Information Technology Reference
In-Depth Information
Fig. 4.5
Dynamics of
potential value
ʦ
when
ʸ
=
x
10
−6
1
*
10
6
Maximum Potential Value
ʦ
0
−1
−2
−3
−4
−5
−6
0
100
200
300
400
500
Iterations
time average interference
ʳ
n
(
a
). It demonstrates that the distributed spectrum access
algorithm can drive users' time average interference decreasing and converging to
an equilibrium such that each user only receives a small interference level. To verify
that the algorithm can approach the SNE of the SGUM game, we show the dynamics
of the potential value
ʦ
(
a
) in Fig.
4.5
. We see that the distributed spectrum access
algorithm can drive the potential value
ʦ
increasing and approach the maximum
potential value
ʦ
∗
. According to the property of potential game, the algorithm hence
can approach the SNE of the SGUM game.
4.5.2
Erdos-Renyi Social Graph
We then consider
N
100 users that randomly scattered across a square area of a
length of 2000 m. We evaluate the SGUM game solution by the distributed spectrum
access algorithm with the social graph represented by the Erdos-Renyi (ER) graph
model [
9
], where a social link exists between any two users with a probability of
P
L
.
We set the strength of social tie
s
nm
=
=
1 for each social link. To evaluate the impact of
social link density of the social graph, we implement the simulations with different
social link probabilities
P
L
0, 0
.
1,
...
,1
.
0, respectively. For each given
P
L
,we
average over 100 runs. To benchmark the SGUM solution, we also implement the
the following two solutions:
=
(1) Non-cooperative spectrum access: we implement the non-cooperative game
based solution such that each user aims to maximize its individual utility, i.e.,
we set
f
n
(
a
)
u
n
(
a
) in the distributed spectrum access algorithm.
(2) Network utility maximization: we implement the social optimal solution such
that the system-wide utility is maximized, i.e., we set
f
n
(
a
)
=
=
n
=
1
u
n
(
a
)in
the distributed spectrum access algorithm.
