## 3 Results and Discussion
### Radiation Pattern Optimization  
To optimize the antenna design, dual-band operation was achieved through a slot configuration, where the dimensions of each notch on the patch were systematically adjusted. Key antenna parameters, particularly S\({}_{11}\) and gain, were analyzed to determine the optimal design. In addition to this optimization process, extensive parametric analyses were conducted for each slot to further refine the radiation pattern. The optimization of the radiation pattern was carried out using two primary approaches: (a) ground plane modifications and (b) radiation pattern enhancement using EBG-like notches. These techniques enabled precise control over the beamforming characteristics, ultimately improving the antenna's overall performance. * Ground plane modifications  
To assess the impact of ground plane modifications on the radiation pattern, parametric analyses were conducted by systematically varying the ground dimensions in increments of approximately 10% in all directions except, for the connector side. Instead of utilizing the CST Parametric Analysis tool, separate CST models were employed to minimize computational complexity and ensure accurate results. The simulation outcomes, including S\({}_{11}\), gain, and sidelobe level (SLL) for different ground plane configurations, are summarized in Table 3. The results demonstrate that variations in the ground plane dimensions significantly affect the antenna's performance, particularly in terms of gain and the sidelobe level. The final design was selected based on an optimal trade-off between resonance stability, gain, and radiation pattern characteristics. Radiation pattern optimization using EBG-like notches  
In addition to slot-based optimization and parametric analyses, electromagnetic bandgap (EBG)-like notches were symmetrically incorporated into the patch to enhance the radiation pattern, particularly by reducing the sidelobe levels. The notch dimensions, defined by parameters y and u, were systematically varied in increments of approximately 10% to evaluate their impact on the radiation characteristics. The primary objective of this optimization was to create a sufficient bandgap to suppress surface waves, thereby  
improving the overall radiation performance of the antenna. The simulation results for different notch configurations are summarized in Table 4.  
To further optimize the notch design, additional parametric analyses were performed for smaller values of y and u. These analyses aimed to achieve an optimal balance between enhanced sidelobe suppression and minimal impact on return loss and gain. The final optimized dimensions were selected based on this trade-off, ensuring improved radiation performance without significant degradation in other key antenna parameters. The simulation results are summarized in Table 5.  
This study adopted a two-pronged approach to optimize the radiation pattern of the proposed antenna. Ground plane modifications were implemented to fine-tune the beamforming characteristics, while EBG-like notches were incorporated to suppress the sidelobes and enhance radiation efficiency. The results confirm that the proposed optimization methodology significantly improves antenna performance at both 28 GHz and 38 GHz, making it a promising candidate for 5G and applications beyond. Figure 14 presents the null angles and gain values at 38 GHz. The purple dotted lines in the figure indicate the beamwidth considering the \(-3\) dB threshold. The suboptimal radiation pattern at this frequency is due to the presence of nulls or sidelobes in certain directions. The antenna design incorporates a directed radiation structure to ensure stable and directional radiation. At 38 GHz, the radiation pattern achieves maximum gain at approximately 70\({}^{\circ}\), with a narrow beamwidth of 27\({}^{\circ}\), providing precise control.