
and
BER
as
a
function
of
SNR
with
IBO=5
2
4
6
8
10
10
−3
10
−2
10
−1
10
0
EbNo (dB)
BER
a. BER as a function of EbNo with IBO=0
Original
with TR
with CL
with TRCL
2
3
4
5
6
7
8
9
10
11
15
20
25
30
35
40
EbNo (dB)
EVM (%)
b. EVM as a function of EbNo with IBO=0
Original
with TR
with CL
with TRCL
Figure
8.
EVM
and
BER
as
a
function
of
SNR
with
IBO=0
where
s(t)represents
the
transmitted
signal.
After
the
addition
of
nois
e,
we
first
calculated
the
percentage
of
Error
V
ector
Magnitude
(EVM)
which
corresponds
to
t
he
error
v
ector’
s
amplitude
between
the
origin
constellation
and
the
recei
v
ed
constellation.
Second,
we
calculated
the
Bit
Error
Rate
(BER)
which
is
the
ratio
between
the
number
of
errors
bits
at
reception
(Ne)
and
the
total
number
of
transmitted
bits
(N).
In
the
first
figures
(7.a
and
7.b),
we
can
sho
w
the
e
v
olution
curv
es
of
the
EVM
and
the
BER
according
to
the
SNR
(Eb/No)
that
v
aries
between
2
dB
and
11
dB
for
a
backw
ard
mo
v
ement
of
I
B
O
=
5
dB,
to
mak
e
a
comparison
between
the
v
arious
methods
for
P
APR
reduction.
F
or
the
lo
w
SNR
v
alues
(
S
N
R
<
7
)
dB,
we
can
see
that
all
BER
and
EVM
curv
es
ha
v
e
almost
the
same
beha
vior
.
F
or
strong
SNR
(
S
N
R
>
7
)
dB,
a
first
remark
concerns
the
Clipping
method
which
de
grades
all
communication
criteria.
W
e
also
see
that
of
TR
which
coincides
with
TRCL
with
a
non-ne
gligible
impro
v
ement
of
BER
and
with
a
slight
impro
v
ement
of
EVM
compared
to
the
other
methods.
After
,
the
amplifier
operate
s
in
the
non-linear
zone
at
the
point
at
1
dB
of
compression
corresponding
to
a
decrease
in
po
wer
of
zero
i
nput
(
I
B
O
=
0
dB).
The
curv
es
in
Figure
8
sho
w
the
comparison
between
the
BER
and
the
EVM
according
to
SNR
(Eb/No)
v
arying
between
2
dB
and
11
dB
to
mak
e
a
comparison
between
v
arious
methods
which
allo
ws
t
o
reduce
the
v
alue
of
P
APR.
From
the
results
of
these
figures,
W
e
can
also
see
that
the
CL
method
de
grades
all
the
criteria
and
the
TRCL
method
maintains
a
good
impro
v
ement
when
the
noise
le
v
el
e
xceeds
E
b=
N
o
=
8
dB.
W
e
can
notice
that
our
TRCL
method
al
w
ays
retains
the
best
le
v
el
of
performance
on
both
criterias.
In
the
follo
wing
figure
9,
we
e
v
a
luated
the
transmission
quality
in
terms
of
BER
and
EVM
for
each
method
by
v
arying
the
v
alue
of
the
amplifier’
s
input
do
wn
IBO
(IBO
v
aries
between
3
dB
and
2
dB
in
a
step
1
dB)
with
fix
ed
SNR
v
alue
=
12
dB.
W
e
noted
the
impro
v
ements
made
by
applying
a
clipping
after
the
TR
method.
Ne
w
T
ec
hnique
Combining
the
T
one
Reservation
Method...
(Hajar
Abdelali)
Evaluation Warning : The document was created with Spire.PDF for Python.
5224
ISSN:
2088-8708
−3
−2
−1
0
1
2
10
−4
10
−3
10
−2
10
−1
IBO (dB)
BER
a. BER as a function of IBO with SNR=12
Original
with TR
with CL
with TRCL
−3
−2
−1
0
1
2
10
15
20
25
30
IBO (dB)
EVM (%)
b. EVM as a function of the IBO with SNR=12
Original
with TR
with CL
with TRCL
Figure
9.
EVM
and
BER
as
a
function
of
the
IBO
−30
−20
−10
0
10
20
30
−80
−70
−60
−50
−40
−30
−20
−10
0
frequency, MHz
power spectral density
Transmit spectrum OFDM (based on 802.16e)
Original
with TR
with CL
with TRCL
mask
Figure
10.
T
ransmit
spectrum
OFDM
based
on
802.16e
without
amplifier
Simulation
results
in
figure
9.a
sho
w
that
when
the
IBO
increases,
the
BER
tends
to
w
ard
zero
with
the
TRCL
method.
It
is
the
proof
that
there
is
less
disruption.
In
ef
fect,
an
IBO
lo
w
engenders
significant
distortions
in
the
signal.
W
e
can
also
observ
e
in
figure
9.b
that
TRCL
impro
v
es
EVM
by
about
3%
when
the
IBO
increases,
that
is
to
say
that,
when
the
amplification
is
done
more
and
more
in
the
linear
area.
Ho
we
v
er
,
lo
w
v
alues
of
the
IBO
mean
that
the
po
wer
amplifier
operates
on
the
limit
of
its
saturation
zone
and
will
cause
distortions
in
the
amplified
signal.
Figure
10
and
11
sho
w
the
signal
spectrum
before
and
after
the
use
of
methods
which
reduce
the
P
APR,
for
a
bandwidth
of
30
MHz.
W
e
can
see
that
the
application
of
TR
and
TRCL
method
lead
to
a
spectrum
broadening
of
the
signal,
this
is
due
to
the
use
of
the
64
free
sub-carriers
of
the
standard.
It
is
v
erified
on
the
spectra
input
and
output
of
the
amplifier
.
In
addit
ion,
at
the
output
of
the
amplifier
,
we
can
see
the
spectral
ascents
in
t
he
bands
due
to
nonlinear
ef
fects.
Ho
we
v
er
,
these
spectral
lifts
stay
belo
w
the
IEEE
802
:
16
standard
mask.
−30
−20
−10
0
10
20
30
−80
−70
−60
−50
−40
−30
−20
−10
0
frequency, MHz
power spectral density
Transmit spectrum OFDM (based on 802.16e)
Original
with TR
with CL
with TRCL
mask
Figure
11.
T
ransmit
spectrum
OFDM
based
on
802.16e
with
amplifier
IJECE
V
ol.
8,
No.
6,
December
2018
:
5215
–
5226
Evaluation Warning : The document was created with Spire.PDF for Python.