## 3 Results and Discussion
### Patch Antenna  
The designed single-element square patch antenna's reflection coefficient refers to the amount of reflected signal delivered to the antenna structure in comparison to the incident signal. Generally, the reflection coefficient, known as S\({}_{11}\), indicates that the reflected signal is greater than the incident signal for port 1, and is expressed in decibels. The results suggest that, for all frequencies with S\({}_{11}\) less than \(-10\) dB, the antenna structure is regarded as radiating. This phenomenon aligns with similar findings in recent research [82; 83] on patch antennas, where a reflection coefficient of less than \(-10\) dB indicates efficient impedance matching and minimal signal loss. Figure 14 depicts the reflection coefficient of a single rectangular patch antenna element. Figure 12: Magnitude of the S-parameter of the crossover for input port 1. Figure 13: Phase of the S-parameter S\({}_{12}\) of the proposed phase shifter. The designed single-element square patch antenna has a bandwidth of 140 MHz from 5.43 GHz to 5.57 GHz, as highlighted in Figure 4, which aligns with other microstrip antenna designs that focus on achieving a wide operational bandwidth through optimization techniques [84]. Similarly, another essential antenna parameter is the far-field radiation pattern, which specifies the direction in which the antenna radiates in the far field [85]. Figure 15 depicts the designed single-element square patch antenna's cross and co-poles of the far-field radiation patterns. At 5.5 GHz, it shows a directed radiation pattern with a gain of 7.78 dBi, a gain value that is consistent with typical patch antennas of this size and configuration [86]. The rectangular patch antenna's directed radiation pattern was caused by the presence of a ground plane on its backside, as also indicated by [PERSON] et al. [87], which has been proven to significantly influence the radiation behavior by enhancing the front-to-back ratio and reducing unwanted reflections. Figure 14: Reflection coefficient of single-element square patch antenna at 5.5 GHz. Figure 15: Far-field radiation co- and cross-pole pattern of a single-element antenna at 5.5 GHz (a) phi = 0, (b) phi = 90, (c) Theta = 0, and (d) Theta = 90. The rectangular patch antenna was circularly polarized by changing its shape and shortening the opposite edge of the patch, which is a common technique for achieving circular polarization in patch antennas [88]. The width of the rectangular patch was reduced to create a square patch. The reflection coefficient of the square patch antenna was also displayed for various antenna widths, as shown in Figure 16. The patch's width was adjusted to 20.45 mm, 19.13 mm, 17.8 mm, and 16.5 mm. Similarly, for 0 mm to 3 mm, the parametric sweep was conducted on the reduced length of the opposing edges of the square patch. Figure 17 depicts the reflection coefficient results for the sweep analysis, a process widely used in antenna design optimization [89]. Figure 17 depicts the reflection coefficient results for parametric sweep analysis with different lengths of Lf (truncated length). The results show that, at Lf = 3 mm, the square patch antenna achieves a wide bandwidth, while for Lf = 4 mm, it exhibits dual-band operation with a narrower bandwidth. Therefore, the value of Lf = 3 mm was selected for the design of the square patch antenna. The final dimensions of the square patch antenna are shown in Table 6. The square patch antenna provides an impedance bandwidth of 400 MHz between 5.52 GHz and 5.99 GHz, which aligns with recent developments in circularly polarized antennas that achieve broad impedance bandwidths [90]. The single-element antenna is right-hand circularly polarized (RHCP) with a circularly polarized bandwidth of 300 MHz between 5.51 GHz and 5.81 GHz, as shown in Figure 18. Circular polarization  
Figure 16: Reflection coefficient of parametric sweep of the width (w) of the single element antenna.