## 4 Large-Scale Path Loss Models  
The purpose of path loss modelling is to evaluate the magnitude of attenuation experienced by broadcasting radio signals over a distance, which is useful for designing communications systems. In order to determine the received signal strength at Rx, a large-scale path loss was utilized between Tx and Rx for both the LOS and the NLOS environments. The path loss model is commonly used to illustrate the channel effects caused by the surrounding environment. It can predict whether the path loss prediction model should be based on theoretical (deterministic), empirical (statistical), or a combination of both methods [65]. However, the ideal channel prediction can be achieved when the path loss model is designed from real-time practical measurements [66]. It differs for varying communication systems, while radio channels can be modelled in a statistical fashion. The path loss formula provided the Friis free space equation can be used for the reference point or measured at distance \(d_{0}\). The conditions assumed for this model attempted to replicate real-life readings from the experiments but could never guarantee a perfect match due to the random nature of obstructions, aerodynamics of buildings depending on weather, reflections from the buildings and ground, as well as terrestrial communication. Thus, in this paper, the two most potential path loss models (CI free space and FI path loss) for the 5G network have been considered. [67; 68]. The CI model is easily implemented in existing 3 GPP models by making a very subtle modification, that is by replacing a floating non-physically based constant with a frequency-dependent constant that represents free space path loss in the first meter of propagation. This model is most suitable for outdoor environments because of its accuracy, simplicity, and superior sensitivity performance due to its physical close-in free-space reference point, given the fact that measured path loss exhibits little dependence on frequency in outdoor environments beyond the first meter of free-space propagation. The CI model relies on a FSRD of 1 m standard value, where its path loss model is expressed in Equation (1) with the presence of a single model parameter, \(n\), which is also stated as the path loss exponent (PLE). The path loss in dB as a function of 3D T-R separation distance, \(d\), and the carrier frequency \(f\), is expressed as:  
\[PL^{CI}(f,d)[dB]=FSPL(f,d_{0})+10n\log_{10}(\frac{d}{d_{0}})+\chi_{g}^{CI} \tag{1}\]where the free space path loss of the anchor point is given by:  
\[FSPL(f,d_{0})=20\log_{10}\left(\frac{4\pi d_{0}f}{c}\right) \tag{2}\]  
and the large-scale signal fluctuations resulting from large obstacles in the surrounding environment were embedded in the model by the shadow factor, \(\chi_{o}^{CI}\), which is a zero mean Gaussian random variable written as:  
\[\chi_{o}^{CI}=PL^{CI}(f,d)[dB]-FSPL(f,d_{0})-10n\log_{10}\left(\frac{d}{d_{0}}\right) \tag{3}\]  
while its standard deviation, \(\sigma^{CI}\), in dB is:  
\[\sigma^{CI}=\sqrt{\frac{\sum\left(\chi_{o}^{CI}\right)^{2}}{N}} \tag{4}\]  
denotes the overall number of measured points in the measurement campaign [69]. The best fit minimum mean square error (MMSE) of the PLE \(n\) and the minimum standard \(\sigma^{CI}_{\min}\) deviation were calculated as in (5) and (6), respectively. \[n=\frac{\sum\left(PL^{CI}(f,d)[dB]-FSPL(f,d_{0})\right)\left(10\log_{10}\left( \frac{d}{d_{0}}\right)\right)}{\sum\left(10\log_{10}\left(\frac{d}{d_{0}} \right)\right)^{2}} \tag{5}\]  
\[\sigma^{CI}_{\min}=\sqrt{\frac{\sum\left(PL^{CI}(f,d)[dB]-FSPL(f,d_{0})-10 \log_{10}\left(\frac{d}{d_{0}}\right)\frac{\sum\left(PL^{CI}(f,d)[dB]-FSPL(f,d _{0})\right)\left(10\log_{10}\left(\frac{d}{d_{0}}\right)\right)}{\sum\left(10 \log_{10}\left(\frac{d}{d_{0}}\right)\right)^{2}}\right)^{2}}{N}} \tag{6}\]  
Another path loss model, which was adopted by WINNER II and 3 GPP standardization bodies [67], and the FI path loss model, also known as the alpha-beta model, were employed in this study.