Communications and Network, 2013, 5, 361-366 Published Online September 2013 (
An Enhanced Difference Method for Multi-objective
Model of Cellular Base Station Antenna Configurations
Xiaofei Wang, Zhipeng Jiang, Suixiang Gao
School of Mathematical Sciences, University of CAS, Beijing, China
Received July, 2013
In this paper, we propose a fine-grained gr id-based multi-objectiv e model which aims at optimizing base station anten-
nas' configurations, such as transmit power, antenna tilt and antenna azimuth, in order to upgrading network perform-
ance in cellular networks. As the model is non-convex, non -smooth and discrete and computationally expensive, we use
decomposition method to solve the MOP problem. We mainly focus on addressing the scalarized sub-problem after
decomposition. For the scalarized sub-problem, we propose an enhanced difference method. First, difference of each
component is calculated, which provides the guidance of optimization. Then an OPSO is applied to search the optimal
step length. The method is applied to GSM network optimization on an area in Beijing. The effect of the application
shows that proposed method has a good performance, and is effective/efficient to solve mobile network optimization
Keywords: Mobile Network Optimization; Multi-objective Optimization; Decomposition, Difference Method, Particle
Swarm Optimization
1. Introduction
Wireless networks such as GSM, UMTS etc. are based
on the same cellular concept. A cellular network is a ra-
dio network distributed over land areas called cells, each
served by at least one fixed-location transceiver, known
as a cell site or base station antenna. Due to the high
costs and the scarcity of radio resources, an accurate and
efficient mobile network planning appears of outmost
importance. With the rapid growth of network size and
number of users, efficient quantitative methods to sup-
port decisions for base station (BS) location have become
essential. This need is now even more acute due to the
increased complexity of the system and the number of
parameters that must be considered [2]. In order to im-
prove the quality of service (QoS) in cellular network s, it
is very important to implement the network planning and
optimization in cellular networks. Network planning re-
fers to the process of designing network structure and
topology subject to various design requirements. Net-
work optimization amounts to finding a network con-
figuration to achieve the best possible performance.
In order to improve the QOS of a cellular network,
some factors have to be considered, e.g. upgrading cov-
erage rate, decreasing interference, increasing coverage
continuity and enhancing cells’ traffic equilibrium. In
real system planning, optimizing BS configuration can
often be more critical than BS location since service pro-
viders may have a very limited set of candidate sites due
to authority constraints on new antenna installation and
on electromagnetic pollution in urban areas. So they are
usually very interested in optimizing the QOS with the
available BSs by adjusting their configurations, adding
new BSs only when it is strictly necessary.
In detailed planning, making major changes in net-
work topology and layout is typically not an acceptable
option for an operator. Instead, the goal is to optimize
antennas’ key configuration parameters [7]. Meanwhile,
the optimization of every one of these parameters is af-
fected by the other parameters and other antennas. Be-
cause of this, it is difficult and even impossible to opti-
mize the three configuration parameters by a manual
approach. Automated network planning and optimization
through mathematical model and algorithms allow op-
erators to better deal with the complexity of cellular
network optimization, a task that is often beyond the
reach of a manual approach. In addition to making the
network optimization process time-efficient, planning
tools incorporating automated optimization can signifi-
cantly reduce network deployment and maintenance
There have been many works on cellular networks
planning and op timization. Almost all the prev ious work s
establish a model with a discrete solution space and
opyright © 2013 SciRes. CN
based on few test points. But as mentioned in [8], the
optimization conducted on few test points can’t ensure
the same good performance for other region. Besides, in
order to improve the QoS of a cellular network, some
objectives/factors have to be considered simultaneously,
e.g. upgrading coverage rate, decreasing interference,
increasing coverage continuity and enhancing cells' traf-
fic equilibrium. These factors or objectives are often de-
pendent and conflict. For instance, decreasing the
transmit power reduce the cell overlap and interference.
On the other hand, coverage problems will arise if the
transmit power becomes too low. So, a multi-objective
optimization problem should be considered to improve
the QoS of mobile network. In this paper, we propose a
multi-objective optimization model of QOS and base
station antenna configurations with fine-grained grid
division developed in [8], and an enhanced difference
method is designed for the proposed MOP.
This paper is organized as follows. Section 2 discusses
the cellular networks planning and optimization prob-
lems on previous work. In Section 3, a multi-objective
optimization model of QOS and base station antenna
configurations is proposed in cellular networks. In Sec-
tion 4, we give the enhanced difference method to solve
the proposed MOP model. Computational results ob-
tained with realistic instances are reported and discussed
in Section 5. The paper is then concluded in Section 6.
2. Previous Work
Many previous works have discussed the optimization of
the location and co nfiguration of base stations.
In [2], the authors proposed discrete optimization
models which consider the signal-to-interference ratio as
quality measure and algorithms aimed at supporting the
decisions in the process of planning where to locate new
BSs. The similar methods are arisen in [3-5], [15]. But all
these studies are about the positio n on which the BSs are
installed without considering the adjustment of the an-
tennas' configuration. In [6] the authors gave a basic
model for pilot power optimization subject to a full cov-
erage constraint as well as its extended version which
considers various coverage levels and to consider user
traffic distribution over the network. In [7] automated
optimization of service coverage and radio base station
antenna configuration is addressed and three key con-
figuration parameters: transmit power of the common
pilot channel (CPICH), antenna tilt and antenna azimuth
are considered. The optimization targ et is minimizing the
total CPICH power under the constraint that every bin
(Each bin is a test point) is in the coverage area of at least
one cell. In [9-11], a mathematical mixed-integer pro-
gramming model for planning cost-efficient radio net-
works under network quality constraints and some net-
work planning methods based on this model are pre-
All these studies suppose that a little area with a given
amount of traffic can be considered as a test point and the
whole optimization area is denoted by all this kind of
points. Meanwhile, all these studies give models with
constraints like that the signal received by all the test
points must be under the given constraints (i.e. the signal
strength received by every point have to be strong
enough, and the signal to in terf erence r atio of ev ery poin t
must be greater than a given threshold.). Then they opti-
mized some other performance parameters (e.g. mini-
mizing the cost or total transmit power) with this con-
straint and some other constraints. But in real application,
constraints like that the signal received by all the test
points must be under the given constraints may not be
satisfied no matter how the antennas' con figuration of the
network being set.
In [12] various parameters of cellular base station (BS)
placement problem such as site coordinates, transmit
power, height and tilt angle are determined using evolu-
tionary multi-objective algorithm to obtain better com-
promised solutions. And the maximization of service
coverage and minimization of cost are considered as
conflicting objectives by satisfying in equality constraints
such as handover, traffic demand and overlap. In [13] the
authors address the design of the network which has been
formulated as a multi-objective constrained combinato-
rial optimization problem and propose a genetic algo-
rithm that aims to approximate the Pareto frontier of the
problem. But the detailed formulas of the objectives are
not given in these studies.
In [14] the authors address the problem of capacity op-
timization in a Universal Mobile Telecommunication
System (UMTS) radio network and present an optimiza-
tion algorithm for finding th e best settings of the antenna
tilt and common pilot channel power of the base station s.
But only an algorithm is presented in this paper without
any model.
3. A Multi-objective Model of QoS and Base
Station Antenna Configurations
In the section, A multi-objective optimization model is
As mentioned in introduction sectio n, there are several
indicators that reflect performance of the network, such
as interference, coverage rate, the connectivity of pri-
mary service area and traffic balance. In this paper, the
objectives we consider are coverage rate, interference
and the connectiv ity of primary serv ice, and the variables
are antenna's azimuth, tilt and transmit power. Traffic
balances are considered as constraints, because the dis-
tribution of grid traffic varies from time to time, it's very
Copyright © 2013 SciRes. CN
X. F. WANG ET AL. 363
difficult to handle all cases. In order to optimize a rec-
tangle region by adjusting some antenn as' para meters, the
region surrounding must be considered. Otherwise, after
optimization, the objectives of region get improved but
the region surrounding may get worse. Besides consider-
ing the optimization region, we also take account of the
region around as protect region.
The main goal is to optimize the objectives of optimi-
zation region by adjusting antennas' parameter and
meanwhile to avoid the objectives of protect regions get-
ting worse. In add ition, antennas must not be ov erloaded.
The antennas selected to be adjusted are determined in
3.1. Multi-objective Model
Consider a rectangle optimization region Z and corre-
sponding protect region '
, divided into I and J grids
with identical or different size respectively. We assume
the strength of the received signal from an antenna at all
the points in a grid is identical and the total traffic of
every grid is received only by one antenna. In order to
make the hypothesis be rational, the grid size have to be
small enough. Suppose there are
K antennas that can
affect the region
and '
. An antenna affect a region
if the strength of the received signal in at least one grid in
the region from this antenna is greater than a given
threshold (e.g. -104dBm) and the strength of the received
signal of all the grids from each antenna can be estimated
according to empirical propagation models such as Hata
and COST-231 or to more precise but computationally
intensive ray tracing techniques. Let the strength of the
received signal in grid i from antenna k be ik . If the
strength of the received signal in grid i from antenna k is
the strongest in all antennas which can affect the grid i,
then antenna k is called the master antenna of grid i and
the strength of the received signal from antenna k is
called the master strength. Let i be the geographic
neighbor of grid i. The antenna is the master antenna
of grid i.
The proposed multi-objective optimization model
OP ) is given below: is a very large number. R
is set of adjusted antenna s. is the set of antennas,
traffic balance of which are considered. u
t represents
the traffic of grid . target is strength threshold.
contains K and TK. AK and TK are determined by K and
propagation model. is total traffic received by an-
tenna k. 0 and represent the traffic received
from optimization region and protect region under the
adjusted antenna's configure 0
TT(Tx()Tx )
and x. k
L is the
maximum traffic load of antenna k, which is determined
by the number of antenna's frequency channels and
maximum capacity of per channel. 0
is the existing
antennas’ configuration of the network.
min( )(( ),( ),( ))
..( ),
|9|/ ,
argmax( ),
(()/ ())
(()/ ())
uu v
ik ik
jk jk
fxfxfxf x
thRP PxuIJ
gk kRuIJ
PxPx E
PxPx E
 
 
() (),
kk kk
 
() ||
()(1 (()/()))
() ||
ik ik
uI Jkk
fx h
fx g
Tx t
 
,,,,,WEBWEB are thresholds that represent the
objective function values of optimization region and
protect region under the existing antenna configuration of
the network respectively.
3.2. Variables, Objectives and Constraints
Three key base station antenna con figuration parameters,
transmit power, antenna tilt and antenna azimuth, are
considered in this model. Then the decision variable x is
set as '
(,,,, , ,)
, where i
is the
antenna azimuth, and i
is antenna tilt, i is
transmit power. p
is the rectangle boundary set of x.
As mentioned in [1], each antenna is configured by some
engineering parameters and the adjustment of every con-
figuration parameters is limited in a special range.
There are three objective functions in this mod el. First
objective is to minimize the weak coverage rate of opti-
mization region Z. If the master strength of grid i is less
than a given threshold target (i.e. -90dBm), the grid i is
called weak-covered grid because master strength is too
weak to be received by receivers. Second objective is to
minimize the interference from other antenna. We evalu-
Copyright © 2013 SciRes. CN
ate this objective by considering the ratio of interference
energy and total receive energy. The third objective is to
reduce the boundary grid rate, which is to decrease the
switching possibility. When a calling moves from a grid
in which the master antenna is antenna k to a grid in
which the master antenna is antenna q and kq
, the
access antenna of this calling may switch from k to q.
The dropped possibility of the calling is increasing dur-
ing the process of switching. So in order to decreasing
the call dropping possibility cau sed by the switching, the
rate of cell boundary g rids has to be re d uced.
Constrains (4)-(6) represent that optimal solution must
outperform the existing configuration in terms of opti-
mization region. Constrains (7)-(9) represent that the
objectives of protect region must not get worse after op-
timization. Constrains (10) represent that antenna traffic
must not be exceed maximum load. In practical optimi-
zation, objectives in optimization region may conflict
with the one in protect region. And if we keep the con-
straint strictly satisfied, there may be no feasible solution.
Thus, in this paper, we consider the relaxation form of
MOP and get
. For the sake of saving space,
the right terms in constraints (7)-(9) are multiplied by
(1 )
. If 0
OP are the same.
4. Enhanced Difference Method
The MOP is difficult to solve because it is nonconvex
nonsmooth and discrete. And the function evaluation is
computationally expensive, so we choose a decomposi-
tion-based multi-objective optimization method. By de-
composition, the MOP is transformed into single objec-
tive problem. Thus, the classical single optimization
methods are used to solve it in a fast convergence. In
this paper, we use the popular decomposition-based
framework-MOEA/D [16] to decompose the MOP. In
this paper, we mainly consider approaches for subprob-
lems, which are taken as an option in [16]. The mail loop
in MOEA/D is used to help subproblems jump out of
local optimal.
As the sub-problem is also a nonconvex, nonsmooth
and discrete, it's difficult to solve it by classical gradi-
ent-based methods. We use the difference instead of gra-
dient to guide the search, but the difference is used in a
different way, no the same with coordinate rotation
method. Thus, an enhanced difference method is pro-
posed. First the penalty NBI method is applied to trans-
form the MOP into single objective function. Then the
difference of every component is calculated. After that
component difference is modified into improved differ-
ence matrix (Algorithm 2). In the last, we use OPSO [17]
to get the step length with the guide of improved differ-
ence matrix (A lgorithm 1);
We list the proposal method -- Enhanced Difference
Method below:
Algorithm 1 Enhanced Difference Method
Input: weight vector
, reference point , penalty
Output: optimal solution
Step 1. Initiate first solution
Step 2. Use Penalty NBI method, scalarize the MOP
|| (())||
(), || ||
||()() ||
tfx z
gxdd d
 
Step 3 Calculate improved difference matrix
of , see Algorithm 2
Step 4. Apply OPSO to search the best step size array
for improved difference of current solution x, which is to
solve the following optimization:
min(( ))
.. 0
st u
where i is max step size for dimension i, is the
improved difference matrix.
Step 5. let 1()
 , . If stopping
condition is satisfied, then stop and output
. Other-
wise, go to Step 2.
Algorithm 2 Improved Difference Matrix
Input: a scalarized function ()
Output: improved difference matrix
Step 1. Initialize 0
, and initialize max differ-
ence matrix 0
Step 2. Calculate each component's forward difference
and backward difference:
ii ii
xe gxgxgxe
 
where i
is the minimum step length of component i.
Step 3. Calculate forward improved value and back-
ward improved value
max(0,), max(0,)
Set ii i
. if , let .
ii ii i
Step 4. for each component i, set
npGpsgn( )
iiii i
sgn( )
is sign function.
In next section, we validate the proposal method with
real operational network.
5. Simulation and Application
In this section, we apply our model and algorithm on the
GSM1800 networks of China Mobile Communications
Corporation. The implementation is on a region in Bei-
jing. The area of the optimization region Z is 1.1km
and the area of protect region is
1.7km 7.5km 7.9km
Copyright © 2013 SciRes. CN
X. F. WANG ET AL. 365
The grid size is . There are 30 antennas are se-
lected to be adjusted. The propagation model used is a
new high-precision propagation model in our previous
work [8]. The average error of the prediction of the field
strength is lower than 6.5dBm. Our work is supported by
China Mobile Group Beijing Limited Company, and the
data of base station antennas' configuration and the elec-
tronic map are provided by them. We execute our work
on a DELL server with 32G memory and 8 CPUs. The
algorithm is implemented by VC++.
The transmit power is set in the range [29dBm,
43dBm], minimum step length is 2dBm. The maximum
change of Azimuth to the left direction is set to , to
the right direction is set to , minimum step length is
. The tilt is in the range , and minimum step
length is . The max step sizes in each iteration for all
components are same to 5, that is . And we set
[0 ,
We select 4 different weight vectors to test the method.
They are
. The
total computation time is about 1 hour, and the optimiza-
tion results are as follows. The functions values listed in
the following tables are the ratio between real function
values and function values of
,0 , 0,1,0
1,0,0,0,1, (1/3,1/3,1/3)
, that is
() ()
x fx
/( ),1,2,3
ffx i.
The results obtained by enhanced difference method
corresponding to the 4 weight vectors are listed in Table
1. We take weight vector (0,1,0) as example, weak cov-
erage rate after optimization is reduced by 11% and
interference energy is reduced by and boundary
grid rate is reduced by . So after applying the pro-
posed method, the performance of GSM1800 network is
improved significantly. The result shows the method is
effective and efficient.
The adju sted result of the anten nas' configuration with
weight vector is listed in Table 2. The ID is
antenna’s identifier. The Ab and Aa represent the azi-
muth before and after optimization respectively. The Tb
and Ta represent the tilt before and after optimization
respectively. The Pb and Pa represent the transmit power
before and after optimization respectively. The blank
grid represents that this type of configuration of the an-
tenna remain unchanged after optimization.
Table 1. The relative objective values of GSM1800
after opti mization .
x '
x '
)0,0,1( 0.93 0.81 0.94
)0,1,0( 0.89 0.8 0.89
)1,0,0( 0.95 0.85 0.96
Table 2. The adjusted result.
ID Ab Aa Tb Ta Pb Pa
30114 40 20 6 22 43 39
30115 205 185
30303 39 43
... ... ... ... ... ... ...
33153180 150 43 31
... ... ... ... ... ... ..
34398 3 25 43 33
34399300 270 3 5 43 33
6. Conclusions
In this paper, we propose a fine-grained grid based
multi-objective model which aims at optimizing base
station antennas' configurations, such as transmit power,
antenna tilt and antenna azimuth, in order to upgrading
network performance in cellular networks. As the model
is nonconvex, discrete and computationally expensive,
we use decomposition method MOEA/D to solve the
MOP problem. We mainly study the optimization of the
subproblem in MOEAD framework. We propose an en-
hanced difference method to solve these subproblems.
First, Penalty NBI scalarization method is used to trans-
form MOP to single objective optimization. Second,
OPSO is coupled with difference method to find best step
size to minimize the scalarized objective. The improved
difference is used only to find which dimension could be
minimized; the real step length in each iteration is gener-
ated by OPSO method. We apply the MOP model and
algorithm to optimize GSM1800 network on a region
which has bad performance in YuQuanlu district in Bei-
jing, collaborated with the China Mobile Group Beijing
Limited Company. The application results show that the
network performance in the region is greatly improved
after optimization. The Model and algorithm are effec-
tive and efficient for real network optimization.
7. Acknowledgements
The authors would like to express their sincere thanks to
CMCC and Engineers working in China Mobile Group
Guangdong Company Guangzhou Branch and Beijing
Limited Company for their kindly suggesting the prob-
lem, providing the data, and for their invaluable support.
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