## 2 Proposed Antenna Design  
### Geometry of Vehicle Window Glass Antenna  
Figure 1 shows the geometry of the proposed printed 5G monopole antenna on the vehicle window glass with the parasitic elements and lattice-structure reflector to improve the bore-sight gain and minimize the radiation pattern distortion. The proposed antenna consists of the CPW feeding structure, the monopole radiator with parasitic elements, and the lattice-structure reflector. The CPW has an inner conductor (length \(l_{2}\times\) width \(w_{4}\)) and grounds (length \(l_{2}\times\) width \(w_{2}\)). The gap between the inner conductor and grounds is \(g_{1}\). The CPW is printed on the top of the thick vehicle window glass substrate (\(\epsilon_{r}=6.9\), \(tan\delta=0.017\) at 28 GHz) with dimensions of \(w_{1}\times l_{1}\times t\) (width \(\times\) length \(\times\) thickness). Note that the guided fields from the CPW line are less affected by substrate thickness compared to other transmission lines (i.e., strip line, microstrip, and CPW with a ground) that induce more electromagnetic fields inside the substrate. This CPW line is fed by a K-type (2.92 mm) connector [21], and we modeled the actual geometry to consider the effects of the connector, as shown in Figure 2. The K-type connector is excited by using a waveguide port at the starting points of the inner and outer conductors, which is directly connected to the coaxial cable, to feed the CPW in the simulation conditions. The monopole radiator is directly connected to the CPW inner conductor and has a length of \(l_{4}\) and a width of \(w_{4}\) for resonance at 28 GHz. This monopole has the LP characteristic that can have advantages for the design and fabrication of an antenna, and in general, it is widely employed for 5G vehicular communications [22; 23; 24; 25]. The parasitic elements have four rectangular patches (\(l_{3}\times w_{3}\)) that are placed at the distances \(g_{1}\) and \(g_{2}\) from the monopole radiator and the CPW ground, respectively. When adjusting these dimensions, the parasitic elements operate as a radiator by indirect coupling with the monopole radiator. Furthermore, the electromagnetic waves radiated from each parasitic element can be combined with those radiated from the monopole radiator that results in increasing the bore-sight gain. The lattice-structure reflector is printed on the opposite side of the monopole radiator. The reflector is composed of multiple square patches with a width of \(w_{5}\), and the distance between the adjacent patches is \(g_{3}\). The number of reflector elements is \(M\times N\), where \(M\) and \(N\) indicate the total number of reflector patches along the \(x\)- and \(y\)-axes. The adjustment of the reflector parameters can effectively minimize the radiation pattern distortion that occurs due to the thick vehicle window glass in accordance with the wavelength at 28 GHz. Herein, design goals for this work are as follows: operating center frequency of 28 GHz, bandwidth of more than 850 MHz, reflection coefficient less than \(-10\) dB, bore-sight gain of more than 0 dBi, LP, and glass substrate thickness of 3.2 mm. To achieve the goals, the proposed antenna was modeled and optimized using the CST Studio Suite full EM simulator, and the optimized design parameters are listed in Table 1.  
Figure 1: Geometry of the proposed printed antenna: (**a**) isometric view; (**b**) top view; (**c**) bottom view; (**d**) side view.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline \(l_{1}\) & 25 mm & \(w_{5}\) & 2 mm \\ \(l_{2}\) & 2 mm & \(g_{1}\) & 0.13 mm \\ \(l_{3}\) & 1.4 mm & \(g_{2}\) & 0.13 mm \\ \(l_{4}\) & 2.03 mm & \(g_{3}\) & 0.5 mm \\ \(w_{1}\) & 25 mm & \(g_{4}\) & 0.5 mm \\ \(w_{2}\) & 9.62 mm & \(t\) & 3.2 mm \\ \(w_{3}\) & 0.8 mm & \(M\) & 4 \\ \(w_{4}\) & 0.5 mm & \(N\) & 6 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimized design parameters of the proposed antenna.