Information Technology Reference
In-Depth Information
In this paper, we consider a system with
K
users sharing
N
sub-channels. The objec-
tive function in the system aims to optimize sub-channel and power allocation to max-
imize system capacity under an aggregate power constraint. Meanwhile, owing to the
introduction of proportional fairness, each user should also satisfy the related propor-
tional rate. The benefit is that different users can achieve their expected data rate based
on their different services.
Mathematically, the optimization problem discussed in this paper is formulated as
2
ρ
|
h
|
p
KN
max
kn
kn
,
kn
,
kn
,
log (1
+
)
2
N
N
B
p
,
ρ
kn
==
11
0
N
,
kn
,
KN
subject to
pPp
≤
≥
0 for all and
k
n
k n
,
total
k n
,
kn
==
11
K
ρ
=
1,
ρ
=
{0,1} for all
n
kn
,
kn
,
k
=
1
RR
:
:...:
R
=
γγ
:
:...:
γ
1
2
K
1
2
K
where K is the number of users, N is the number of sub-channels, and
k
h
and
k
p
are the channel gain and power allocated to user k in sub-channel n, respective-
ly. Further,
ρ , which is either 0 or 1, indicates whether sub-channel n is assigned
to user k,
N
is the power spectral density of additive white Gaussian noise
(AWGN), and B is the available bandwidth and
kn
{}
K
ii
P
is the total power. Here,
γ
total
=
1
is a set of values indicating the data rate ratio among users.
3
Sub-channel Allocation and Power Allocation
3.1
Sub-channel Allocation
The sub-channel is first allocated under the assumption of equal power allocation to
all the sub-channels based on a genetic algorithm to maximize system capacity
using a rough rate constraint. A genetic algorithm is an evolutionary intelligent search
technique that has been successfully used to solve many troublesome optimization
problems. Fig. 2 depicts the flow chart, while each of the procedures is described
below.
1) The number in each cell denotes which user is occupying the associated sub-
channel. For example, in the chromosome shown in Fig. 3, cell number 3 contains the
number 5, which means that sub-channel 3 is assigned to user 5. Different sub-
channel allocation schemes can be represented by different chromosomes. Initially, W
chromosomes are randomly generated.
