Information Technology Reference
In-Depth Information
Fig. 2.1
Illustration of the social group utility maximization (SGUM) framework
2.2
Physical Network Graph Model
We consider a set of wireless users
where
N
is the total number
of users. We denote the set of feasible strategies for each user
n
N
={
1, 2,
...
,
N
}
∈
N
as
X
n
.For
instance, a strategy
x
∈
X
n
can be choosing either a channel or a power level for
wireless transmission. Subject to heterogeneous physical constraints, the strategy
set
X
n
can be a set of feasible
relay users that are in vicinity of user
n
for cooperative communication.
To capture the diverse physical coupling among the users in the physical domain,
we introduce a
physical graph
X
n
can be user-specific. For example, the strategy set
p
p
G
={
N
,
E
}
(see Fig.
2.1
for an example). Here
(
n
,
m
):
e
nm
=
p
the set of users
N
is the vertex set, and
E
≡{
1,
∀
n
,
m
∈
N
}
is the
edge set where
e
nm
1 if and only if users
n
and
m
have physical coupling (e.g.,
cause interference to each other). We also denote the set of users that have physical
coupling with user
n
as
=
n
:
e
nm
=
N
≡{
m
∈
N
1
}
.
∈
n
=
1
X
n
be the strategy profile of all users. Given the
strategy profile
x
, the individual utility function of user
n
is denoted as
u
n
(
x
), which
represents the payoff of user
n
, accounting for the physical coupling among users. For
example,
u
n
(
x
) can be the achieved data rate or the satisfaction of quality of service
(QoS) requirement of user
n
under the strategy profile
x
. Note that in general the
underlying physical graph plays a critical role in determining the individual utility
u
n
(
x
). For example, users' achieved data rates are determined by the interference
graph and channel quality.
Let
x
=
(
x
1
,
...
,
x
N
)
2.3
Social Network Graph Model
To capture the diverse social coupling among the users in the social domain, we
introduce a
social graph
s
s
G
={
N
,
E
}
to model their social ties. Here the edge set
s
(
n
,
m
):
e
nm
=
where
e
nm
=
is given by
E
={
1,
∀
n
,
m
∈
N
}
1 if and only if users
