## 3 Results and Discussion
### Radiation Pattern Optimization
None of the nulls (located at 4\({}^{\circ}\), 28\({}^{\circ}\), 52\({}^{\circ}\), 118\({}^{\circ}\), 142\({}^{\circ}\), 162\({}^{\circ}\), and 178\({}^{\circ}\)) fall within the main lobe (approximately between 60\({}^{\circ}\) and 87\({}^{\circ}\)), so they do not impact system stability, which is governed by the main lobe. The CST simulation reports a sidelobe level of \(-6.4\) dB at 38 GHz, even at the highest sidelobe, with the first sidelobe significantly lower than the main lobe level, as is commonly observed in the literature. This behavior, potentially caused by asymmetrical slot placement, is considered to be controlled. While the radiation pattern is not perfectly symmetrical, it remains highly functional. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Analysis Number**} & \multirow{2}{*}{**Notch Parameter y**} & \multirow{2}{*}{**Notch Parameter u**} & \multirow{2}{*}{**S\({}_{11}\) (dB)**} & \multirow{2}{*}{**Resonant Frequencies**} & \multirow{2}{*}{**Gain (dBi)**} & \multirow{2}{*}{
\begin{tabular}{c} **SLL** \\ **(dB)** \\ \end{tabular} } \\  & & & **28** & **38** & **(GHz)** & & **28** & **38** \\  & & & **GHz** & **GHz** & & **GHz** & **GHz** & **GHz** \\ \hline
1 & 3.26 & 1.52 & \(-19.45\) & \(-21.93\) & 28.26 & 37.79 & 9.3 & 7.22 & \(-15.7\) & \(-8.1\) \\ \hline
2 & 3.09 & 1.44 & \(-19.54\) & \(-24.14\) & 28.23 & 37.73 & 8.99 & 6.92 & \(-15.6\) & \(-8.2\) \\ \hline
3 & 2.93 & 1.36 & \(-20.77\) & \(-29.33\) & 28.15 & 37.75 & 8.68 & 6.71 & \(-15.5\) & \(-7.8\) \\ \hline
4 & 2.77 & 1.29 & \(-21.93\) & \(-47.34\) & 28.10 & 37.74 & 8.39 & 6.77 & \(-15.5\) & \(-7.3\) \\ \hline
5 & 2.60 & 1.21 & \(-23.60\) & \(-32.47\) & 28.10 & 37.79 & 8.10 & 7.12 & \(-15.6\) & \(-7.0\) \\ \hline
6 & 2.44 & 1.14 & \(-25.18\) & \(-28.69\) & 28.06 & 37.79 & 7.86 & 7.64 & \(-1.1\) & \(-6.8\) \\ \hline
7 & 2.28 & 1.06 & \(-27.95\) & \(-28.74\) & 28.08 & 37.83 & 7.7 & 8.15 & \(-1.5\) & \(-6.6\) \\ \hline
8 & 2.12 & 0.98 & \(-30.36\) & \(-30.88\) & 28.09 & 37.86 & 7.74 & 8.52 & \(-1.8\) & \(-6.5\) \\ \hline
9 & 1.95 & 0.91 & \(-35.12\) & \(-35.09\) & 28.06 & 37.90 & 7.77 & 8.76 & \(-2.0\) & \(-6.4\) \\ \hline
10 & 1.79 & 0.83 & \(-41.72\) & \(-42.02\) & 28.07 & 37.90 & 7.79 & 8.89 & \(-2.1\) & \(-6.4\) \\ \hline Proposed Antenna & 1.63 & 0.76 & \(-53.00\) & \(-83.64\) & 28.07 & 37.90 & 7.82 & 8.98 & \(-2.2\) & \(-6.4\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parametric analysis of radiation pattern optimization using EBG-like notches. The designed antenna's radiation pattern at 38 GHz is specifically intended to fulfill the need for directional and compact radiation, critical for 5G mmWave applications. Since the antenna is directional and the nulls are situated far from the main radiation direction, they do not affect the effective coverage area or orientation. These nulls result naturally from resonance. For 5G and mmWave applications, directional, high-gain antennas are required due to free space losses, and omnidirectional radiation external antennas can be broadly used. This study emphasizes S\({}_{11}\) and gain values for optimal antenna design, and passive pattern optimization can be achieved with four different slot configurations, ground plane modifications, and EBG-like notch structures on the antenna patch. Parametric analysis of the antenna design enables this flexibility. The antenna has a gain of 8.98 dBi at 38 GHz. The half-power beamwidth is \(27^{\circ}\), and the maximum gain occurs at \(71^{\circ}\). The \(-3\) dB limits are approximately between \(60^{\circ}\) and \(87^{\circ}\), with the nulls positioned outside the main radiation direction, as shown in Figure 14.  
Figure 14: Nulls, beamwidth, and gain characteristics at 38 GHz.