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5)Gen=300?: Gen defines the maximum number of generations. If the number of
cycle operations satisfies the predefined number, the genetic algorithm terminates and
returns the optimal solution.
Applying the above procedures will generate an optimal sub-channel allocation
scheme with a rough rate constraint. The simulation results are presented in Section 4.
3.2
Power Allocation
After sub-channel allocation, the system has an optimal sub-channel scheme. Next,
power allocation is carried out to ensure proportional fairness. The basic strategy is to
assign power to the users according to the optimal solution, while power for the sub-
channels owned by each user is allocated equally. The basic process flow, shown in
Fig. 4, is similar to that depicted in Fig. 3. The optimization problem can be simpli-
fied as follows:
2
|
h
|
p
K
1
max
kn
kn
,
kn
,
log (1
+
)
2
N
N
B
p
,
ρ
knA
=∈
1
0
N
,
kn
,
K
K
subject to
p
≤
Pp
,
≥
0 for all and
k
n
kn
,
total
kn
,
knA
=∈
1
k
RR
:
:...:
R
=
γγ
:
:...:
γ
1
2
K
1
2
K
where
A
is the sub-channel distribution for the k-th user.
Compared with sub-channel allocation, power allocation is a multiple object optimi-
zation problem that includes maintaining system capacity, ensuring that the total power
is consumed, and achieving proportional fairness.
Randomly generate initial chromosomes: A series of K elements, representing the
power values for the users, with values ranging from 0 to 1 is randomly generated.
Evaluate the fitness function of each chromosome: There are two fitness functions:
one is for system capacity, and the other is for proportional fairness. The chromo-
somes should, therefore, be divided into two groups, to which the respective fitness
function is applied. The number of chromosomes allocated to each group is based on
the weight. Here, the process focuses on the realization of proportional fairness. The
specific method first calculates the user rates according to the power and sub-channel
distributions. Next, it generates the user proportional rate by dividing the user rate by
the proportion
γ
. Finally, the difference between the maximum and minimum user
proportional rates is obtained, and if the absolute value of the difference is optimized
to 0, proportional fairness has been achieved. So, the principle of ranking fitness con-
siders the maximum system capacity and the minimum of the absolute value of the
difference between the maximum and minimum user proportional rates.
k
