## 3 Results
### Patch Antenna Arrays  
When an antenna is located in the vicinity of a scatter, its matching and radiation are altered. To exclude the effect of the antenna mismatch, TPD\({}_{7}\) is normalized to (1-S\({}_{11/\mathrm{PH}}\)2) and TPD\({}_{5}\) to (1-S\({}_{11/\mathrm{FS}}\)2), where S\({}_{11/\mathrm{Ph}}\) and S\({}_{11/\mathrm{FS}}\) are S\({}_{11}\) of the antenna in the presence of the phantom and in free space, respectively. Note that modern wireless devices are equipped with matching networks designed to compensate for the mismatch.  
The changes in the TPD due to the antenna/phantom coupling (scenarios 5 and 7) are shown in Figure 10. For d \(<\) d\({}_{\mathrm{r}}\), where d\({}_{\mathrm{r}}\) denotes the interface between the reactive and radiating near-field regions, the changes in term of the absolute value of TPD are more pronounced (Figure 10a-d). In terms of the relative variations, for this range of d, the TPD increases up to 79.2%, 71.6%, and 43.8% and decreases down to 4.4%, 9.75%, and 9.84% for 2 \(\times\) 2 PAA, 2 \(\times\) 4 PAA, and 4 \(\times\) 4 PAA, respectively (Figure 10e-h). The results shown in Figure 10i demonstrate that there is no direct correlation between Y\({}_{(7,5)}\) and the source directivity. Note that Y\({}_{(7,5)}\) is lower compared to Y\({}_{(6,5)}\). This difference is attributed, to a smaller extent, to losses inside the antenna (15.7%, 18.6%, 27.8%, 33% in respect to the total accepted power at d = 2.25 mm and for SPA, 2 \(\times\) 2 PAA, 2 \(\times\) 4 PAA, and 4 \(\times\) 4 PAA, respectively) and, to a larger extent, to the scattering properties of the antennas. The higher the scattering, the lower the TPD variations.  
For d \(>\) d\({}_{\mathrm{r}}\), the TPD increases up to 84.11%, 79.2%, 95.5%, and 53.3% and decreases down to 25.7%, 30.1%, 20.3%, and 23.9% for SPA, 2 \(\times\) 2 PAA, 2 \(\times\) 4 PAA, and 4 \(\times\) 4 PAA, respectively (Figure 10e-h). The variations are higher for wet skin (increase up to 98.25% and decrease down to 32.5%) and children (increase up to 103.3% and decrease down to 33.7%). Y\({}_{(7,5)}\) converges to Y\({}_{(6,5)}\). For d \(\gg\) d\({}_{\mathrm{r}}\), Y\({}_{(7,5)}\)\(\simeq\) Y\({}_{(6,5)}\)\(\simeq\) Y\({}_{(4,3)}\) as the power density decreases as 1/d2 in the far-field (Figures 7 and 10e-h). The antenna substrate in scenario 7 introduces a phase shift between Y\({}_{(7,5)}\) and Y\({}_{(6,5)}\) (Figure 10e-h). The maximum values of max\(\overline{Y}_{(7,5)}\) are obtained for 2 \(\times\) 4 PAA (i.e., increase up to 52%, 25%, 21% for \(\Delta\)d = 1 mm, 3 mm, 5 mm, respectively) (Table 4). It is worthy to note that the ground plane size impacts the TPD variations. For instance for the SPA, the TPD variations increase with size until the ground plane becomes large enough (e.g., for ground plane dimensions of \(2.5\times 2.5\) to \(10\times 10\) mm2, Y\({}_{(7,5)}\) increases from 10% to 79%).  
Figure 8 top line (scenario 5) and bottom line (scenario 7) show that the spatial distribution of TPD\({}_{7}\) is altered by the antenna/phantom interactions in a similar way as in scenario 6. This suggests that the exact distribution of TPD cannot be retrieved from measurements of the incident power density in free-space in absence of the body model.