## 2 Antenna Design and Performance
### 2 \(\times\) 2 Ka-Band Patch Antenna Array Design and Performance  
In a millimeter wave band, a high gain is required in order to compensate for the high path loss caused by atmospheric absorption [8]. Therefore, we considered the antenna array in order to enhance the radiation gain in the Ka-band. Figure 2a shows the geometry of the designed 2 \(\times\) 2 patch antenna array for V-pol. The center-to-center spacing of the array is 4.3 mm (0.5 \(\lambda_{0}\) at 35 GHz). As shown in Figure 2b, the simulated surface current distributions of all patch antennas have the same directions (V-pol characteristics). Figure 2c shows the simulated reflection coefficient performances of the 2 \(\times\) 2 patch antenna array. The \(-\)10 dB reflection coefficient bandwidths of all ports sufficiently cover the 35 GHz target band. As shown in Figure 2d, the simulated maximum gain and FBR at 35 GHz are 10.89 dBi and 15.31 dB, respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Frequency Band** & **P** & **L** & **S** & **C** & **X** & **Ku** & **Ka** \\ \hline Frequency (GHz) & 0.3–1 & 1–2 & 2–4 & 4–8 & 8–12 & 12–18 & 27–40 \\ \hline \end{tabular}
\end{table} 
Table 1: Frequency bands used in SAR systems. Figure 1: Single patch antenna: (**a**) geometry of antenna, (**b**) perspective view, (**c**) side view, (**d**) simulated surface current distribution at 35 GHz, (**e**) simulated S-parameters, (**f**) simulated radiation patterns at 35 GHz when Port 1 is excited, and (**g**) simulated radiation patterns at 35 GHz when Port 2 is excited. Figure 3a shows the geometry of the antenna array for H-pol. The spacing of the patch antennas is the same as that for V-pol. As shown in Figure 3b, the surface current distributions show that the antenna array has H-pol characteristics. Figure 3c shows that the simulated \(-10\) dB reflection coefficients cover the target band. Figure 3d shows the simulated radiation pattern of the H-pol case. The simulated maximum gain and FBR at 35 GHz are 10.66 dBi and 13.28 dB, respectively. Figure 4a,b show the antenna array with the feeding network used for fabrication. The feeding network has \(180^{\circ}\) phase-delay lines for in-phase excitation. As shown in Figure 4c, the simulated 10 dB \(1S_{11}\) and \(1S_{22}\) \(|\) bandwidths are 5.43 GHz (32.77-38.2 GHz) and 5.63 GHz (31.61-37.24 GHz), respectively. In the V-pol case (Port 1 excitation), the simulated maximum gain and FBR at 35 GHz are 10.04 dBi and 5.74 dB, respectively. In the H-pol case (Port 2 excitation), the simulated maximum gain and FBR at 35 GHz are 10 dBi and 12.11 dB, respectively. Each slot aperture can be considered to be a slot antenna. Since the slot antenna radiates in both directions perpendicular to the substrate, the backlobe is mainly due to the radiation from the slot apertures. Therefore, a reflector is required to enhance the FBR performance. Figure 2: \(2\times 2\) patch antenna array for V-pol: (**a**) geometry of antenna array, (**b**) simulated surface current distribution at 35 GHz, (**c**) simulated reflection coefficient performances, and (**d**) simulated radiation patterns at 35 GHz. Figure 4: \(Cont\). Figure 3: \(2\times 2\) patch antenna array for H-pol: (**a**) geometry of antenna array, (**b**) simulated surface current distribution at 35 GHz, (**c**) simulated reflection coefficient performances, and (**d**) simulated radiation patterns at 35 GHz. Figure 5a,c show the patch antenna array with a reflector. The reflector is made of a 1.6 mm thick FR4 substrate (\(\varepsilon_{\rm r}=4.4\), tan \(\delta=0.02\)) with a metal plane on the top side. As shown in Table 2, the radiation performance of the proposed antenna can be optimized by changing the gap distance (\(h\)) between the antenna and the reflector.