## 2 Antenna Design  
Figure 1 shows the environment of the mobile handset used in this study. The dimensions of the touchscreen display are the same as the PCB, namely, 74 \(\times\) 150 mm\({}^{2}\). The touchscreen is emulated by using a capacitive resistive approach [23], which uses optically transparent microwires made of copper [24]. Since the conductivity of the transparent copper microwires varies depending on the manufacturing process, this study emulates the conductivity (\(\sigma\)) in a worst-case scenario, namely, \(\sigma\) = 5.8 \(\times\) 10\({}^{7}\) S/m. The spacing between the conductive touchscreen display and the PCB is 5.8 mm. The 28 GHz, 38 GHz, and 2.45 GHz antennas are located on the upper, right, and left flanks, respectively, whereas the lower half is reserved for a hand-held position. Figure 2a shows the geometry of the 28 GHz antenna array, which comprises 12 identical elements printed on a 0.787 mm-thick Rogers RT5880 substrate (dielectric constant \(\varepsilon_{r}\) = 2.2 and loss tangent tan\(\delta\) = 0.0009). The distance between the phase centers of two adjacent elements is 6.2 mm. Figure 2b depicts the proposed element, a revised capacitive coupled patch. It consists of three patches, namely, a left coupled patch with a rectangular notch, a feed strip, and a right coupled patch. This configuration is different from an earlier design [4] owing to the rectangular notch. In comparison with a design without the notch [4], the proposed unit element reduces the vertical dimension by 33% and the horizontal dimension by 11%; therefore, the proposed antenna is capable of fitting in a slim and low-profile handset. Besides this modification, this element inherits the characteristic broad bandwidths of the earlier design [4], which is significantly larger than conventional patch antennas. Figure 2c depicts the simulated surface current distributions using HFSS. When the feed strip is excited, the horizontal edges of the left coupled patch produces strong currents in the same direction. Such current distributions are comparable with a conventional patch antenna excited along the z-axis, thereby creating broadside radiation with y-axis polarization. Figure 3a depicts the geometry of the 38 GHz 8-element antenna array printed on a 0.787-mm-thick Rogers RT5880 substrate where the adjacent elements are separated by 5.1 mm. Detailed dimensions for the unit element are provided in Figure 3b. This element is also a capacitive coupled patch antenna [25], where only two patches--a feed strip and a right coupled patch--are employed. When the strip is fed by a 38 GHz signal, it couples electromagnetic energy to the adjacent patch antenna. The simulated current distributions for the patches are shown in Figure 3c. In contrast to the previous design for the 28 GHz antenna, strong and in-phase currents flow along the vertical edges of the two patches,  
Figure 1: Design environment for the three antenna modules. creating z-axis polarization radiation. This configuration provides a broader impedance bandwidth as compared to microstrip-line-fed patch antennas, albeit at the cost of a slight asymmetry in its radiation characteristics. Although designing millimeter-wave elements with dual polarization can achieve polarization diversity, this study utilizes single linear polarization to reduce the footprint of the antenna. By arranging the proposed antenna with dual-polarized base stations [26; 27], the communication system can still be operated with enhanced spectral efficiency. Figure 3: _Cont._  
Figure 2: Geometry of (**a**) the 28 GHz 1 \(\times\) 12 coupled patch antenna array and (**b**) the unit element (all measurements are in mm). (**c**) The surface current distributions at 28 GHz. Figure 4a details the topology of the 2.45 GHz antenna. Along with the current pathway on the PCB ground, the proposed antenna has a half-wavelength loop printed on a 0.6-mm-thick FR4 substrate (\(\epsilon_{r}\) = 4.4 and tan\(\delta\) = 0.02).