JOURNAL OF TELECOMMUNICATIONS, VOLUME 16, ISSUE 1, SEPTEMBER 2012

© 2012 JOT

www.journaloftelecommunications.co.uk

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An Educational Model Cellular Shape Convertor (EMCSC): A Tool That

Demonstrates and Calculates the Size and Shapes of Cells in Cellular Networks

Jameson Mbale

Abstract: This paper introduces the Educational Model Cellular Shape Convertor (EMCSC) a tool which demonstrates and

calculates the sizes and shapes of various models of cellular network cells. The size and shape of the cell is the most critical

factor in a cellular system design. The tool computes the area covered, distance around, ratio of boundary length and unit area,

ratio of unit area with N channels with cells, channel increased by a factor K and cell reduced by a factor M. The computed data

can be used to determine the ideal shape and use the information to guide the setting up and operation of the wireless cellular

network. The EMCSC tool has four major components: the Heterogeneous Shape Cell Model (HSCM), which holds the various

shape models; the Automated Equation Formula Calculator (AEFC), the automated part which evaluates the formulas; the

Mathematical Sorter (MS), which sorts the calculated data and User Repository (UR) which stores the data for later use by the

user.

Index Terms: Cells, mathematical formulas, increased factors and reduced factors.

—————————— ——————————

1 INTRODUCTION

ireless technology has emerged as one of the most convenient for establishing networks, especially in areas where it is difficult to install physical equip-

ment. Wireless equipment can easily be deployed in inac-cessible areas or terrain, such as base stations, Access Points (AP), backup power for access points, repeaters, laptops, solar panels, inventers and batteries.

The sizes and shapes of the cells are the most im-portant factors in designing a cellular network. It is with this in mind that the Educational Model Cellular Shape Convertor (EMCSC) tool has been developed to calculate the sizes of the various cell shapes. The computed data can be used to assess and determine the locations and sizes of the cells that comprise the network. The tool as-sists the telecommunications engineers to determine the areas to be covered, with minimum overlap of area cover-age within cells.

Various cell shapes are envisaged including polygons, squares, triangles, and circles. Appropriate models of cells would be designed before a cellular system is established. Cell boundaries need to be carefully considered because some shapes may leave larger areas uncovered. Similarly, a larger coverage that extended well outside the cell would be a waste of resources. Therefore, the need to adopt the cellular model shape which would cover ninety

percent of the site leaving only a small portion not cov-ered, which would be covered by the neighbouring cells. This implies that a particular cellular shape would be de-termined by the geographical terrain.

1.1 EMCSC Overview

The tool has a number of model shapes whose meas-urements are calculated taking radius R meters for circu-lar shapes and side R meters for equilateral triangles, squares and polygons. The EMCSC tool has an automated component which calculates the area covered, circumfer-ence, ratio of boundary length and unit area, ratio of unit area with N channels with cells, channel increased by a factor K and cell reduced by a factor M. The tool performs calculations on the various shape models. Based on the geography of the area, the engineer can assess from the computed figures the right shape model to use. Table 1 shows the various formulas used for each model within the EMCSC tool.

1.2 Study Outline

This study is organised as follows. Section 2 gives

highlights of other research that has focused on cellular

innfrastructure. The EMCSC system architecture is pre-

sented in Section 3. Section 4 discusses the implementa-

tion of the EMCSC and includes two illustrative case

studies. Section 5 draws some conclusions.

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J. Mbale is with the University of Namibia, Centre of Excelence in Tele-communications and Information Technology, Department of Computer Science, P/B, 13301, Windhoek, Namibia.

W

2 RELATED WORK

The desire to develop communication infrastructure in an

inaccessible areas is one of the factors that has driven the

emergence of cellular technologies. Recently much re-

search has focused on the development of cellular infra-

structure in inaccessible areas.

In [1] they illustrated that in a cellular system the most

important factor is the size and shape of the cell. They

define a cell as the radio area covered by a transmission

station or a base station. All users in the cell are served by

the base station. The authors point out that in ideal radio

environments, the shape of the cell will be circular cen-

tred at the microwave transmitting tower and with radius

equal to the reachable range of the transmitted signal. The

cell area and periphery are determined by the signal

strength within the region, which in turn depend on

many factors, such as the contour of the terrain, height of

the transmitting antenna, presence of hills, valleys, and

tall buildings and atmospheric conditions. The authors

emphasized that the actual shape of the cell would nor-

mally be irregular with a zigzag boundary. However, for

practical purposes, the cell could be approximated by a

regular hexagon, which is itself a good approximation of

a circular region. Using regular hexagonal shapes allows

a larger region to be divided into nonoverlapping hexag-

onal sub-regions of equal size, with each one representing

a cell area. The authors also gave some further examples,

including the square and the equilateral triangle, as alter-

native shapes that can be used to represent a cell area.

Octagons and decagons are shapes that better approxi-

mate a circular area. Figure 1 is taken from [1] and illus-

trates a cell with a base station and mobile stations (MS).

The Figure shows the circular, hexagonal and square cell

models.

Base Station

MS

CellMS

Ideal cell area

(2 - 10) km radius

Cell a

rea u

sed

in m

ost m

odelsA

ltern

ati

ve

sh

ap

e o

f a c

ell

Figure 1. Illustration of a Cell with a Base Station and Mobile Sta-tions

Although in [1], many cellular systems technologies

are discussed, less attention is given to the determination

of the size of cells. The EMCSC operates as a tool to com-

pute the cell size, the unit area when number of channels

is increased by a factor, and unit area when size of cell is

reduced by a factor. Such statistical data will aid tele-

communications and mobile engineers to determine

which cell model to use.

In [2], the cell is defined as the geographic area where

a mobile station is preferentially served by its base sta-

tion. It is pointed out that the cell shape can be defined as

a circle and its radius was determined so as to have a cir-

cular area within which base station and mobile stations

receive a signal power exceeding a given threshold. It is

emphasized that a mobile station moving out of its serv-

ing cell and into a neighbouring cell must be provided

with sufficient resources from these cells so that the al-

ready established communication will not be discontin-

ued. However, it is argued that circles, on the other hand,

cannot fill a plane without leaving gaps (holes) or exhibit-

ing overlapping areas. It was acknowledged that the use

of circular geometry may impose difficulties in the design

of a cellular network, whereas regular polygons, such as

equilateral triangles, squares, and regular hexagons

would not exhibit these constraints. The authors also clar-

ified that the choice for one or another cellular format

depends on the application, and noted that in practice,

the coverage area differs substantially from the idealized

geometric figures and that amoeboid cellular shapes are

more likely to occur.

The EMCSC presented in the present paper is an au-

tomated system which calculates the areas covered by the

cell shape and enables the engineer to make assessments

from the computed data.

In [3] the concept cells are defined as normally roughly

circular, but they are easier to model as hexagons. The

cells are all of the same size and grouped in units of seven

cells. At the centre of each cell is a base station to which

all the telephones in the cell transmit. It is further dis-

cussed that the base station consists of a computer and

transmitter/receiver connected to an antenna. At any in-

stant, each mobile telephone is logically in one specific

cell and under the control of that cell’s base station. When

a mobile telephone physically leaves a cell, its base station

notices the telephone’s signal fading away and asks all the

surrounding base stations how much power they are re-

ceiving from it. The base station then transfers ownership

to the cell getting the strongest signal, that is, the cell

where the telephone is then located. The telephone is then

informed of its new “boss”, and if a call is in progress, it

will be asked to switch to a new channel. It is emphasised

that base stations are really just radio relays.

In [4], it is pointed out that a synonym for “cell site” is

“cell tower”, although many cell site antennas are mount-

ed on buildings rather than on towers. However in GSM

networks, the technically correct term is a base transceiver

station (BTS), and colloquial British English synonym are

“mobile phone mast” or “base station”. It was also ex-

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plained that a cell site was a term used primarily in North

America for a site where antennas and electronic commu-

nications equipment were placed to create a cell in a net-

work. It was further pointed out that each cell requires a

tower or other elevated structure for mounting antennas,

and one or more sets of transmitter/receivers, transceiv-

ers, digital signal processors, control electronics, a GPS

receiver for timing (for CDMA2000 or IS-95 systems),

regular and backup electrical power sources, and shelter-

ing.

The authors of [4] regard a cellular network as a radio

network made up of number of radio cells (or just cells)

each served by at least one fixed-location transceiver

known as a cell site or base station. These cells cover dif-

ferent land areas to provide radio coverage over a wider

area than the area of one cell, so that a variable number of

portable transceivers can be used in any one cell and

moved through more than one cell during transmission.

The authors point out that cellular networks offer a num-

ber of advantages over alternative solutions such as: in-

creased capacity, reduced power usage, larger coverage

area, and reduced interference from other signals.

3 EMCSC SYSTEMS ARCHITECTURE

The EMCSC demonstrated in Figure 1 has four major

components: the Heterogeneous Shape Cell Model

(HSCM), Automated Equation Formula Calculator

(AEFC), Mathematical Sorter (MS) and User Repository

(UR). These are discussed in the following sections.

3.1 The Heterogeneous Shape Cell Model

The Heterogeneous Shape Cell Model is composed of

various cell shape models: the circle, the hexagon, the

square and the triangle. The size of a circle is specified as

the radius in kilometers, while the size of a hexagon,

square and triangle are specified as the length of a side in

kilometers. The user may choose one model at a time or

choose all to compute the cell size or sizes. The cell shape

information is forwarded to the EFC, where it is added to

other input data to commence the calculations.

Automated Equation Formula Calculator (AEFC)

User Respository

Distance

Length

Unit Area

.R R

RR R

. . Other

Shapes

Channel N,

Increased Factor K

Reduced Factor M

Mathematical

Sorter

Area

Covered

Distance

Around

Unit Area

/ Cells

Increased

Factor by

K

Reduced

Factor by

M

Heterogeneous Shape Cell Model

Figure 2. Educational Model Cellular Shape Convertor Systems architecture

3.2 The Automated Equation Formula Calculator (AEFC)

For The Automated Equation Formula Calculator (AEFC)

is an automated component of the tool that is pro-

grammed to evaluate the formulas shown in Table 1. The

AEFC receives the channel and factor data that is com-

bined with that from the Heterogeneous Cell Shape Mod-

el. This tool component calculates the area covered, cir-

cumference, distant length per unit area, channels per

unit area with N channels/cells, channels per unit area

when number of channels increased by a factor K and

channels per unit area when size of cell is reduced by a

factor M for all the cell shape models. The user may calcu-

late one shape model at a time or all at once. When the

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calculations are complete, the computed data is forward- ed to the Mathematical Sorter.

TABLE 1. EDUCATIONAL MATHEMATICAL MODEL CELLULAR FORMULA USED IN EMCSC

Cell

Shape

(side = R)

Area-

Covered

Distant-

Around

Dist Length

/Unit Area

Unit Area/

Cells

Channels

by Fact. K

Reduced

Fact. M

Circular

Cell 2R R2

R

2 2R

N

2R

NK

2

2

R

NM

Hexagonal

Cell 2

2

33R 6R

R3

4

235.1 R

N

235.1 R

KN

2

2

35.1 R

NM

Square

Cell 2R 4R

R

4

2R

N

2R

KN

2

2

R

NM

Triangular

Cell 2

4

3R 3R

R

34

23

34

R

N

23

34

R

NK

2

2

3

34

R

NM

3.3 Mathematical Sorter (MS)

The Mathematical Sorter (MS) receives the computed data

from the AEFC, sorts the data according to its category

and forwards them to the User Repository.

3.4 Using Repository

The User Repository (UR) receives the sorted data from

the MS. In the UR, the sorted data is stored according to

its category as shown in Figure 2. This is where the user

can use the calculated data to assess which Cell Shape

model is suitable for the site.

4 IMPLEMENTATION OF THE EDUCATIONAL MODEL

CELLULAR SHAPE CONVERTOR (EMCSC)

The tool is designed to calculate circular, hexagonal,

square and triangular cell shape models. The user may

choose either to calculate individual cell shape models or

all of them at once.

4.1 Case Study 1: Calcualte Hexagonal Cell Shape

In the tool, the user selects the hexagonal cell radio button

as illustrated in Figure 3a. The tool displays the hexago-

nal cell row with its six formulas under the respective

fields.

Figure 3a. Calculation of Hexagonal Cell Shape

Then the user enters the input data, for example: number of channels (N) = 3, channel increased by a factor

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K = 2, the length side of a hexagon (R) = 10, reduced factor

M = 4. Once the input has been entered correctly, the user

presses the calculate button to have the tool compute the

output. The calculated values are displayed as shown in

Figure 3b as: area covered is = 259.80m2; distant around is

= 60.00m; distant length per unit area is = 0.23; unit area

with N channels per cells is = 0.011 m; unit area channels

increased by factor K is =0.023m; and unit area-size of cell

reduced by factor M is = 0.185m. The displayed results

may be cleared by pressing the clear button. To quit from

the whole system, an exit button may be used.

Figure 3b. Calculation of Hexagonal Cell Shape – Showing Results

For clarity, the Hexagonal cell row would have its val-

ue be presented column by column as follows:

Area-Covered = 2

2

33R

= 259.81m2 (1)

Distant-Around = 6R = 60m (2)

Dist. Length/Unit Area =R3

4

= 0.23m (3)

Unit-Area N Channels/Cells =235.1 R

N= 0.011m

(4)

Unit Area-Channels Increased by a Factor

K = 235.1 R

KN

= 0.023m (5)

Unit Area-Size of Cell Reduced by Factor

M = 2

2

35.1 R

NM

= 0.185m (6)

The other options: Circular, Square and Triangular

cells may be calculated as for the Hexagonal cell. Thereaf-

ter the computed values would be compared to assess the

cell model which would best suit the particular site.

4.2 Case Study 2: Calcualte for All the Cell Shapes

For In the tool there is also an option to calculate at once

for all the cell shapes Circular, Hexagonal, Square and

Triangular as shown in Figure 4. In this case the user

presses the Compare button, which will prompt for the

various inputs: number of channels (N) = 3, channel in-

creased by a factor K = 2, the length side of a hexagon (R)

= 10, reduced factor M = 4.

Figure 4a. Calculation of All Cell Shape

Once all the prompted input is completed, the results are displayed as indicated in Figure 4b.

Figure 4b. Calculation of All Cell Shape – Showing Results

From Figure 4b, the user can make comparisons. For

the same input data, the circular cell had the greatest area

covered and distant around, followed by Hexagonal cell,

third is Square cell and last is the Triangular cell.

The Circular cell covered more areas and distant

around. However, it is less successful when it comes to

distant length per unit area, channels per unit area per

cell and cell size reduced by factor M, for which attributes

the other model shapes do better, in order of hexagonal,

square and triangular.

With this mathematical comparison, the circular shape

and hexagonal shapes are preferred as the most appropri-

ate models. Though the circular shape tends to have more

space than the hexagonal, the latter has more added ad-

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vantages. Though the shapes with higher area and distant

around, they have the least cell size reduced by factor M,

channels per unit area per cell and distant length per unit

area. One of the greatest disadvantages of the circular

shape is when there are multiple cells to be covered, as

circles leave larger gaps between the boundaries as indi-

cated in Figure 5a. By contrast, the hexagonal in Figure 5b

leaves no gaps at all. For this reason, the hexagonal shape

is more preferred than the circular one in the design of

cellular wireless networks.

Gaps

between

circular cells

No gaps

between

hexagonal

cells

Figure 5a. Circular Cells Figure 5b. Hexagonal Cells

5 CONCLUSION

The size and shape of a cell is the most important factor in

a cellular network. In fact the cell area and the distant

around are the most critical parameters that affect the

handoff from a cell to an adjacent cell. Therefore, this pa-

per introduces the EMCSC tool that calculates the size

and shape of the various cell models. The study has en-

visaged that the size and capacity of the cell per unit area

and the impact of the shape of a cell on service character-

istics is the cornerstone to develop a cellular system. It is

obvious from the calculations that when the cell area is

increased, the number of channels per unit area is re-

duced for the same number of channels. Therefore it is

ideal for less populated areas with fewer cell phone sub-

scribers. Note that if the number of cell phone users is

increased, then the obviously the number of channels

may be increased. The other alternative is to reduce the

cell size so that the number of channels per unit area is

kept comparable to the density of subscribers.

The calculations done also showed that the hexagonal

model shape was the most ideal for the cellular system.

Apart from the calculated data, Figure 4b demonstrated

that the hexagonal shape could fit tightly just likes tiles on

the floor.

REFERENCES

[1] D. P. Agrawal and Q. Zeng, “Introduction to Wireless

and mobile Systems,” Thomson, Canada, 2006.

[2] M. D. Yacoub, “Wireless Technology, Protocols,

Standards, and Techniques,” CRC Press LLC, United

State of America, 2002.

[3] A. S. Tanenbaum, “Computer Networks,” Fourth

Edition. Prentice Hall PTR, New Jersey, United State

of America: 2003.

[4] Wikipedia, the free encyclopedia.

Http://en.wikipedia.org/wiki/

Jameson Mbale received his PhD Degree in Computer Science

from Harbin Institute of Technology, China, in 2003. He obtained

M.Sc. Degree in Computer Science from Shanghai University in

1996 and B.A. in Mathematics and Computer Science at University

of Zambia in 1993 in Zambia. He is a Senior Lecturer in the Depart-

ment of Computer Science at the University of Namibia. He is the

founder and coordinator of Centre of Excellence in

Telecommunications and Information Technology. His research

interest in network security, wireless networking, telecommunications

and e-Learning and he has published papers in these areas.

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