2005
IEEE
16th
International
Symposium
on
Personal,Indoor
and
Mobile
Radio
Communications
utting
Plane
Optimization
Algorithm
for
Intracell
Link
Adaptation
Problem
Alireza
Babaei(1)
rezababaci aec.,i
st.ac.
Mansoor
Isvand
Yousefil2
tnansoor(
ee..shari
fledL
Bahman
Abolhassani(t)
abolhassania
iust c
ir
Naser
Sadati
sadati caishari
fedu
1 :
College
of
Electrical
Engineering,
Iran
University
of
Science
and
Technology,
Tehran,
Iran,
FAX:
(9821)7454055
2 :
Department
of
Electrical
Engineering,
Sharif
University
of
Technology,
Tehran,
Iran
Abstract
Link
adaptation
of
a
wireless
cellular
network
is
of
much
attention
due
to
the
desire
of
maximizing
both
the
a
erage
lin
throughput
and
coerage
reliability,
which
have
conflicting
effect
on
each
other.
In
this
paper,
the
intracell
lin
adaptation
problem
is
formulated
as
a
nondifferentiable
constrainedoptimization
problem
to
maximize
average
link
throughput
while
guaranteeing
the
best
possible
coverage
reliability.
To
achieve
this,
a
cutting
plane
optimization
algorithm
is
employed.
The
performance
of
our
method:adaptive
modulation/coding
with
power
management
AMCWPM)
using
proposed
algorithm
is
compared
with
that
of
an
adaptive
modulation/coding
AMC)
with
no
power
management.
Simulation
results
show
that
the
performance
ofour
method
improves
bothaverage
link
throughputand
coverage
reliability
by
at
least
10
while
in
each
case
the
other
parameter
i.e.
respectively,
coverage
reliability
and
average
link
throughput
is
hold
as
much
as
that
of
the
M
with
no
powermanagement.
Keywords
Adaptive
modulation/coding,
power
distribution
management,
decomposition
techniques,
nondifferentiable
optimization,
convex
analysis.
I.
INTRODUCTION
Future
wireless
mobile
communication
networks
are
expected
to
provide
extremelyhigh
data
rate
applications,especially
in
the
downlink.
Themain
obstacle
to
satisfying
this
expectation
is
the
mobile
wireless
channels,
which
is
quite
harsh.
mobile
channel
usually
consists
of
multiplepaths
whose
parameters
(attenuations,
timedelays
and
phases)
are
highly
timevariant.
Providing
reliable
communication
links
over
these
channels
necessitates
thatthe
system
is
designed
forthe
worstchannel
conditions,
which
is
resource
wasting.
To
avoid
this,
system
designers
have
to
applyadaptivemethods.
Of
these
methods
is
adaptation
of
the
modulation/coding
with
or
without
power
control
in
the
base
station
transmitter,
basedon
link
conditions.
The
performance
of
adaptive
transmitters
has
been
studied
for
both
singleuser
and
multiuser
environments.
In
[1],
the
Shannon
capacity
of
a
fading
channel
is
obtained
fora
single
user,
in
the
presence
ofchannel
side
information
(CSI)
at
both
thereceiver
and
transmitter.
As
well,
joint
adaptation
of
transmitted
power
and
rate
is
proposed
using
idealcase
of
infinite
number
of
coding
rates.
In
[2],
a
sequel
of
[1],
a
variablerate
variablepower
MQ M
modulation
is
proposed
to
remove
the
impracticality
of
[1].
Moreover,
it
is
shown
that
there
is
a
constant
gap
between
the
Shannon
capacity
and
the
throughput
provided
by
the
method
proposed
in
[2].
References
[3]
and
[4],
considering
multi
user
case,
propose
new
iterative
methods
to
maximize
aggregate
throuighput
of
a
channel,
which
results
in
maximizing
aggregate
throughput
of
the
network.
In
[5],
considering
practical
conditions
such
as
SINRmin,
SINRmax
and
finite
number
of
modulation/coding
rates,
performance
of
different
intracell
link
adaptation
strategies
is
studied.
It
is
shown
that
waterfilling
algorithm
is
optimal
and
provides
the
greatest
amountof
average
link
throughput,
at
the
expense
of
loosing
coverage
reliability
i.e.,
reduction
in
the
number
ofmobiles
that
can
be
supported).
To
compensate
this
coverage
reliability,in[56],
different
link
adaptation
methods
are
analyzed
to
provide
equations
for
the
network
capacity.
As
well,
a
hybrid
of
both
M
and
power
control
is
also
proposedand
its
performance
is
addressed.
Yet,
the
performanceof
optimal
intracelllink
adaptation,
considering
the
practical
constraints,
has
not
been
investigated.
Optimal
intracell
link
adaptation
with
practical
constraints
is
a
hard
optimization
problem.
In
this
paper,
we
propose
a
new
method
(adaptive
modulation/coding
with
powermanagement
AMCWPM))
for
maximization
of
both
the
average
link
throtughput
and
coverage
reliability,
which
have
conflicting
effect
oneach
other.
We
formulate
the
problem
with
practicalconstraints
asa
constrained
nonconvex
nonsmooth
optimization
problem.
A
decomposition
technique
is
used
to
solve
the
srcinal
largescale
problem:
replacing
it
by
a
sequenceof
reduceddimensional
local
problems
that
are
coordinated
by
a
master
program.
A
cutting
planeoptimization
algorithm
is
proposed
to
overcome
the
nonsmoothness
arising
in
the
master
program.
Since
locations
of
mobiles
are
random,
the
constraints
of
the
problem
sometimes
cannot
be
met,
and
therefore
no
feasible
solution
can
be
found.
To
overcome
this,
we
are
obliged
to
relax
some
of
theconstraints
corresponding
to
links
having
sm ll
SINR
values.
Performance average
link
throughput
andcoverage
reliability)
of
the
proposed
method
AMCWPM)
is
9783800729098/05/ 20.00
©2005
IEEE
1
895
2005IEEE
16th
International
Symposium
on
Personal,
Indoor
and
Mobile
Radio
Communications
compared
with
that
of
the
AMC
with
no
power
management,
through
computer
simulations.
The
remainderof
this
paper
is
organized
as
follows.
Section
1I
describes
mathematical
model
of
the
problem.
Section
III
briefly
describes
the
exploited
decomposition
technique
and
thecutting
plane
algorithm.
The
proposed
method
is
evaluated
through
computer
simulations
in
Section
IV,
and
conclusions
are
presented
in
Section
V.
II.
MATHEMATICAL
MODEL
OFPROBLEM
In
this
section,
the
mathematical
model
of
the
problem,
used
forthe
maximizationof
average
link
throughput,
is
presented.
Themodel
of
throughput
is
a
modification
of
Shannon
capacity
for
AWGN
channels.
In
this
direction,the
capacity
is
divided
by
the
bandwidth,
and
a
link
degradation
parameter
a,
where0<a<1,
is
used
in
the
model,
to
consider
any
practical
link
degradation
from
ideal
Shannon
case.
It
is
notable
that
the
model
used
for
throughput
inthis
paper,
is
the
one
employed
in[56].
The
link
throughput
t
is
given
by
t
=
log2
1
or.SINR),
1)
where
SINR
is
the
signal
to
noise
and
interference
ratio.
Optimal
intracelllink
adaptation
problem
is
the
bestdistribution
of
power
among
the
N
downlinks
of
a
specific
cell,
whichmaximizes
the
average
link
throughput
and
meanwhile
satisfies
theconstraints.
It
is
desirable
to
giveservice
to
all
links
ina
cell.
This
requires
that
the
SINR
of
each
link
to
be
larger
than
a
threshold
value.
There
are
K
modulations/coding
rates
available
at
the
transmitter
i.e.
ri,...,rK,
where
rl<r2<..
.<rK).
Each
modulation/coding
rate
r
i
1,2,
,K,
corresponds
to
a
SINR
value
denoted
by
y
i
1,2,
,K.
Moreover,
the
base
station
BS
initially
obtains
a
primary
profile
of
each
link
SINR
i.e.
[SINRk,...,SINRN]),
by
transmitting
an
equal
amount
of
power
i.e.
P/N
in
each
of
N
active
links
and
receiving
a
feedback
from
each
mobile.
The
modulation/coding
ratein
each
link
is
chosen
to
be
r
if
the
measured
SINR
of
the
link
<SINR<
y±i
The
power
distribution
should
result
in
SINR
values
that
lie
in
the
interval
[Yi
7K].
That
is
because,
links
with
SINR
values
less
than
y,
will
be
considered
out
of
service,
and
links
with
SINR
values
more
than
YK
are
just
wasting
power;because
such
links
are
assigned
the
modulation
coding
rate
rK,
no
matter
howmuch
their
SINR
values
are
more
than
YK.
The
base
stationdistributes
its
composite
transmitted
power
P
among
links
such
that
to
maximize
total
downlink
throughput.
For
this
purpose,
as
was
mentioned
in
previousparagraph,
the
base
station
initially
distributes
the
total
transmitted
power
ofP
equally
among
N
active
links
to
obtain
a
profile
ofeach
link
SINR.
Then,
it
changes
the
transmitted
power
assigned
to
link
i
from
P/N
to
P/N)
+xi,
where
xi
is
the
power
variation
according
to
the
measured
SINR
of
link
i.
This
modification,
in
the
transmitted
power,
causes
the
SINR
of
link
i
changes
from
SINRk
to
SINR Il+xiN/P).
The
objective
function
T
i.e.
total
throughput)
to
be
maximized
is
given
by
Max
T
=
E
fIlog2Il+
a.SINRtp
i=
2)
where
0
x<rl
r1
r
x<r2
f x)
=
r2
r2
<
x
<
r3
rKl
rK1
x
rK
r,K
x
2rK
Solution
must
satisfy
the
following
constraints:
N
1)
Zx,=0.
i=1
This
guarantees
that
the
total
transmitted
power
remains
equal
toP.
2 x>
x,
where
x=[xl
x2
...
xN]T
is
the
vector
of
power
corrections
applied
in
each
link,
and
x
=[x*l
x
...
XN]T
is
the
minimum
threshold
for
power
correction
vector
to
assure
that
the
SINR
of
link
i
after
adaptation
remains
above
71,
and
its
i h
l
SINRi
p
element
is
=
S
SINRi
N
3 x<
x,
**
K
SINRi
p
where
x
with
itch
element
as
x
=i
SINR.
N
the
maximum
threshold
for
power
correctionvector
to
guarantee
that
the
SINR,
after
adaptation,
remains
below
YK.
4)
x> e
where
e=[1IlI...,]T.
N
This
constraint
is
to
guarantee
that
thetransmitted
power
from
each
link
is
nonnegative.
The
objectivefunction,
given
by
2),
is
discontinuous
since
function
f
is
discontinuous.
Therefore,
this
is
a
constrained
nonconvex
nonsmooth
optimization
problem,
which
is
hardly
tractable.
Using
a
decomposition
technique,
we
will
split
this
largescale
program
to
a
set
of
simpler
subproblems
coordinated
by
a
master
program.
Then,
we
propose
a
simple
iterative
algorithm
to
solve
the
problem
efficiently.
III.
SOLUTION
METHOD
As
mentioned,
our
optimization
problem
is
a
largescale
problem
with
a
nonsmooth
objective
function.
This
problem
is
quite
difficult
to
be
solved
by
classical
algorithms.
So,other
algorithms
appropriate
for
our
optimization
problem
must
be
employed.
One
of
these
algorithms
is
cutting
plane,
which
is
described
below.
9783800729098/05J 20.00
©2005
IEEE
1
896
2005
IEEE
16th
International
Symposium
on
Personal,Indoor
and
Mobile
RadioCommunications
To
achieve
a
better
solution,
in
the
cutting
plane
algorithm,
a
generalized
concept
of
derivative
for
objectivefunction
is
employed.
Rather
than
using
a
gradient
of
the
objective
function
at
a
given
x,
the
vector
containing
thevariables
that
must
be
found,
a
certain
set
will
be
associated
with
x.
This
set
is
calledthe
generalized
Clarke
sub
differential
at
x,
which
is
defined
as
follows
[7],
af x)
:=
conv{
lim
Vf
x )
Vx ;
Vf
x )
exist
},
where
conv
stands
for
convex
hull.
Each
elementof
x
is
called
a
subgradient.
Forconvex
functions
f
is
minimized
at
i
if
and
only
if
0
e
af x)
[7].
Cutting
plane
based
algorithms
are
first
proposed
by
Kelly
[8],
and
they
are
to
minimize
a
constrained
convex
non
smooth
objective
function.
These
algorithms
rely
on
using
information
from
pastiterations
to
find
a
polyhedral
approximation
of
convex
functions,
and
using
this
approximation
to
find
a
search
direction
for
the
new
iteration.
In
fact,
it
will
transform
the
initial
problem
to
a
set
of
linear
programs
with
a
number
of
affine
constraints,
which
increase
as
the
algorithm
progresses.
Keeping
track
of
past
information
allows
defining
a
model
for
the
objective
function.
Denoting
an
arbitrary
element
of
subdifferential
of
f
at
xi
by
s ,
cutting
plane
method
uses
k
values
off
so
far
obtained,
which
are
given
by
fi
:=
f x ),
s
:=
s xi);
i
=
I.k,
to
construct
the
following
piecewise
linear
model
for
f:
fk
Y)
=
max
{fi+ Yx
s
}
3)
i=il..k
The
minimization
of
the
objective
function
model
Ik
on
a
convex
compact
set
S
to
be
determined
in
advance,
gives
a
new
vector
of
variables
for
iteration
k+1
i.e.,
gives
xk+1
).
A
variant
of
this
algorithm
appropriate
for
our
problem
is
employedwhose
steps
are
given
below.
A.
ProposedAlgorithm
cutting
planes)
Let
tol
.
0
be
a
givenstopping
tolerance
and
let
S
X
0
be
a
compact
convex
set
containing
a
minimum
point
of
f
Choose
x
E
S
and
set
k
=
1
Define
A
STEP
1
Implement
stopping
test):
k
ik
computeda
:=
f x
f
x
).If
6s,
<
tol,
stop.
k
k
I
STEP
2
Find
candidatesearch
direction):findthe
search
direction
d
by
solving
the
following
linear
program
LP)
min
d,r
r.2/+ x
x
)
s
+d
s,
I
k
4)
xk
+dESand
re
RSTEP
3
skipping
Linesearch):
set
tk
=
1.
k+I
k
k
STEP
4
Loop):
define
x
=
X
+tkd
Change
k
to
k+land
go
to
1.
The
key
idea
is
to
incorporate
inequality
constraints
in
the
reference
set
X.
With
this
setting,
our
maximization
problem
changes
to
the
minimization
of
the
opposite
sign
of
the
objectivefunction,
given
by
2),
that
is
N
N
xeMX

jf
log
2
1
+
aSINR
i
aSINR
i
xi
N
s.t.
E
xi
=
O
i=1
where
5)
N
iA
=l
P
SINRmi
SINR
SINRmi
IR
_xE
R
max 
min
)<X<
min

SINR
N
SINRiSINRi
in
this
setting
the
Lagrangianof
3)
has
a
simple
separable
structure[7]
N
p
N
L x,
A)
=
af Iog2
1
SINR,
+
axSINRi
xi
))
+
Z
xi)
6)
i=1
N
i=
with
A
E
R.
According
to
[9],
solving
5)
is
equivalent
to
solving
inf
sup
L x,
A
Interchanging
order
of
inf
and
x
A
sup
under
no
assumptions)
we
have
dualproblem
sup
0 A)
AieR
where
O A)
inf
L x,A)
xeX
7)
8)
is
the
associate
dual
function.
Note
that,
L x,
A),
X
and
thus0 A)
have
separable
structure.
Price
decomposing
technique
is
used
to
solvelargescale
problem
5),
replacing
it
by
N
one
dimensional
local
problems
linked
by
a
master
program,
0 A)f=
n
[ log
ai
+
bi
xi))
+
Axi
J}
9)
Typically,
the
master
program
will
choose
a
multiplier
A
price)
sent
to
the
ocal
solvers.
Once
thesolutions
x
of
9)
are
obtained
for
all
i,
the
master
program
evaluates0 A)
and
computes
a
new
A
using
a
cutting
plane
scheme.Note
that
both
master
and
local
programs
are
nonsmooth.
Each
local
problem
can
be
solved
by
searching
for
all
possible
states
of
function
f,
which
is
veryeasy
to
solve
and
may
be
performed
analytically.
Using
these
local
solutions,
the
value
of
dual
function
o A)
is
found
by
9),
and
according
to
proposition
2.2.2
in
chapter
XIIof
[7],
an
arbitrary
subgradient
is
now
available:

E
9 2
10
i=l
Once
the
value
of
the
dual
function
o A)
and
an
arbitrary
element
of
its
subdifferential
determined,
a
blackbox
optimization
technique
such
as
cutting
plane
methodmaybe
9783800729098/05/ 20.00
©2005
IEEE
1897
2005IEEE
16th
International
Symposium
on
Personal,Indoor
and
Mobile
Radio
Communicationsadopted
to
solvedual
problem
(7)
andcompute
a
new
iterate
k+I.
Thisprice
2k+
is
then
given
to
the
slave(local)
programs
and
this
procedure
is
repeated
until
the
convergence
criterion
is
met.
It
can
be
shown
[7]
that
the
algorithm
converges
linearly
only
if
number
of
affine
functionsdefining
the
model
(3)
goes
toinfinity.
Note
that,
although
our
optimization
problem,
given
by
(5),
is
nonconvex,
after
solving
slave
programs
the
dual
function
in
(8)
would
be
affine
(and
therefore
concave)
in
2,
and
therefore,
using
a
convex
optimizationtechnique
makes
no
problem.
However
the
aforementioned
dual
approach
is
ultimatelysuccessful
if
an
initial
solution
can
be
recovered
from
a
dual
solution
(7).
The
difference
between
optimalobjective
values
in(5)
and
(7)
is
calledthe
duality
gap
and
measures
how
good
the
dualization
scheme
is.
Complete
recovery
corresponds
to
a
zero
duality
gap.
This
occurs
if
and
only
if
(5)
has
convex
data
and
a
constraint
is
satisfied.
In
our
problem,
although
the
duality
gap
is
nonzero,
the
numerical
resolution
of
(7)
generates
a
sequence
{
k
converging
to
2*,
with
subgradients
hopefully
close
to
zero
for
large
k
(see
(10)).
hen
by
(10)
there
will
be
primal
points
xk
:=
x
for
which
s Ak
is
close
to
zero.
Theorem
2.1.1
of
[7]
then
implies
that
those
x
kare
very
good
approximation
of
a
primal
optimum.
A
serious
drawback
of
thecutting
plane
method
is
the
infinite
accumulation
of
affine
function
defining
the
model
3 .
More
precisely,
as
k
grows,
the
LP
(4)
has
more
andmore
constraints
and
many
of
them
are
similar.
So
in
general
the
LP
will
become
extremely
difficult
to
solve.
As
our
formulation
shows,
incorporating
complete
decoupled
constraints
in
thereference
set
X
and
thenpass
them
to
the
local
problems
allows
Lagrangian
(6)
to
be
one
dimensional
inA
.
Inthis
way
LP
(4)exits
vector
notation
and
will
be
very
easy
to
solve
even
manually
so
that
the
aforementioned
tailing
off
effect
will
not
manifest
itself.
IV.
SIMULATION
RESULTS
Inthis
section,
the
performance
of
adaptivemodulation/coding
AMC),
with
no
power
management,
as
well
as
the
performance
of
our
method
with
power
management
AMCWPM),
are
compared
through
computer
simulations.
We
have
considered
a
cellular
hexagonal
system
with
frequency
reuse
of
1.
Fading
effects
are
assumed
to
be
removed
by
a
sufficient
number
of
diversity
branches
at
the
transmitter
or
receiver.
A
distance
dependent
path
loss
model,
using
a
path
loss
exponent
is
employed
for
our
propagationmodel.
The
system
alsosuffers
fromlognormal
shadowing
with
a
standarddeviation
of
10
dB.
The
value
of
link
degradation
parameter
is
set
to
0.398,
which
corresponds
to
4
dB
deviation
from
Shannon
capacity
limit.
The
supported
modulation/coding
rates
along
their
corresponding
SINR
intervals
havebeen
listedin
table
I.
TABLE
I
SUPPORTED
MOD/COD
RATES
AND
THEIR
CORRESPONDING
SINR
INTERVALS
mod/cod
rate
initial
SINR
dB)
final
SINR
dB)
0.375
1.27
2.33
0.75
2.33
6.62
1.5
6.62
12.45
3
12.45
17.35
4.5
17.35
22
6
22
The
transmitted
power
of
the
base
station
is
considered
to
be
100
and
the
number
of
links
in
each
cell
is
set
to
be
100.
It
is
considered
that
the
BS
has
a
primary
profile
of
each
link s
SINR
by
transmitting
an
equal
amount
of
power
i.e.
1W)
in
each
link.
In
order
to
include
the
effect
of
the
randomnessof
users locations,
we
have
averaged
the
parameter
of
interest
over
a
number
of
different
users
locations
in
our
simulations.
We
havefound
the
coverage
reliability
and
average
link
throughput
of
adaptive
modulation/coding
AMC)
through
simulation
and
have
listed
them
in
table
II.
In
this
case,
the
vector
of
power
correction
i.e.
x)
equals
0.
TABLE
II
COVERAGE
RELIABILTY
AND
AVERAGE
LTNK
THROUGHPUT
OF
AMC
n
2.5
3
3.5
4
4.55
Average
link
throughput
0.93
1.33
1.71
2.092.432.74
(bit/s/Hz)
reliability
(0)
45
53 60 66 70 74
Employing
the
primary
profile,
the
BS
uses
the
optimization
method
discussed
in
the
pervious
section,
to
findthe
optimal
vector
x
which
leads
to
maximum
throughput.
Since
locations
of
users
are
random,
the
resulting
SINR
values
may
lead
to
an
empty
feasiblespace.
In
this
case,
someof
the
weak
links
i.e.
links
with
low
SINR
values)should
be
considered
out
of
service
sequentially.
By
doing
this
the
coverage
reliability
reduces
from
ideal
coverage
of
100 .
The
power
of
theselinks
is
allocated
to
the
remaining
active
links,
resulting
to
a
newproblem
withreduced
number
of
dimensions.
In
order
to
compare
the
performance
of
the
M
and
M WPM
for
each
path
loss
exponent
n,
we
set
the
same
coverage
reliabilityfor
both
link
adaptation
methods.
For
this
purpose,
using
table
II,
a
proper
number
of
the
weakest
linksare
considered
out
of
service
to
have
a
coverage
reliability
which
is
at
least
as
good
as
AMC.
Then
our
algorithm
maximizes
the
average
link
throughput
within
the
remaining
links.
Figure
1
illustrates
the
improvement
in
average
link
throughput
of
the
M WPM
over
that
of
the
M
when
the
coverage
reliability
ofboth
is
equal
for
each
n).
As
it
can
be
seen,
the
use
of
power
management
has
led
to
a
significant
improvement
in
the
average
link
throughput,
while
the
coverage
reliability
is
at
least
as
much
asthat
of
the
AMC.
Coverage
reliability
of
M WPM
and
M
with
no
power
control
is
compared
in
Figure
2.
Foreach
path
loss
9783800729098/05/ 20.00
©2005
IEEE
1
898
2005IEEE
16th
International
Symposium
on
Personal,
Indoor
and
Mobile
Radio
Communications
exponent
n,
the
same
average
link
throughput
is
considered
for
both
link
adaptation
methods.
To
provide
the
same
average
link
throughput
for
AMCWPC,
some
of
the
weakest
links
should
be
considered
out
of
service.
It
can
be
seen
that
while
both
of
AMC
and
AMCWPM
provide
the
same
average
link
throughput,
the
coverage
reliability
of
AMCWPM
is
at
least
10%
more
than
that
of
the
AMC
with
no
power
control.
V.
CONCLUSIONS
In
this
paper,
we
formulated
the
intracell
link
adaptation
problem
considering
all
practicallimitations
as
a
nonconvex
nonsmooth
constrainedoptimization
problem.Exploiting
the
problem
structure,
a
price
decomposition
techniquealong
a
cutting
plane
optimization
algorithm
was
used
to
solvetheresulting
problem.Simulation
results
showed
more
than
10%
improvement
in
the
coverage
reliability
and
0.5
bits/S/Hz
improvement
in
the
average
link
throughput
obtained
from
our
proposed
methodcompared
to
those
of
the
AMC
with
no
power
control.IV.
REFERENCES
[1]
A.
J.
Goldsmith
and
P.
Varaiya,
Capacity
of
fading
channelswith
channel
side
information,
IEEE
Trans.
Inform
Theory,
vol.43,
Nov.
1997.
[2]
A.
J.
Goldsmithand
S.
G
Chua,
Variablerate
variablepower
MQAM
for
fading
channels,
IEEE
Trans.
Commun.,
vol.45,
Oct.1997.
[3]
X.
Qiu
andK.
Chawla,
On
the
performance
of
adaptive
modulation
in
cellular
systems,
IEEE
Trans.
Commtin.,
vol.47,June.
1999.
[4]
A.
Babaeiand
B.
Abolhassani,
A
new
iterative
method
forjoint
powerand
modulation
adaptation
in
cellular
systems,
Proceedingsof
WOCN2005,
Dubai,
UAE,
March
2005.
[5]
K.L.
Baum,
T.A.
Kostas,
P.J.
Sartori,
and
B.K.
Classon,
Performance
Characteristics
of
Cellular
Systems
with
Different
Link
Adaptation
Strategies,
IEEE
Trans.
Veh.
Technol,
Vol.
52,
NOV
2003.
[6]
B.
Abolhassani
and
A.
Babaei,
Capacity
enhancement
of
wireless
networks
using
adaptivemodulation/coding,
Proceedingsof
IEEEGCC
2004
Bahrain,
Nov.
2004.
[7]
J.B.
HiriartUrruty
and
C.
Lemarechal,
Convex
Analysis
and
Minimization
Algorithms(volumes
I
and
II
SpringerVerlag,
Berlin,
1993.
[8]
J.E.
Kelly,
The
Cutting
Plane
Method
for
Solving
Convex
Problems,
Journal
of
SIAM,
1960.
[9]
S.Boyd,
L.Vandenbergh,
Convex
Optimization,
Cambridge
universitypress,
2004.
z
;Z
I
C
:3
0
z
Iz
2
Z
a
r
AMCWPM
24
2
_1
2.
,
ot
,3
_____ ______L___S__
_
____
/
,
,,,

X
__
.

.,/
/,,
..
'
,/
,,
_,
_

X



r

1
,/
_____ ______e______I______
PATHLOSS
E
PONENT
n)
Fig.
1.
Average
link
throughput
of
AMC
and
AMCWPM
at
the
same
coverage
reliability
I
AMC
AMCWPM
_I
/
I
_
I
m
lY
co
4
UC
2
e
PATH
LOSS
E
PONENT
n)
Fig.
2.
Coverage
reliability
of
AMC
and
AMCWPM
at
the
same
average
link
throughput
9783800729098/05/ 20.00
©2005
IEEE
^
1899