FORMULATION OF THE PROBLEM OF MATHEMATICAL ANALYSIS OF CELLULAR COMMUNICATION BASIC STATIONS IN RESIDENTIAL AREAS FOR STUDENTS OF IT-PREPARATION

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International Journal of Advanced Research in Engineering and Technology (IJARET)
Volume 13, Issue 7, July 2022, pp.12-18 Article ID: IJARET_13_07_002
Available online at https://iaeme.com/Home/issue/IJARET?Volume=13&Issue=7
ISSN Print: 0976-6480 and ISSN Online: 0976-6499
DOI: https://doi.org/10.17605/OSF.IO/SM2N6
© IAEME Publication Scopus Indexed
FORMULATION OF THE PROBLEM OF
MATHEMATICAL ANALYSIS OF CELLULAR
COMMUNICATION BASIC STATIONS IN
RESIDENTIAL AREAS FOR STUDENTS OF
IT-PREPARATION
Sabbi Simhachalam Naidu1 and Syed Shahnawaz Ali2
1Research Scholar, Department of Mathematics, Sri Satya Sai University of Technology and
Medical Science (SSSUTMS), Madhya Pradesh, India
2Professor, Department of Mathematics, Sri Satya Sai University of Technology and Medical
Science (SSSUTMS), Madhya Pradesh, India
ABSTRACT
The importance of examining mathematical modelling concerns in the training of
students in IT-related fields stems primarily from trends in the growth of the artificial
intelligence sector, as well as modelling in general. It is now obvious that using
mathematical models to investigate and anticipate diverse processes and conditions can
greatly lower the cost of introducing new technologies and products, as well as the time
it takes to implement and test them. This led us to the conclusion that students in the IT
areas of training should be taught modelling approaches as well as how to pose
modelling issues, analyse source data, and build interconnections in designing models.
On the example of modelling the position of cellular base stations in residential areas,
the article explores the broad concept of the formulation of the problem of mathematical
modelling. The fundamental concepts of estimating are discussed, each of which can be
elaborated on depending on the tasks at hand. KPIs and a system of indicators can be
created based on the criteria and attributes chosen, and then used to solve various
electromagnetic hazard analysis problems. At this time, we can only discuss the study's
preliminary findings. At the time of writing, the research was still under progress. The
findings, on the other hand, can be successfully used to educate students in IT-related
fields mathematical modelling.
Key words: mathematical modelling, university teaching, student teaching, information
technology, mathematical model, base stations, cellular communication, placement
model, geometric model, mathematical model.

Formulation of the Problem of Mathematical Analysis of Cellular Communication Basic Stations
in Residential Areas for Students of IT-Preparation
Cite this Article: Sabbi Simhachalam Naidu and Syed Shahnawaz Ali, Formulation of
the Problem of Mathematical Analysis of Cellular Communication Basic Stations in
Residential Areas for Students of IT-Preparation, International Journal of Advanced
Research in Engineering and Technology (IJARET), 13(7), 2022, pp. 12-18.
https://iaeme.com/Home/issue/IJARET?Volume=13&Issue=7
1. INTRODUCTION
The effects of electromagnetic fields and radiation on the human body and other living species
have piqued the interest of experts all around the world for more than three decades. This issue
took on new significance at the turn of the twenty-first century, when the cellular
communications industry began to expand at a breakneck pace, making cell phones available
to a wider range of people, and as a result. The number of cell phone towers- base stations(BS)-
has rapidly increased in residential areas, that is, territories intended for land intended for the
construction of residential and public buildings, roads, streets, squares within cities and urban-
type settlements. On the one hand, mobile carriers are concerned with their positioning inside
the cellular network and other applications [1][2]. The solution to this problem is dependent on
a variety of factors, many of which are unrelated. The signal's quality and stability will be
determined mostly by how the BS is networked. However, this does not simplify the work of
mathematical modelling of BS placement to a simple geometric placement problem, as it may
appear at first glance. One of the most significant aspects to consider while placing the BS is
the degree of electromagnetic radiation. As a result, the architecture of placements is reduced
to a minimum number of BSs, maximum coverage of the needed coverage area, and maximum
subscriber access to the network, while reducing the impact on residential areas. This brings us
to the conclusion that early mathematical modelling of the level of exposure to electromagnetic
radiation on the population and workers in residential areas is both necessary and practical. It
is interesting to put the task of mathematical modelling of the position of cellular base stations
in residential areas in the context of training students in IT-areas of training. We chose it as a
real topic for scientific practical research since it is multifactorial and allows you to look at it
with varied initial data. The building of mathematical models is a vital educational practise in
the training of students in IT-related fields, as it builds the foundation for the algorithmic
thinking that they will need in their professional job. In the preparation of bachelors and masters
in IT-related fields of study, mathematical modelling receives a lot of attention. I ) Methodology
A mathematical model is a set of mathematical equations that reflect the relationship between
uantitative variables[3][5].The purpose of constructing a mathematical model is to produce a
model that depicts reality accurately but simply: student behaviour during the educational
process. Mathematical models are frequently used in science to describe and predict the nature
of events. Behavioral researchers develop mathematical models to convey descriptive thoughts
using mathematical concepts. Two of the most important advantages of building mathematical
models explaining theories are the verification of theoretical statements and the assessment of
the extent to which the models match empirical facts collected to explore a certain field of
study. Two requirements can be used to describe the BS layout in general [6]. The first is the
condition of minimizing the number of BS and, as a result, their total cost:
where Ci is the cost of the i-th station; Ki is the number of stations of the i-th type. The
second condition is the condition of maximum coverage of a given territory [1]:

Sabbi Simhachalam Naidu and Syed Shahnawaz Ali
where P (x, y) is the signal power at (x, y); (a, b)-coordinates of the deviation from the
point(x,y).
This condition assures that the average power in a 5 m radius zone does not fall below the
specified value. We provide this formula as is since the author in [6] set the target radius to 5
metres, but this radius can be altered and established depending on the provided criteria in the
interests of the computational model or any research.
2. RESULT
In this paper, we look at how to formulate the topic of mathematical modelling of cellular base
station deployment in residential areas for students in IT training in this work. This formulation
is due to the fact that most computer equipment emits its own, often significant, electromagnetic
radiation, which is an important element of the BS's location. Physiotherapeutic techniques, for
example, are commonly utilised in the treatment of a wide range of illnesses today [7]. An
electromagnetic field of a specified frequency and strength is used to accurately achieve the
therapeutic effects of several devices on the patient's body. As a result, medical facilities have
strict criteria for infrastructure, equipment operation, and treatment protocols.
The staff of physiotherapy departments (PEF) must undergo mandatory medical
examinations when they arrive at work, as well as periodic medical examinations once a year
and once every two years, depending on the frequency range of the device, according to the
order of the Ministry of Health and Social Development of 12.05.2013 No 302n [8]. To meet
safety regulations, patients and FTO employees should be separated into cabins that are
insulated from each other and from the corridor with sufficient shielding material. According
to the same directive" There are extra booth size regulations in all three dimensions: height –
not less than 2.0 m; length – not less than 2, 2 m; and width – not less than 1.8 – 2.0 m." (The
width of the cabin must be at least 2.0 m for inductothermy, MKV-therapy, and UHF-generators
with a power of more than 200 W). Each cabin should only have one device and one patient.
"Any medical equipment used in the FTO must be certified by a certificate of conformity,
passport, and registration certificates, and must be regularly monitored for proper operation
(electrical connection, grounding, equipment serviceability), with documentary confirmation of
the test results (inspection report or mark maintenance log)." [7]. All of this emphasises the
importance of the task. Cross-electromagnetic radiation from neighbouring BS can have a
harmful impact on medical workers and even patients who attend on a frequent basis in such
cases. Continuous exposure can lead to the development of dangerous diseases of varying
severity. According to the findings, even brief exposure to electromagnetic fields above the
maximum permitted level might result in headaches, nausea, and other symptoms. awareness
turbidity [8, 9], [11].
According to Russian standards, base stations (BS) are "radio receiving and transmitting
objects emitting electromagnetic energy in the UHF range (500-1800 MHz)." "Against the
backdrop of a higher frequency of complaints of irritability, drowsiness or insomnia, headaches
pain, etc., among persons residing or working in residential areas in the immediate vicinity of
the BS, changes in the state of the nervous, cardiovascular, and neuroendocrine systems were
erased." As a result, when defining the boundaries of the so-called sanitary zone, the BS

installation necessitates measurements at multiple points, which are typically performed along
specific measurement paths (routes), and other permanent sources of electromagnetic radiation,
such as medical institutions, are considered.To simulate the impact, the area where the BSs is
mounted is divided into sectors, with each sector choosing a radial measuring trajectory with
respect to the item. A measurement point list is constructed. The need to reduce population
exposure at the sites where it exists, both within and outside the sanitary zone, as well as
duplicate radiation and cross-electromagnetic radiation, drives the creation of a register of
measurement points.
Consider the issue of locating the smallest number of BSs while considering topography
and population density in the area where the health care institution is located. We'll go over the
requirement for reducing the amount of BS in more detail:
What determines the average signal power over an R-radius circular zone centred at (a, b).
This allows measuring the total cross-electromagnetic radiation in the residential area where
the health care facility is located. In this formulation, the task has a clear practical orientation,
which has a positive impact on the development of relevant competencies among students in IT
training fields. Many academics and practitioners have previously studied this issue, allowing
us to propose a formula for a pessimistic estimate of the average total intensity of
electromagnetic radiation generated at an observation point on the earth's surface by the entire
set of N BS cellular communications randomly located nearby.

Z∑BS is the overall EMF intensity [W / m2] produced by the BS at the observation site,
defined as the scalar sum of the power flux density BSi values of all N BS at the observation
point. HOP - height of the observation point above the surface;  - BS radiation wavelength
LTBS is the electromagnetic load on the territory created by BS near the observation point,
measured in units of [W / m2]; BS is the mean territorial density of BS near the observation
point, measured in units of [BS / m2]; PeBS is the equivalent isotropically radiated power of
BS electromagnetic radiation. E∑BS denotes the overall intensity of electromagnetic radiation
in units of electromagnetic field intensity [V / m].Following receipt of the data, it is summed
by observation points with the obtained measurement values, and the result is already analysed
in terms of safety or harm to people's health in residential areas. Considering the availability of
publications [11], [14], and [16], The formula can be used to calculate the intensity of
electromagnetic radiation using published data and estimations of the electromagnetic burden
on the land caused by the cellular communication BS in the locations of these measurements
[6], [9], [14], [19]. It is best to take the maximum of the measured values after doing many (at
least three) independent measurements [20][21]. The method of measuring electromagnetic
field parameters is critical in the environmental monitoring of telecommunications firms and
necessitates increasing attention and careful planning [6], [9], [22],[26].
3. CONCLUSION
The challenge of optimal placement of the fewest number of BS is reduced to solving both
difficulties. The generated relationships can be utilised to solve problems using the simulation
method. Russia currently lacks a state framework for monitoring the electromagnetic
environment. Systematic observations are only performed on individual objects, and are used
less frequently in relatively big distinct residential areas. However, using the calculations in the
article and following the measuring process will allow you to simulate the radiation level even
before installing the BS near residential areas where there is a possibility of exceeding the
allowable level of electromagnetic radiation.
The organisation of current control in compliance with sanitary laws, followed by analysis
of the data collected in the format of mathematical models, will ensure the prevention of
hazardous and dangerous diseases of the population and individuals working in residential
areas. It would be preferable to do a preliminary investigation of the background
electromagnetic radiation in residential areas where BS installation is proposed. Unfortunately,
because it is not regulated at all at the legislative level, the majority of mobile operators rely
solely on geometric coverage metrics to maintain the quality of client service. It is not
commonplace for residents or staff of organisations located in residential areas to conduct an
expert assessment of the level of electromagnetic radiation, which indicates that standards have
been exceeded, at their own expense. As a result, the BSs are dissolved after lengthy litigation,
causing significant harm to mobile operators. The implementation of a cellular base station
location model near various areas will, first and foremost, protect public health.
In addition, reduce the costs associated with BS installation breaches. In terms of the
educational component of the problem of mathematical modelling of cellular base station
position in residential areas for students of IT-training areas, the practice-oriented nature of this
job, as well as its research worth, is significant. When we look at professional standards in
information technology, as well as the relevant GEF, we can see that mathematical modelling,
the capacity to synthesise and explain data, and the ability to parameterize are among the
important competences expected of current specialists in this sector.

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FORMULATION OF THE PROBLEM OF MATHEMATICAL ANALYSIS OF CELLULAR COMMUNICATION BASIC STATIONS IN RESIDENTIAL AREAS FOR STUDENTS OF IT-PREPARATION