Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
7,
No.
5,
October
2017,
pp.
2651
–
2660
ISSN:
2088-8708
2651
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
A
P
APR
Reduction
f
or
OFDM
Signals
Based
on
Self-Adapti
v
e
Multipopulation
DE
algorithm
Hocine
Ait-Saadi
1
,
J
ean-Yv
es
Chouinard
2
,
and
Abderrazak
Guessoum
3
1,3
D
´
epartement
de
l’
´
electronique,Uni
v
ersit
´
e
de
Blida1,
Algeria
2
D
´
epartement
de
g
´
enie
´
electrique
et
de
g
´
enie
informatique,
Uni
v
ersit
´
e
La
v
al,
Qu
´
ebec,
Canada
Article
Inf
o
Article
history:
Recei
v
ed:
Mar
6,
2017
Re
vised:
May
30,
2017
Accepted:
Jun
16,
2017
K
eyw
ord:
OFDM
Peak-to-a
v
erage
po
wer
ratio
P
artial
transmit
sequence
Dif
ferential
e
v
olution
algorithm.
ABSTRA
CT
One
of
major
dra
wbacks
of
orthogonal
frequenc
y
di
vision
multiple
xing
(OFDM)
systems
is
the
high
peak-to-a
v
erage
po
wer
ratio
(P
APR).
A
signal
with
high
P
APR
leads
to
nonlinear
distortion
caused
mainly
by
po
wer
amplifiers
in
wireless
transmitters.
P
artial
transmit
se-
quence
(PTS)
is
one
of
the
most
attracti
v
e
methods
to
reduce
the
P
APR
in
OFDM
systems.
It
achie
v
es
consi
derable
P
APR
reduction
without
distortion,
b
ut
it
requires
an
e
xhausti
v
e
search
o
v
er
all
the
combinations
of
the
gi
v
en
phase
f
actors,
which
results
in
a
computational
comple
xity
that
increases
e
xponentially
with
the
number
of
partitions.
F
or
this
optimiza-
tion
problem,
we
propose
in
this
pape
r
a
suboptimal
PTS
method
based
on
the
self-adapti
v
e
multipopulation
dif
ferential
e
v
olution
algorithm
(SAMDE).
The
self
adaptation
of
control
parameters
and
structured
population,
is
able
to
obtain
high
quality
solutions
with
lo
w
com-
putational
cost
by
e
v
olving
each
sub-population
of
indi
viduals
o
v
er
successi
v
e
generations.
Copyright
c
2017
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Hocine
Ait-Saadi
D
´
epartement
de
l’
´
electronique
Uni
v
ersit
´
e
de
Blida1,
Route
de
Soumaa,
BP
270,
Blida
Algeria
(+213)
25
43
38
50
Email:
h
aitsaadi@uni
v-blida.dz
1.
INTR
ODUCTION
Orthogonal
frequenc
y
di
vision
multiple
xing
(OFDM)
is
widely
used
for
high
speed
transmission
technolo-
gies
such
as
WIMAX,
L
TE,
WIFI,
D
AB-T
and
D
VB-T
.
The
OFDM
concept
is
based
on
spreading
the
high
speed
data
to
be
transmitted
o
v
er
a
lar
ge
number
of
subcarriers.
OFDM
is
useful
and
rob
ust
ag
ainst
multipath
f
ading
channels.
Ho
we
v
er
,
the
generation
of
OFDM
signals
typically
induces
lar
ge
en
v
elope
fluctuations,
kno
wn
as
Peak-to-A
v
erage
Po
wer
Ratio
(P
APR).
The
P
APR
is
defined
as
the
ratio
of
the
maximum
instantaneous
po
wer
and
the
a
v
erage
po
wer
of
the
signal
to
analyze.
An
OFDM
signal
with
high
P
APR
transmitted
through
a
nonlinear
de
vice,
such
as
a
high-po
wer
amplifier
(HP
A),
leads
to
in-band
or
out-of-band
signal
distortion
such
as
spectral
re
gro
wth,
intermodulation,
or
con-
stellation
tilting
and
scattering
[1],
[2].
The
P
artial
T
ransmit
Sequences
(PTS)
method
is
one
of
the
most
attracti
v
e
in
reducing
the
P
APR
for
OFDM
systems.
It
is
a
distortionless
scheme
for
P
APR
reduction
in
OFDM
systems
and
it
w
orks
with
an
arbitrary
number
of
subcarriers
and
an
y
modulation
scheme.
The
principle
of
the
PTS
met
hod
is
to
partition
the
input
data
of
N
symbols
into
M
disjoint
subblocks
[3].
The
subcarriers
in
each
subblock
are
weighted
by
a
phase
f
actor
selected
from
a
set
of
W
f
actors
for
that
subblock.
The
phase
f
actors
are
selected
such
that
the
P
APR
of
the
combined
signal
is
minimized.
The
con
v
entional
partial
transmit
sequence
technique
(C-PTS)
has
e
xpo-
nentially
increased
search
comple
xity
.
Man
y
methods
ha
v
e
been
proposed
to
reduce
the
number
of
candidate
signals,
which
means
decreasing
the
number
of
searches
in
the
PTS
scheme
b
ut
wi
th
a
compromise
in
P
APR
reduction
ef
fi-
cienc
y
.
Among
them,
there
are
iterati
v
e
and
simplified
search
methods
such
as,
the
flipping
iterati
v
e
method
(IF-PTS)
proposed
in
[4]
or
a
gradient
descent
search
(GD-PTS)
proposed
in
[5].
Ev
olutionary
algorithms
ha
v
e
been
also
considered
by
man
y
researchers
for
reducing
the
number
of
candi-
date
signals
in
PTS
scheme.
Genetic
algorithms
are
used
for
searching
rotation
f
actors
while
reducing
the
P
APR
in
PTS
scheme
(GA-PTS)
[6].
The
bee
colon
y
optimization
algorithm
(BCO-PTS)
has
been
proposed
in
[7].
In
this
J
ournal
Homepage:
http://iaesjournal.com/online/inde
x.php/IJECE
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
, DOI: 10.11591/ijece.v7i5.pp2651-2660
Evaluation Warning : The document was created with Spire.PDF for Python.
2652
ISSN:
2088-8708
article,
we
propose
a
Self-Adapti
v
e
Multipopulation
Dif
ferential
Ev
olution
(SAMDE)
algorithm
for
searching
the
optimal
phase
f
actors
v
ector
required
in
the
PTS
scheme.
The
population
in
SAMDE
algorithm
is
partitioned
into
small
sub-populations
kno
wn
as
islands
.
In
this
model,
each
sub-population
is
e
v
olving
independently
from
the
oth-
ers.
The
sub-populations
e
xchange
information
between
them
in
a
process
called
migration.
The
dynamic
adaptation
of
control
parameters
and
the
use
of
a
structured
population
pro
vide
a
w
ay
to
increase
the
amount
of
potential
search
mo
v
es.
Simulation
results
demonstrate
that
the
performances
of
the
SAMDE-PTS
method
are
better
in
terms
of
P
APR
reduction
with
lo
wer
numbers
of
candidate
signals
when
compared
to
other
optimization
algorithms.
2.
OFDM
SIGN
AL
AND
P
APR
In
OFDM
systems,
the
in
v
erse
f
ast
F
ourier
transform
(IFFT)
is
used
to
get
the
compl
e
x
en
v
elope
in
discrete
time-domain
x
n
which
is
gi
v
en
by:
x
n
=
1
p
N
N
1
X
k
=0
X
k
e
j
2
k
n
LN
;
n
=
0
;
1
;
:
:
:
;
LN
1
;
(1)
where
N
is
the
number
of
subcarriers,
L
is
the
o
v
ersampling
f
actor
and
X
=
f
X
k
;
k
=
0
;
:
:
:
;
N
1
g
is
a
block
of
N
input
symbols.
Therefore,
the
P
APR
of
transmitted
OFDM
signal
x
n
defined
as
the
ratio
of
the
maximum
po
wer
to
the
a
v
erage
po
wer
,
is
e
xpressed
as
P
APR
=
max
0
n
LN
1
j
x
n
j
2
P
av
(2)
where
P
av
=
E
j
x
n
j
2
is
the
a
v
erage
po
wer
and
E
[
]
denotes
the
e
xpectation
operation.
The
o
v
ersampling
is
done
by
inserting
(
L
1)
N
zeros
before
IFFT
module.
The
o
v
ersampling
f
actor
must
be
(
L
4
)
for
a
good
approximation
of
the
P
APR
of
continuous-time
OFDM
signal
[8].
The
distrib
ution
of
P
APR
can
be
e
xpressed
in
terms
of
complementary
cumulati
v
e
distrib
ution
function
(CCDF),
which
is
also
used
to
e
v
aluate
the
performance
of
P
APR
reduction
in
OFDM
systems.
It
represents
the
probability
that
the
P
APR
of
an
OFDM
symbol
e
xceeds
a
gi
v
en
threshold
P
APR
0
,
which
is
denoted
as
=
CCDF
(
z
0
=
P
APR
0
)
=
Prob
f
P
APR
>
z
0
g
(3)
A
relati
v
ely
accurate
approximation
of
the
CCDF
is
proposed
in
[9],
by
emplo
ying
the
e
xtreme
v
alue
theory
:
CCDF
(
z
0
)
=
1
exp
N
e
z
0
r
3
ln
N
(4)
Thus,
for
a
gi
v
en
probability
and
from
(4)
the
threshold
z
0
could
be
formulated
as
z
0
=
ln
ln(1
)
N
p
3
ln(
N
)
(5)
The
Solid
State
Po
wer
Amplifier
(SSP
A)
is
an
often
used
model
of
the
nonlinear
HP
A.
The
SSP
A
produces
no
phase
distortion
and
the
AM/AM
con
v
ersion
function
is
gi
v
en
by
A
(
j
x
(
t
)
j
)
=
j
x
(
t
)
j
[1
+
(
j
x
(
t
)
j
=
A
0
)
2
p
]
1
=
2
p
(6)
where
is
the
amplification
g
ain,
A
0
=
A
sat
,
A
sat
denotes
the
amplifier
input
s
aturation
and
p
determines
the
smoothness
of
the
transition
from
the
linear
re
gion
to
saturation
re
gion.
The
operating
point
of
the
SSP
A
in
relation-
ship
with
the
nonlinearity
of
the
HP
A
on
a
signal,
depends
on
a
quantity
called
the
input
back-of
f
(IBO),
defined
as
I
B
O
=
10
log
10
A
2
sat
=E
j
x
(
t
)
j
2
in
dB.
An
OFDM
signal
with
high
P
APR,
leads
to
nonlinear
distortions
which
increase
the
BER.
An
HP
A
with
high
IBO
has
a
lar
ge
linear
amplifier
re
gion
with
lo
w
distortion,
b
ut
this
leads
to
a
poor
po
wer
ef
ficienc
y
.
An
HP
A
with
lo
w
back-of
f
v
alues
increases
nonlinear
distortions
as
inter
-modulation,
in-band
distortion
and
out-of-band
radiation.
These
distortions
result
also
in
BER
de
gradation.
T
o
pre
v
ent
the
occurrence
of
such
problems,
a
suboptimal
v
ersion
of
PTS
technique
reducing
the
P
APR
of
the
transmitted
signal,
can
be
en
visaged.
IJECE
V
ol.
7,
No.
5,
October
2017:
2651
–
2660
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
2653
3.
CONVENTION
AL
PTS
AND
OPTIMIZA
TION
PR
OBLEM
In
the
con
v
entional
PTS
(C-PTS)
scheme,
the
input
data
block
X
is
e
v
enly
di
vided
i
nto
M
disjoint
subblocks,
which
are
X
m
=
[
X
m;
0
;
X
m;
1
;
:
:
:
;
X
m;N
1
]
T
,
such
that
X
=
M
X
m
=1
X
m
(7)
with
m
=
1
;
2
;
:
:
:
;
M
.
The
IFFT
output
of
each
subblock
(i.e.,
x
m
=
[
x
m;
0
;
x
m;
1
;
:
:
:
;
x
m;LN
1
]
T
is
mult
iplied
by
a
rotation
f
actor
(
b
m
)
selected
from
a
W
-element
set,
with
b
m
=
e
j
m
,
m
=
1
;
2
;
:
:
:
;
M
,
and
m
2
[0
2
)
.
F
or
W
=
2
,
the
allo
wed
phase
f
actors
b
m
belong
to
t
he
set
f
1
g
,
while
for
W
=
4
the
y
belong
to
the
f
1
;
j
g
set.
Figure
1
sho
ws
the
block
diagram
of
a
OFDM
system
using
the
con
v
enti
on
a
l
PTS
technique.
The
PTS
OFDM
symbol
is
formed
by
adding
the
M
partitions
as
follo
ws
:
x
n
(
b
)
=
M
X
m
=1
b
m
x
m;n
;
n
=
0
;
1
;
:
:
:
;
N
L
1
(8)
where
x
(
b
)
=
[
x
0
(
b
)
;
x
1
(
b
)
;
:
:
:
;
x
N
L
1
(
b
)]
T
.
Assuming
that
W
is
the
number
of
allo
wed
phase
f
actors,
the
deter
-
mination
of
optimal
v
ector
with
the
phase
rotation
f
act
ors
b
opt
=
[
b
1
;
b
2
;
:
:
:
;
b
M
]
T
minimizing
the
P
APR
of
the
PTS
OFDM
signal,
requires
an
e
xhausti
v
e
search
o
v
er
C
=
W
M
1
combinations.
b
opt
=
arg
C
min
c
=1
max
0
n
LN
1
j
x
n
(
b
)
j
2
P
av
(9)
The
optimal
set
of
phase
f
actors
is
sent
to
the
recei
v
er
as
a
side
information
for
correct
decoding
of
the
signal.
It
is
I
F
F
T
I
F
F
T
I
F
F
T
P
h
a
s
e
o
p
t
i
m
i
z
a
t
i
o
n
S
e
r
i
a
l
t
o
p
a
r
a
l
l
e
l
p
a
r
t
i
t
i
o
n
s
u
b
b
l
o
c
k
s
X
1
X
2
X
M
x
1
x
2
x
M
N
L
-
p
o
i
n
t
N
L
-
p
o
i
n
t
N
L
-
p
o
i
n
t
i
n
t
o
s
i
d
e
i
n
f
o
r
m
a
t
i
o
n
´
x
(
b
)
b
1
b
2
b
M
X
Figure
1.
OFDM
signal
generation
using
the
PTS
technique.
possible
to
reduce
the
number
of
samples
required
for
P
APR
calculation
by
using
a
reduced
comple
xity
PTS
scheme
(RC-PTS)
as
proposed
by
[10].
Calculating
the
po
wer
of
x
(
b
)
in
(8)
and
applying
the
Cauch
y-Schw
artz
inequality
j
x
n
(
b
)
j
2
=
M
X
m
=1
b
m
x
m;n
2
M
X
m
=1
j
b
m
j
2
M
X
m
=1
j
x
m;n
j
2
=
M
Q
n
(10)
where
Q
n
=
P
M
m
=1
j
x
m;n
j
2
is
the
sum
of
po
wer
of
the
samples
at
time
n
in
the
M
subblocks.
Suppose
that
N
is
the
minimum
possible
peak
po
wer
among
the
dif
ferent
time-domain
symbols
in
an
OFDM
system
with
N
subcarriers,
then
we
can
write
M
Q
n
max
0
n
LN
1
j
x
n
(
b
)
j
2
N
(11)
and
thus
Q
n
N
M
=
(12)
A
P
APR
Reduction
for
OFDM
Signals
Based
on
Self-Adaptive
...
(Hocine
Ait-Saadi)
Evaluation Warning : The document was created with Spire.PDF for Python.
2654
ISSN:
2088-8708
Based
on
the
abo
v
e
inequality
and
if
N
is
kno
wn,
it
is
possible
to
consider
only
the
samples
with
Q
n
=
N
=
M
for
P
APR
calculation
during
the
e
xhausti
v
e
search
of
optimal
set
of
phase
f
actors
in
PTS
scheme.
In
practice
it
is
not
possible
to
get
the
true
v
alues
of
N
and
,
b
ut
an
estimation
of
this
threshold
for
selecting
samples
can
be
determined
by
using
the
CCDF
function
of
the
peak
po
wer
similar
to
(4).
=
Prob
max
0
n
LN
1
j
x
n
(
b
)
j
2
>
z
0
P
av
(13)
where
is
the
probability
that
the
peak
po
wer
e
xceeds
a
gi
v
en
threshold
N
;
this
threshold
is
obtained
by
using
(5)
as
N
=
z
0
P
av
=
P
av
ln
ln(1
)
N
p
3
ln(
N
)
(14)
The
probability
of
e
v
ent
Q
n
>
is
e
xpressed
as
[10],
p
=
M
P
av
M
1
e
M
P
av
(
M
)
M
1
+
P
av
M
(
M
1)
M
2
+
P
av
M
2
(
M
1)(
M
2)
M
3
+
+
P
av
M
M
1
(
M
1)!
(15)
where
(
)
is
the
g
amma
function.
In
RC-PTS
scheme,
the
a
v
erage
number
of
samples
used
for
P
APR
calculation
is
then
gi
v
en
by
p
L
N
for
each
candidate
signal,
and
therefore
the
computational
comple
xity
is
reduced.
The
comple
xity
reduction
is
more
significant
for
small
v
alues
of
M
(i.e.
M
=
4
).
4.
PR
OPOSED
PTS
SCHEME
B
ASED
ON
DIFFERENTIAL
EV
OLUTION
ALGORITHM
In
this
section,
we
describe
the
self-adapti
v
e
multipopulation
dif
ferential
e
v
olution
algorithm
(SAMDE).
This
algorithm,
based
on
a
multiple
populations
structure
and
self
adaptation
of
control
parameters,
is
used
to
search
the
optimal
phase
rotation
f
actors
v
ector
.
4.1.
Differ
ential
e
v
olution
algorithm
The
dif
ferential
e
v
olution
algorithm
(DE)
is
a
population
based
search
approach
introduced
by
[11]
and
considered
as
an
impro
v
ed
v
ersion
of
the
original
genetic
algorithm
introduced
by
[12].
The
DE
in
v
olv
es
se
v
eral
control
parameters
such
as
mutation
weighting
f
actor
F
,
crosso
v
er
control
parameter
CR
,
population
size
NP
and
fitness
function
to
minimize
f
.
A
population
P
consists
of
NP
parameter
v
ectors
i;G
,
(
i
=
1
;
2
;
:
:
:
;
NP
for
each
generation
G
)
and
each
v
ector
is
called
an
indi
vidual.
The
initial
population
is
chosen
randomly
and
should
co
v
er
the
entire
parameter
space,
whereas
the
ne
w
indi
viduals
are
generated
by
using
the
follo
wing
operators:
1.
Mutation
is
an
important
operator
which
consists
in
adding
a
perturbation
on
the
population.
Basically
during
each
generation
G
,
mutant
indi
vi
duals
v
i;G
+1
are
produced
by
adding
the
weighted
dif
ference
between
tw
o
or
more
population
v
ectors,
resulting
in
a
third
v
ector
.
There
are
se
v
eral
v
ariant
strate
gies
of
DE
[13]:
DE
=
rand
=
2
:
v
i;G
+1
=
r
1
;G
+
F
(
r
2
;G
r
3
;G
+
r
4
;G
r
5
;G
)
(16)
DE
=
b
est
=
1
:
v
i;G
+1
=
best;G
+
F
(
r
1
;G
r
2
;G
)
(17)
DE
=
b
est
=
2
:
v
i;G
+1
=
best;G
+
F
(
r
1
;G
r
2
;G
+
r
3
;G
r
4
;G
)
(18)
DE
=
rand
to
b
est
=
1
:
v
i;G
+1
=
i;G
+
F
(
best;G
i;G
)
+
F
(
r
1
;G
r
2
;G
)
(19)
DE
=
rand
to
b
est
=
2
:
v
i;G
+1
=
i;G
+
F
(
best;G
i;G
)
+
(20)
F
(
r
1
;G
r
2
;G
+
r
3
;G
r
4
;G
)
where
r
1
6
=
r
2
6
=
r
3
6
=
r
4
6
=
r
5
6
=
i
(
2
f
1
;
2
;
:
:
:
;
NP
g
)
are
random
inde
x
es
and
best;G
is
the
best
indi
vidual
in
the
population
at
current
generation
G
.
P
arameter
F
2
[0
;
1]
controls
t
he
amplification
of
the
dif
ference
v
ector
of
the
randomly
chosen
indi
viduals.
2.
Crosso
v
er
is
a
genetic
operator
designed
to
increase
the
di
v
ersity
of
the
population
using
the
follo
wing
scheme:
u
i;G
+1
=
v
i;G
+1
if
r
[0
;
1]
CR
i;G
if
r
[0
;
1]
>
CR
(21)
IJECE
V
ol.
7,
No.
5,
October
2017:
2651
–
2660
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
2655
where
CR
(
CR
2
[0
;
1]
)
is
the
crosso
v
er
probability
or
crosso
v
er
control
parameter
and
r
denotes
a
random
number
.
The
ne
w
trial
indi
viduals
u
i;G
+1
of
the
ne
xt
generation
are
produced
by
e
xchanging
indi
viduals
from
the
pre
vious
generation
population
i;G
with
the
mutated
v
ectors
v
i;G
+1
.
3.
Selection
is
a
DE
operator
applied
to
select
the
fittest
indi
viduals
o
f
the
resulting
of
fspring
u
i;G
+1
for
the
ne
xt
generation
according
to
their
fitness
scores
f
as
e
xpressed
by:
i;G
+1
=
u
i;G
+1
if
f
(
u
i;G
+1
)
<
f
(
i;G
)
i;G
otherwise
(22)
The
control
parameters
of
the
DE
algorithm
F
;
CR
and
NP
are
generally
fix
ed
during
the
whole
optimization
proces
s.
But
with
fix
ed
v
alues,
after
a
number
of
generations,
the
search
is
performed
mainly
in
the
neighborhood
of
the
promising
solutions,
this
reduces
the
e
xploration
of
the
whole
search
space
and
in
v
olv
es
a
sta
gnation
ef
fect.
4.2.
Self-Adapti
v
e
Multipopulation
DE
algorithm
The
main
dra
wback
of
the
cl
assical
DE
algorithm
after
a
number
of
generations
is
its
limited
capability
to
produce
ne
w
promising
solutions
by
e
xploring
correctly
the
decision
space.
Therefore,
the
optimization
process
requires
more
search
mo
v
es
to
find
the
optimal
or
the
suboptimal
solution,
which
is
not
suitable
for
our
objecti
v
es.
T
o
o
v
ercome
the
problem
of
stagnation
and
dynamically
adjust
the
control
parameters
F
and
CR
,
we
adopt
tw
o
approaches.
The
first
one,
is
to
use
a
self-adapti
v
e
v
ersion
of
DE
algorithm
(SADE)
de
v
eloped
by
[14];
the
control
parameters
are
determined
in
accordance
with
the
e
v
aluation
of
the
uniform
random
numbers:
F
i;G
+1
=
F
l
ow
+
F
upp
r
and
1
if
r
and
2
<
1
F
i;G
otherwise
(23)
CR
i;G
+1
=
r
and
3
if
r
and
4
<
2
CR
i;G
otherwise
(24)
where
1
,
2
denote
the
probabilities
to
a
d
j
ust
the
control
parameters
F
and
CR
.
The
numbers
r
and
1
to
r
and
4
are
random
v
alues
in
the
interv
al
[0
;
1]
.
F
or
the
v
alues
F
l
ow
=
0
:
1
and
F
upp
=
0
:
9
,
the
ne
w
parameters
F
and
CR
are
randomly
generated
within
interv
als
[0
:
1
;
1]
and
[0,
1],
respecti
v
ely
.
The
updates
are
obtained
before
the
mutation
is
performed.
The
objecti
v
e
is
to
reach
the
best
solution
with
a
minimum
number
of
searches.
The
second
one,
to
increase
the
population
di
v
ersity
and
to
enhance
the
space
search
e
xploration,
is
to
use
a
structured
population
or
multipopulation
structure.
The
space
problem
is
subdi
vided
into
separated
optimized
sub-spaces.
Man
y
v
ariants
of
the
DE
algorithm
with
a
structured
populations
and
dif
ferent
topologies
ha
v
e
been
proposed
in
literature
[15],
[16].
4.3.
Suboptimal
sear
ch
of
PTS
phase
factors
based
on
the
SAMDE
Algorithm
In
this
section,
a
detailed
description
of
the
SAMDE
algorithm
used
for
searching
the
nearly
optimal
phase
f
actors
v
ector
for
P
APR
reduction
with
PTS
scheme
(SAMDE-PTS),
is
e
xamined.
The
phase
f
actors
search
can
be
considered
as
a
combinatorial
optimization
problem.
The
objecti
v
e
is
to
find
out
the
best
weighting
f
actors
v
ector
b
that
minimizes
the
P
APR
function.
The
fitness
function
is
directly
related
to
the
P
APR
and
is
defined
as:
f
(
b
)
=
max[
j
x
n
(
b
)
j
2
]
E
[
j
x
n
(
b
)
j
2
]
with
0
n
LN
1
subject
to
b
2
e
j
m
M
where
m
2
2
k
W
j
k
=
0
;
1
;
:
:
:
;
W
1
(25)
T
o
reduce
the
samples
required
for
P
APR
calculation
at
this
step,
R-PTS
scheme
is
used.
A
gi
v
en
probability
to
find
the
peak,
and
a
threshold
is
deduced
by
using
(14).
This
threshold
is
used
to
find
the
sample
required
for
P
APR
calculation
by
using
(12),
only
an
a
v
erage
of
p
LN
samples
are
needed
instead
of
LN
samples.
The
first
step
of
SAMDE-PTS
algori
thm
is
to
generate
randomly
an
initial
population
P
of
NP
v
ectors
or
indi
viduals
i;G
and
each
v
ector
contains
M
real
phases
randomly
initialized
with
im
2
[0
;
2
)
.
In
this
w
ork,
the
population
P
is
structured
in
S
sub-populations
of
n
p
indi
viduals.
Each
sub-population
P
j
(
j
2
f
1
;
2
;
:
:
:
;
S
g
),
e
v
olv
es
independently
to
w
ards
a
solution
as
per
the
self-adapti
v
e
DE
algorithm.
The
population
generated
contains
phases
with
real
v
alues,
b
ut
the
phase
f
actors
b
i;m
required
for
fitness
e
v
aluation
in
(25)
being
in
discrete
form,
we
need
to
transform
(or
to
map)
each
ne
w
phase
into
the
set
of
discrete
allo
wed
phases
f
m
g
and
determine
the
corresponding
phase
f
actors
f
b
i;m
g
.
W
e
A
P
APR
Reduction
for
OFDM
Signals
Based
on
Self-Adaptive
...
(Hocine
Ait-Saadi)
Evaluation Warning : The document was created with Spire.PDF for Python.
2656
ISSN:
2088-8708
Algorithm
1
SAMDE-PTS
algorithm
1:
Set
the
OFDM-PTS
scheme
parameters
:
N
,
L
,
M
and
W
.
2:
Set
the
population
size
NP
,
the
initial
mutation
weighting
f
actor
F
i;
1
,
upper
bound
F
upp
and
lo
wer
bound
F
l
ow
,
the
crosso
v
er
control
parameter
CR
i;
1
and
the
maximal
number
of
generations
G
max
and
set
G
=
1
.
3:
Randomly
generate
an
initial
population
P
with
NP
indi
viduals
of
M
real
phases
i;G
and
split
it
into
S
sub-
populations
of
n
p
indi
viduals
4:
while
the
stopping
criterion
G
max
is
not
met
do
5:
f
or
Each
sub-population
P
j
,
j
=
1
;
2
;
:
:
:
;
S
do
6:
f
or
Each
v
ector
i;G
=
[
i;
1
;
i;
2
;
:
:
:
;
i;M
]
,
i
=
1
;
2
;
:
:
:
;
n
p
do
7:
Mutation:
Generate
4
random
inde
x
es
r
1
,
r
2
,
r
3
and
r
4
2
f
1
;
2
;
;
NP
g
and
dif
ferent
from
inde
x
i
.
Generate
a
mutant
v
ector
v
i;G
+1
by
using
the
scheme
DE/rand-to-best/2
gi
v
en
by
(20).
8:
Cr
osso
v
er:
Choose
a
random
number
r
2
[0
;
1]
,
and
generate
the
ne
w
indi
viduals
u
i;G
+1
as
per
(21).
9:
Ev
aluation:
Calculate
the
fitness
function
f
v
alue
for
the
ne
w
indi
viduals
by
using
the
mapping
gi
v
en
by
(26)
and
fitness
calculation
(25).
Memorize
the
best
indi
viduals.
10:
Selection:
Perform
a
selection
of
indi
viduals
according
the
fitness
function
(22).
11:
self
adapting:
Update
the
control
parameters
F
and
CR
using
(23).
12:
end
f
or
13:
if
G
=
i
,
with
i
2
f
;
2
;
:
:
:
G
max
g
then
14:
(P
erf
orm
the
migration
pr
ocess)
:
Send
a
cop
y
of
the
best
indi
viduals
to
the
ne
xt
sub-population
P
j
+1
.
Replace
the
w
orst
indi
viduals
by
the
incoming
ones
from
the
pre
vious
sub-population
P
j
1
.
15:
end
if
16:
end
f
or
17:
T
est:
if
G
=
G
max
,
then
output
the
best
results
and
stop.
Otherwise
increment
G
=
G
+
1
and
return.
18:
end
while
consider
the
case
where
W
=
4
and
the
allo
wed
phases
f
actors
are
f
+1
;
+
j
;
1
;
j
g
.
This
mapping
operation
i
s
performed
only
for
e
v
aluating
the
objecti
v
e
function,
without
o
v
erwriting
the
populations
and
e
xpressed
as:
b
i;m
=
8
>
>
<
>
>
:
1
if
7
=
4
i;m
<
=
4
j
if
=
4
i;m
<
3
=
4
1
if
3
=
4
i;m
<
5
=
4
j
if
5
=
4
i;m
<
7
=
4
(26)
During
one
generation,
for
each
v
ector
of
each
sub-population,
a
self-adapti
v
e
DE
is
emplo
yed
with
mutation,
crosso
v
er
and
selection
operations
to
produce
an
of
fspring
and
to
select
one
of
these
v
ectors
with
the
best
fitness
v
alue.
Updating
the
sub-populations
independently
with
a
migration
process
ensures
a
better
e
xploration
of
the
de-
cision
space.
The
mutation
adopted
for
each
sub-population
is
the
DE/rand-to-best/2
scheme.
Initially
the
control
parameters
are
randomly
generated
for
each
sub-population
and
updated
in
each
generation
using
(23
and
24).
The
multiple
populations
structure
decreases
the
risk
of
stagnation
which
might
occurs
with
the
DE
algorithm
after
a
number
of
generations.
F
or
each
sub-population
P
j
,
a
migration
mechanism
is
performed
e
v
ery
generations,
by
sending
a
cop
y
of
the
best
indi
viduals
to
the
ne
xt
sub-population,
where
2
N
is
called
the
migration
interv
al
and
2
N
represents
the
migration
rate
defined
as
the
number
of
indi
viduals
which
migrate
between
sub-populations.
At
the
same
time,
each
sub-population
recei
v
es
the
best
indi
v
i
duals
from
the
pre
vious
sub-population
which
will
replace
the
same
number
of
the
w
orst
indi
viduals,
e
v
en
if
the
y
are
not
better
.
This
mechanism
adds
ne
w
search
mo
v
es
and
enhances
the
algorithm
performance.
The
proposed
SAMDE
algorithm
can
be
summarized
in
Algorithm
1
and
a
flo
w
chart
is
gi
v
en
by
Figure
2
with
4
sub-populations
and
unidirectional
topology
ring.
4.4.
Complexity
analysis
The
C-PTS
method
re
qu
i
res
a
high
comple
xity
search
by
trying
C
=
W
M
1
candidate
signals
to
find
the
optimum
set
of
phase
f
actors.
The
computational
comple
xity
is
(
LN
M
C
+
LN
C
)
comple
x
multiplications
and
(2
LN
C
(
M
1)
+
LN
C
1)
real
additions.
The
amount
of
P
APR
reduction
increases
with
the
number
of
subblocks
M
and
the
number
of
allo
wed
phase
f
actors
W
,
b
ut
at
the
cost
of
high
computational
comple
xity
.
F
or
R-PTS
scheme
[10],
the
a
v
erage
number
of
samples
required
for
P
APR
calculation
is
reduced
to
p
LN
,
such
that
the
comple
xity
is
around
(
LN
M
+
p
(
LN
M
+
LN
)
C
)
comple
x
multiplications
and
(3
LN
M
+
p
(2
LN
M
LN
)
C
2
LN
)
IJECE
V
ol.
7,
No.
5,
October
2017:
2651
–
2660
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
2657
N
o
G
=
G
m
a
x
s
u
b
-
p
o
p
u
l
a
t
i
o
n
Y
e
s
F
i
,
CR
i
s
u
b
-
p
o
p
u
l
a
t
i
o
n
1
2
i
n
d
i
v
i
d
u
a
l
s
f
r
o
m
N
o
G
=
G
m
a
x
s
u
b
-
p
o
p
u
l
a
t
i
o
n
M
u
t
a
t
i
o
n
S
e
l
e
c
t
i
o
n
C
r
o
s
s
o
v
e
r
M
i
g
r
a
t
i
o
n
Y
e
s
F
i
,
CR
i
γ
,
ρ
3
i
n
d
i
v
i
d
u
a
l
s
f
r
o
m
N
o
G
=
G
m
a
x
s
u
b
-
p
o
p
u
l
a
t
i
o
n
Y
e
s
F
i
,
CR
i
3
4
i
n
d
i
v
i
d
u
a
l
s
f
r
o
m
N
o
G
=
G
m
a
x
s
u
b
-
p
o
p
u
l
a
t
i
o
n
Y
e
s
s
u
b
-
p
o
p
u
l
a
t
i
o
n
4
1
i
n
d
i
v
i
d
u
a
l
s
f
r
o
m
O
ut
put
t
he
b
e
s
t
re
s
ult
s
b
b
e
s
t
2
s
u
b
-
p
o
p
u
l
a
t
i
o
n
s
u
b
-
p
o
p
u
l
a
t
i
o
n
F
i
t
n
e
s
s
e
v
a
l
u
a
t
i
o
n
F
i
,
CR
i
S
e
l
e
c
t
i
o
n
M
i
g
r
a
t
i
o
n
γ
,
ρ
M
u
t
a
t
i
o
n
C
r
o
s
s
o
v
e
r
F
i
t
n
e
s
s
e
v
a
l
u
a
t
i
o
n
S
e
l
e
c
t
i
o
n
M
i
g
r
a
t
i
o
n
γ
,
ρ
M
u
t
a
t
i
o
n
C
r
o
s
s
o
v
e
r
F
i
t
n
e
s
s
e
v
a
l
u
a
t
i
o
n
S
e
l
e
c
t
i
o
n
M
i
g
r
a
t
i
o
n
γ
,
ρ
M
u
t
a
t
i
o
n
C
r
o
s
s
o
v
e
r
F
i
t
n
e
s
s
e
v
a
l
u
a
t
i
o
n
Figure
2.
Flo
w
chart
of
multipopulation
DE
algorithm
with
4
sub-populations
and
unidirectional
ring
topology
.
real
additions.
F
or
all
suboptimal
PTS
methods
trying
to
reduce
the
candidate
signals,
the
computational
comple
xity
is
proportional
to
the
number
of
phase
f
actors
searches.
F
or
heuristic
methods,
such
as
the
gradient
descent
search
(GD-PTS)
algorithm
used
in
[5],
the
number
of
searches
is
gi
v
en
by
C
r
(
M
1)
W
r
I
,
where
r
is
the
radius
of
the
neighborhood,
I
is
the
number
of
iterations
and
C
k
n
is
the
binomial
coef
ficient
.
W
ith
the
iterati
v
e
flipping
algorithm
for
PTS
(IF-PTS)
[4],
the
search
comple
xity
is
proportional
to
(
M
1)
W
.
F
or
stochastic
methods
based
on
population
search
as
the
proposed
method
(SAMDE-PTS),
the
artificial
bee
colon
y
algorithm
(ABC-PTS)
[7],
the
dif
ferential
e
v
olution
algorithm
(DE-PTS)
considered
in
[17],[18]
and
the
genetic
algorithm
(GA-PTS)
[6],
a
P
APR
calculation
is
needed
at
each
iteration
for
each
candidate,
so
the
number
of
searches
is
gi
v
en
by
the
population
size
times
the
number
of
iterations
(c
ycles
C
or
generations
G
)
NP
I
.
The
computational
comple
xity
of
the
proposed
scheme
is
also
e
v
aluated
by
using
the
CCRR
(computational
comple
xity
reduction
ratio)
defined
as
follo
ws:
C
C
R
R
=
1
complexity
of
proposed
PTS
complexity
of
C-PTS
100%
(27)
5.
SIMULA
TION
RESUL
TS
Extensi
v
e
simulations
ha
v
e
been
conducted
to
v
erify
the
performance
of
the
SAMDE-PTS
scheme
for
searching
the
optimal
combination
of
phase
f
actors.
An
OFDM
system
with
16-QAM
modulation
and
N
=
1024
subcarriers
with
an
o
v
ersampling
rate
of
L
=
4
is
simulated.
T
o
generate
the
CCDF
of
P
APR,
10
4
random
OFDM
symbols
are
used.
F
or
P
APR
reduction
technique
with
PTS
scheme,
the
allo
wed
rotation
phase
f
actors
are
described
in
section
3.
2
3
4
5
6
7
8
9
10
11
12
10
−3
10
−2
10
−1
10
0
PAPR
0
dB
Prob(PAPR > PAPR
0
)
Original OFDM
SAMDE−PTS
C−PTS
1600
searches
W=4
M=4
32
searches
W=2
M=16
W=4
M=8
Figure
3.
CCDF’
s
of
original
OFDM,
con
v
entional
PTS
and
the
proposed
SAMDE-PTS
method
7
7.2
7.4
7.6
7.8
8
8.2
8.4
8.6
8.8
9
9.2
9.4
9.6
10
−3
10
−2
10
−1
10
0
PAPR
0
Prob(PAPR > PAPR0)
Original OFDM
IF−PTS.
GD−PTS,r=1, I=3
GD−PTS,r=2, I=2
GA−PTS
DE−PTS
BCO−PTS
SAMDE−PTS
C−PTS
R−PTS
ζ
=0.99, p
α
ζ
= 0.6880
Figure
4.
CCDF’
s
comparison
of
P
APR
reduction
with
con
v
entional
PTS,
SAMDE-PTS
and
some
other
heuristic
and
meta-heuristic
methods
Figure
3
sho
ws
the
CCDF
curv
es
of
the
original
OFDM
signal
(without
an
y
P
APR
reduction
method),
the
A
P
APR
Reduction
for
OFDM
Signals
Based
on
Self-Adaptive
...
(Hocine
Ait-Saadi)
Evaluation Warning : The document was created with Spire.PDF for Python.
2658
ISSN:
2088-8708
T
able
1.
Search
cost
of
the
dif
ferent
methods
and
the
P
APR
v
alues
when
CCDF
=
10
3
.
Method
Number
of
searches
CCRR
%
P
APR
dB
C-PTS
C
=
W
M
1
=
16384
0
8.00
R-PTS
(
=
0
:
99
,
p
=
0
:
68
)
[10]
C
=
16384
31.1
8.0
R-PTS
(
=
0
:
4
,
p
=
0
:
3735
)
[10]
C
=
16384
62.64
8.0
SAMDE-PTS
(
=
0
:
99
,
p
=
0
:
68
)
S
n
p
G
=
1600
93.27
8.137
SAMDE-PTS
(
=
0
:
4
,
p
=
0
:
3735
)
S
n
p
G
=
1600
96.34
8.156
SAMDE-PTS
S
n
p
G
=
1600
90.23
8.12
BCO-PTS
[7]
NP
C
=
1600
90.23
8.17
DE-PTS
[17,
18]
NP
G
=
1600
90.23
8.20
GA-PTS
[6]
NP
G
=
1600
90.23
8.27
GD-PTS(
r
=
2
;
I
=
2
)
[5]
C
2
7
W
2
2
=
672
95.89
8.41
GD-PTS(
r
=
1
;
I
=
3
)
[5]
C
1
7
W
1
3
=
84
99.48
8.84
IF-PTS
[4]
(
M
1)
W
=
28
99.82
9.35
OFDM
only
0
-
11.7
P
APR
reduction
is
achie
v
ed
by
using
the
con
v
entional
PTS
(C-PTS)
and
the
proposed
SAMDE-PTS
method.
The
C-
PTS
method
requires
C
=
W
M
1
candidate
signals.
This
corresponds
to
64
,
16384
and
32768
searches
for
(
W
;
M
)
gi
v
en
by
(4,4),
(4,8)
and
(2,16),
respecti
v
ely
.
The
P
APR
reduction
is
enhanced
by
increasing
M
,
b
ut
at
the
e
xpense
of
an
e
xponential
increase
in
the
search
computational
comple
xity
.
F
or
the
proposed
SAMDE-PTS
method
and
for
(
M
=
8
or
16
,
S
=
4
,
n
p
=
10
,
NP
=
40
,
=
1
,
=
10
),
dif
ferent
v
alues
of
F
and
CR
are
initially
assigned
to
each
subpopulation
after
a
fe
w
generations,
self
adaptation
is
performed
with
a
search
cost
of
1600
.
Whereas,
for
(
M
=
4
,
S
=
2
,
np
=
4
,
G
=
4
)
the
total
search
cost
is
32
.
F
or
almost
the
same
P
APR
reduction
performance,
the
computational
comple
xity
has
been
considerably
reduced
with
CCRR’
s
=
95
:
11%
,
90
:
24%
and
50%
for
M
=
16
,
8
and
2
respecti
v
ely
.
Figure
4
sho
ws
the
dif
ferent
CCDF
simulated
curv
es
of
the
P
APR
with
a
v
ariety
of
heuristic
and
meta-
heuristic
methods.
T
able
1
gi
v
es
the
P
APR
at
CCDF
=
10
3
and
lists
the
search
costs
for
(
N
=
1024
,
L
=
4
,
W
=
4
,
M
=
16
).
The
IF-PTS
method
with
only
28
searches
and
CCCR=
99
:
829%
,
presents
the
lo
wer
computational
comple
xity
b
ut
with
considerably
the
w
orst
performance
in
P
APR
reduction.
The
meta-heuristic
methods
gi
v
e
a
better
performance
in
P
APR
reduction
with
the
same
search
comple
xity
,
which
corresponds
to
CCRR=
90
:
24%
.
But,
the
best
performance
is
achie
v
ed
by
the
proposed
SAMDE-PTS
method
with
a
P
APR
equal
to
8
:
125
dB.
It
can
be
seen
that
the
proposed
method
outperforms
all
the
other
methods
in
P
APR
reduction
while
k
eeping
a
lo
w
comple
xity
of
1600
.
7
7.2
7.4
7.6
7.8
8
8.2
8.4
8.6
8.8
9
10
−3
10
−2
10
−1
10
0
PAPR
0
Prob(PAPR > PAPR
0
)
SAMDE−PTS,
ζ
=0.1, p
α
ζ
= 0.205
R−PTS
ζ
=0.1, p
α
ζ
=0.2050
SAMDE−PTS
ζ
=0.4, p
α
ζ
=0.3735
SAMDE−PTS
ζ
=0.99, p
α
ζ
=0.688
SAMDE−PTS
R−PTS
ζ
=0.4, p
α
ζ
=0.3735
R−PTS
ζ
=0.99, p
α
ζ
= 0.6880
C−PTS
Figure
5.
Comparison
of
P
APR
reduction
performance
for
the
C-PTS,
R-PTS
and
the
proposed
method
SAMDE-PTS
based
on
R-PTS
scheme
with
W
=
4
,
M
=
8
.
Figure
5
sho
ws
the
performance
of
the
con
v
entional
PTS
and
R-PTS
scheme
with
e
xhausti
v
e
search
o
v
er
16384
candidate
signals,
and
the
proposed
method
SAMDE-PTS
with
1600
searches.
F
or
the
P
APR
calculation
required
for
each
generation
in
optimization
process,
the
simulations
are
done
by
taking
all
LN
samples,
and
also
by
taking
about
p
LN
samples
and
with
dif
ferent
v
alues
of
.
The
proposed
PTS
scheme
with
(
0
:
40
)
can
achie
v
e
IJECE
V
ol.
7,
No.
5,
October
2017:
2651
–
2660
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
2659
almost
the
same
P
APR
reduction
perform
ance
b
ut
with
lo
wer
computational
comple
xity
reaching
a
CCRR
of
96
:
34%
.
Figure
6
depicts
the
BER
v
ersus
E
b
=
N
0
performance
of
OFDM
signals
o
v
er
the
A
WGN
channel
when
SSP
A
has
been
considered
with
dif
ferent
parameters
p
=
2
and
3
and
operating
at
IBO
=
3
and
6
dB.
The
best
performance
bound
curv
e
is
obtained
with
no
SSP
A;
the
nonlinearity
ef
fects
of
SSP
A
are
ne
glected.
The
SSP
A
with
lo
w
input
back-of
f
v
alue
(
I
B
O
=
3
dB)
increases
the
BER
of
the
system.
The
small
IBO
v
alues
(IBO
=
0,
3,
6
dB)
lead
to
inband
distortion
that
increases
the
BER
of
the
system.
P
arameter
p
controls
the
AM/AM
sharpness
of
the
saturation
re
gion
and
af
fects
the
BER
performance.
The
proposed
SAMDE-PTS
scheme
with
=
0
:
4
;
p
=
0
:
3735
of
fer
an
impro
v
ed
BER
performances
o
v
er
A
WGN
channel
compared
with
the
original
OFDM
system
with
SSP
A,
and
almost
the
same
BER
performance
as
that
obtained
with
the
C-PTS
scheme.
4
6
8
10
12
14
16
18
20
22
24
10
−5
10
−4
10
−3
10
−2
10
−1
E
b
/N
0
(dB)
BER
No
S
S
P
A
O
r
i
g
i
n
a
l
O
F
D
M
S
AM
D
E
-
P
T
S
,
ζ
=
0
.
4
,
p
ζ
α
=
0
.
3
7
3
5
C
-
P
T
S
IBO = 3 dB
IBO = 6 dB
p
=
2
p
=
3
p
=
2
p
=
3
Figure
6.
BER
vs
E
b
=
N
0
performance
of
SAMDE-PTS
and
C-PTS
methods
with
W
=
4
M
=
8
,
o
v
er
an
A
WGN
channel
and
by
using
an
SSP
A
(
p
=
2
and
3
,
IBO
=
3
and
6
dB).
6.
CONCLUSION
In
this
paper
,
we
ha
v
e
proposed
a
ne
w
approach
to
reduce
the
P
APR
in
OFDM
systems
by
using
a
Self-
Adapti
v
e
Multipopulation
Dif
ferential
Ev
olution
P
artial
T
ransmit
Sequence
algorithm
(SAMDE-PTS)
for
search-
ing
the
optimal
combination
of
phase
f
actors
in
PTS
technique.
Simulation
results
ha
v
e
sho
wn
that
the
proposed
method
achie
v
es
almost
the
same
P
APR
reduction
and
the
same
BER
performance
as
that
of
the
con
v
ent
ional
PTS
scheme
while
significantly
reducing
computational
comple
xity
by
10
.
Furthermore,
simulation
results
ha
v
e
sho
wn
that
SAMDE-PTS
method
outperforms
others
heuristic
and
meta-heuristic
methods.
In
f
act,
the
performance
of
the
algorithm
is
enhanced
by
adopting
a
dynamic
adaptation
of
control
parameters
and
a
multipopulation
structur
e.
This
approach
accelerates
con
v
er
gence
and
a
v
oids
stagnation
by
adding
a
ne
w
search
mo
v
es
and
maintaining
the
popula-
tion
di
v
ersity
.
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BIOGRAPHY
OF
A
UTHORS
Hocine
AIT
-SAADI
is
a
lecturer
with
the
department
of
Electronics,
Uni
v
ersit
´
e
de
BLID
A.
His
research
interests
are
focused
on
digit
al
signal
processing,
Bayesian
estimation,
digital
communi-
cation,
multicarrier
systems,
wireless
communic
ation
systems,
metaheuristic
algorithms.
has
re-
cei
v
ed
a
BS
de
gre
e
in
electrical
engineering
from
the
Uni
v
ersit
´
e
de
BLID
A,
Algeria,
in
1998
and
M.Sc
De
gree
in
2001.
He
then
attended
Institut
National
Polytechnique
de
la
lorraine
in
Nanc
y
,
France,
where
he
obtained,
a
M.Sc
in
Communications,
Control
&
signal
processing
in
2002.
In
2010
he
w
as
a
visiting
researcher
at
La
v
al
Uni
v
ersity
LR
TS
laboratory
.
J
ean-Yv
es
Chouinard
is
a
Professor
with
the
Department
of
Electrical
and
Computer
Engineer
-
ing
at
Uni
v
ersit
´
e
La
v
al,
Quebec
city
,
Canada.
His
research
interests
are
wireless
communications,
secure
communication
netw
orks
and
signal
processing
for
radar
applications.
He
is
the
author/co-
author
of
more
than
200
journal,
conference
papers
and
technical
reports.
He
w
as
co-recipient
of
the
1999
Neal
Shepherd
Best
Propag
ation
P
aper
A
w
ard
from
the
IEEE
V
ehicular
Society
and
of
the
2004
Signal
Processing
Best
P
aper
A
w
ard
from
the
European
Journal
of
Signal
Proc
essing.
He
is
an
editor
of
a
book
on
information
theory
and
co-author
of
book
chapters
on
MIMO
wireless
communication
systems
and
on
OFDM-based
mobile
broadcasting.
He
is
an
Editor
for
the
IEEE
T
ransactions
on
V
ehicular
T
echnology
and
Associate
Editor
for
the
IEEE
T
ransactions
on
Broad-
casting.
Abderr
ezak
GUESSOUM
has
recei
v
ed
a
BS
de
gree
i
n
electronics
from
the
Ecole
Nationale
Poly-
technique
d’Alger
,
Algeria,
in
1976.
He
then
attented
Geor
gia
Institute
of
T
echnology
in
Atlanta,
Ga,
USA,
where
he
obtained,
a
PhD
in
electr
ical
engineering,
in
1984.
He
w
ork
ed
as
an
Assistant
Professor
in
the
School
of
Computer
Science
at
Jackson
State
Uni
v
ersity
,
Mississippi,
USA,
from
1984
to
1985.
He
has
been
with
the
Uni
v
ersit
´
e
de
Blida,
Algeria,
as
a
Professor
in
the
department
of
Electronics,
since
1988.
He
is
the
head
of
the
Digital
Signal
and
Image
Processing
Research
Laboratory
.
His
current
research
interests
include
e
mbedded
signal
processing
algorithms,
digital
filter
design,
intelligent
control,
neural
netw
orks,
genetic
algorithms,
and
fuzzy
logic.
IJECE
V
ol.
7,
No.
5,
October
2017:
2651
–
2660
Evaluation Warning : The document was created with Spire.PDF for Python.