## 2 Methodology and Data Collection
### Kriging-Based Channel Model Development
Additionally, this novel technique provides the best fit to the measured data with respect to the standard models presented by [PERSON] et al. in [6]. Kriging, as a geostatistical technique, assumes that there is an implied connection between the measured data value at a point and its location in space. Therefore, it was possible to estimate shadowing from the best set of available sample points (tuning dataset) yielding the K model as the most accurate of those exposed in Table 6, where the metrics and the CDFs illustrated in Figures 7-9 suggest the efficiency of the proposed model, since, unlike the others, it considers the characteristics of the selected link. Even though the R model tunes the parameters \(n\), \(e\) and \(L_{\text{s}}\) from the tuning dataset and is considered in telecommunication society as the most traditional model, the WINNER+ is quite accurate for the SS link with an RMSE of 4.11 dB, and the COST231, WINNER+ and 3 GPP for the OS case with an RMSE of no more than 3.4 dB. In Figure 7 it is possible to validate the outstanding K model performance. From the 2000 tests that were carried out, it is possible to conclude that, when estimating the path

Figure 8: CDFs of standard deviation for path loss predictions based on different models: (a) SS O2I links; (b) OS O2I links. Figure 9: CDFs of RMSE for path loss predictions based on different models: (a) SS O2I links; (b) OS O2I links. loss with Kriging-aided shadowing, there is a 95% probability that the mean error of the prediction is less than 1 dB and 1.3 dB for SS and OS links, respectively. Regarding Figure 9, the stability and the confidence to predict the path loss more accurately is guaranteed when the K model is used, with a 95% probability that the RMSE is less than 3.1 dB and 3.25 dB for SS and OS links, respectively. The applicability of the standard model results presented in Figures 7-9 is discussed as follows: the COST231, 3 GPP, and WINNER+ models are more accurate for the OS than for SS links, with median errors less than or equal to 1.16 dB and RMSEs of no more than 3.49 dB. The results presented in Table 6 demonstrate the WINNER+ model as the most consistent and the ITU-R as the least accurate compared to the other standard models for both types of links. Regarding SS results and considering the resulting scenario geometry by locating the BS as low as 0.7 m from the building wall, the standard models present higher standard deviations compared to the OS deviations. By taking into account these results and the following two considerations: the standard models were based on measurements at different frequencies: 850 MHz, 1.8 and 1.9 GHz for COST 231; 450 MHz to 6 GHz for WINNER; 2 to 6 GHz for ITU-R; and 0.5 to 100 GHz for 3 GPP. Additionally, the formulation of each standard model was originally conceived for cells of up to 1 Km radius. It is important to improve the accuracy of the standard models for a specific application, in this case, for O2I NLOS links at the 3.5 GHz band, one of the candidate frequencies considered for 5G communications. In [15] it was validated through different indoor approaches that the path loss prediction accuracy was significantly better when Kriging was included as part of the tuning process for frequencies in the ultra-high-frequency (UHF) band. This study validated the potential of this geostatistical technique for O2I scenarios at 3.5 GHz against standard models. Therefore, it is an interesting future line of research to consider other setups to validate and compare Kriging performance against the existing standard models at difference frequencies. ## 4 Conclusions

It was validated that the methodology and the model proposed in this paper for O2I applications such as 5G communications at 3.5 GHz, with a proposed accurate combined path loss and shadowing-aided model, were more accurate and versatile compared to both the conventional linear path loss plus log-normal shadowing model and the existing standard models.