# Path Loss Model for Outdoor Parking Environments at 28 GHz and 38 GHz for 5G Wireless Networks
## 3 Path Loss Model for Single Frequency  
Path loss (PL) is the fundamental characteristic of electromagnetic wave propagation. It is used in any wireless communication system design (i.e., link budgets) to estimate the expected Rx power [31]. The Rx power in dBm in free space can be given by the Friis transmission formula [32]:  
\[P_{r}=\frac{P_{t}G_{t}G_{r}}{\left(4\pi d/\lambda\right)^{2}} \tag{1}\]  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Frequency & 28 GHz and 38 GHz \\ Transmit Power & 20 dBm \\ Antenna Gain (28, 38 GHz) & 19.18 dB, 21.10 dB \\ Tx Antenna Type / Beam-width (28, 38) & Horn/(18.88\({}^{\circ}\), 15.23\({}^{\circ}\)) \\ Rx Antenna & Omni-directional \\ Tx Antenna Height & 2 m \\ Rx Antenna Height & 1.7 m \\ \hline \end{tabular}
\end{table}
Table 1: Measurement setup parameters.  
\begin{table}
\begin{tabular}{c c} \hline
**Setting** & **Description** \\ \hline SPL & Rx antenna was moved in one parking lot \\ DPL & Rx antenna was moved along two parking lots. \\ \hline \end{tabular}
\end{table}
Table 2: Terminology for directional parking lots scenarios.  
Figure 2: Measurement environment: (**a**) photo of parking lots; (**b**) floor plan of the environment.  
where \(P_{r}\) and \(P_{t}\) are the received and transmitted power, respectively. The \(G_{t}\) and \(G_{r}\) are the Tx and Rx antenna gain, respectively. The \(d\) is the link distance, and \(\lambda\) is wavelength for the frequency \(f_{c}\). In trying to estimate path loss models, it is necessary to test for model accuracy and other path loss model parameters. Engineers will inevitably need to calculate the propagation models when designing new applications and factors like distance estimation or any other unforeseen scenarios (i.e., original forecasted or predicted in the experimental model used to determine path the loss model). Researchers are still conducting several field measurements to ensure that modeled system is stable, accurate and useful. In this paper, the 5G channel was characterized based on different path loss models for parking lot case study. Propagation path loss can be modeled using the close-in (CI) free space reference distance path loss model provided in Equation 2 with the single model parameter path loss exponent (PLE) (\(n\)):  
\[PL^{CI}(f,d)[dB]=FSPL(f,d_{0})+10n\log_{10}\biggl{(}\frac{d}{d_{0}}\biggr{)}+ \chi_{\sigma}^{CI} \tag{2}\]  
where \(\chi_{\sigma}^{CI}\) is a zero mean Gaussian random variable with standard deviation \(\sigma\) in dB. The free space path loss model is expressed as \(FSPL(f,d_{0})=\left(\frac{4\pi d}{\lambda}\right)^{2}\); \(d_{0}\) is a physical reference distance.  
Using the minimum mean square error (MMSE) [2] optimizing technique, the path loss was modeled by obtaining the PLE in CI model that matches the measured data along with the smallest error using a real-time practical reference point.  
The WINNER II and 3 GPP standards have been used the floating-intercept (FI) path loss model. It is not a physically-based model, as it has no anchor point constraint as with the CI model. The FI path loss model is a mathematically-based model that provides the floating-intercept (\(\alpha\)) and line slope (\(\beta\)) as follow:  
\[PL^{FI}(d)[dB]=\alpha+10\cdot\beta\log_{10}(d)+\chi_{\sigma}^{FI} \tag{3}\]  
where \(\chi_{\sigma}^{FI}\) is a zero mean Gaussian (in dB) random variable, which presents large-scale signal fluctuations about the mean path loss over a Tx-Rx separation distance. As a CI model, the MMSE is used as a best-fit that involves solving \(\alpha\) and \(\beta\) to minimize \(\sigma\)[33].