## 3 Numerical Analysis
### Effect of Ground Cavity Sidewall Height  
For a cavity-backed antenna, its radiation performance is heavily dependent on the ground cavity [13]. Two key parameters of a ground cavity are its aperture size (\(L_{g}\)) and cavity height (\(H_{sw}\)). Since the excitation ports of the antenna are located on the cavity sidewalls, the feedline length is directly correlated with the aperture length. In other words, the impedance bandwidth is very sensitive to changes in the aperture length. To improve the radiation performance with minimal impact on its impedance bandwidth, here, we only investigate the effect of the ground cavity sidewall height. To determine this, we varied the sidewall height \(H_{sw}\) from 70 mm to 140 mm in 10 mm increments while keeping all other antenna dimensions constant (i.e., \(L_{g}=165\) mm, \(g=11\) mm, \(s=3\) mm, \(l=53\) mm, \(w=30\) mm, \(l^{\prime}=1\) mm, and \(w^{\prime}=3.6\) mm). Simulated differential reflection coefficient (S\({}_{\text{dd11}}\)) results for different sidewall heights are shown in Figure 6a. Lower and upper frequencies for S\({}_{\text{dd11}}\leq-10\) dB are \(f_{1}\) and \(f_{2}\). A center frequency, \(f_{c}\), was calculated as the mean value of \(f_{1}\) and \(f_{2}\) and these values were used to calculate the impedance bandwidth. For all sidewall heights, there was a notch at 1.2 GHz and approximately 1.83 GHz. As the height was increased from 70 mm to 140 mm, the notch at 1.2 GHz increased, and the notch at 1.83 GHz deepened. Simultaneously, the impedance bandwidth slightly decreased from 55.2% to 50.0%. Sidewall heights around 80 mm showed a good balance between the two notch depths, and the curve remained below \(-10\) dB. The effect of varying the sidewall height on the gain and the diagonal plane (\(\Phi=45^{\circ}\)) cross-polarization ratio is shown in Figure 6b. The gain at the low end of the impedance bandwidth (\(f_{1}\)) is around 6.5 dBi and increases to a peak of 10.7 dBi at the upper frequency (\(f_{2}\)). There are small variations in gains in relation to different sidewall heights, and the trend is relatively consistent between the simulation results. As the sidewall height increases from 70 mm to 140 mm, the cross-polarization bandwidth significantly increases from 25.8% to 49.2%. Varying the sidewall height had little effect on the cross-polarization at the lower end of the operating band but significantly affected the cross-polarization in the mid and upper sections of the operating band. The minimum cross-polarization at \(f_{1}\) occurs when the sidewall height reaches 100 mm. Beyond this height, the cross-polarization ratio rises in the mid-section of the operating band. The minimum cross-polarization at \(f_{2}\) occurs when the sidewall height reaches 120 mm. Figure 5: OCROP with different air gaps: (**a**) Differential reflection coefficient; (**b**) Peak cross-polarization ratio. The bandwidth of operation is summarized in Table 1. As the sidewall height increases, impedance bandwidth (for \(\mathrm{S_{dd11}}\leq-10\) dB) decreases while cross-polarization bandwidth (for \(\mathrm{X\text{-}pol}\leq-25\) dB) increases. In column 4, we present the combined bandwidth, where we took the minimum and maximum frequencies that met both requirements. In all cases, the lower frequency bound, \(f_{1}\), is limited by the cross-polarization ratio. The upper frequency bound, \(f_{2}\), is limited by the impedance bandwidth for \(H_{sw}\leq 90\) mm and the cross-polarization bandwidth for \(H_{sw}\geq 100\) mm. Once the sidewall height reaches 90 mm, there is very little change in the overall operating bandwidth (42.7 \(\pm\) 0.7%). The aperture field distribution for the antenna, with \(g=11\) mm and \(H_{sw}=80\) mm, at 1.5 GHz on a fictitious square surface with a length of 4 \(\lambda\), located 1 \(\lambda\) above the aperture, as shown in Figure 7 exhibits a uniform characteristic, with large peak electric field magnitudes immediately above the antenna.