Information Technology Reference
In-Depth Information
Non−Cooperative Spectrum Access
Social Group Utility Maximization
Network Utility Maximization
1.4
1.3
1.2
1.1
1
200
300
400
500
600
Number of Users
Fig. 4.7
Normalized system-wide interference with different number of users
4.6
Summary
In this chapter, we study the SGUM-based database assisted spectrum access. We
show that the SGUM-based spectrum access game is a potential game and thus
always admits a SNE. Then we design a distributed spectrum access algorithm that
can achieve an SNE. We also derive the upper-bound of the performance gap of the
SNE from the NUM solution. Numerical results demonstrate that the performance
gap between the SGUM solution and the NUM solution is at most 15 %.
Appendix
Proof of Theorem
4.1
Suppose that a user
k
changes its channel
a
k
to
a
k
such that the channel selection
profile changes from
a
to
a
. We have that
ʦ
(
a
)
ʦ
1
(
a
)
ʦ
2
(
a
)
−
ʦ
(
a
)
=
−
ʦ
1
(
a
)
+
−
ʦ
2
(
a
)
.
(4.15)
For the part
ʦ
1
, we have that
2
n
=
k
1
2
1
ʦ
1
(
a
)
P
m
d
−
ʱ
P
k
d
−
ʱ
−
ʦ
1
(
a
)
=−
mk
I
{
a
k
=
a
m
}
−
kn
I
{
a
n
=
a
k
}
p
k
p
n
m
∈
N
k
∈
N
1
2
P
m
d
−
ʱ
ˉ
k
−
a
k
+
mk
I
{
a
k
=
a
m
}
p
k
m
∈
N
2
n
1
P
k
d
−
ʱ
ˉ
a
k
.
+
kn
I
{
a
n
=
a
k
}
+
(4.16)
