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Overshooting and Cost Minimization in LTE Cellular Network
Using Non-dominate Sorting Genetic Algorithm based on
Laplace Crossover
Mohamed Amine Ouamri
LIMED Laboratory,
Department of Electrical Engineering,
University of Bejaia
Bejaia, Algeria
mouhamedamineouamri@gmail.com
Mohamed Azni
LIMED Laboratory,
Department of Electrical Engineering,
University of Bejaia
Bejaia, Algeria
mohamed.azni@gmail.com
ABSTRACT
In cellular networks design, cell planning is the primary and most
important phase before the deployment of the network’s infrastruc-
ture. Cell planning aims to determine the best Base Stations (BS)
placement in a given area, in order to meet trac and coverage
requirements, and to minimize overshooting that may aect user
equipments. Overshooting consists in a signal from a given cell
forming a discontinuous coverage area in another adjacent cell. In
this paper, we develop a novel optimization method for BS plan-
ning. Our objective is to reduce the number of deployed BS while
minimizing signal overshooting, under capacity constraint. In the
proposed approach, cell planning is formulated as a multi-objective
problem. Then, a non-dominate sorting genetic algorithm based
on Laplace Crossover is applied in order to solve the problem. The
proposed algorithm is implemented and simulations under real con-
ditions are conducted. The performance of the proposed algorithm
is compared with that of a real deployed network infrastructure.
The results obtained show that the number of required BS can be
reduced with a lower rate overshooting.
KEYWORDS
Planning, cellular network, coverage, optimization, genetic algo-
rithm
ACM Reference Format:
Mohamed Amine Ouamri and Mohamed Azni. 2019. Overshooting and Cost
Minimization in LTE Cellular Network Using Non-dominate Sorting Genetic
Algorithm based on Laplace Crossover. In Proceedings of ACM International
Conference on Future Networks and Distributed Systems (ICFNDS). ACM, New
York, NY, USA, 6 pages. https://doi.org/10.1145/nnnnnnn.nnnnnnn
1 INTRODUCTION
In recent years, exponential growth of trac in cellular networks
forces operators to improve their network infrastructures in order
to meet the requirements of quality of service (QoS). The essential
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ICFNDS, July 2019, Paris, France
©2019 Association for Computing Machinery.
ACM ISBN 978-1-4503-7163-6. . . $15.00
https://doi.org/10.1145/nnnnnnn.nnnnnnn
tasks identied by operators are coverage and cell planning. Gener-
ally, cell-planning process starts by determining the number and
location of Base Stations (BS) as well as choosing judicious antenna
parameters [
2
]. Once set, the modication of those parameters
may have negative impact on networks, such as the overlapping
and overshooting phenomena. Overshooting consists in a signal
from a given cell forming a discontinuous coverage area in another
adjacent cell [
15
]. The main cause of this phenomenon is due to
bad antenna parameters settings. Indeed, in the initial network
planning, high power transmission and large antenna heights are
chosen in order to cover a large area. Consequently, overlaps are
observed between cell sites. Therefore, inappropriate location of
base stations can lead to an overshooting problem.
Overshooting has been extensively studied in the literature, from
dierent perspectives. In [
1
], authors proposed an algorithm for
coverage and cell planning, where the objective is to increase capac-
ity and throughput by adjusting antenna parameters. To perform
cell planning, authors in [
9
] employed third generation Genetic
Algorithm. Optimal base stations planning in LTE networks using
Genetic Algorithm was introduced in [
11
]. The authors formulated
the approach as a multi-objective problem, where the main objec-
tive aims to increase coverage while using a minimum number of
BS. In [
6
], an optimization technique was developed in order to
maximize outdoor coverage and minimize the number of BS; Meta-
Heuristic based on Partical Swarm Optimization (PSO) and Grey
Wolf Optimizer (GWO) was implemented. Furthermore, the work in
[
12
] proposed a method to reduce overshooting in mobile networks.
The authors give practical ways to reduce overshooting by central-
ized adjustment of antenna parameters such as transmission power,
or tilt and azimuth. Similarly, to eliminate overshooting in LTE
network, [
4
] provides an algorithm that aims to self-adjustment
of antenna parameters in fourth generation (4G) networks. More
recently, a new priority based coverage optimization technique
has been depicted in [
8
] for femtocells. The technique supports
reduction of coverage gaps and improvement of Signal to Noise
Ratio (SNR).
In this paper, we develop an optimisation method to model the
cell planning problem. Our objective is to minimize overshooting
and cost deployment while reducing the number of BS in LTE
cellular network, under capacity and handover constraints. We
formulate this as a mutiobjective problem, then a non-dominate
sorting genetic algorithm based on Laplace Crossover is applied in
order to estimate the optimal location of BS leading to minimum
ICFNDS, July 2019, Paris, France Trovato and Tobin, et al.
discontinuous coverage. Simulations are then conducted in a real
environment in order to investigate how antenna parameters can
be chosen to reduce overshooting.
The rest of the article is organized as follows. In section 2, the
system model description is presented. Section 3 sets the problem
statement and presents the proposed algorithm. Simulations and
numerical results are given in section 4. Finally, conclusion and
perspectives are drawn in section 5.
2 SYSTEM MODEL
In this section, we describe the system model where macro cells
are involved. Let
MBS ={MBS1,MBS2
2
, . . . , MBSn}
bet the set of
candidate Macro Base Stations (MBS). Assume that all MBS are
distributed on the coverage area according to Poisson Point Process
(PPP) of intensity
λBS
[
14
]. Assume also that Mobile Stations (MS)
are distributed in the coverage area according to PPP of intensity
λMS
. Each MS in the set
MS ={MS1,MS2, . . . , MSm}
of mobile
stations connects with the nearest MBS. Let
φ={φ1,φ2, . . . , φz}
be
the set of antenna parameters. The antenna conguration consists
of power transmission, height and tilt. Let the maximum transmis-
sion power of a MBS be
Pmax
M BS =
46
dBm
. Hence, a MS must have
a reception power above a certain predened threshold
Pth
MS
. The
received power at
MSk
from Base Station
MBSj
is expressed by
equation (1) as follows (see [10]):
Pk,j=10 log10 PM BS j−PLk,j(1)
where
PM BS j
is the transmission power of
MBSj
and
PLk,j
is the
pathloss between MBSjand MSk.
The propagation model that is used to determine pathloss, in this
case, is formulated by equation (2) (see [7])
PLk,j=69.55 +26.16 log10 (f)−13.82 log10 hM B Sj+
44.9−6.55 log10 hM BS jlog10 dk,j−ahMSk(2)
where
f
denotes frequency,
hM BS j
and
hMS k
are the heights of
MBSj
and
MSk
respectively, and
dk,j
is the Euclidian distance be-
tween MBSjand M Skand calculated using equation (3).
dk,j=q(xj−xk)2+(yj−yk)2(3)
where
(xj,yj)
and
(xk,yk)
are the cartesian coordinates of
MBSj
and MSk, respectively.
Figure 1 represents the model desciption of the network in-
frastructure for this approach. Nevertheless, we assume that each
base station
MBSj
operates with directional beamforming antenna
whose particularity is a high gain G(θj,Ψj)and low side lobes.
In our approach, we use orthogonal frequency division multi-
ple access. Therefore, intracellular interference is not taken into
consideration, i.e. we assume perfect orthogonally. Nevertheless,
interference depends only on signals received from other base sta-
tions. The signal-to-interference-and-noise-ratio (SINR) is modeled
as follows:
γk=
Pk,j
Pn
i=1,i,jPk,i+N2
0
(4)
Figure 1: Model description of network infrastructure
where
I=Pn
i=1,i,jPk,i
is the interference caused to
MSk
by neigh-
boring
MBSi
and
N2
0
represents the thermal noise power. A partic-
ular
MSk
is said to be covered by
MBSj
if and only if its SINR level
exceeds a threshold value γth =−10dB.
2.1 Probability density function of SINR
Note that mobile stations are assigned to base stations that provide
an appreciable SINR. In this context, we calculate the cumulative
distribution function of SINR received by
MSk
, which is aected
by inter-cellular interference
I=Pn
i=1,i,jPk,i
from adjacent cells.
Pr{γk≤γth |I,Pk,j}=Pr{Pk,j≤γt hr (N2
0+I)|I,Pk,j}(5)
Pr{γk≤γth |I,Pk,j}=1−exp *
,−γth (N2
0+I)
Pk,j
+
-(6)
By calculating the cumulative distribution function, we derive
the probability distribution function, which is given by the follow-
ing formula (equation (7)):
fyk{γk≤γth |I,Pk,j}=d
dγth
Pr{γk≤γth |I,Pk,j}
=
N2
0+I
Pk,j
exp *
,−γth (N2
0+I)
Pk,j
+
-(7)
2.2 Rate overshooting probability
The main idea is to calculate the probability of overshooting in
the network, i.e. the discontinuous coverage in each base station.
Let
g
Pk,l
be the received power by a given MS from neighboring
base station in the network (see Figure 2). The rate overshooting
probability is denoted by
ω
and is dened as
ω≜Pr{g
Pk,i≥Pth
k,j}
.
In addition, a mobile station is in overshooting when its SINR from
the nearest MBS is larger than SINR of its serving base station. i.e.,
γk,i≥γk,j(8)
Overshooting and Cost Minimization in LTE Cellular Network Using Non-dominate Sorting Genetic Algorithm based on Laplace Crossover ICFNDS, July 2019, Paris, France
Figure 2: Illustration of overshooting phenomenon
3 PROBLEM STATEMENT AND PROPOSED
ALGORITHM
3.1 Problem statement
In network cell planning, the goal is to maximize coverage by max-
imizing the number of user equipments while reducing the cost
of installation and maintenance. This represents in fact a great
challenge for network operators. However, during the optimization
phase, interference needs to be minimized in order to eliminate
overlap from other antennas, thereby minimizing the overshooting
phenomenon. Our approach consists in reducing overshooting and
nding the optimal number of base stations necessary to cover
a dense urban area, while satisfying capacity and handover con-
straints.
We dene three binary variables as follows:
vj=(1if MBSjis deployed with conguration φ
0otherwise (9)
uk=(1if MSkis covered by a neighboring M BSi
0otherwise (10)
дk=(1if MSkis covered by MBSj
0otherwise (11)
We now move to formulate the objective functions. In this ap-
proach, LTE network planning will be rst performed, and then
a multi-objective genetic algorithm will be introduced. According
to the problem formulated in the previous section, the rst goal is
to choose the minimum number of candidate base stations, while
satisfying a series of constraints. Such constraints include cover-
age of all users by the network, positive transmission power and
the available bandwidth allocated to MBS. Mathematically, this
optimization can be formulated as follows:
min
n
X
j=1
vjCj(12)
Subject to:
m
X
k=1
дk≥m(13)
PM BS j≥0(14)
X
j∈{1, . . .,n}
bj≤Bal l oc at e d (15)
Where
Cj=Cjm+Cja
is the total cost of deployment of base
sation
MBSj
.
Cjm
and
Cja
represent the maintenance cost and an-
tenna cost, respectively.
The second objective we would like to optimize is overshooting.
To this end, the main objective is to reduce the discontinuous cov-
erage by minimizing the total number of MS that are aected by
signals coming from neighboring MBS. The constraints imposed
on this optimization problem include handover in the rst instance.
Indeed, a change in the antenna parameters can decrease the cov-
erage of an aected base station, thus eliminating overshooting.
Furthermore, a change of parameters leads to a reduction in the
overlap zone, which is important for the Handover mechanism. The
second constraint is relative to network capacity. The capacity of
each base station should not exceed 43 Erlang. This optimization
problem can be formulated using the objective function below.
min
n
X
j=1
uk(16)
subject to:
Pk,i>Pk,j+Ψ(17)
where
Pk,j
and
Pk,i
are the received power of the target cell and
the serving cell, respectively. Ψrepresents handover margin.
3.2 Proposed algorithm
In this work, a Meta-heuristic algorithm is proposed and imple-
mented to solve our optimization problem and evaluate its per-
formance.
Algorithm 1
is introduced in order to predict initial
coverage.
Algorithm 1 General procedure for overshooting
Input: MBS ={MBS1,MBS2, . . . , MBSn},MS =
{MS1,MS2, . . . , MSm}
for j=1 : n,k=1 : mdo
Step 1: Calculate distance between MBSjand M Sk
Step 2:
Calculate
PLk,j
using equ.(2) and evaluate received
power Pk,jby equ.(1) at each MS
Step 3: Compare Pk,jto Pth
k,j
if Pk,j>Pth
k,jthen
MSkis covered by M BS j
end if
end for
Step 4:
if MS receive g
Pth
k,j>Pth
k,jthen
overshooting is observed and calculate min Pn
j=1uk
end if
Step 5: Apply NSGAII to nd optimal solution
Output: MBSop t ,minover s hoo t in д
The rst step consists in distributing the base stations as well
as the users according to PPP. Each base station operates with a
well-dened conguration, chosen from the set
φ
. In the second
step, the received power and pathloss are calculated for each user.
Then, users covered by nearby base stations and users aected by
ICFNDS, July 2019, Paris, France Trovato and Tobin, et al.
overshooting are selected. Finally, an evaluation of the functions in
equations (12) and (16) is made. Once the initial procedure is com-
pleted, the algorithm proceeds to optimize with a Multi-Objective
genetic algorithm. Our choice is based on the use of Non-dominate
Sorting Genetic Algorithm II (NSGAII) applied in [
11
]. Proposed
by [
13
], this algorithm is characterized by a fast non-dominated
sorting approach, fast crowded distance estimation procedure and
simple crowded comparison operator. Asfor any Genetic Algorithm
search, the way to encode candidate solutions is very important.
The real coding for chromosome is applied to code the initial pop-
ulation, where the chromosomes representation is as shown in
Table 1. Moreover, in our case we use the Laplace crossover (LX)
Table 1: Chromosomes representation
Chromosome 1 2 3 4
Representation (xj,yj)θjPM BS jhj
based on the Laplace distribution whose density function is given
by equation (18) (see [3]):
f(x)=1
2be−|x−a|
b,−∞ <x<∞(18)
The Laplace’s distribution function is given by
F(x)=
1
2e−|x−a|
b,x≥a
1−1
2e−|x−a|
b,x>a
(19)
The result obtained after crossover is as expressed by equations
(20) and (21)
x(1)
i=y(1)
i+δ|y(1)
i−y2
i|(20)
x(2)
i=y(2)
i+δ|y(1)
i−y2
i|(21)
where a random number
δ
is generated, following a Laplace dis-
tribution by simply reversing the Laplace distribution function as
follows [5]:
δ=(a−bloдe(u),u≥1
2
a+bloдe(u),u>1
2
(22)
4 SIMULATION RESULTS
In this part, the performance of the proposed optimization algo-
rithm is evaluated. We validate the approach while comparing the
algorithm convergence with dierent crossover operator. The sim-
ulation is realized in 8
×
8
km2
Voronoi service area as shown in
gure 3. There are 80 candidate MBS distributed by PPP of intensity
2
/km2
in the same area. Frequency reuse is used in the cell after
600
m
distance between Base Stations. Moreover, as discussed in
previous sections, the users are distributed with dierent PPP
λMS
,
and dense deployment is considered. In this realistic case, only the
downlink is considered. Figure 3 illustrates the geographical area,
and Table 2 shows the simulations parameters.
Figure 4 describes the Pareto fronts achieved by NSGAII with
two crossover types, namely Laplace Crossover and two-points
crossover, where the probability of crossover is equal to 0
.
7. It can
be observed that our model based on LX crossover is always better
Figure 3: Voronoi geographical area for BS deployment
Table 2: Simulation parameters
Parameter value
PM BS j26 −46 dbm
γth −10 d B
Pth
MS 90 dbm
θj0to −15
hj5−30 m
than the two-points crossover. Indeed, lower overshooting solutions
with lower cost are given as optimal solution.
Figure 4: Comparison of Pareto fronts achieved by Laplace
crossover and two-points crossover
In gure 5 we plot the overshooting probability
ω
for
λMS =
30
/km2
and
λMS =
60
/km2
. As expected, it can be seen that the
overshooting probability decreases as the receiver power threshold
increases (which means less receiver sensitivity). However, when
Overshooting and Cost Minimization in LTE Cellular Network Using Non-dominate Sorting Genetic Algorithm based on Laplace Crossover ICFNDS, July 2019, Paris, France
users intensity increases, and are located in the cell edge, overshoot-
ing is more likely to be observed.
Figure 5: Overshooting probability vs receiver power thresh-
old
We now evaluate our objective optimization, which consists
in minimizing overshooting and the number of base stations to
guarantee coverage constraint. Figures 6 and 7 show the required
number of Macro Base Station necessary for coverage of the users
and minimum overshooting, using respectively
λMS =
30
/km2
and
λMS =
60
/km2
. The optimum number of MBS to ensure that all
users are connected with minimum discontinuous coverage using
λMS =
30
/km2
and
λMS =
60
/km2
is obtained at the end of simu-
lation. Figure 6 compares the results of the two experiments. We
can note that the number of base station deployed is minimized
after 800 generations. Nevertheless, with the growth in user inten-
sity, the number of base stations deployed increases. In gure 7 we
can observe the minimum overshooting values obtained at the last
generation, where only 29% of users are in discontinuous coverage.
Users thus aected by overshooting are located at the coverage
radius boundary of serving Base Station.
In order to demonstrate the performance of the proposed Genetic
algorithm optimization method, we conducted a test on a real LTE
network deployed in an urban area. To do this, we chose a site af-
fected by an overshooting problem during the RSRP measurements
in this area (see gure 8). Then we apply the Genetic Algorithm
with Laplace crossover to choose antenna parameters and decrease
overshooting. Figures 9 and 10 show the results from our investiga-
tion. We can see that after the application of our genetic algorithm
and that the parameters were modied, the overshooting recorded
in site was eliminated.
5 CONCLUSION
In this paper, we considered the problem of LTE cellular network
planning, using meta-heuristic algorithm. We provided a math-
ematical model to describe this problem, using a multiobjective
optimization approach to attain the double objective of reducing
Figure 6: Evolution of the required number of BS during op-
timization process
Figure 7: Evolution of overshooting during optimization
process
the discontinuous coverage and the number of deployed Base Sta-
tions. Poisson Point Process is applied in order to distribute both
mobile stations and base stations on the coverage area. An NSGAII
genetic algorithm based on Laplace crossover is then implemented
in order to nd Pareto fronts of optimal solution. The algorithm
also looks for the right parameters to use in order to achieve the
best possible solution. The results obtained through simulation
show that this approach provides better results compared to the
two-points crossover. The application of the approach to a real
deployed network shows also that improvements to the network
can be made.
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