## 3 Results and Discussion  
Figure 1 depicts the structure of a single port antenna array constructed on a low-loss Rogers RT-5880 substrate with the thickness (h) of 0.787 mm, a dielectric constant (\(\varepsilon_{\rm r}\)) of 2.2, and a loss tangent of 0.0009. This antenna array comprises 1\(\times\)8 rectangular patch elements fed via a microstrip feedline. Each antenna element consists of a modified single radiating patch with dimensions W\({}_{\rm p}\)\(\times\) L\({}_{\rm p}\). The combination of inset feeders of each dimension, W\({}_{\rm inset}\)\(\times\) L\({}_{\rm inset}\), improves the impedance matching of the antenna. Aimed to enhance the bandwidth of antenna, two rectangular slots, W\({}_{\rm slot}\)\(\times\) L\({}_{\rm slot}\), were plunged at distances W\({}_{\rm p}\)/4 from left and right edge of the patch. The slotted patches were fed through a 50 \(\Omega\) microstrip feedline, defined by width W\({}_{\rm mf}\) and length L\({}_{\rm mf}\). The substrate and ground plane are defined by dimensions W\({}_{\rm s}\), L\({}_{\rm s}\) and W\({}_{\rm g}\), L\({}_{\rm g}\), respectively. All slot dimensions were carefully adjusted to achieve the best impedance matching at the desired resonant frequency. Insets in rectangular patch antennas play an important role in adjusting the input impedance of antenna arrays for proper impedance matching. By strategically placing insets within the patch structure, the input impedance is adjusted according to Equation (9). This adjustment is crucial for efficient power transfer from the transmission line to the antenna element, minimizing signal reflections and optimizing performance parameters. In case of insufficient impedance matching, additional stubs with calibrated lengths (L\({}_{\rm stub}\)) and positions can be added to the transmission line feeder to fine-tune the impedance. In this regard, we performed a geometric parametric sweep to optimize the lengths of inset feeders and stubs. From simulation results, it was found that these dimensions are the most influential factor in impacting the input impedance of the antenna array. Table 1 and Figure 1 offer a detailed overview of all design parameters. The impedance matching was achieved using insets created in the first patch, in addition to two stubs placed before that patch. The insets and stub dimensions were critical for achieving impedance matching and controlling the bandwidth, as indicated in the parametric sweeps of L\({}_{\rm inset}\) and L\({}_{\rm stub}\) in Figure 2, where the reflection coefficient S\({}_{11}\) of the antenna structure was computed. The parametric sweep analysis reveals that among all the dimensions outlined in Table 1, the inset length (L\({}_{\rm inset}\) or y\({}_{0}\)) stands out as the most critical parameter. Altering L\({}_{\rm inset}\) from 0.2 mm to 1.0 mm resulted in significant variations in the resonance frequencies throughout the operating band, as well as in the bandwidth values and reflection coefficients, as illustrated in Figure 2. These changes arise from the intricate interplay between the two inset lengths and the antenna's input impedance. Adjusting the inset length leads to noticeable shifts in the impedance characteristics, subsequently influencing the resonance behavior, bandwidth efficiency, and reflection properties of the antenna system. Optimal performance was attained with inset and stub lengths set at 0.7 mm. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Parameter** & \(W_{mf}\) & \(L_{mf}\) & \(W_{f}\) & \(L_{f}\) & \(W_{p}\) & \(L_{p}\) & \(W_{s}\) & \(L_{s}\) & \(W_{g}\) & \(L_{g}\) & \(W_{gs}\) & \(L_{gs}\) \\ \hline
**Value (mm)** & 0.6 & 6 & 0.5 & 4.16 & 3.72 & 3.61 & 12 & 65 & 11 & 59 & 0.5 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Antenna array dimension parameters.