## 2 Antenna Design  
### The Design of Unit Cell and Proposed Series-Fed Antenna  
Figure 1 shows the configurations of the proposed series-fed antennas. The proposed antennas are designed on a Taconic RF-35 dielectric substrate, which at 1.9 GHz exhibits a relative permittivity of 3.5 and a loss tangent of 0.0018, with a thickness of 0.76 mm. The design positions the radiating elements on the substrate's top side and a ground plane on the bottom side. As depicted in Figure 1, each unit cell within the array includes a patch with truncated corners to facilitate CP radiation towards the \(+z\)-direction. These patches are interconnected through transmission lines, ensuring series feeding across the 12-unit cells comprising the antenna array. The characteristic impedance of these transmission lines is maintained at approximately 100 \(\Omega\), which reduces radiation loss that occurs in the transmission lines [29]. In the beam-tilted antenna configuration (Figure 1a), the transmission lines below and above the patch in the unit cell include U-shaped bends in opposite directions. The U-shaped bends in opposite directions are proposed to reduce the coupling between parallel microstrip lines in a series-fed array arrangement. In contrast, the unit cell of the broadside antenna, described in Figure 1b, contains a U-shaped bend transmission line below the patch and a straight upper transmission line. The U-shaped bend transmission  
Figure 1: Configuration of the proposed series-fed antennas: (**a**) beam-tilted antenna, (**b**) broadside antenna. line is chamfered at the corners to reduce losses, enhancing the overall antenna efficiency, as shown in Figure 1a,b. The length of the upper U-shaped bend in each unit cell determines a progressive phase value between each radiating patch that is required to implement the beam tilting. The proposed series-fed array antennas, comprising 12 series-connected unit cells, incorporate patches with truncated corners and transmission lines that link these patches, supported by a ground plane underneath. To maintain a compact size and avoid grating lobes, the distance between each patch is fixed at \(L_{sub}=25\) mm (0.487 \(\lambda_{0}\), where \(\lambda_{0}\) is the free space wavelength at 5.84 GHz). Table 1 shows the detailed values of design parameters, all of which have been optimized. Simulations were carried out using CST Studio Suite. Figure 2 presents the simulation results of the reflection coefficient, axial ratio (AR), and RHCP realized gain patterns of the proposed antenna's radiating patch. As shown in Figure 2a, the reflection coefficient is below \(-10\) dB across the frequency band of 5.77-5.88 GHz. This band also corresponds to the antenna's 3-dB AR bandwidth, as indicated in Figure 2b, ranging from 5.81-5.85 GHz. Figure 2c,d show the radiation patterns of the patch as realized RHCP gain in the \(\phi=90^{\circ}\) plane and \(\phi=0^{\circ}\) plane at 5.84 GHz, respectively. The patch has directional characteristics and maximum radiation in the \(+z\)-direction with a gain of 6.2 dBic, and half-power beamwidths (HPBW) of \(90^{\circ}\) and \(89^{\circ}\) in the \(\phi=90^{\circ}\) and \(\phi=0^{\circ}\) planes, respectively. Figure 3 shows the simulated surface current distributions of the radiating patch of the unit cell observed in the proposed \(+z\)-direction to confirm the RHCP radiation at different times \(t=0\), \(T/4\), \(T/2\), and \(3T/4\), where \(T\) is the oscillation period at 5.84 GHz. The direction of current distribution rotates counterclockwise with increasing time, indicating RHCP radiation in the \(+z\)-direction. Figures 4 and 5 shows parameter study of the unit cell for varying \(L_{p}\) and \(a\). Figure 4a reveals that increasing the patch length \(L_{p}\) from 13.5 mm to 13.9 mm causes the resonance frequency to lower, refining the resonance quality as demonstrated by a deeper and sharper reflection coefficient. Meanwhile, Figure 4b indicates a marginal degradation in circular polarization purity with increasing \(L_{p}\).