## 3 Numerical Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Skin** & **Brain Grey Matter** & **Cerebellum** \\ \hline
**QDC** & 67.4\% & 74.6\% & 76.0\% \\
**\% \textgreater{} 0.7 maximum** & 3.3\% & 4.2\% & 2.8\% \\
**Range H-plane** & From \(-5^{\circ}\) to \(5^{\circ}\) & From \(-10^{\circ}\) to \(6^{\circ}\) & From \(-5^{\circ}\) to \(5^{\circ}\) \\
**Range E-plane** & From \(-11^{\circ}\) to \(4^{\circ}\) & From \(-5^{\circ}\) to \(10^{\circ}\) & From \(-4^{\circ}\) to \(8^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The QDC values, the percentage of \(SAR_{10g}\) higher than the 70% of the maximum values and the variation range extremes of the two input parameters for the skin, for the brain grey matter and for the cerebellum. close to each other with values that were around half of the values obtained for the skin (precisely, max = 95.24 mW/kg, median = 4.89 mW/kg, mean = 13.30 mW/kg for the brain grey matter and max = 105.32 mW/kg, median = 4.37 mW/kg mean = 10.86 mW/kg for the cerebellum). Figure 7 reports, analogously to Figure 5, a map of the values on the plane of the 1000 combinations of azimuth angles, in the range (\(-50^{\circ}\), \(+50^{\circ}\)), and elevation angles in the range (\(-25^{\circ}\), \(+25^{\circ}\)), and two graphs, one varying the azimuth angles of the beam, fixed the elevation angle to \(0^{\circ}\), and the other one varying the elevation angles fixed the azimuth angle to \(0^{\circ}\). The results of the deeper statistical analysis, i.e., the QDC values, the percentage of \(SAR_{10g}\) values higher than 70% of the maximum and the ranges of elevation and azimuth angles corresponding to these highest exposure levels are reported in Table 3.  
In addition, for \(SAR_{10g}\), the QDC values remained high (from a maximum value of 76% for the cerebellum to a minimum of 67.4% for the skin), whereas the percentage of highest values is really low. For the skin this percentage was only 3.3%, the brain grey matter was 4.2%, and the cerebellum only 2.8%. It can be noticed again that the highest \(SAR_{10g}\) levels corresponded to beams concentrated in a symmetrical small range around \(0^{\circ}\) in the azimuth plane for the skin and the cerebellum, while for the brain grey matter the range was slightly unbalanced (\(-10^{\circ}\), \(6^{\circ}\)). A slightly larger variability on the exposure levels was measured varying the beam direction on the elevation plane, but the amplitude of ranges remained small, varying from \(12^{\circ}\) to \(15^{\circ}\). Finally, a global sensitivity analysis based on Sobol indices was conducted for all the \(SAR\) distributions here considered, and the results are reported in Figure 8. The normalized Sobol indices for the azimuth angles showed high values, from 70% and 80%, definitely higher than the values measured for the elevation angles. Moreover, the Sobol indices for the elevation angles showed non-negligible values, especially for the brain tissues (i.e., the whole brain, the brain gray matter, and the cerebellum), where are around 30%. This is a quite interesting result, that highlights how the azimuth angles of the main beam of antenna arrays with 3D beamforming capability have a predominant role on the exposure levels, even if also the elevation angles have a non-negligible impact on exposure levels especially for the brain area. These considerations obviously derive from the relative position between the UPA antenna and the model and from the 3D shape of the human body model. Figure 8: The normalized Sobol indices for the six \(SAR\) distributions under investigation.