Information Technology Reference
In-Depth Information
Algorithm 1
Distributed Spectrum Access Algorithm For Social Group Utility
Maximization
1:
initialization:
2:
set
theparameterʸandthechannelupdaterate˄
n
.
3:
choose
achannel
a
n
∈ M
n
randomlyforeachuser
n
∈ N .
4:
endinitialization
5:
loop
foreachuser
n
∈ N
inparallel:
6:
a
n
.
7:
generate
atimervaluefollowingtheexponentialdistributionwiththemeanequalto
˄
n
.
8:
countdown
untilthetimerexpires.
9:
compute
thesocialgrouputility
f
n
(
a
n
,
a
−
n
)
onthechosenchannel
if
thetimerexpires
then
10:
choose
anewchannel
a
n
∈ M
n
randomly.
11:
compute
thesocialgrouputility
f
n
(
a
n
,
a
−
n
)
onthenewchannel
a
n
.
exp ʸ
f
n
(
a
n
,
a
−
n
)
12:
stay in
the new channel
a
n
with probability
,Or
(
ʸ
f
n
(
a
n
,
a
−
n
)
)
,
exp
(
ʸ
f
n
(
a
n
,
a
−
n
))
}
max
{
exp
exp ʸ
f
n
(
a
n
,
a
−
n
)
moveback
totheoriginalchannel
a
n
withprobability1
−
.
(
ʸ
f
n
(
a
n
,
a
−
n
)
)
,
exp
(
ʸ
f
n
(
a
n
,
a
−
n
))
}
max
{
exp
13:
endif
14:
endloop
a
a
a
={
∈
|{
∪
}\{
∩
}| =
}
|·|
as
ʔ
a
denotes the size of a set.
According to (
4.3
), a user
n
can compute the social group utility
f
n
(
a
) by locally
enquiring the users having social ties with it about their received interferences. Then
user
n
will randomly choose a new channel
a
n
∈
M
n
and stay in this channel with
a probability of
ʩ
:
a
a
2
, where
exp
ʸf
n
(
a
n
,
a
−
n
)
exp
ʸf
n
(
a
n
,
a
−
n
)
,exp
(ʸf
n
(
a
n
,
a
−
n
)
)
}
.
(4.10)
max
{
The underlying intuition behind (
4.10
) is as follows. When
f
n
(
a
n
,
a
−
n
)
≥
f
n
(
a
n
,
a
−
n
) (i.e., the new channel
a
n
offers the better performance), user
n
will
stay in the new channel
a
n
with probability one. According to the property of poten-
tial game in (
4.4
), we know that choosing the new channel
a
n
can help to increase
both user
n
's social group utility
f
n
(
a
) and the potential function
ʦ
(
a
) of the SGUM
game. When
f
n
(
a
n
,
a
−
n
)
<f
n
(
a
n
,
a
−
n
) (i.e., the original channel
a
n
offers the better
performance), user
n
will switch back to the original channel
a
n
with a probability of
1
exp
ʸf
n
(
a
n
,
a
−
n
)
exp
(ʸf
n
(
a
n
,
a
−
n
)
)
. That is, the probability that user
n
will switch back to the original
channel
a
n
increases with the performance gap
f
n
(
a
n
,
a
−
n
)
−
−
f
n
(
a
n
,
a
−
n
). We would
like to emphasize that such probabilistic channel selections are necessary such that
all the users can explore the feasible channel selection space to prevent the algorithm
from getting stuck at a local optimum.
Then from a system-wide perspective, the probability of transition from state
(
a
n
,
a
−
n
)to(
a
n
,
a
−
n
) due to user
n
's channel selection update is given as
exp
ʸf
n
(
a
n
,
a
−
n
)
1
|
M
n
|
exp
ʸf
n
(
a
n
,
a
−
n
)
,exp
(ʸf
n
(
a
n
,
a
−
n
)
)
}
.
(4.11)
max
{
