## 2 Design of a Unit Cell for the Single-Layer Shared-Aperture Antenna  
Figure 1 presents the geometry of the S/X-band single-layer shared-aperture antenna for the MFRs of military ships. A unit cell of the proposed antenna consists of one S-band element and a 2 \(\times\) 2 X-band array, both of which are printed on the same layer. Since this configuration does not include an upper stacked element, the performance degradation of the antenna due to the blockage effect can be prevented compared to a stacked structure antenna. Herein, the S-band patch element contains a small size radiator with a length \(l_{1}\) and a width \(w_{1}\) to avoid physical interference with the X-band elements. However, the small size radiator has narrow bandwidth characteristics [19; 20]. Therefore, the S-band element consists of one feeding patch and a pair of parasitic patches, which have a mutual complementary configuration to the X-band elements. A mutual complementary configuration means that two different shapes have a maximum area without overlapping within a limited area. Therefore, this configuration can maximize the area of the radiator, which can improve the bandwidth of the S-band element. Herein, the gap size between the feeding patch and the parasitic patches is \(g\), and the antenna bandwidth can be further improved by adjusting the gap size \(g\). The parasitic elements have a half-cross shape obtained by combining two rectangular structures of different lengths. In this element, the long rectangle has a width \(w_{2}\) and a length \(l_{2}\), and the short rectangle has a width \(w_{3}\) and a length \(l_{3}\). The X-band elements are rectangular patch antennas with a width \(w_{x}\) and a length \(l_{x}\). In general, the length of the patch antenna can be calculated using the wavelength and the dielectric constant [18]. However, because of the coupling characteristics, the length of the X-band element is adjusted more by the S-band patch parameters. To obtain the wide antenna bandwidth of the X-band elements without causing physical interference to the S-band element, an RF-60 substrate (\(\varepsilon_{r}\) = 6.05, tan \(\delta\) = 0.0018) with a thickness \(h\) is applied to the proposed antenna. In addition, the unit cell of the proposed antenna is designed in a symmetrical structure, which can be flexibly extended to a full array configuration. The design parameters are obtained using the CST electromagnetic simulator [21] and are provided in Table 1.  
Figure 1: Geometry of the proposed single-layer shared-aperture antenna: (**a**) isometric view of the S-band element; (**b**) isometric view of the X-band array; (**c**) isometric view of the unit cell; (**d**) side view of the unit cell. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Dimension (mm)** \\ \hline \(s\) & 17.0 \\ \(h\) & 3.2 \\ \(l_{1}\) & 21.0 \\ \(l_{2}\) & 21.6 \\ \(l_{3}\) & 8.7 \\ \(g\) & 2.5 \\ \(w_{1}\) & 5.5 \\ \(w_{2}\) & 3.2 \\ \(w_{3}\) & 10.1 \\ \(l_{x}\) & 4.2 \\ \(w_{x}\) & 4.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometrical parameters of the proposed antenna. Figure 2 illustrates the comparison of antenna performances according to the S-band element configurations. Figure 2a (Case 1) shows a small size radiator for the S-band to avoid physical interference with the X-band elements, which has narrow bandwidth characteristics. To improve the antenna bandwidth, the mutual complementary configuration can be applied to the S-band element, as shown in Figure 2b (Case 2). The use of a mutual complementary configuration for X-band elements can maximize the area of the radiator, which can improve the antenna bandwidth. To further improve the antenna bandwidth, the S-band element is separated into one feeding patch and a pair of parasitic patches, as shown in Figure 2c (Case 3).