## 2 Antenna Design
### Cylindrical Reflector Antenna  
The reflector is a singly curved offset parabolic cylinder, measuring 110 mm in width and 149 mm in length (equivalent to 6.3\(\lambda\)\(\times\) 8.5\(\lambda\), where \(\lambda\) represents the free space wavelength at the center frequency of 17.2 GHz). The arrangement of the offset cylindrical reflector system, along with the feed patch array, is illustrated in Figure 7. The illustration includes details of the geometric parameters and coordinate system. Due to its cylindrical shape, the antenna has a focal line that necessitates a line source rather than a point source to provide proper illumination. The 2 \(\times\) 8 patch antenna array serves as the feed for the reflector antenna and is positioned along the focal line of the reflector. The antenna aperture is rectangular-shaped, with dimensions of 6.3\(\lambda\)\(\times\) 8.5\(\lambda\) and a focal length of \(F\) = 98 mm (\(F/D\) = 0.65). The clearance height is \(H\) = 13 mm (cf. Figure 7a). The feed should exhibit a proper pattern in the parabolic cut to provide illumination along the cylindrical axis (\(y\)-axis). Additionally, ensuring that the feed source is lightweight is crucial to meet potential launching constraints. This can be achieved by designing the array feed on lightweight substrates such as Rogers, as discussed in Section 2.2. The feed is offset and tilted by 45\({}^{\circ}\), as illustrated in Figure 7b, to illuminate the reflector. An offset configuration was employed to prevent gain loss resulting from feed blockage. In this setup, the feed remains along the axis of the reflector, but the reflector itself is cut halfway as shown in Figure 7a. The feed with two rows ensures proper illumination of the reflector cut along the \(y\)-axis. Minimizing taper and spillover losses required optimizing the feed to achieve a minimum feed taper of \(-10\) dB at 33\({}^{\circ}\) (cf. Figure 6a). Proper adjustment of the feed position and its tilting angle enables the achievement of maximum directivity. The maximum directivity can be calculated by  
\[D_{max}=10\ log_{10}\ (\frac{4\pi}{\lambda^{2}})\ A_{P} \tag{1}\]  
where \(A_{P}=L_{r}\times W_{r}\) is the physical area (the aperture dimensions). The maximum calculated directivity, as per (1), is 28.3 dBi. However, the simulated directivity is 25.4 dBi, resulting in an efficiency of 52%. The discrepancy of 2.9 dB is attributed to taper and spillover losses, along with feed and mismatch losses. When considering the ideal reflector, the overall efficiency \(\epsilon\)= \(e_{T}\cdot e_{S}\) can theoretically reach up to 81% (i.e., \(-1\) dB) [25]. This efficiency is derived from the product of taper efficiency (\(\epsilon_{T}\)) and spillover efficiency (\(\epsilon_{S}\)), the two primary contributors to aperture efficiency. The taper and spillover losses exhibit a  
Figure 7: The offset cylindrical reflector system: (**a**) optical specifications for the offset-fed cylindrical reflector with the key parameters (the dimensions are \(W_{r}\) = 110 mm, \(L_{r}\) = 149 mm, \(F\)= 98 mm, and \(H\) = 13 mm) and (**b**) the cross-section of the reflector system.  
slight increase compared to the ideal scenario. The simulated radiation patterns in both the E- and H-planes at 17.2 GHz are depicted in Figure 8. The simulated half-power beamwidth (HPBW) in the E- and H-planes are \(8^{\circ}\) and \(9.6^{\circ}\), respectively. In the E-plane, the sidelobe level (SLL) is \(-16\) dB, whereas in the H-plane, it is \(-14\) dB. Additionally, the cross-polarization level is below \(-30\) dB in both cuts. It is worth mentioning that the simulated radiation patterns exclude the blockage effects caused by the feed support. Additionally, the cross-polarization shows as null at the boresight, demonstrating the precise alignment of the feed on the reflector.