## 2 Methodology and Data Collection
### Kriging-Based Channel Model Development
In other words, from the N shadowing tuning samples at the coordinates \(\mathrm{c}_{\mathrm{i}}\), the dataset vector defined by (6) is extracted, leading Kriging to estimate an unknown shadowing value \(L_{\mathrm{s}}(\mathrm{c}_{0})\) at a random location \(\mathrm{c}_{0}\) from the known samples \(L_{\mathrm{s}}(\mathrm{c}_{\mathrm{i}})\):  
\[L_{\mathrm{s}}(\mathrm{c}_{\mathrm{i}})=(L_{\mathrm{s}}(\mathrm{c}_{1}),\ L_{ \mathrm{s}}(\mathrm{c}_{2}),\ \ldots,\ L_{\mathrm{s}}(\mathrm{c}_{\mathrm{N}}))^{T}. \tag{6}\]  
To provide these predictions, [PERSON] employs the variography to understand and find a pertinent threshold of neighboring samples to the interpolation. In order to summarize the central shadowing tendency, an exponential model function is fitted to the variogram estimator to further visualize the shadowing spatial process. The selection of the exponential function is focused on both theoretical reasons, which highlight the properties that a function selected as a variogram model must fulfil, and practical reasons, for which evidence from multiple studies [15; 24; 25] demonstrates that the exponential function provides the best fits. In Figure 6, it is possible to observe that the parametric curve (exponential function, Exp) fits reasonably well over the first three 5 m lags for both SS and OS NLOS links. \begin{table}
\begin{tabular}{c c c} \hline \hline
**O2I Link** & \(\mathbf{n}\) & \(\mathbf{\epsilon}\) \\ \hline SS & 1.93 & 24.73 \\ OS & 2.41 & 15.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Median Path Loss. Figure 5: O2I path loss measurements. According to geostatistics [26], this is appropriate for Kriging due to near points, such as shadowing neighboring samples, carry more weight than more distant ones to the unknown shadowing values. Thereby, considering the characteristics of the data, ordinary Kriging is employed to interpolate and then predict shadowing at each grid location in the scenario area. Ordinary Kriging uses a weighted average of the neighboring points to estimate the value of an unobserved point. To guarantee that the estimates are unbiased this Kriging determines the weights under the constraint described below in Algorithm 1. As is illustrated in Figure 4, at the end of the methodology proposed, the estimated path loss is assessed by (3) at the testing locations in order to proceed with the validation of the shadowing measured at those points. All the supporting information for the Kriging-aided method was analyzed and described in greater depth in [15]; however, an overview is presented in the algorithm below. ```
1:\(\quad\)\(\



on the mean error, standard deviation and root mean square error (RMSE) of the predicted path loss values, \(\hat{L}_{\text{i}}\), at the testing measured locations, \(t_{\text{N}}\), relative to the corresponding testing measured path loss values, \(L_{\text{i}}\). The mean error (ME), the standard deviation of the error (S) and the RMSE are given by:

\[\text{ME}=\frac{1}{t_{\text{N}}}\sum_{\text{i=1}}^{t_{\text{N}}}\left(L_{\text {i}}-\hat{L}_{\text{i}}\right), \tag{7}\]

\[\text{S}=\sqrt{\frac{1}{t_{\text{N}}-1}\sum_{\text{i=1}}^{t_{\text{N}}}\left| \left(L_{\text{i}}-\hat{L}_{\text{i}}\right)-ME\right|^{2}}, \tag{8}\]

\[\text{RMSE}=\sqrt{\frac{1}{t_{\text{N}}}\sum_{\text{i=1}}^{t_{\text{N}}}\left( L_{\text{i}}-\hat{L}_{\text{i}}\right)^{2}}. \tag{9}\]

Furthermore, these results are compared with those of the most traditional assumption of \(L=L_{50}+L_{\text{s}}\), where the shadowing, \(L_{\text{s}}\), is a random variable with a zero mean and a standard deviation \(\sigma\) extracted from the tuning dataset behavior, labeled as \(R\).