## 3 Results and Discussion
### Final Design Overview
The resulting antenna model incorporating these optimized parameters is presented in Figure 9. The final design was selected based on a comprehensive S\({}_{11}\) and gain performance evaluation, ensuring the antenna meets the desired specifications. The detailed dimensions of the optimized antenna are summarized in Table 2, providing an in-depth breakdown of the critical measurements. An S\({}_{11}\) graph was generated to assess the reflection performance across a broad range of frequencies after optimizing the antenna design. As shown in Figure 10, the graph clearly represents the antenna's return loss over the operating frequencies, confirming that the design achieved significantly low S\({}_{11}\) values, particularly at the targeted frequencies. This validates the antenna's efficiency and overall performance stability, thereby underscoring the success of the design optimization. Figure 9: Antenna model of the final design. The simulation results reveal outstanding performance, with S\({}_{11}\) values as low as \(-\)53.04 dB at 28.08 GHz and \(-\)83.65 dB at 37.9 GHz. The antenna also maintained a return loss below \(-\)10 dB over two critical frequency bands: 27.63-28.75 GHz and 37.33-38.60 GHz, corresponding to bandwidths of 1.12 GHz and 1.27 GHz, respectively. These bandwidths are centered around the target frequencies of 28 GHz and 38 GHz, ensuring optimal operation across both bands. A comprehensive 3D model illustrating the optimized antenna configuration is presented in Figure 11, which presents the final design in greater detail. The presence of side lobes in the 3D radiation patterns is primarily attributed to the equal dimensions of the ground and insulator layers, along with the use of Rogers 5880 RT/duroid, a low dielectric material. This material was deliberately chosen to optimize S\({}_{11}\) and enhance gain performance at 28 GHz and 38 GHz. Although the design exhibits pronounced side lobes, it achieves a significantly higher gain than the literature average. Furthermore, side lobe levels can be effectively mitigated using established techniques, such as feed optimization, as documented in previous studies. In terms of directivity, the antenna achieved an impressive value of 8.02 dBi at 28 GHz and 9.17 dBi at 38 GHz. The antenna also demonstrated exceptional efficiency, with total efficiencies of 96.02% at 28 GHz and 95.50% at 38 GHz, highlighting its superior operational performance. These results underscore the antenna's ability to maintain high performance and efficiency across both frequency bands. A detailed depiction of the antenna's overall realized gain and efficiency is provided in Figure 12. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Dimension (mm)** & **Parameter** & **Dimension (mm)** \\ \hline a & 16.50 & 1 & 1.40 \\ \hline b & 13.50 & m & 0.55 \\ \hline e & 13.75 & o & 0.70 \\ \hline f & 17.68 & p & 4.45 \\ \hline g & 0.83 & r & 2.05 \\ \hline h & 5.41 & s & 2.35 \\ \hline i & 1.55 & u & 0.76 \\ \hline j & 0.60 & y & 1.63 \\ \hline \end{tabular}
\end{table} 
Table 2: Antenna dimensions of the final design. Figure 10: S\({}_{11}\) performance at different frequencies. Figure 13 illustrates the 2D radiation patterns of the designed antenna in the E-plane and H-plane at 28 GHz and 38 GHz. Figure 13a represents the E-plane radiation patterns at 28 GHz and 38 GHz, while Figure 13b shows the corresponding H-plane patterns, respectively. Figure 11: Three-dimensional radiation pattern of the final antenna design at (**a**) 28 GHz and (**b**) 38 GHz. Figure 12: Realized gain and total antenna efficiency of the designed antenna. Figure 13: Two-dimensional radiation pattern: (**a**) E-plane (28/38 GHz); (**b**) H-plane (28/38 GHz).