947

https://doi.org/10.37815/rte.v34n3.947

Original articles

Comparison of radio propagation models in five LTE coverage cells i= n Riobamba

Comparación de modelos de propagación de radio en cinco celdas de cobertura LTE de Riob= amba

Brayan Vique<= /span>¹ <= /span>^{https://orcid.org/0000-0=
001-6283-0884},

Carlos Bayas^{1 =}^{https://orcid.org/0000-0=
002-3037-3954}, Martin Escobar¹^{https://orcid.org/0000-0=
001-7033-2914}, Adrián Infante^=
1^{https://orcid.org/0000-0=
001-8754-9239}, Allison Proańo^=
1^{https://orcid.org/0000-0=
002-8587-2099}

¹Escuela Superior Politécnica de Chimborazo, Facult= ad de Informática y Electrónica, Riobamba, Ecu= ador

brayan.vique@espoch.edu.ec, carlos.bayas@espoch.edu.ec, nicolas.escobar@espoch.edu.ec, adrian.infante@espoch.edu.ec, allison.proanio@espoch.edu.ec

Sent: 2022/06/19<= o:p>

Accepted: 2022/09/16

Published: 2022/11/30

Abstract

This article performs a comparative analysis of the power intensity levels measured with the Network Cell Info Lite application and the perform= ance of the different propagation models: Log-Normal, Okumura Hata, COST 231, Walfish Bertoni<= /span>, and SUI in the 4G LTE Frequency Band. The study was conducted in five LTE coverage cells located in the southern area of the city of Riobamba. The mo= del that best fits each cell was chosen by means of absolute error analysis, th= us obtaining an empirical correction factor for the proposed models. For the analysis of the absolute error, three measurement campaigns were carried out with 50 samples where the mean value was obtained. After applying the aforementioned models, the Log-Normal model yielded th= e most favorable results, being the one that achieved the best adaptation in Rioba= mba, since the power levels vary in the range (-80; -106) dBm at a coverage area= not exceeding 200m.

= Keywords: Coverage cells, frequency band, multiscreen diffraction loss, cells and open spatial propagation model, Friis.

Summary: Introduction, Theoretical Framework, Methodology, Results and Conclusions.

= ;

How to= cite: Vique, B.,= Bayas, C., Escobar, M., Infante, A. & Proańo, A. (2022). Comparación de modelos de propagación de radio en cinco celdas de cobertura LTE de Ri= obamba. Revista Tecnológica - Espol, 34(3), 171-190. http://www.rte.espol.e= du.ec/index.php/tecnologica/article/view/947

Resumen

Este artículo realiza un análi= sis comparativo de los niveles de intensidad de potencia medidos con la aplicac= ión Network Cell Info Lite y el desempeńo de los diferentes modelos de propagac= ión: Log-Normal, Okumura Hata, COST 231, Walfish Bertoni y SUI, en la Banda de Frecuencia 4G LTE. El estudio se realizó en cinco celdas de cobertura LTE ubicadas en la zona sur de la ciudad de Riobamba. Se eligió el modelo que m= ejor se ajusta a cada celda mediante el análisis de error absoluto, con ello se obtuvo un factor empírico de corrección para los modelos propuestos. Para el análisis del error absoluto se realizaron tres campańas de medición con 50 muestras donde se consiguió el valor medio. Después de aplicar los modelos antes mencionados, el modelo Log-Normal arrojó los resultados más favorables siendo este, el que logró una mejor adaptación en Riobamba ya que los nivel= es de potencia varían en el rango (-80; -106) dBm a una zona de cobertura no superior a los 200m.

Pa= labras clave: Celdas de cobertura, banda de frecuencia, pérdi= da de difracción multipantalla, celdas y modelo de propagación espacial abierta, Friis.

Introduction

The growing demands on mobile services have encouraged many research= ers toward achieving multi- services with low latency. To illustrate that, Zhang (2012) = = pointed out that LTE (Long Term Evolutio= n) is a standard for high-speed wireless data communications which is maintained = as a project of the 3rd Generation Partnership Project (3GPP). In addition, to c= over the requirements of the mobile migrations of Internet applications, such as VOIP, video streaming, music downloading, and mobile TV, LTE networks offer= the capacity to tolerate the throughput explosion for the connection from mobile devices customized to those new mobile applications. A propagation model is= a set of mathematical expressions, diagrams, and algorithms used to represent= the radio characteristics of a given environment (Bekele, 2017).

In 2004, an initial study of long-term evolution (LTE) was introduced and viewed as a path for migration to 4G networks (Rao, 2009). With the rap= id development of LTE (4G) technology in recent years, 4G terminals like mobile phones have been widely used for communication. LTE (4G) signals have cover= ed indoor and outdoor environments in modern cities. Inspired by the advances = in wireless sensing that have enabled a large variety of new applications such= as indoor localization (Li, 2016).

LTE aims to increase the speed and capacity of wireless networks by utilizing signal processing techniques and modulations (Hadi, 2015). 4G technology is supported by the 3GPP (third generation) standard, which bases its system on IP, that is, it is a system of systems and a netw= ork of networks, and is subsequently overcome in the convergence between cable networks or wireless networks, computers, electrical devices -electronic, I= CT among others to provide access speeds between 100Mbps in movement and 1Gbps= at rest, but the most important thing is to maintain the quality of service (Q= oS) from point to point (end-to-end), with high security to massify the number of additional ser= vices in any place betting on having the lowest possible cost (Tomažič, 2009).

Path loss models are sophisticated tools for predicting coverage are= a, interference analysis, frequency assignments, and cell parameters which are= the basic elements for the network planning process in mobile radio systems (Blaunstein, 2006).

The Okumura-Hata model is the most widel= y used empirical propagation prediction model. In 1980, Hata<= /span> introduced an empirical formula for propagation loss that was derived from Okumura's report to put the propagation prediction method into computational use in system planning software. The propagation loss is presented in the simple form A + B log(R), where A and B are functions of frequency and heig= ht of the antenna and R is the distance (Y., 1967). This simplicity of the mod= el has made it the most widely used propagation prediction model and it is even standardized for international use (Union, 1995).

The European Cooperative for Scientific and Technical Research (Euro-Cost) developed the Cost 231 model, in which the Hata model is extended to the 2 GHz range, covering the VHF and UHF bands. CM is= a correction factor to fit the model by extending the frequency range for whi= ch the Hata model operates; CM (0 dB) for medium c= ities and suburban areas; CM (3 dB) for metropolitan centers; and that correspond= s to the equations presented in the Hata model. One = of the contributions of this model is to consider losses due to dispersion (Garcia, 2004).

Stanford University Interim (SUI) model derived from Hata, with corrections for frequencies above 1900MHz. It includes the path loss exponent, it proposes three different types of terrain: urban, suburban, and rural. The height of the antenna of the proposed base station is between 10= and 80 meters, that of the mobile from 2 to 10 meters, and the extension of the cell from 0.1 to 8 km (Shahajahan, 2009).<= /o:p>

The model, proposed by Joram Walfisch and Henri Bertoni, considers the losses produced by the diffractions that occur on the roofs of buildings (Walfish, 1988). It is a model that d= oes not consider the existence of a line of sight between the transmitter and t= he receiver, it uses the phenomenon of diffraction to describe the losses suff= ered by the signal before reaching the receiver located low above the street. The contribution of the rays that penetrate the buildings and of those that suf= fer multiple diffractions is neglected. The separation between the buildings mu= st be less than their height and they are supposed to be arranged in parallel rows. The frequency range in which this model applies is from 300 to 3,000 = MHz, with a separation between transmitter and receiver of 200 to 5,000 m. It is= not applicable when the base station antenna is below the average height of buildings (Hernando, 2013).

The log-normal distribution is a function distributing a dependent variable in a normal or Gaussian fashion on a logarithmic scale of the independent variable. This function has been used for a long time to descri= be size distributions of particle properties in atmospheric aerosols. Foitzik (1964) used this functional relationship for = the description of optical aerosol properties. Later, Whitby (1974) built a gen= eral concept for the multimodal nature of the atmospheric aerosol on this approa= ch by fitting measured particle size distributions in a combination of three log-normal distributions (Heintzenberg, 1994).<= o:p>

To determine the performance of the previously proposed propagation models, a comparative analysis of the power intensity levels measured with the Network Cell Info Lite application in the 4G Frequency Band was carried out at 5 LTE coverage cells located in the southern zone of the Riobamba city and the mo= del that best adapts to the conditions of the area will be extinguished by appl= ying an empirical correction factor to the proposed models. The document details= the absolute error for the calculation of this correction factor, considering t= hree measurement campaigns with 50 samples where the mean value was obtained. Fr= om the study carried out, it was concluded that the model Log-Normal is the be= st estimator of power levels considering the environment of the city, which is= a residential area.

Theoretical Framework

Log-Normal Model

It is an empirical model based on a reference of the losses at a pre-established distance, and applicable in closed environm= ents by factors of correction. It is expressed in an equation as a function of t= he distance between transmitter and receiver as:

(1)<= o:p>

Where is the path loss variable due to the mult= iple trajectories; is the- loss to one near reference distance and it is calculated using the space propagation model open, Friis formula, or taking measurements field; is a random variable expressed in dB and experimentally validated and statistica= lly. The model is simple but absorbs the random effects of shadows and multipath that occur for different measurement locations with the same distance between the Tx-Rx, but with different obstructions in the path of propagation comparing with a reference value (Yepez, 2012).

Okumura Hata Model

The = Hata model is an empirical formulation of the graphical path loss data provided = by Okumura and is valid from 150 MHz to 1500 MHz. = Hata presented the urban area propagation loss as a standard formula and supplied correction equations for application to other situations. The standard formula for median path loss in an urban area is given:

<= /p>

=

(2)<= o:p>

Where is the frequency (MHz) from 150 MHz to 1= 500 MHz, is the effective transmitter (base station) antenna height (meters) ranging from 30 m to 200= m, is the effective receiver (mobile) anten= na height (meters) ranging from 1 m to 10 m, is the T-R separation distance (km), and= is the correction factor for effective m= obile antenna height which is a function of the size of the coverage area. For a small to medium-sized city, the mobile antenna correction factor is given b= y:

<= /span>

(3)<= o:p>

and for a large city, it is given by:

for MHz

(4)<= o:p>

for MHz

(5)<= o:p>

The predictions of= the Hata model compare very closely with the origin= al Okumura model if d exceeds 1 km. This model is well suited for large cell mobile systems, but not personal communications systems (PCS) which have ce= lls on the order of a 1km radius (Anonymous, 1968).

<= /span>

Cost 231 Walfish-Ikegami Model

The COST 231 model is a semi-empirical path loss prediction model. It is recommended for macro-cells in urban and sub-urban scenarios, with good path loss results for transmitting antennas located ab= ove average rooftop height. However, the error in the predictions increases considerably as the transmitter height approaches rooftop height, leading to very poor performance for transmitters below that level. Compared to previo= us models such as Okumura-Hata, the COST 231 model includes a series of additional parameters to the calculation process, in addition to expanding the frequency range in which it can be used (800 - 20= 00 MHz). The model performs a more detailed calculation of the attenuation, ba= sed on four additional parameters:

· = Height of buildings.

· = Width of streets.

· = Separation between buildings.=

· = Orientation of the street concerning the direction of propagation.

For LOS scenarios, the propagation loss conside= rs only the free space loss, where:

		(6)<= o:p>
		=

is expressed in km and in MHz.

The typical NLOS path described in the COST 231 model is shown in Figure 1 and Figure 2.

Figure 1

Typical NLOS Propagation Scenario Profile view<= o:p>

Figure 2

Typical NLOS Propagation Scenario Top view

The parameters defined in the COST 231 model (<= /span>Figure 2= ) are t= he following:

· : average height of buildings (meters)

· : width of the street (meters)

· : average distance between buildings (meters)

· : angle formed by the direction of propagation and the axis of the street.

· = : base station antenna height (meters)

· = : height of the mobile device antenna (meters)

·&n= bsp; =3D (meters)<= /span>

· : total distance between the first and the last building on the path (meters)=

· : distance between the base station and mobile device (km)<= /span>

· : frequency (MHz)

The basic propagation loss for the NLOS scenari= o is given by:

(7)<= o:p>

The propagation loss in free space conditions, = L0, is obtained according to the expression:

(8)<= o:p>

The term considers the width of the street and it= s orientation concerning the direction of ray propagation.

The expression for the calculation of L<= /span>rts is given by:

(9)<= o:p>

where:

(10)<= o:p>

The term is a correction factor that quantifies losses due to street orientation. In case the value of < 0, =3D 0 should be considered.

The multiscreen diffraction loss, , is a function of the frequency, the distance between the mobile device and the base station, as well as the hei= ght of the base station and the height of buildings. Like , if is negative, =3D 0 is considered. Its value is calculated using the expression:

(11)<= o:p>

where:

(12)<= o:p>

Is a term that depends on the height of the base station. In addition, the following parameters are defined:

(13)<= o:p>

(14)<= o:p>

(15)<= o:p>

The term presents the increase in path loss for the case of base stations located be= low the average height of the buildings. The terms and control the dependence of on distance and frequency, respectively. If there is no data on the buildings on the route, the COST 231 model recommends using: (Aguilar, 2010).

		(16)<= o:p>
		=
		(17)<= o:p>

Walfish-Berton= i Model

It is valid when there is no line of sight betw= een the base station and the mobile. Buildings are modeled as a set of diffract= ion and absorption screens buildings of a uniform height and width are consider= ed, require that the transmitting antenna is above the highest ceiling.

The path loss is given by:

(18)<= o:p>

where:

· : frequency (MHz)

· : distance between transmitter and recei= ver (km)

· : average height of the antenna concerni= ng the height of the buildings (m)

· : variable that expresses the influence = of buildings on the signal

Figure 3

Typical propagation Scenario

The influence of buildings on the signal (Figure 3).=

(19)<= o:p>

where:

· = : height of buildings (m)

· = : receiver height (m)<= /p>

· : distance between buildings (m)

In a real environment, the geometry of the buildings is irregular, causing this model to have less certainty in predic= ting the received power; however, this model is applicable in radio propagation simulation software (Cell View) if adaptations are made to the equations or= if an average density and height of buildings are obtained (Shabbir, 2011).

SUI Model

Stanford University Interim (SUI) model is developed for IEEE 802.16 by Stanford University. It= is used for frequencies above 1900 MH. In this propagation model, three differ= ent types of terrains or areas are considered. These are called terrain A, B, a= nd C. Terrain A represents an area with the highest path loss, it can be a very densely populated region while terrain B represents an area with moderate p= ath loss, a suburban environment. Terrain C has the least path loss which descr= ibes a rural or flat area. In , these different terrains and different factors used in the SUI model are described (Table 1).

<= /span>

Table 1

Different terrains and their parameters

PARAMETERS=	TERRAIN A<= b>	TERRAIN B<= b>	TERRAIN C<= b>
a	4.6	4	3.6
b (1/m)	0.0075	0.0065	0.005
c (m)	12.6	17.1	2= 0

&n= bsp;

The pat= h loss in the SUI model can be described as

&n= bsp;

(20)<= o:p>

where PL represents Path Loss in DBS, d is the distance between the transmitter and receiver, do is the reference distance, is the frequency correction factor, is the correction factor for base station height, S is shadowing and γ is the path loss component and it is described as

(21)<= o:p>

where is the height of the base station and a, b and c represent the terrain for whi= ch the values are selected from the above table.

(22)<= o:p>

where is free space path loss while do is the distance between Tx and Rx and = is the wavelength. The correction factor for frequency and base station height= are as follows:

(23)<= o:p>

(24)<= o:p>

where is the frequency in MHz, and is the height of the receiver antenna. This expression is used for terrain typ= es A and B. For terrain C, the blow expression is used.

(25)<= o:p>

(26)<= o:p>

Here, dB for rural and suburban environments (Terrain A & B) and 6.6 dB for urban environments (Terrain C) CITATION Sha11 \l 3082 (Shabbi= r, 2011).

Meth= odology

The comparative analysis was carried out on 5 LTE coverage cells in the South Z= one of the city of Riobamba in 3 different campaigns, taking 50 reference sampl= es from which, the arithmetic means of said measurements were taken to have an estimate of the reception power of each cell.

Figure 4

Location of LTE coverage cells

The southern area of the= city of Riobamba was taken by the Google Maps application where the 5 cells were located, and the power data was collected for the study of the propagation models that can be applied in said area. Each antenna works with different operators (Figure 4).

The applicability of this document was carried out using 2 software programs: Microsoft Excel for the development = of mathematical operations and obtaining numerical data, and MATLAB for the management of graphs and the statistical study of results.

To determine which model best fits, we= apply the equations of the different propagation models considering the correction factor and the parameters that each model requires.

Coverage Cell = 1

The first cell is located on José Oroz= co and Bernardo Darquéa streets from Riobamba City it belongs to the Tuenti operator and works with an operating frequency of 1900MHz. Next, the considerations for the use of propagation models are detailed (Table 2).

Table 2=

Para= meters Cell 1

PARAMETERS<= /o:p>	VALU= E
Base station antenna height = (m)	30
Mobi= le device height (m)<= /o:p>	1.5<= o:p>
Distance (m)=	47–1= 70
Stre= et width (m)	4
Elevation ang= le	14.4= 7°-40.79°
Buildings height (m)	9
Distance between buildings (m)	4

Fuente: <= span style=3D'mso-bookmark:_Toc38966068'>https://www2.ulpgc.es/hege/almacen/downlo= ad/27/27199/propagacion.pdf

Coverage Cell = 2

The second cell is in the Sabún Sports Complex, located on Av. October 9 = and Atenas street from the Riobamba city, it belongs to Tuenti operator and works with an operating frequency= of 1900MHz. Next, the considerations for the use of propagation models are detailed (Table 3).

Table 3=

Para= meters Cell 2

PARAMETERS	VALUE
Ba= se station antenna height (m)	32
Mobile device hei= ght (m)	1.5
Distance (m)=	48.62 – 205.02
Street width (m)	4
Elevation ang= le	20° - 63°
Buildings height (m)	9
Distance between buildings (m)	3.5

Coverage Cell 3

The third cell is located at Celso Rod= ríguez Avenue and París street from Riobamba city, it belongs to the Tuenti operato= r and works with an operating frequency of 1900MHz. Next, the considerations for = the use of propagation models are detailed (Table 4).

Table 4=

Para= meters Cell 3

PARAMETERS	VALUE
Base station antenna height = (m)	18
Mobi= le device height (m)<= /o:p>	1.5
Distance (m)	49 – 211
Stre= et width (m)	4
Elevation angle	25° - 63°
Buildings height (m)<= /o:p>	9
Distance between buildings (m)	4.5

Coverage Cell 4

The fourth cell is located at Leopoldo Freire Avenue and Lisboa Street from Riobamba c= ity, it belongs to the CNT operator and works with an operating frequency of 1900MHz. Next, the considerations for the use of propagation models are detailed (Table 5).

Table 5=

Para= meters Cell 4

PARAMETERS	VALUE
Ba= se station antenna height (m)	30
Mobile device hei= ght (m)	1.5
Distance (m)=	49 – 226
Street width (m)	4
Elevation ang= le	25°-72°
Buildings height (m)	9
Distance between buildings (m)	3.5

Coverage Cell 5

The fifth cell is located at 9 de Octubre avenue and Noruega street from Riobamba city, it belongs to the Claro operator and works with an oper= ating frequency of 1700MHz. Next, the considerations for the use of propagation models are detailed (Table 6).

Table 6=

Para= meters Cell 5

PARA= METERS	VALUE
Base station antenna height = (m)	25
Mobi= le device height (m)<= /o:p>	1.5
Distance (m)	48.62 – 205.02
Stre= et width (m)	4
Elevation angle	17° - 70°
Buildings height (m)<= /o:p>	9
Distance between buildings (= m)	4

Finally, the losses obtained by each o= f the models mentioned above are replaced in the general formula that is given by= :

(27)

where:

·&n= bsp; : transmission potency

·&n= bsp; : transmission= gain

·&n= bsp; : reception ga= in

·&nb= sp;

(= 28)

w= here:

·&nb= sp; := absolut mistake

·&nb= sp; := average power value

· : power value for each propagation model

&= nbsp;

Results

The following graphs obtained show the approximate curves of the propagation mo= dels without a correction factor in each of the five LTE coverage cells concerni= ng the average power whose data was collected in the southern zone of the city= of Riobamba.

Figure 5

Coverage cell 1 without correction factor

= Figure 5I= n cell 1 (Figure 5). It is possible to observe that without= the corrections to the different propagation models, the samples obtained resem= ble the Log Normal model, in addition to the other models such as Okumura-Hata and the Walfish-Bertoni model, giving results very far from the values measured.<= /span>

Figure 6

Coverage cell 2 without correction factor

In cell 2 (Figure 6) it is possible to observe that the samp= les obtained are similar to the Log Normal model within 100 meters, which is wh= ere there is a great concentration of powers, so it can be said that it is wher= e it is best has been coupled to the prediction model, considering that the different attenuations are due to being in an area full of vegetation. On t= he other hand, the other models do not coincide with the powers collected beca= use the area where the samples were taken does not meet the characteristics of = the different models, which is why it is seen that both the Okumura-Hata, Cost 231 and Walfish-Berto= ni are far apart with respect to the powers obtained and compared with the data obtained in the other radio bases, it is observed that these 3 models are m= uch further away from each other.

Figure 7

Coverage cell 3 without correction factor

In cell 3 (Figure 7<= !--[if gte mso 9]> 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200= 650066003100300036003500320034003000380035000000 ) it is observ= ed that the data collected is very similar to the Log Normal model, especially between 80 and 118 meters there is coupling with respect to this model, but= at the same time, it is possible to observe that the powers collected at from = 130 to 190 meters they resemble the SUI model, these power losses are because t= he area where the data was collected was an area where there are many houses between 2 and 3 floors.

Fi= gure 8

Coverage cell 4 without correction factor=

In cell 4 (Figure 8<= !--[if gte mso 9]> 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200= 650066003100300036003500320034003100390038000000 ) where it is observed that it resembles two models, firstly, the collected data tend to = have a coupling with the SUI model between 47 to 78 meters, and from 83 to 140 meters they are coupled to the model. Log Normal, considering that from 140 meters these tend to suffer more attenuations, therefore they move away from the results of the models, this is because the data obtained were in a place full of buildings within the main street.

<= /span>

Figure 9

Coverage cell 5 without empirical correct= ion factor<= /o:p>

In cell 5 (Figure 9= <= !--[if gte mso 9]> 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200= 650066003100310035003100390032003600380033000000 ) it is observ= ed that it resembles the Log Normal model within 50 to 96 meters of distance, where there is a great concentration of powers between 70 to 94 meters, in addition to that manages to observe that there is an intersection between t= he SUI model and Log Normal, so that within 130 to 135 meters the data collect= ed resembles the SUI model.

Next, the graphs of the propagation models are presented with a correction factor so that they are coupled to the power measurements of the 5 different LTE coverage cells located in the southern = zone of the city of Riobamba, in this way having a prediction of attenuation in = that area. =

<= /span>

Fi= gure 10

Coverage cell 1 with correction factor

In cell 1 shown in (= Figure 10) the correcti= on factor was applied to 3 propagation models: Okumura-Ha= ta, Cos 231, and the Walfish-Bertoni model, the correction values were: -20.69 dBm, -13.34 dBm, -21.23 dBm respectively. When applying the correction factor, the graphs of the propagation models are better coupled to the power samples taken with the mobile, however, the model that is more coupled in cell 1 is the Log-normal model.

In the first 100 meters, many powers were collected, finally, it was visualized that at a greater distance the samples suffer an attenuation that is caused by the presence of different infrastructures. It is possible to observe that, without the corrections to= the different propagation models, the samples obtained are = similar to the Log Normal model, in addition to other models such as the Okumura-Hata model and the Walfish-Bertoni model, giving results very far from those obtained. measured values. Accord= ing to Pérez, within his investigation he affirms the following:

A= ttenuation as a result of energy absorption by the medium o= ccurs as a consequence of the electromagnetic characteristics of the material thr= ough which the wave propagates and is the fundamental cause of energy losses in = the case of material media. (p. 111). Pérez (2001)

That is why within the first 100 meters different powers were collected, finally it was visualized that at a greater distance the samples suffer an attenuation that is caused by the presence of different infrastructures.

Fi= gure 11

Coverage cell 2 with correction factor

In cell 2 shown in (= Figure 11) the correcti= on factor was applied to 3 propagation models: Okumura-Ha= ta, Cos 231, and the Walfish-Bertoni model, the correction values were: -30.35 dBm, -19.40 dBm, - 26.20 dBm respectively. When applying the correction factor, the graphs of the propagation models performed better than the power samples taken with the mobile, however, the model that best fits cell 2 is the Log-Normal with variations less than 5dBm.

In cell 2 (Figure 6) = it can be seen that the samples obtained are similar to the Log Normal model within 100 meters, which is where there is a large concentration of powers,= so it can be said that it is where there is a better coupling to the prediction model, considering that the different attenuations are due to being in an a= rea full of vegetation. According to Recommendation ITU-R P.833-3, it states:

In certain cases, vegetation attenuation may be important, both for terrestrial systems and for Earth-to-space systems. But the great diversity of conditio= ns and types of foliage makes it difficult to develop a general prediction procedure. In addition, there is a lack of adequately verified experimental data. (p.1). Recommendation UIT-R P.833-3 (2001)

On the other hand, the other models do not coincide with the powers collected because the area where the samples were taken does not meet the characteristics of the different models, so it is s= een that both the Okumura-Hata, Cost 231, and Walfish- Bertoni are very= far apart concerning the powers obtained and comparing with the data obtained in the other radio bases, it is observed that these 3 models are much further = away from each other.

In cell 3 shown in (= Figure 12) correction f= actor was applied to 4 propagation models: Okumura-Hata, Cos 231, the Walfish-Bertoni model, and the SUI model, the correction values were -34.20 dBm, - 27.28 dBm, -3= 4.42 dBm, and -6.69 dBm respectively. When applying the correction factor, the graphs of the propagation models performed better than the power samples ta= ken by the mobile, however, we see that almost all the models fit correctly, be= ing the one that stands out the most are the Cos 231 model and the Cos 231 mode= l. Log-Normal with differentiation between the measured value and that of the power of the models not greater than 6 dBm.=

Fi= gure 12

Coverage cell 3 with correction factor

In cell 3 (Figure 7= <= !--[if gte mso 9]> 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200= 650066003100300036003500320034003000380035000000 ) it is observ= ed that the collected data are very similar to the Log Normal model, especially between 80 and 118 meters there is coupling concerning this model, but at t= he same time it is possible to observe that the powers captured from 130 to 190 meters are similar to the SUI model, these power losses are because the area where the data was collected is an area where there are many houses between= 2 and 3 floors. For this reason, Anonymous (2019), suggests that "whenev= er there is a refraction of the electromagnetic wave, we will have a reflectio= n of energy on the separation surface, for which the energy of the refracted wave will be less than that of the incident" (p.2). Anonymous (2019).

= =

Figure <= span style=3D'mso-bookmark:_Ref106524743'>13

Cove= rage cell 4 with= correction factor

In cell 4 show= n in (Figure 13) the correction factor was applied to 3 propagation models: Okumura-Hata, Cos 231, the = Walfish-Bertoni model, the correction values were: -31.84 dBm, -14.43 dBm, -20.64 dBm, respectively. When applying the repair factor, the graphs of the propagation models are better coupled to the power samples taken by the mobile, however, the curve of the Okumura-Hata model, together with the normal Log model, was the most adapted, even though between 140m and 200m there is a significant dispersion in the measurements whose differentiation is less th= an 8 dBm.

In cell 4 (Figure 8<= !--[if gte mso 9]> 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200= 650066003100300036003500320034003100390038000000 ) where it is observed that it resembles = two models, first of all, the collected data tend to have a coupling with the S= UI model between 47 to 78 meters, and from 83 to 140 meters are coupled with t= he Log Normal model, considering that from 140 meters these tend to suffer more attenuation, according to Recommendation ITU-R P.1407-1, states:=

In radio systems with low antenna heights, there are often multiple indirect paths between the transmitter and receiver due to reflection from surrounding objects, in addition to the direct path = when there is a line of sight. This multipath propagation is particularly import= ant in urban environments where building walls and paved surfaces generate stro= ng reflections. (p.1). Recommendation UIT-R P.1407-1 (2003)<= /span>

Therefore, the= y are far from the results of the models, this is because the data obtained was i= n a place full of buildings within the main street.

Figure 14

Coverage cell = 5 with correction factor

In cell 5 shown in (Figure 14) correction f= actor was applied to 3 propagation models: Okumura-Hata, Cos 231, and the Walfish-Bertoni model, the correction values were: -30.29 dBm, -21.97 dBm, -29.48 dBm, r= espectively. When applying the correction factor, the graphs of the propagation models a= re better coupled to the power samples taken by the mobile, however, the one t= hat best fits is the normal Log model curve with a differentiation between the measurements taken and the model less than 5dBm.

One of the technologies and methods used = is the repeater or signal amplifier. In this case, the signal received from a cellular operator is amplified to provide coverage inside a building. The building or area to be covered can be any building, house, garage, or facto= ry where the mobile phone signal is weak, and we want to amplify it. (p.n). Ubierna (2018)=

In addition to= the fact that it is possible to observe that there is an intersection between t= he SUI model and Log Normal, this is because these models do not consider loss= es due to reflection from different infrastructures, and within 130 to 135 met= ers the data collected resembles the SUI model.

Conclusions

· The use of these models and the application of the correction factor allowed us to analyze the values of reception power and real propagation lo= sses in particular environments of the southern zone of Riobamba city.

· The samples obtained show a significant improvement with the use of = the Correction Factor, thus increasing the accuracy of predicting power levels.=

· In the southern part of Riobamba city, as it is a residential area without the existence of large buildings, the signal loss does not exceed -= 106 dBm. Despite also the existence of natural topographic factors that influen= ce it.

· According to the results obtained, it was concluded that the Log-Nor= mal model is the best predictor of power in the southern area of the city of Riobamba considering the different scenarios where there were propagation losses.

· In the case of using these prediction models in practice, the data m= ust be modeled by software to determine the coverage and power of the signal th= at the physical equipment must emit.

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