# Design of Multi-Mode Antenna Array for Use in Next-Generation Mobile Handsets
## 4 Characteristics of the Handset Antenna Array  
Figure 6 shows the S parameters of the designed handset antenna. As illustrated, the antenna exhibits good S parameters at three operation bands with acceptable mutual coupling at less than \(-\)10 dB [5; 60]. According to the obtained results in Figure 6, slight variation can be observed in the S\({}_{\mathrm{nn}}\) results of the antenna elements, especially in the lower band (2.6 GHz). This variation is mainly due to different placements, feeding points, neighboring, and also unsymmetrical configurations of the employed elements in the main design (smartphone PCB), as shown in Figure 1. Besides this, the smartphone PCB is in a rectangular shape (with a size of 150 \(\times\) 75 mm\({}^{2}\)) which could cause some discrepancies on the frequency responses and couplings, mainly between even and odd port numbers (antennas 1 and 2, for example). However, due to the flexible frequency behavior of the antenna elements (explained in Figure 4), by modifying the design parameters of the antenna element, the frequency response can be easily adjusted to the desired frequency bands [61].  
Figure 5: Radiation characteristics of the PIFA element versus its operation bands.  
The side view of the design radiation patterns for a single-element radiator at different operation frequencies is illustrated in Figure 7. Clearly, the antenna radiation elements exhibit high symmetric radiation patterns covering the different sides of the handset mainboard and increasing the radiation coverage [62; 63; 64; 65]. The 3D radiation patterns for the eight PIFAs of the main design are displayed in Figure 8. As illustrated, the gain level of the design varies from 3 to more than 4 dBi. Besides, due to the placements of the PIFA element, four horizontally and vertically polarized radiation patterns are achieved to improve the MIMO performance of the design [66; 67].  
The envelope correlation coefficient (ECC) and total active reflection coefficient (TARC) characteristics are substantial in MIMO/diversity antenna systems [68; 69]. These parameters can be extracted from the S-parameter results using the below formulas, respectively:  
\[ECC=\frac{\left|S_{mm}^{*}S_{nm}+S_{mm}^{*}S_{m}\right|^{2}}{\left(1-\left|S_{ mm}\right|^{2}-\left|S_{m}\right|^{2}\right)\left(1-\left|S_{mm}\right|^{2}- \left|S_{m}\right|^{2}\right)} \tag{3}\]  
\[TARC=-\sqrt{\frac{\left(S_{mm}+S_{mm}\right)^{2}+\left(S_{mm}+S_{m}\right)^{2 }}{2}} \tag{4}\]  
Figure 6: (**a**) \(\mathrm{S_{m}}\) and (**b**) \(\mathrm{S_{mm}}\) properties of the proposed 5G handset antenna.  
Figure 7: Side views of the antenna radiation patterns at (**a**) first (2.6 GHz), (**b**) second (3.6 GHz), and (**c**) third (5.8 GHz) resonances.  
The ECC and TARC results of the presented multi-mode MIMO antenna design are calculated and plotted in Figure 9. As seen from Figure 9a, the calculated ECC results of PIFA pairs are very low over the entire multi-operation bands (less than 0.01). Additionally, it can be observed from Figure 9b that the TARC value of the diverse PIFA pairs is less than \(-20\) dB at different frequencies.