Computational Intelligence - February 2014 - 49
algorithm 2: Power control in uplink
direction: p ui
Input: I jkv , C jkv obtained by Algorithm 1;
The propagation gain G = 6g ijk@ .
Output: The state of the connection S ij ;
The transmitted power p ui .
Initial the maximum number of iteration
maxiter and the transmitted power of the
each mobile station p ui ;
for n =1: maxiter do
Compute the system interference h bjv
by Eq. (22)
for each C jkv do
Check the connection state
S tj , t d C jkv ; Compute the transmitted
power p ut by Eq. (23) of the mobile
stations in TP t d C jk with s tj =1;
end for
end for
u dt s tj hlmh
+ hlmi f 1 - ~
Ut + ~
/
~
t ! C jki
v
p dji =
(U i + ~) f 1 - ~
3) power Control in
Downlink Direction:
A similar procedure is also used to estimate the emitted power in the downlink
direction. Let U i = W SIR di R di , and
we can transform the SIR constraint
(17) into the following linear equations:
(U i + ~) p dji - ~ / u dt p djt s tj = hlmi (24)
t ! C jki
v
for i ! I, j ! J where
= 3.9811, then Q . 79. That is, there is
no way to accommodate more than 79
users at the desired QoS requirement in
uplink direction.
The system interference h vbji and s tj
in Eq. (23) are not available in advance.
Hence, an iterative approach is presented
to solve it. It is composed of three procedures as follows:
1) As p ui , i ! I, is given, we can easily
obtain the system interference h vbj for
each cell of the active BSs according
to Eq. (22).
2) For each cell C vjk, check the connection state s tj, t ! C vjk to guarantee the
SIR constraint (16). We always give
priority to TPs with a greater propagation gain. Specifically, we sort the
TPs i ! C vjk in descending order
according to the propagation gain
g ijk, and then compute the transmitted power of the TPs one by one
according to Eq. (23). If the transmitted power of mobile stations in TP t
satisfies the SIR constraint, i.e.
p ut < p umax, then s tj = 1, otherwise,
s tj = 0.
3) For each cell C vjk, compute the
transmitted power of the mobile stations in TP t ! C vjk with s tj = 1 by
Eq. (23).
More precisely, the power control in
uplink is described in Algorithm 2,
where maxiter is the maximum number
of the iteration. We set it at 3 and let the
initial transmitted power of each mobile
station be zero in this paper.
t
h mi + p j g ijk +
/
p dl vi g ilk
l ! J i, l ! j
. (25)
g ijk
As discussed in the uplink power control method, Eq. (25) can be extended by
the equation c = /
u dt p djt s tj with an
t ! C jk
additional variable c. Substituting this
into Eq. (24), we have that
~c + hlmi
p dji =
Ui + ~
and
hlmi
=
vi
c = ~c
/
t ! C jki
v
u dt s tj
+
Ut + ~
/
t ! C jki
v
u dt s tj hlmt
.
Ut + ~
Hence, p dji can be calculated as
shown in (26) at the top of this page.
From Eq. (26), we can find that p dji
depends on hlmt and s tj, t ! C vjki . It is
independent of the variable p dji in the
same cell. Hence, we can use the similar
method described above to solve it.
Please note that there is no way to
accommodate more than 23 users at the
desired QoS requirement.
As a result, the state of the connection
s ij just depends on the values of the BSs'
state X. It means that s ij can be expressed
as a latent function of X, denoted as
s ij = fij (X) ! {0, 1} . Moreover, the constraints (12)-(19) are satisfied when we
solve the state of the connection s ij .Then,
the model can be formulated as follows:
max Tcap (X) = / / u i fij (X)
i!I
min C cos (X) =
j ! Ji
/ / c jk x jk
j!J k!K
Tcap
s.t.
/ u i $ 0.9.
i!I
(27)
/
t ! C jki
v
/
t ! C jki
v
u dt s tj
Ut + ~ p
u dt s tj
Ut + ~ p
.
(26)
III. Moea/d-M2M for wcdMa
Network Planning
A. Presentation Based on
Orthogonal Design
Four configuration parameters for each
BS are taken into account in this paper.
Sine each BS has a specific lower bound
of the antenna height according to the
terrain variation, the antenna height is
just a fine adjustment configuration. We
consider the antenna height above the
lower bound in meter, i.e. h !
{0, 1, 2, 3, 4, 5} . It is assumed that the
antenna tilt of each sector of a BS also
has six possible values in degree, i.e.
b i ! {0, 3, 6, 9, 12, 15} with i = 1, 2, 3.
The sector orientation which defines the
sets I vjk and C vjk has the following six
possible values in deg ree: c !
{0, 20, 40, 60, 80, 100} . The pilot power
tp also has six possible values in watt tp
{1, 1.2, 1.4, 1.6, 1.8, 2} . This indicates
that there are 6 6 = 46656 combinations
levels of configuration parameters for
each BS. The search space of configuration parameters combinations of the
model is 46656 n . It is very time consuming to find the best configuration
combination level. Therefore, it is desirable to sample a small, but representative
set of combination levels. The orthogonal design [30] is used to reduce the
search space of the model in this paper. A
series of orthogonal array are provided in
[30]. Orthogonal array L 36 (6 6) is utilized
in this paper. Then, there are only 36
combination levels for each BS. It greatly
reduces the search space of the model.
We propose an encoding method
based on orthogonal design. Specifically,
a vector y = (y 1, y 2, g, y n) records the
combination level of BSs' configuration
parameters in a solution. y j = k
expresses that a BS is installed in CS j
with combination level k of configuration parameters, i.e. x jk = 1. For example, y 2 = 10 implies that a BS is installed
February 2014 | Ieee ComputatIonal IntellIgenCe magazIne
49
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