## 2 Methodology and Data Collection
### Kriging-Based Channel Model Development
Based on the approach that a typical O2I path loss prediction model considers: the main large-scale propagation loss in line-of-sight (LOS) or NLOS up to the building wall, is a penetration factor that adds wall losses and an indoor path loss term, and that this structure is shared by the most widely used standard models for O2I: COST231 Building Penetration LOS model [7], WINNER+ O2 Ia/LOS model [8], ITU-R O2I model [9] and 3 GPP 3D-UMi O2I model [10]. The \(K\) model predictions are also compared with those of the standard models. The path loss estimated trough the standard models is calculated using (7), where each component is in dB and is described in Table 5:

\[L_{sm}=L_{1}+L_{2}+L_{3}, \tag{10}\]

The path loss components, described in Table 5, were extracted from the setup and results of the O2I NLOS measurement campaign, i.e., the distances of the x, y, and z axes were given by the location of each measurement, the frequency \(f\) in Hz (\(3.5\times 10^{9}\) Hz) and the room depth \(w\) in m by the measurement setup. In each room where the measurements were performed the receiver antenna was placed at three different room depths: around 1 m from the exterior university wall, in the center of the room, and around 1 m from the interior university wall. \begin{table}
\begin{tabular}{c c} \hline \hline
**Standard Model** & **Path Loss Components 1** \\ \hline
3 GPP & \(L_{1}=22\log\left(\sqrt{x^{2}+y^{2}+z^{2}}\right)+28+20\log f\) \\ \(\frac{L_{2}}{L_{3}}=\frac{w}{w}\) \\ \hline ITU-R & \(L_{1}=22\left(\log\sqrt{x^{2}+\left(y-w\right)^{2}+z^{2}}\right)+28+20\log f\) \\ \(L_{2}=\frac{14+15\cdot(1-\theta)^{2}}{L_{3}}\) \\ \hline WINNER & \(L_{1}=22\cdot 7\log\left(\sqrt{x^{2}+\left(y-w\right)^{2}+z^{2}}\right)+27+20\log f\) \\  & \(L_{2}=17.64+14\cdot(1-18.\log f)+15\cdot(1-\theta)^{2}\) \\  & \(L_{3}=\frac{w}{w}\) \\ \hline COST231 & \(L_{1}=20\log\left(\sqrt{x^{2}+\left(y-w\right)^{2}+z^{2}}+w\right)+32.4+20\log f\) \\  & \(L_{2}=7+20\cdot\left(1-\frac{y-w}{\sqrt{x^{2}+\left(y-w\right)^{2}+z^{2}}+w} \right)^{2}\) \\  & \(L_{3}=0.6\cdot(w-2)\cdot\left(1-\frac{y-w}{\sqrt{x^{2}+\left(y-w\right)^{2}+z^ {2}}+w}\right)^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Standard Models. To make a robust analysis to the choice of the 60/40 rate for tuning and testing datasets, a uniform random sampling method was performed 2000 times to estimate the corresponding path loss according to the Kriging-aided model proposed. The average of the 2000 iterations for the mean error, the standard deviation of the error and the RMSE is presented in Table 6 for each link described in Table 2.

In addition, after the 2000 iterations are performed to select a different 60/40 rate from measurements to estimate the path loss, the model-based results are presented in terms of the cumulative distribution function (CDF) of the mean error, the standard deviation of the error and the RMSE in Figures 7-9, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**O2I Link** & **Model** & **Mean Error** & **Standard Deviation** & **RMSE** \\ \hline \multirow{5}{*}{SS} & R & \(-\)0.04 & 4.73 & 4.73 \\  & K & 0.30 & 2.82 & 2.85 \\  & 3 GPP & 3.43 & 3.52 & 4.91 \\  & ITU-R & 5.26 & 3.82 & 6.49 \\  & WINNER+ & 1.29 & 3.91 & 4.11 \\  & COST231 & \(-\)3.81 & 3.31 & 5.04 \\ \hline \multirow{5}{*}{OS} & R & 0.00 & 4.81 & 4.81 \\  & K & 0.47 & 2.78 & 2.84 \\ \cline{1-1}  & 3 GPP & 0.55 & 3.46 & 3.49 \\ \cline{1-1}  & ITU-R & 5.20 & 3.02 & 6.00 \\ \cline{1-1}  & WINNER+ & 1.16 & 3.03 & 3.23 \\ \cline{1-1}  & COST231 & 1.14 & 3.02 & 3.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Path Loss Models Accuracy. Figure 7: CDFs of mean error for path loss predictions based on different models: (**a**) SS O2I links; (**b**) OS O2I links. According to Table 6 and Figure 9, in both links, with an RMSE of 2.8 dB, the Kriging-aided model estimates the path loss with a higher level of confidence than the other approaches evaluated.