## 3 Results and Discussion  
### Single-Array Antenna  
Figure 1 shows the design of a single-port antenna array built on a substrate material of Rogers RT-5880, which has a dielectric constant (\(\epsilon_{r}\)) of 2.2, a thickness of 0.787 mm, and a loss tangent of 0.0009. The array consists of 1 \(\times\) 8 rectangular elements, and each patch is fed by a microstrip feedline. Every element features a main radiating patch with dimensions \(\text{W}_{p}\times\text{L}_{p}\). The antenna impedance was calibrated using inset feeders, each sized \(\text{W}_{\text{inset}}\times\text{L}_{\text{inset}}\), to improve impedance matching. To enhance the antenna's bandwidth, two rectangular slots with dimensions \(\text{W}_{\text{slot}}\times\text{L}_{\text{slot}}\) were incorporated, positioned at a distance of \(\text{W}\text{p}/4\) from the right and left patch edges. The patches were fed using a 50 \(\Omega\) feedline, with dimensions of \(\text{W}_{\text{mf}}\times\text{L}_{\text{mf}}\). The substrate and ground plane were designed with dimensions \(\text{W}_{\text{s}}\times\text{L}_{\text{s}}\) and \(\text{W}_{\text{g}}\times\text{L}_{\text{g}}\), respectively. The precise optimization of the slot dimensions was performed to achieve optimal impedance matching at the target resonant frequency. Through parametric sweep and optimization, it was identified that the length of the inset feeders, \(\text{L}_{\text{inset}}\), was the most effective dimension that greatly influenced the antenna array input impedance. Table 1 provides a comprehensive summary of all the design parameters. Figure 1 displays details of the proposed design. In the antenna's reflection coefficient described by the scattering parameter, \(\text{S}_{11}\), depicted in Figure 2, resonance is observed at a frequency of 28.8 GHz, reaching \(-\)28.5 dB reflection coefficients. The bandwidths surrounding this resonant frequency is determined to be \(\sim\)1 GHz (from 28.3 to 29.3 GHz). These simulation results are essential for predicting and assessing the antenna's performance before fabricating a prototype of the proposed design. The parametric examination highlights that, among all the design dimensions, the lengths of insets (\(\text{L}_{\text{inset}}\) or \(\text{Y}_{0}\)) constitute the most key parameter that directly influences the input impedance of the antenna. Varying \(\text{L}_{\text{inset}}\) from 0.1 to 0.6 mm caused substantial resonance frequency shifts and additionally altered bandwidth and reflection coefficient values, as demonstrated in Figure 3. These changes arise from the complex interchange between the antenna's input impedance and the two inset lengths. Modifying these lengthssignificantly alters the impedance characteristics, which in turn affects the resonance, bandwidth, and the antenna reflection properties. The optimized performance was observed when the inset length was set to 0.3 mm. Figure 4 presents the computed peak gain of the proposed antenna as a function of frequency. The series-fed antenna array comprising 1 \(\times\) 8 elements achieves a peak gain of 13 dBi at the resonance frequency of 28.8 GHz. This demonstrates the antenna's capability \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline
**Parameter** & \(W_{p}\) & \(L_{p}\) & \(W_{s}\) & \(L_{s}\) & \(W_{f}\) & \(L_{f}\) & \(W_{mf}\) & \(L_{mf}\) & \(W_{g}\) & \(L_{g}\) & \(W_{sq}\) & \(W_{slot}\) & \(L_{slot}\) & \(W_{inset}\) & \(L_{inset}\) \\ \hline
**Value (mm)** & 4.65 & 3.06 & 20 & 68 & 0.5 & 4.16 & 0.6 & 9.02 & 18 & 67 & 1 & 0.25 & 1.5 & 0.2 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimized dimensions of single-array antenna. Figure 1: (**a**) Front, (**b**) back view of single-port antenna; and (**c**) dimensions of slots created in each single-patch. to focus electromagnetic (EM) energy in a specific direction within the investigated band, highlighting its fitness for the N261 band operation.