## 2 Methodology and Data Collection
### Kriging-Based Channel Model Development  
The overall methodology for both SS and OS channel modelling links is illustrated in Figure 4 and described as follows. As a first step, from the resulting O2I measurements, SS and OS NLOS links, the path loss L is extracted in dB as a classical link budget:  
\[L=P_{\text{Rx}}+G_{\text{tx}}+G_{\text{rx}}-\overline{P_{\text{rx}}}. \tag{2}\]  
To properly choose tuning samples that accurately reflected the characteristics of the larger measurement campaign, the selections suggested by the authors in [15] about the method and dataset size for tuning selection were considered: first, four classification methods were addressed and compared in terms of the mean absolute error (MAE); the results showed the first method as the most accurate with the lowest MAE of 2.16 dB. This method divided the target area of each scenario into representative zones bounded by concentric circles every 5 m from the position of the BS; and second, five approaches were addressed in order to select the least amount of tuning dataset, obtaining the best goodness of fit. The conclusion for this test was to recommend the rate of 60/40 to extract tuning and testing datasets. Considering both suggestions, the measurements were divided into areas defined by rings with radius \(r=5\)k in m (where \(k=1,\ 2,\dots,\ n\), and \(n\) depends on the maximum separation distance between transmitter and receiver) centered at the position of the BS. Then, a 60/40 rate was extracted from each zone: 60% exclusively used for driving the measurement-based prediction process using Kriging (tuning dataset), and 40% to perform the validation of the estimated path loss at those testing placements (testing dataset). For the model tuning process, the path loss extracted in (2) was defined by two components [22]: median path loss \(L_{50}\) and shadowing \(L_{\text{s}}\) in dB:  
\[L=L_{50}+L_{\text{s}}. \tag{3}\]  
The median path loss described how the transmitted signal was attenuated during the path, in terms of the free space path loss \(L_{\text{fs}}=20\log_{10}(d_{0})+20\log_{10}(f\ [\text{MHz}])-28\)[23], the distance-dependent relation, and specific sources from wall attenuations. In this channel modeling proposal, the median path loss was calculated as:  
\[L_{50}=L_{\text{fs}}+10n\log_{10}\left(\frac{d}{d_{0}}\right)+e, \tag{4}\]  
where \(L_{fs}=42.9\) dB, \(d_{0}\) is the reference distance of 1 m, \(n\) denotes the path loss exponent, \(d\) is the Euclidean distance in a three-dimensional space in m, and \(e\) is strictly related to attenuation sources such as floor and walls attenuations. The variables \(n\) and \(e\) are found  
Figure 4: Channel model methodology. by fitting a linear equation to the path loss extracted in (2); the linear regression results are shown in Table 4.  
In Figure 5 the path loss extracted from (2) is illustrated in blue circles markers for the SS links and in red cross markers for the OS links (where the marker points are already averaged over all 60 samples per received position) along with the median path loss calculated by (4) with the values presented in Table 4 for the SS and OS NLOS O2I links. For shadowing extraction and continuing with the second component for path loss, the shadowing is extracted from (3) as follows:  
\[L_{\mathrm{s}}=L-L_{50}. \tag{5}\]  
The shadowing generation process employs the shadow values previously obtained in (5) to interpolate the known data \(L_{\mathrm{s}}(\mathrm{c}_{\mathrm{i}})\) in unknown locations \(\mathrm{c}_{0}\), achieving the accurate shadowing values through the Kriging-aided channel.