## 4 Optimal Design and Simulation of Antenna  
The establishment of the antenna model and simulation test were carried out in the electromagnetic software. The basic function of the antenna is to achieve low impedance and axial ratio bandwidth in the upstream and downstream frequency band of BeiDou-1, limited by the shape of the gap (that is, the coupling between the X-shaped gap and the influence of the surface on its amplitude), and the electric field value strength of the two radiation gaps \(\hat{z}\
eq\hat{y}\), that is, the circular polarization can only be achieved by optimizing the mutual coupling between the radiation field and the gap unit in the waveguide. Since the coaxial end of the feed is connected to the waveguide wall, forming a short-circuit structure, the X-shaped gap is treated with a cutting angle at the end of the antenna, which can optimize the impedance at the end of the antenna, so that the coaxial line of the shorted end is equivalent to an impedance matching device under the action of the X-shaped gap at the cutting angle, further reducing the reflection of the end signal and preventing the formation of standing waves [15]. During the antenna simulation testing, a comprehensive comparison was conducted between the corner-truncated and non-truncated models in terms of axial ratio (AR) performance, as illustrated in Figure 4a. The upper-left corner presents a comparative schematic of the two simulation configurations. The truncated design demonstrates AR values approaching 3 dB within both 1.6-1.62 GHz and 2.4-2.5 GHz bands, with the yellow-shaded regions (1.59-1.62 GHz and 2.4-2.5 GHz) effectively covering the predetermined operational frequency bands. To intu \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Size (mm)** & **Parameter** & **Size (mm)** & **Parameter** & **Size (mm)** \\ \hline H & 71.5 & H7 & 6 & W3 & 44 \\ H1 & 40 & H8 & 6 & L1 & 11 \\ H2 & 65 & t & 2 & L2 & 7 \\ H3 & 75 & H9 & 22 & L3 & 9 \\ H4 & 26.5 & W & 1 & L4 & 10 \\ H5 & 15.5 & W1 & 40 & L5 & 16 \\ H6 & 6 & W2 & 4 & L6 & 1.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimized parameters of omnidirectional antenna. Figure 3: Schematic diagram of the omnidirectional CP antenna: (**a**) side view of the antenna; (**b**) schematic diagram of the main body of the antenna; (**c**) schematic diagram of the coaxial structure. itively demonstrate the AR characteristics in uplink/downlink frequency ranges, magnified views of the truncated model's corresponding bands are provided in subfigures (b) and (c). Comparative analysis reveals that the truncated configuration exhibits significantly mitigated performance degradation relative to the non-truncated counterpart, achieving superior circular polarization characteristics. This improvement is particularly evident through reduced AR fluctuations and enhanced stability across targeted spectral regions, confirming the efficacy of corner truncation in optimizing polarization purity for dual-band antenna operation. In order to further understand the electric field distribution around the gap, assuming a period of T and a phase of 360 deg, the electric field distribution around the gap at 0, T/4, T/2 and 3T/4 is shown in Figure 5, which shows the specific process of radiating circularly polarized waves. The electric field is opposite at 0 and T/4, and at T/2 and 3T/4. Based on the principles of antenna array design, equidistant spacing of array elements (typically half-wavelength) was conventionally adopted to ensure in-phase radiation from the slot elements. However, in this design, the corner-truncated slots at the array terminals alter the radiation environment, necessitating a deviation from the strict half-wavelength spacing criterion. Additionally, due to the polytetrafluoroethylene (PTFE) filling between the inner and outer conductors, the effective inter-element spacing was reduced to 70% of the original design.