Information Technology Reference
In-Depth Information
Fig. 3.4
Illustration of the
physical interference model
h
1
g
12
g
21
T
1
R
1
T
2
R
2
h
2
We can see that the SGUM solution for the ER model based social graph always
dominates that of the NCG, with a substantial performance gain up to 22 %. On the
other hand, it performs almost as well as the NUM solution. This demonstrates that
system efficiency can be significantly improved by exploiting social ties. We observe
that the SGUM solution for the real data based social graph is worse than that for the
ER model based social graph due to that social ties are weaker in the real data than in
the ER graph with link probability 0
.
5. However, it still can achieve a performance
gain up to 13 % over that of the NCG solution.
3.3
SGUM-based Power Control
3.3.1
System Model
We consider a set of users under the physical interference model, where each user
i
is a link consisting of a transmitter
T
i
and a receiver
R
i
. The channel gain of
communication link
i
is
h
i
, and the channel gain of the interference link between
transmitter
T
i
and receiver
R
j
is
g
ij
(as illustrated in Fig.
3.4
). The noise at receiver
R
i
is
n
i
. Then the signal tointerference and noise ratio (SINR)
ʳ
i
of link
i
is given by
h
i
p
i
n
i
+
j
=
1
g
ji
p
j
ʳ
i
(
p
i
,
p
i
)
=
−
where
p
i
denotes the transmit power of
T
i
. We assume that the individual utility
u
i
of player
i
is given by
=
−
u
i
(
p
i
,
p
−
i
)
log (
ʳ
j
)
c
i
p
i
where
c
i
denotes the cost of per unit power consumption. Similar to Sect.
3.2
,we
also use the logarithmic function to model the utility of a user. For example, log (
ʳ
i
)
can be a good approximation for the channel capacity log (1
+
ʳ
i
) under the high
SINR regime. Also, log (
ʳ
i
) can be used to quantify the satisfaction of wireless
users' requirements in terms of SINR. Then, under the SGUM framework, we define
the SGUM game for power control as
G
(
N
,
{
p
i
}
,
{
f
i
}
), where
log
h
i
p
i
n
i
+
j
=
i
g
ji
p
j
f
i
(
p
i
,
p
−
i
)
=
−
c
i
p
i
+
