PROPAGATION MODELS APPLIED IN OPEN AREAS UNDER LTE TECHNOLOGIES AND FITTING WITH MEASUREMENTS

ABSTRACT

improved the connectivity and data transmission speed.The first generation of mobile cellular technology, 1G, was characterized by limited voice quality and network capacity.Subsequently, 2G technology improved voice quality and added features such as text messaging and international roaming.3G technology added data capabilities and enabled simultaneous voice and data transmission.4G technology offered faster data speeds and improved data handling capacity for high-demand applications such as video conferencing and online video streaming.[1] Long Term Evolution (LTE) technology is a mobile communication technology that has had a significant impact on how people communicate and access information.LTE is considered like an advanced version of 4G technology and has significantly improved data transmission speeds, mobile network capacity, and energy efficiency of mobile devices.[2] It has enabled the transmission of high-definition services and fast downloading of large files.Additionally, its ability to support multiple users simultaneously has enhanced the capacity of mobile networks, allowing more users to connect and enjoy advanced services without affecting connection stability.LTE is a wireless broadband technology capable of reaching speeds of up to 300 Mbps.[3] Presently, Propagation models are used to predict the strength of signal power between a base and a receiver.These models consider various factors, such as distance, frequency, and environmental conditions.Among the most used models are the renowned Ericsson 999 model, [4] which stands out for its precision in urban environments when VOLUMEN 5, N˚2 / JULIO -DICIEMBRE 2023 / e -ISSN: 2661

A. Log-Distance Model
A radio propagation model that predicts the path loss encountered by a signal within a building or in densely populated areas over distance.In many cases, empirical results agree with Friis on a logarithmic decay with distance, however, the quadratic exponent is not the best fit to the data in many real propagation environments.Path loss is generally expressed as a function of distance by an exponent n according to: [7] B. Cost 231 Walfish-Ikegami Model The COST 231 model is a semi-empirical path loss prediction model.It is recommended for macrocells in urban and sub-urban scenarios, with good path loss results for transmitting antennas located above 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 previous 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 -2000 MHz).The model performs a more detailed calculation of the attenuation, based on four additional parameters.[8] [9] • Height of buildings.
• Width of streets.
• Orientation of the street concerning the direction of propagation.
For LOS scenarios, the propagation loss considers only the free space loss, Lb = Lo(los) Where:

Pr(d):
The signal propagation power loss at a distance d.
The typical NLOS path described in the COST 231 model is shown in Figure 1 and Figure 2.
Where:  The propagation loss in free space conditions, L0, is obtained according to the expression: The k a term presents the increase in path loss for the case of base stations located below the average height of the buildings.The terms k d and k f control the dependence of L msd on distance and frequency, respectively.If there is no data on the buildings on the route, the COST 231 model recommends using the following values [10]: The term L rts considers the width of the street and its orientation concerning the direction of ray propagation.
The expression for the calculation of L rts is given by: The parameters defined in the COST 231 model (Figure 2) are the following: • hr: Average height of the buildings (m).
• ϕ: Angle formed by the direction of propagation and the axis of the street.• hb: Height of the base station antenna (m).
• hm: Height of mobile device antenna (m).Where: Is a term that depends on the height of the base station.
In addition, the following parameters are defined: "The L ori term is a correction factor that quantifies losses due to street orientation.If the value of L rst ¡ 0, it should be considered as L rst = 0.The multiscreen diffraction loss, L msd , is a function of the frequency, the distance between the mobile device and the base station, as well as the height of the base station and the height of buildings.Similar to L rst , if L msd is negative, it is considered as L msd = 0. Its value is calculated using the following expression:" Considering that: Where: f : Frequency (GHz) d : Distance between transmitter and receiver (m).h b : Height of buildings (m).h r : Receiver height (m).

C. Ericsson 9999 Model
The Ericsson 9999 model, developed by the company Ericsson, is used for network addressing.
It is an extension of the Hata model.The advantage of this model is that it allows for parameter adjustments according to the specific scenery in which the model is being applied.[11] The mathematical expression that describes the loss predicted by this model is as follows: where free space approximation is used d < d 0 for.Values for l 0 , γ, and s are defined in tables 2 and 3 .

D. Erceg Model
Erceg et al. [12] proposed a model derived from a vast amount of data at 1.9 GHz, which makes it a preferred model for PCS and higher frequencies.The model was in particular adopted in the 802.16 [13] study group and is popular with WiMAX suppliers for 2.5 GHz products, and even 3. The Where PL represents Path Loss in DBS, d is the distance between the transmitter and receiver, d 0 is the reference distance, X f is the frequency correction factor, X h is the correction factor for base station height, S is shadowing and γ is the path loss component and it is described as [14]: The Figure 4 shows the Movistar LTE base station located next to ESPOCH, with an EIRP of 46 dBm at coordinates -1.656432, -78.680327.The location is determined by the Network Cell Info Lite application, which allows you to identify it based on power intensity levels, taking as reference the criteria of shortest distance and highest power level.[16] Show in Figure 5  where A is free space path loss while d0 is the distance between Tx and Rx and λ is the wavelength.The correction factor for frequency and base station height are as follows: where f is the frequency in MHz, and hr is the height of the receiver antenna.This expression is used for terrain types A and B. For terrain C, the blow expression is used.
For rural and suburban environments (Terrain A and B): For urban environments (Terrain C): α = 6.6 dB.) [15] Shown in Figure 3 is the block diagram in which the steps that were carried out to perform the power intensity measurements outside the Computer and Electronics Department were specified in order to later compare them with the propagation models.The parameters of the transmitting antenna are shown in Table 5, where a frequency of 1940MHz.
To obtain the measurements of the power intensity levels at each point, the Network Cell Info Lite application was used.Three measurement campaigns were carried out at similar times and in similar scenarios to analyze the power variations in each campaign.This allowed obtaining an average value of the power intensity at each point.Figure 7 shows the results of the three measurement campaigns carried out on different days of the week in the Computer and Electronics Department.In the campaigns, the relationship between power and distance is observed without the presence of factors affecting the measurements in open spaces.In each of the campaigns it was analyzed how the power varies as the distance increases.Knowing the location of the base radio, 14 radios were plotted obtaining a total of 145 points covering all the exteriors of the Department of Informatics and Electronics in which the measurements of the receiving power were taken, Google Earth was used to mark the 14 radios shown in Figure 6 .
The distances of the radios are shown in Table 6.The distance from the transmitting antenna to the outer space of the Department of Computer Science and Electronics was considered.The number of radios was determined to cover all this area, obtaining a total of 14 radios.

A. Log-distance Model
In this propagation model, equation 1 was used, which depends on data shown in Table 6.Substituting the values in the equation, the results in terms of n could be obtained.This process was applied to the 14 radii, then the mean square error was calculated, which is the sum of squared errors divided by the number of measurements.Once this process was completed, an equation was obtained for the mean squared error which is a function of n to minimize the mean squared error, the mean squared error was derived and equaled to zero, resulting in the optimum value of n, which in this case is n = 3.6395.And with this value determine the powers calculated for each radius.

B. Cost 231 Walfish-Ikegami Model
The Cost 231 Ikegami model was designed using a frequency of 1940 MHz, with a transmitting antenna located at a height of 20 meters and a receiving antenna at a height of 1.5 meters.To obtain more accurate data, the IT and Electronics department was divided into two scenarios, and measurements were taken to determine the

C. Ericsson 9999 Model
The current model was developed using a frequency of 1940 MHz, with a transmit antenna height of 20 m and a receive antenna height of 1.5 m.In addition, an EIRP (Equivalent Isotropic Radiated Power) of 52 dBm and a receiver gain of 2 dBi were found.It is important to highlight that in this model the specific parameters of a suburban environment that are shown in the table 1 have been taken into account.

D. Erceg Model
This model was developed using a frequency of 1940 MHz, with a transmitting antenna height of 20 m and a receiving antenna height of 1.5 meters.The effective isotropically radiated power (EIRP) has a value of 52 dBm and the receiver gain is 2 dBi.It should be noted that this model takes into account the parameters established in Table 2 and Table 3, specifically in Table 3, For the Faculty of Computer Science and Electronics it was ruled that it is a suburban environment, based on that category C is used (density of light trees and flat terrain).

E. SUI Model
The model developed was based on a frequency of 1940 MHz, with a transmitting antenna located at a height of 20 meters and a receiving antenna at a height of 1.5 meters.The EIRP used was 52 dBm and the receiver gain was set to 2 dBi.It is important to note that additional parameters specific to a suburban environment were considered in this model, such as the 5.2 dB attenuation due to the presence of obstacles and other factors.These additional considerations may affect the results average width of the streets and the average height of the buildings.These additional parameters were considered in order to improve the accuracy of the results and allow a more appropriate comparison with other available models.In the model, an Equivalent Isotopic Radiated Equivalent Radiated Power (EIRP) of 52 dBm was used, while the receiver gain was estimated at 2 dBi.Taking into account these additional parameters and performing measurements in the two scenarios mentioned above, a higher accuracy in the results and a better application in similar scenarios is achieved.I am sorry for the above confusion and hope this answer is clearer and more accurate.
obtained, which explains the differences with the initial expectations.
A comparison between different propagation models, including Log-Distance, Erceg, Ericsson 9999, SUI and the Walfish-Ikegami model, along with the average measured values, is presented in Figure 8.
The figure is divided into two categories: points with direct line of sight and points without direct line of sight.
The results reveal that generally points with direct line of sight present better average power values compared to points without line of sight.It is observed that the maximum value recorded is -104 dBm, while the minimum value is -71.7 dBm.
In terms of the fit of the models to the scenario, it was determined that the Erceg model fits more accurately to the measurements made.The mean square error (MSE) was used to evaluate the quality of the models' fit, and the Erceg model obtained the lowest MSE, with a value of 3.62, compared to the other models.
On the other hand, the Ericsson 9999 model tends to overestimate the values in relation to the measurements made, which implies that it predicts mean powers higher than those observed.In contrast, the SUI model underestimates the values, i.e., it predicts mean powers lower than those observed.The Walfish-Ikegami model also shows some degree of fit to the scenario, although not as accurate as the Erceg model.
These results emphasize the importance of selecting an appropriate propagation model to improve accuracy in the planning and optimization of telecommunication networks.In this case, the Erceg model proved to be the most suitable for the evaluated scenario due to its adjustment capacity and accuracy in predicting propagation losses.
In summary, the Erceg model more accurately fits the measured data in this scenario, showing better agreement with the observed mean powers.This indicates that the Erceg model is able to more accurately capture the propagation characteristics in the specific environment evaluated.On the other hand, both the SUI model and the Ericsson 9999 model show discrepancies compared to the measured mean powers.These discrepancies can be attributed to the limitations and simplifications inherent in these models.The SUI model, despite its versatility and adaptability, may overlook environment-specific

Fig. 3 .Fig. 4 .
Fig. 3. Process Block Diagram the device used to measure the field strength (NARDA), obtaining a result of 0.5 v/m at a distance of 142 meters from the radio base, with the recommendation ITU-R P.525-4 the EIRP was determined from the electric field obtaining an EIRP of 52dBm.where h b is the height of the base station and a, b and c represent the terrain for which the values are selected from the above table.

TABLE 1 :
Factor of correction for different sectors

TABLE 2 :
Values for Erceg model.

TABLE 3 :
Values for Erceg model parameters in various terrain categories.

TABLE 4 :
Different terrains and their parameters.
hr = 3m * (No .ofFloors) + ceiling height TABLE 1 below shows the correction factor values for different sectors: