Int.
J.
Electron.
Commun.
(AEÜ)
70
(2016)
204–209
Contents
lists
available
at
ScienceDirect
International
Journal
of
Electronics
and
Communications
(AEÜ)
j
ourna
l
h
omepage:
www.elsevier.com/locate/aeue
SHORT
COMMUNICATION
Overlapping
coalition
formation
games
based
interference
coordination
for
D2D
underlaying
LTE-A
networks
Shaoyi
Xu
a,∗
,
Chunmei
Xia
a
,
Kyung
Sup
Kwak
b
a
School
of
Electronics
and
Information
Engineering,
Beijing
Jiaotong
University,
Beijing
100044,
China
b
UWB-ITRC,
Inha
University,
Republic
of
Korea
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
29
April
2015
Accepted
19
October
2015
Keywords:
Device-to-device
(D2D)
LTE-Advanced
(LTE-A)
Overlapping
coalition
formation
game
(OCFG)
Interference
coordination
Resource
sharing
a
b
s
t
r
a
c
t
In
the
device-to-device
(D2D)
underlaying
LTE-Advanced
(LTE-A)
systems,
unlike
the
existing
works
which
formulate
the
resources
sharing
problem
as
a
disjoint
coalition
formation
game,
in
this
letter
we
propose
a
novel
overlapping
coalition
formation
game
(OCFG)
based
scheme
to
coordinate
the
interfer-
ence
between
these
two
subsystems.
By
sharing
uplink
spectrums,
in
this
game
each
D2D
pair
is
allowed
to
join
multiple
coalitions
simultaneously
to
improve
the
spectral
efficiency
and
maximize
the
system
utility.
The
merge-and-split
rule
is
designed
to
adapt
to
the
dynamic
environment
and
a
discrete-time
Markov
chain
based
analysis
is
utilized
to
present
the
stability.
Compared
with
traditional
methods,
sim-
ulations
demonstrate
the
significant
performance
enhancement
of
the
proposed
algorithm
in
terms
of
the
complexity
and
D2D
system
sum
throughput.
©
2015
Elsevier
GmbH.
All
rights
reserved.
1.
Introduction
To
adapt
to
the
explosive
upsurge
of
mobile
services
and
user
demands,
3GPP
provided
some
technologies
to
improve
the
spectral
efficiency
and
increase
system
capacity
for
coming
LTE-
Advanced
(LTE-A)
systems.
Among
them,
device-to-device
(D2D)
which
utilizes
physical
proximity
to
enable
high
date
rates,
low
power
consumption
and
delay
is
one
of
the
key
components
and
receives
much
attention
recently.
However,
sharing
uplink
(UL)
or
downlink
resources
with
cellular
networks,
D2D
users
impose
interference
to
the
cellular
devices
and
suffer
interference
from
them
as
well.
Most
existing
work
focused
on
the
scenarios
of
a
single
D2D
pair
sharing
spectrums
with
only
one
cellular
user
equipment
(CUE)
and
proposed
centralized
methods
by
allowing
the
evolved
NodeB
(eNB)
to
coordinate
such
interference
such
as
power
control
[1],
spectrums
allocation
[2],
transmission
modes
selection
[3],
spatial
multiplexing
[4]
or
interference
alignment
[5].
Although
distributed
methods
are
investigated
in
[3,6,7],
the
inter-
ference
problem
is
formulated
as
a
noncooperative
game
in
[7]
by
considering
co-channel
interference
between
a
CUE
and
a
D2D
pair.
In
[3,6],
resources
are
assigned
by
using
a
cooperative
coalition
for-
mation
game,
however,
authors
assume
that
the
finally
formatted
coalitions
are
disjoint
which
means
that
one
D2D
pair
only
partic-
ipates
in
one
coalition
at
most.
∗
Corresponding
author.
Tel.:
+86
10
51684628.
E-mail
address:
shyxu@bjtu.edu.cn
(S.
Xu).
From
the
practical
perspective,
it
is
a
more
general
scenario
to
consider
multiple
D2D
pairs
and
CUEs
by
allowing
D2D
pairs
to
autonomously
decide
which
coalitions
they
can
join
in
order
to
maximize
the
system
utility.
As
a
result,
the
final
coalitions
are
not
disjoint
and
a
D2D
pair
may
belong
to
several
coalitions
simul-
taneously
to
further
improve
the
spectral
efficiency
and
enable
higher
flexibility
by
cooperation.
Fig.
1
illustrates
the
basic
concept
of
overlapping
and
non-overlapping
coalitions.
In
this
context,
different
from
prior
works,
we
address
the
interference
coordination
by
introducing
a
cooperative
overlapping
coalition
formation
game
(OCFG)
when
UL
spectrums
are
reused.
In
this
game,
a
single
D2D
pair
is
allowed
to
join
multiple
coali-
tions
and
to
cooperate
with
other
D2D
user
equipments
(DUEs)
within
the
same
coalition
to
maximize
the
system
utilities
in
terms
of
the
D2D
system
sum
throughput
meantime
guaranteeing
cellu-
lar
users’
quality
of
service
(QoS).
The
proposed
distributed
OCFG
makes
the
eNB’s
involvement
unnecessary
and
it
has
lower
compu-
tation
complexity
compared
with
the
exhaustive
search
method.
Specifically,
the
proposed
scheme
only
requires
partial
channel
state
information
(CSI)
which
further
decreases
the
system
real-
ization
complexity.
We
analyze
the
properties
of
the
developed
algorithm
and
show
the
stability
of
the
finally
formatted
overlap-
ping
coalition
structure.
Simulations
demonstrate
the
effectiveness
of
our
proposed
scheme
compared
with
the
existing
methods.
2.
System
model
and
problem
formulation
Consider
a
single-cell
scenario
where
there
exist
M
CUEs
and
N
D2D
pairs
to
reuse
L
UL
subchannels
with
L
≥
M.
The
sets
of
http://dx.doi.org/10.1016/j.aeue.2015.10.007
1434-8411/©
2015
Elsevier
GmbH.
All
rights
reserved.
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