## 2 Design of Antenna
### Antenna Parameterisation Process  
Figure 3 confirms the approximate coefficients of the Vivaldi antenna in this paper. Using electromagnetic simulation software to integrate the Vivaldi, the gain of the array is enhanced in a confined space. Antennas should be placed as closely together as feasible. However, if the spacing between antennas is excessively narrow, the overall isolation of the antennas deteriorates, resulting in a reduction in the performance of the antenna array. A parameter analysis is carried out on the W\({}_{1}\) and L\({}_{1}\) dimensions of the antenna to determine the impact of the radiating element's size on its performance, aiming to identify the optimal antenna length. This approach also allows for the study of the interplay between the cavity and the antenna, as well as the search for the optimal performance of the antenna [12, 16, 18]. Firstly, a parameter analysis is conducted on the radiating element of a single antenna, as shown in Figure 4a. In Figure 4b, when L\({}_{2}\) = 217 \(\upmu\)m, S11 is below \(-10\) dB at 114.63 GHz, the deepest point being \(-11.63\) dB, and the bandwidth is from 114.63 to 124.03 GHz. When L\({}_{2}\) = 221 \(\upmu\)m, S11 is below \(-10\) dB at 115.27 GHz, the deepest point being \(-11.22\) dB, and the bandwidth is 115.27-123.52 GHz. When L\({}_{2}\) = 225 \(\upmu\)m, S11 is below \(-10\) dB at 113.43 GHz, with the deepest point being \(-12.28\) dB, and the bandwidth is from 113.43 to 124.67 GHz. Therefore, after the parameter analysis, when the length of the radiating element L\({}_{2}\) is 225 \(\upmu\)m, the bandwidth is the widest and the reflection coefficient has the  
Figure 3: (a) Antenna analysis; (b)antenna analysis S-parameter stacked plot. lowest value. Furthermore, the parameter analysis is performed on W\({}_{1}\) as shown in Figure 4a. In Figure 5b, when W\({}_{1}\) = 192 \(\upmu\)m, S11 is below \(-\)10 dB at 116.11 GHz, the deepest point being \(-\)12.5 dB, and the bandwidth is from 116.11 to 125.82 GHz. When W\({}_{1}\) = 206 \(\upmu\)m, S11 is below \(-\)10 dB at 115.76 GHz, with the deepest point being \(-\)12.02 dB, and the bandwidth is from 115.76 to 125.79 GHz. When W\({}_{1}\) = 220 \(\upmu\)m, S11 is below \(-\)10 dB at 112.72 GHz, with the deepest point being \(-\)13.04 dB, and the bandwidth is 112.72-124.66 GHz. Therefore, after the parameter analysis, when the width of the radiating element W\({}_{1}\) is 220 \(\upmu\)m, the bandwidth is the widest and the reflection coefficient has the lowest value [21]. To ensure that the antenna impedance matching performance meets the required standards, a parametric analysis was performed on the W\({}_{7}\) part of the power divider, Figure 6a. Figure 6b shows the results of the S11 parameter analysis, while Figure 7a shows the results of the S21 one, and Figure 7b shows the S31 parameter analyses. The results indicate that S21 and S31 exhibit no significant differences, as both are \(-\)3.5 dB. However, when W\({}_{7}\) = 5 \(\upmu\)m, S11 has the deepest resonance point at 78 GHz, with a value of \(-\)30.8 dB. Therefore, W\({}_{7}\) = 5 \(\upmu\)m is chosen as the design parameter for the power divider. Figure 4: (a) Diagram of L\({}_{2}\)’s location; (b) simulation of L\({}_{2}\)’s S-parameter. Figure 5: (a) Diagram of W\({}_{1}\)’s location; (b) simulation of W\({}_{1}\)’s S-parameter. Next, the Vivaldi antenna array is configured in a \(1\times 2\) format and then the parameter analysis is performed on the radiating elements of the antenna, as shown in Figure 8a. In Figure 8b, when W4 = 22 \(\upmu\)m, S11 is below \(-10\) dB at 93.21 GHz, with the deepest point being \(-33.24\) dB, and the bandwidth is 93.21-113.67 GHz. When W4 = 18 \(\upmu\)m, S11 is below \(-10\) dB at 84.73 GHz, with the deepest point being \(-10\) dB at 84.73 GHz, with the deepest point being \(-25.07\) dB, and the bandwidth is 84.73-102.15 GHz. When W4 = 14 \(\upmu\)m, S11 is below \(-10\) dB at 89.92 GHz, with the deepest point being \(-37.1\) dB, and the bandwidth is from 89.92 to 109.72 GHz.