## 3 Results and Discussion
### Antenna Array with BM Network  
The \(4\times 4\) Butler Matrix (BM) provides four distinct beams when one port is excited. For example, when one port is activated, it produces a beam at \(-45^{\circ}\), and when another port is excited, it produces a beam at \(45^{\circ}\), with reciprocal beams for the other two ports. This behavior is consistent with previous studies that utilized the Butler Matrix for beamforming applications, where discrete beams are generated depending on the port excitation, as seen in millimeter-wave and sub-6 GHz systems [92]. The results of the BM network with the antenna array, tested at 5.5 GHz, showed consistent performance across different input ports. Figure 19 shows the return loss for port 1, port 2, port 3, and port 4, each showing minimal signal loss when only one port is excited. This aligns with established findings that demonstrate the ability of Butler matrices to maintain low return loss and high isolation between ports, which is important for ensuring efficient beam switching and steering without excessive signal degradation [93]. The far-field beam pattern, depicted in Figure 20, demonstrates the directional capabilities of the BM network. The deviation in beam angles between different ports, such as port 3 (beam at \(-12^{\circ}\)) and port 4 (beam at \(16^{\circ}\)), is likely due to slight imperfections in the phase shift introduced by the Butler Matrix. This is not uncommon in practical systems, where minor phase errors can occur due to manufacturing tolerances or component mismatches, as also indicated by [PERSON] et al. [94]. The difference in the angles of port 3 and port 4 is due to incorrect progressive phase difference in the ports by \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Length (mm)** \\ \hline L & 55.20 \\ L1 & 17.6 \\ L2 & 10 \\ L3 & 10 \\ Lf & 3.0 \\ GL & 55.20 \\ W & 35.0 \\ W1 & 17.6 \\ W2 & 1 \\ W3 & 4.91 \\ GW & 35.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimized dimensions for a single-element antenna. Figure 18: Axial ratio of the single-element square patch antenna. the components of the BM network and asymmetric response of the BM network [95]. The gain of the individual beams for all ports varied between 8.38 dBi and 9.69 dBi, indicating strong directional radiation. Higher gain values suggest that the antenna efficiently directs energy into narrow beams, which is advantageous for communication systems in complex environments, such as underground mines. The variation in gain is in line with other studies that demonstrate slight differences in gain across different input ports due to phase and amplitude variations in the Butler Matrix [96] ([PERSON] et al., 2023). This enhanced directional radiation is particularly beneficial in underground mining environments, where obstacles and signal interference are major challenges. By directing the antenna's beam towards specific angles, the system can mitigate signal reflections and improve signal-to-noise ratios, leading to better overall communication performance. Moreover, the ability to steer beams in multiple directions without physical movement of the antenna makes the system well-suited for dynamic environments where the direction of communication may frequently change. This adaptability is a key advantage of using a Butler Matrix for beamforming applications in underground mines, where traditional omnidirectional antennas may struggle with coverage and interference issues. The proposed antenna, depicted in Figure 9, steers the direction of the far-field radiation through a Butler Matrix (BM). This antenna design enables the transmission of beams in four distinct directions, which is a key characteristic of Butler matrix-fed arrays used for beamforming and steering applications [93]. The antenna can be conveniently mounted on the roof of an underground mine tunnel. When a mobile device, such as a miner or a vehicle, enters the antenna's range, the BM automatically steers the beam to track the device's movement within the tunnel.