Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
9,
No.
3,
June
2019,
pp.
2057
2063
ISSN:
2088-8708,
DOI:
10.11591/ijece.v9i3.pp2057-2063
r
2057
Equity-based
fr
ee
channels
assignment
f
or
secondary
users
in
a
cogniti
v
e
radio
netw
ork
Said
Lakhal
1
,
Zouhair
Guennoun
2
1
Mohammadia
School
of
Engineering,
Mohammed
5
Uni
v
ersity
in
Rabat,
Morocco
2
ERSC
formerly
kno
wn
as
LEC,
research
Center
E3S,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
May
31,
2018
Re
vised
No
v
15,
2018
Accepted
No
v
23,
2018
K
eyw
ords:
Cogniti
v
e
radio
netw
ork
Jain’s
equity
inde
x
Scheduler
Channels
allocation
ABSTRA
CT
The
present
paper
addresses
the
equity
issue
among
the
secondary
users
in
a
cogniti
v
e
radio
netw
ork.
After
using
a
multi
scheduler
algorithm
and
a
f
airness
metric
namely
Jain’
s
Equity
Inde
x;
we
enhance
the
equity
between
the
secondary
users’
transfer
rates
by
0.64
in
a
v
erage,
relati
v
e
to
a
pre
vious
w
ork.
Copyright
c
2019
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Said
Lakhal,
Mohammadia
School
of
Engineering,
Mohammed
5
Uni
v
ersity
in
Rabat,
ERSC
formerly
kno
wn
as
LEC,
research
Center
E3S,
Mohammadia
School
of
Engineering,
Ibn
Sina
A
v
enue,
B.P
765,
Agdal,
Rabat,
Morocco.
Email:
said.lakhal.rech@gmail.com
1.
INTR
ODUCTION
In
a
cogniti
v
e
radio
netw
ork
(CRN)
[1],
the
primary
users
(PUs)
ha
v
e
priority
to
use
the
s
pectra,
without
pri
v
atization;
while
the
secondary
users
(SUs),
w
ait
the
cessation
of
acti
vities
of
some
PUs,
for
trans-
mitting
data.
The
design
of
CRN
e
x
ecutes
four
functions,
by
using
one
of
four
techniques,
in
the
aims
to
reach
at
some
objecti
v
es.
These
functions
are
called
in
the
follo
wing
order
[2,
3,
4]:
spectrum
sensing,
spectrum
management,
spectrum
mobility
and
spectrum
sharing
[5,
6,
7].
The
Auctions,
Game
theory
,
Mark
o
vian
queu-
ing
model
and
Multi-agent
systems
(MAS)
represent
the
f
amous
used
techniques
for
modeling
a
CRN
[8,
9],
all
to
achie
v
e
some
objecti
v
es,
characterizing
the
performance
of
a
CRN.
These
aims
are
e
xpressed
in
terms
of
some
quantities
to
maximize
[10,
11,
12],
such
as:
the
equity
,
transfer
rate
and
the
spectrum
use.
These
requirements
are
also
e
xpressed
in
terms
of
other
quantities
to
minimize,
lik
e:
the
ener
gy
consumption
[13],
to
e
xtend
the
lifetime
of
electrical
de
vices;
the
interference
[14,
15],
to
enhance
the
quality
and
quantity
of
transmission
[8,
9].
The
Figure
1
illustrates
altogether
the
CRN
functions,
techniques,
and
objecti
v
es.
The
SUs’
pack
et
transmission
phase
be
gins
as
soon
as
some
channels
are
released
by
the
PUs.
Each
of
these
SUs
seeks
to
be
the
first
to
transmit.
As
a
result,
conflicts
are
created
and
the
netw
ork
can
be
block
ed,
as
well
as
no
licensed
user
will
be
able
to
send
their
data.
In
front
of
this
situation,
the
installation
of
a
scheduler
becomes
essential,
to
manage
the
channel
allocation
for
dif
ferent
SUs,
based
on
performance
criteria
whose
the
equity
represents
an
important
component.
This
scheduler
must
tak
e
into
consi
deration
the
w
ay
of
pack
et
transmission
and
the
properties
of
the
used
equity
metric.
The
w
ay
is
e
xplicit
by
the
distrib
ution
of
SUs
on
the
free
channels
according
to
the
time
slots,
and
the
properties
of
the
metric
are
four:
population
and
Scale
independence,
boundedness
as
well
as
Continuity
.
The
authors
of
[6,
13]
addressed
the
equity
issues,
based
on
a
metric
measurement.
In
the
tw
o
w
orks,
the
abo
v
e
properties
are
not
mentioned
as
well
as
the
w
ay
of
the
pack
et
forw
arding
w
as
not
clarified.
In
[5],
the
authors
studied
the
equity
by
using
the
JEI
as
a
metric,
which
satisfied
the
four
properties,
b
ut
J
ournal
homepage:
http://iaescor
e
.com/journals/inde
x.php/IJECE
Evaluation Warning : The document was created with Spire.PDF for Python.
2058
r
ISSN:
2088-8708
the
y
did
not
mak
e
a
com
parison
with
another
w
ork
also
the
y
treated
the
groups
of
SUs
rather
than
the
SUs
themselv
es.
In
[7,
16],
the
authors
used
one
channel
transmission.
In
[7],
the
standard
de
viation
is
adopted
as
metric,
which
not
satisfies
the
abo
v
e
four
properties.
In
[16],
the
single
channel
transmission
decreases
the
equity
,
despite
the
consideration
of
the
JEI
as
a
metric.
In
our
present
w
ork,
we
tak
e
adv
antage
of
the
benefits
of
these
w
orks,
and
we
impro
v
e
them
to
remo
v
e
their
limit
ations.
Explicitl
y
,
on
one
hand,
we
implement
the
multi
scheduler
algorithm
in
a
multi
channel
netw
ork,
to
produce
the
scheduling
chain.
On
the
other
hand,
we
use
JEI
as
a
metric,
since
it
satisfies
the
four
properties.
As
a
result,
we
impro
v
e
equity
by
an
a
v
erage
of
0.64
for
pre
vious
w
ork.
Figure
1.
The
functions,
objecti
v
es
and
techniques
of
CRN
The
rest
of
this
paper
is
structured
as
follo
ws:
Section
2
discusses
some
related
w
orks
and
our
contri-
b
utions.
Section
3
e
xposes
our
approach.
W
e
present
the
e
xperimental
results
in
section
4,
and
we
conclude
in
section
5.
2.
SCHEDULING
AND
EQ
UITY
CONCEPT
:
A
LITERA
TURE
REVIEW
2.1.
Scheduling
The
SUs
and
their
pack
ets
appear
randomly
on
the
CRN.
The
y
require
the
installation
of
a
sched-
uler
,
able
to
managing
this
flo
w
.
This
scheduler
can
be
implemented
in
softw
are
or
hardw
are
platform.
It
tar
gets
multiple
purposes,
depending
on
the
priorities
and
constraints.
F
or
e
xample:
the
priorities
can
be
e
xpressed
by
the
maximization
of
throughput
or
equity
,
while
the
constraints
can
be
represented
by
the
netw
ork
infrastructure
and
architecture.
Se
v
eral
pre
vious
w
orks
treated
the
throughput
maximization
problem
[11,
17].
Based
on
constant
input
and
output
rates
of
queues
[11],
the
authors
e
xposed
an
opportunistic
scheduler
to
enhance
the
SUs’
transmission
rates.
By
referring
to
the
first-dif
ference
filt
er
clustering
and
correlation
based
PU
modeling
[17],
the
authors
e
xposed
a
QoS-based
spectrum
coordinator
for
the
CR
user
cohabitation
in
or
-
der
to
achie
v
e
high
throughput
and
f
airness.
In
addition,
the
equity
criterion
between
the
SUs
’
transfer
rates
attracted
much
attention
of
researchers
[13,
18,
5,
7].
So,
by
taking
into
account:
the
current
and
prior
history
of
user
e
xperience,
as
well
as
the
respect
of
QoS
[13],
the
authors
proposed
a
f
airness
approach,
by
using
the
JEI.
Their
aims
are
to
determine
the
optimal
po
wer
and
rate
distrib
ution
choices
for
each
SU,
while
maintaining
the
f
airness
across
all
SUs.
In
other
equity
study
[18],
the
authors
presented
a
resource
allocation
algorithm,
in
order
to
m
aximize
the
f
airness.
The
y
used
a
proportional
f
airness
constraint,
to
assure
that
each
SU
can
achie
v
e
a
required
data
rate,
with
QOS
guarantees.
Certainly
,
the
adopted
architecture
af
fects
the
netw
ork
performance.
In
this
re
g
ard,
we
can
distin-
guish
between
tw
o
major
architectures:
distrib
uted
[19,
20,
21]
and
centralized
[22,
7,
5,
19].
Both
architec-
tures
are
considered
in
[19].
The
authors
proposed
an
incenti
v
e-a
w
are
spectrum
sharing
scheme,
for
taking
in
IJECE,
V
ol.
9,
No.
3,
June
2019
:
2057
–
2063
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
r
2059
the
adv
antages
of
these
tw
o
architectures,
and
o
v
ercoming
their
weaknesses.
The
distrib
uted
aspect
requires
no
central
control
entities,
which
can
independently
be
implemented
within
a
distrib
uted
spectrum
mark
et.
By
cons,
the
centralized
aspect
assigns
the
socially
optimal
contracts
for
all
PUs
and
SUs,
for
attaining
the
eco-
nomic
rob
ustness.
In
[20],
the
authors
proposed
a
distrib
uted
clustering
algorithm
based
on
the
soft-constraint
af
finity
propag
ation
message
passing
model
(DCSCAP).
So,
without
depending
on
predefined
common
control
channel
(CCC),
DCSCAP
relies
on
the
distrib
uted
message
passing
among
the
SUs,
through
their
a
v
ailable
channels,
for
applying
the
algorithm
on
lar
ge
scale
of
netw
orks.
In
a
centralized
architecture,
the
authors
of
[22]
proposed
a
h
ybrid
spectrum
sensing
method,
after
creating
one
of
t
h
e
most
trusted
spectrums
sensing
mechanism.
The
suggested
model
sho
wed
an
impro
v
ement
after
comparison
with
v
arious
spectrum
sensing
methodologies.
Figure
2.
The
operating
of
the
mono-scheduler
and
multi-scheduler
algorithms
2.2.
Principles
of
the
mono
and
multi
scheduler
algorithms
In
[7],
the
authors
implemented
a
first
algorithm,
namely
mono-scheduler,
to
assign
the
only
free
channel
to
dif
ferent
SUs.
This
algorithm
produced
a
Scheduling
String
(
SS
)
and
used
the
standard
de
viation
as
a
metric
for
e
v
aluating
the
f
airness
among
the
groups
of
SUs.
Its
comple
xity
is
of
order
2,
in
terms
of
the
total
number
of
pack
ets.
The
same
authors
proposed
in
[5]
another
algorithm,
as
an
e
xtension
of
the
first,
namely
multi-scheduler
,
with
a
comple
xity
of
order
3.
This
second
v
ersion
impro
v
ed
the
mono-scheduler
in
terms
of
the
number
of
the
free
used
channels.
In
the
same
paper
,
the
y
used
the
SS
,
the
States
matrix
noted
S
,
and
the
JEI
to
af
fect
the
free
channels
to
the
SUs,
based
on
the
equity
measure,
between
the
groups
of
SUs.
Both
[5,
7],
considered
the
f
airness
among
the
groups
of
SUs,
b
ut
not
between
the
SUs
themselv
es.
Because
of
the
importance
of
these
tw
o
algorithms,
i.e.
mono-scheduler
and
multi-scheduler
,
in
the
present
w
ork;
we
propose
to
e
xplain
the
operating
principles.
T
o
do
this,
we
consider
an
e
xample
of
CRN
containing:
(i)
T
w
o
groups
of
SUs:
G
1
and
G
2
,
such
as:
G
1
has
tw
o
SUs:
S
U
11
and
S
U
12
,
each
one
has
three
pack
ets;
while
G
2
has
four
SUs:
S
U
21
,
S
U
22
,
S
U
23
and
S
U
24
;
with
tw
o
pack
ets
for
each
one
as
sho
wn
in
Figure
2;
(ii)
Eight
for
both:
number
of
PUs
and
that
of
channels;
After
the
application
of
the
mono-scheduler
algorithm,
we
obtained:
SS
=
(
G
1
;
1)(
G
2
;
1)(
G
1
;
2)(
G
2
;
1)
.
The
first
component
(
G
1
;
1)
of
SS
signifies
that
G
1
transmits
one
line
of
pack
ets.
This
line
cont
ains
tw
o
pack
ets,
because
G
1
has
tw
o
SUs.
The
second
component
(
G
2
;
1)
indicates
that
after
the
transmission
of
the
first
line
of
G
1
,
G
2
transmits
one
line,
which
contains
four
pack
ets,
since
G
2
has
four
SUs,
and
so
on.
On
the
other
hand,
the
application
of
the
multi-scheduler
algorithm
took
tw
o
ar
guments:
SS
and
S
.
This
last
indicates
the
state
of
each
channel,
during
each
time
slot.
T
o
simplify
the
study
,
we
considered
that,
the
channels
ha
v
e
the
same
capacity
.
In
this
case,
we
were
interested
only
,
in
the
number
of
the
free
channels
during
each
time
slot,
while
all
channels
operated
in
the
same
manner
.
Therefore,
S
becomes
a
ro
w
v
ector
,
containing
in
each
component,
the
number
of
the
free
channels,
during
a
gi
v
en
time
slot.
Then,
for
the
e
xample
illustrated
in
Figure
2,
we
can
write:
S
=
(3
;
2
;
3
;
4
;
3
;
2
;
1
;
5)
T
.
After
applying
the
multi-scheduler
algorithm
for
such
e
xample,
we
c
o
ul
d
distrib
ute
the
pack
ets,
on
the
free
channels,
as
sho
wn
in
Figure
2.
In
[16],
the
authors
treated
the
f
airness
between
the
transfer
rates
of
SUs,
rather
than
that
betwe
en
the
transfer
rates
of
groups
[5,
7].
The
y
are
tw
o
Contrib
utions
of
the
present
paper:
Equity-based
fr
ee
c
hannels
assignment
for
secondary
...
(Said
Lakhal)
Evaluation Warning : The document was created with Spire.PDF for Python.
2060
r
ISSN:
2088-8708
(i)
Application
of
the
multi-scheduler
algorithm
[5],
for
treating
the
SUs’
transfer
rates
rather
than
that
of
groups.
(ii)
Enhancement
of
the
SUs’
f
airness
by
0.65,
relati
v
e
to
[16].
2.3.
Equity
concept
In
this
w
ork,
we
are
interested
in
calculating
the
equity
between
the
transfer
rates
of
the
SUs,
after
the
application
of
a
scheduler
algorithm.
In
the
literature,
se
v
eral
w
orks
ha
v
e
treated
the
f
airness
c
omputation,
i.e.
f
airness
metric,
among
the
components
of
a
v
ector
.
These
w
orks
ha
v
e
also
studied
the
properties
of
this
metric.
Let
x
=
(
x
1
;
:;
x
i
;
:;
x
n
)
T
be
a
v
ector
in
R
n
+
,
with
homogeneous
components
in
terms
of
measurement
unit.
In
[23],
the
authors
distinguished
between
four
properties
of
the
f
airness
metric:
P1,
P2,
P3
and
P4.
P1:
Population
size
independence:
The
inde
x
should
be
applicable
to
an
y
number
of
components
of
x
,
finite
or
infinite.
P2:
Scale
and
metric
independence:
The
metric
should
be
independent
of
the
scale
of
all
components.
P3:
Boundedness:
The
inde
x
should
be
bounded
by
tw
o
finite
v
alues.
P4:
Continuity:
An
y
slight
change
in
this
metric
v
alue,
should
sho
w
a
change
of
at
least
one
component
v
alue.
The
y
proposed
a
ne
w
f
airness
metric
namely
JEI,
which
v
erifies
together
these
four
properties:
J
E
I
(
x
)
=
"
n
X
i
=1
x
i
#
2
"
n
n
X
i
=1
x
2
i
#
1
.
A
v
alue
of
J
E
I
(
x
)
close
to
1
e
xpresses
that
most
of
x
components
are
close
to
their
a
v
erage.
By
cons,
if
the
y
are
dispersed
around
their
a
v
erage,
J
E
I
(
x
)
will
be
close
to
0.
3.
MODELING
THE
EQ
UITY
The
y
are
man
y
parameters,
which
define
the
modeling
of
equity
.
Before
be
ginning
this
formulation,
we
prefer
to
e
xpose
these
parameters
in
T
able
2.
T
able
1.
Symbols
and
Their
Meanings
Symbols
Meanings
m,
n
Number
of
PUs
or
channels,
and
number
of
current
SUs,
resp.
MaxSUs,
q
j
,
MaxP
ack
Max
number
of
SUs,
size
queue
of
S
U
j
,
Max
number
of
pack
ets
in
a
queue,
resp.
P
,
Q
,
e
V
ector
containing
the
size
queue
of
each
SU,
v
ector
defined
based
on
P
,
size
of
Q
,
resp.
g
j
,
G
,
S
if
Number
of
SUs
in
group
G
j
,
v
ector
of
all
g
j
,
state
of
channel
i
during
time
slot
f,
resp.
u
f
,
u
,
s
Number
of
free
channels
during
time
slot
f,
v
ector
of
all
v
alues
of
u
f
,
size
of
u
,
resp.
QG
i
,
t
i
,
r
i
Number
of
pack
ets
of
G
i
,
time
for
sending
all
pack
ets
of
G
i
,
transfer
rate
of
G
i
,
resp.
t
ij
,
r
ij
T
ime
spent
to
transmit
all
pack
ets
of
S
U
ij
,
transfer
rate
of
S
U
ij
,
resp.
P
=
(
q
1
;
:;
q
j
;
:;
q
n
)
T
(1)
W
e
note
that
during
a
time
fraction,
a
SU
may
send
one
pack
et
or
not.
W
e
or
g
anize
the
SUs
by
groups
[7],
according
to
the
number
of
pack
ets;
such
as,
a
gi
v
en
group,
contains
all
SUs
who
ha
v
e
the
same
number
of
pack
ets.
T
o
do
this,
we
define
a
ne
w
v
ector
Q
based
on
v
ector
P
:
Q
=
(
q
1
;
:;
q
j
;
:;
q
e
)
T
;
q
i
6
=
q
j
;
8
(
i
6
=
j
;
j
)
2
f
1
;
:;
e
g
2
;
(
e
n
)
;
G
=
(
g
1
;
:;
g
j
;
:;
g
e
)
T
(2)
W
e
ha
v
e
m
channels,
and
during
each
time
slot,
we
can
find
a
certain
number
of
free
channels.
Lik
e
that,
the
state
of
the
CRN
is
defined
by
the
states
of
all
channels.
These
states
are
or
g
anized
in
the
matrix
S
:
S
if
=
8
>
<
>
:
1
if
channel
i
is
free
;
during
time
slot
f
;
0
if
not
:
(3)
The
number
of
free
channels
during
a
time
slot
is
stored
in
v
ector:
u
=
(
u
1
;
:;
u
f
;
:;
u
s
)
T
(4)
IJECE,
V
ol.
9,
No.
3,
June
2019
:
2057
–
2063
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
r
2061
During
the
time
slot
f,
we
ha
v
e
u
f
free
channels:
u
f
=
m
X
i
=1
S
if
;
f
2
f
1
;
:;
s
g
(5)
The
total
number
of
pack
ets
of
the
group
G
i
in
noted
QG
i
.
It
is
obtained
by
summing
the
number
of
pack
ets
of
all
SUs
form
group
G
i
.
By
using
(2),
we
can
write:
QG
i
=
q
i
g
i
(6)
T
o
calculate
the
transfer
rates
of
groups
and
those
of
SUs,
we
must
kno
w
the
necessary
number
of
passing
time
slots,
for
sending
all
pack
ets.
Let
t
i
and
r
i
be
the
necessary
number
of
passing
time
slots
for
sending
all
pack
ets
and
the
transfer
rate
of
G
i
,
resp.
r
i
=
QG
i
t
1
i
=
(
q
i
g
i
)
t
1
i
(7)
Let
S
U
ij
be
the
j
th
SU
of
G
i
.
W
e
consider
that
S
U
ij
needs
t
ij
time
slots,
for
sending
all
his
pack
ets.
So,
the
transfer
rate
r
ij
of
S
U
ij
,
will
be
gi
v
en
by:
r
ij
=
q
i
t
1
ij
(8)
Since
S
U
ij
is
a
member
of
G
i
.
Then,
this
last
completes
the
transmission
of
his
pack
ets,
only
after
the
trans-
mission
of
all
pack
ets
of
his
SUs.
Thus,
we
ha
v
e
the
follo
wing
inequality:
t
i
(
g
i
1)
t
ij
t
i
;
8
j
2
f
1
;
:;
g
i
g
(9)
Let
r
and
r
be
the
v
ectors
containing
all
transfer
rates,
of
all
groups
and
SUs,
respecti
v
ely
.
r
=
(
r
1
;
:;
r
i
;
:;
r
e
)
T
;
r
=
(
r
11
;
:;
r
1
g
1
;
:
;
r
i
1
;
:;
r
ig
i
;
:
;
r
e
1
;
:;
r
eg
e
)
T
(10)
J
E
I
(
q
)
=
"
n
X
i
=1
q
i
#
2
"
n
n
X
i
=1
q
2
i
#
1
;
J
E
I
(
QG
)
=
"
e
X
i
=1
QG
i
#
2
"
e
e
X
i
=1
QG
2
i
#
1
(11)
J
E
I
(
r
)
=
"
e
X
i
=1
r
i
#
2
"
e
e
X
i
=1
r
2
i
#
1
;
J
E
I
(
r
)
=
"
e
X
i
=1
g
i
X
k
=1
r
ik
#
2
"
n
e
X
i
=1
g
i
X
k
=1
r
ik
2
#
1
:
(12)
4.
EXPERIMENT
A
TIONS
W
e
consider
four
scenarios,
containing
tw
o,
three,
four
and
fi
v
e
groups
of
SUs,
respecti
v
ely
.
After
,
we
apply
the
mono
and
multi-scheduler
algorithms.
As
a
result,
we
deduct
the
JEI
of
the
users’
rates,
which
are
e
xposed
in
Figures
3
and
4.
In
all
the
Figures,
we
can
easily
notice
that
the
equities
obtained
by
using
our
model
are
v
ery
important
compared
to
those
of
the
model
[16].
On
a
v
erage,
this
dif
ference
reaches
0.64,
which
is
e
xplained
by
the
parallel
transmission
of
se
v
eral
pack
ets
via
se
v
eral
channels
in
our
model.
As
a
result,
the
users’
transfer
rates
are
v
ery
close
and
the
equities
are
v
ery
important.
By
cons,
the
model
of
[16]
used
a
single
transmission
channel,
therefore,
the
standard
de
viation
of
the
users’
transfer
rates
is
v
ery
important;
then,
the
equities
are
v
ery
lo
w
.
Figure
3.
Groups’
equities,
obtained
by
using
the
tw
o
models
Equity-based
fr
ee
c
hannels
assignment
for
secondary
...
(Said
Lakhal)
Evaluation Warning : The document was created with Spire.PDF for Python.
2062
r
ISSN:
2088-8708
Figure
4.
SUs’
equities,
obtained
by
using
the
tw
o
models
5.
CONCLUSION
In
this
w
ork,
we
ha
v
e
impro
v
ed
the
equity
of
a
pre
vious
w
ork,
by
using
a
ne
w
model.
The
performance
impro
v
ement
can
be
e
xplained
by
the
increase
of
the
number
of
used
channels
processed
by
the
multi
scheduler
algorithm.
W
ithout
for
getting
the
importa
nce
of
the
monoscheduler
,
which
resides
in
the
establishment
of
the
scheduling
chain.
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9,
No.
3,
June
2019
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2057
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IJECE
ISSN:
2088-8708
r
2063
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BIOGRAPHIES
OF
A
UTHORS
S.
Lakhal
obtained
the
diploma
of
application
engineer
in
computer
sciences
in
1998,
from
the
Uni
v
ersity
Sidi
Mohamed
Ben
Abdelah,
Fes,
Morocco,
M.Sc.
de
gree
in
modelization
in
2006,
from
Moha
mmadia
School
of
Engine
ering.
He
is
currently
a
researcher
at
the
Labora-
tory
of
Electronics
and
T
elecommunications,
Mohammadia
School
of
Engineers
(EMI),
Rabat,
Morocco.
His
current
research
interests
are
Computing,
Radio
cogniti
v
e,
Algorithmic
and
com-
ple
xity
,
Modelization.
Z.
Guennoun
recei
v
ed
his
engineering
de
gree
in
Electronics
and
T
elecommunications
from
the
Electronics
and
Electrical
Montefiore
Institute,
ULG
Lie
ge,
Belgium
in
1987;
his
M.Sc.
de
gree
in
Communication
Systems
from
the
EMI
School
of
Engineering,
Rabat,
Morocco
in
1993;
and
his
PhD
de
gree
from
the
same
school
in
1996.
He
visited
the
Centr
e
for
Communication
Research
(CCR)
in
Bristol
Uni
v
ersity
,
UK,
during
the
period
of
1990-1994
to
prepare
a
split
PhD.
Dur
-
ing
1988-1996
he
w
ork
ed
as
an
Assistant
Lecturer
in
the
EMI
School
of
engineering,
and
from
1996
he
is
w
orking
in
the
same
school
as
a
Professor
Lecturer
.
His
fields
of
interest
are
digital
signal
processing,
error
control
coding,
speech
and
image
processing.
Currently
in
char
ge
of
the
laboratory
of
Electronics
and
T
elecommunications
(LEC)
at
EMI.
IEEE
member
since
1990;
and
member
of
the
Moroccan
IEEE
section
e
x
ecuti
v
e
committee.
Equity-based
fr
ee
c
hannels
assignment
for
secondary
...
(Said
Lakhal)
Evaluation Warning : The document was created with Spire.PDF for Python.