Information Technology Reference
In-Depth Information
1
2
N
mn
I
{
a
n
=
a
m
}
−
I
{
a
n
=
a
m
}
P
m
d
−
ʱ
+
n
=
1
p
n
sp
n
m
∈
N
\
N
N
N
1
2
1
2
s
nm
)
P
m
d
−
ʱ
P
m
d
−
ʱ
≤
(1
−
mn
+
mn
.
sp
n
p
n
sp
n
n
=
1
n
=
1
m
∈
N
m
∈
N
\
N
Theorem
4.4
indicates that the upper-bound of the performance gap
ˁ
decreases as the
strength of social tie
s
nm
among users increases. When
s
nm
=
∈
N
(i.e., all users are selfish), the social group utility maximization game
ʓ
degenerates
to the non-cooperative spectrum access game and the upper-bound of the performance
gap
ˁ
reaches the maximum of
0 for any user
n
,
m
2
n
=
1
m
∈
N
1
P
m
d
−
ʱ
mn
. When
s
nm
=
1 for any user
p
n
n
,
m
(i.e., all users are fully altruistic), the SGUM becomes the NUM and
the performance gap
ˁ
∈
N
0. In Sect.
4.5
, we also evaluate the performance of the
SGUM solution by real social data traces. Numerical results demonstrate that the
performance gap between the SGUM solution and the NUM solution is at most 15 %.
=
4.5
Numerical Results
In this section, we evaluate the SGUM solution for database assisted spectrum access
by numerical studies based on both Erdos-Renyi social graphs and real trace based
social graphs.
4.5.1
Social Graph with 8 White-Space Users
We first consider a database assisted spectrum access network consisting of
M
=
5
channels and
N
8 white-space users, which are scattered across a square area of
a length of 500 m (see Fig.
4.2
). The transmission power of each user is
P
n
=
=
100
4, and the background interference power
ˉ
m
for
each channel
m
and user
n
is randomly assigned in the interval of [
mW [
1
], the path loss factor
ʱ
=
90]
dBm. Each user
n
has a different set of vacant channels by consulting the geo-
location database. For example, the vacant channels for user 1 are
−
100,
−
{
2, 3, 4
}
. For the
p
, we define that the user's transmission range
ʴ
interference graph
1000 m and
two users can generate inference to each other if their distance is not greater than
ʴ
.
The social graph
G
=
s
is given in Fig.
4.2
where two users have social tie if there is
an edge between them and the numerical value associated with each edge represents
the strength of social tie.
We implement the proposed distributed spectrum access algorithm for the SGUM
game with different parameters
ʸ
in Fig.
4.3
. We see that the convergent potential
function value
ʦ
of the SGUM game increases as the parameter
ʸ
increases. When the
parameter
ʸ
is large enough (e.g.,
ʸ
≥
G
10
6
), the algorithm can approach the maximum
potential function value
ʦ
∗
=
max
a
ʦ
(
a
). Figure
4.4
shows the dynamics of user's
