## 4 Simulation Results  
In this section, we show the simulation results of the multi-dimensional satellite resource scheduling strategy. We assume that the satellite beam areas are adjacent to each other, and the beam radius can be calculated by \(r=H\tan\theta_{\text{3 dB}}\). The location of UEs in each beam area is randomly generated. We set five beam areas corresponding to five UEs, including two CUEs. Specifically, we set UE 4 and UE 5 as CUE 1 and CUE 2. As for the location of UEs and the LEO satellite, we establish a plane coordinate system; the origin (0,0) corresponds to the ground projection point of the LEO satellite. The center point coordinates of the five beam areas are listed as follows: (\(-150\) km, 0), (0, 0), (\(150\) km, 0), (\(-75\) km, \(-150\) km), (\(75\) km, \(-150\) km). In the communication scenario, UEs transmit uplink signals through two frequency bands, with two optional power levels and five transmission time slots. According to the characteristics of the LEO satellite communication system, the signal frequency \(f\) is set to \(20\) GHz and the bandwidth \(B\) is \(400\) MHz. Since the location of each UE is randomly generated, the simulation results are, unless otherwise stated, averages of five experiments. The detailed parameter settings are shown in Table 1 below. The impact of bandwidth \(B\) and the number of beams \(N_{0}\) on the total communication rate of CUEs is shown in Figure 2. It can be seen that increasing bandwidth can significantly improve the total rate of CUEs. With the increase in \(N_{0}\), UEs can transmit signals through more beams; thus, the total rate of CUEs is also improved. It is worth noting that according to our proposed covertness constraint (18), increasing bandwidth makes this constraint more strict. Therefore, it is necessary to limit the bandwidth within a certain range when the number of transmit power is limited. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Number of UEs & \(I\) & \(5\) \\ Number of CUEs & \(J\) & \(2\) \\ Number of bands & \(M\) & \(2\) \\ Bandwidth & \(B\) & \(400\) MHz \\ Number of beam areas & \(N\) & \(5\) \\ Number of beams & \(N_{0}\) & \(3\) \\ Transmit power & \(P_{k}\) & [\(10\) W \(100\) W] \\ Number of time slots & \(T\) & \(5\) \\ Length of each time slot & \(\delta\) & \(10\) ms \\ Rate threshold for NUEs & \(D\) & \(4\) Mbps \\ Signal carrier frequency & \(f\) & \(20\) GHz \\ LEO satellite altitude & \(H\) & \(1000\) km \\ GEO satellite altitude & \(H_{e}\) & \(35\),\(786\) km \\
3 dB beam angel & \(\theta_{3 dB}\) & \(5^{\circ}\) \\ Beam radius & \(r\) & \(87\) km \\ Receiving antenna gain & \(Gr\) & \(30\) dB \\ Eavesdrop antenna gain & \(Gr_{e}\) & \(40\) dB \\ Transmitting antenna gain & \(Gt\) & \(20\) dB \\ Noise power of LEO channel & \(\sigma^{2}\) & \(-90\) dBW \\ Noise power of GEO channel & \(\sigma^{2}_{e}\) & \(-90\) dBW \\ Covertness parameter & \(\varepsilon\) & \(0.1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. The impact of the covert parameter \(\varepsilon\) on the rate of each UE is illustrated in Figure 3. It is shown that the increase in \(\varepsilon\) corresponds to the increase in communication rates for both CUE 1 and CUE 2. This phenomenon can be attributed to the fact that a higher \(\varepsilon\) value relaxes the covertness constraint (18), thereby enhancing the communication rates. However, it should be noted that this relaxation comes at the expense of reducing the covertness of the communication system. Therefore, it is also necessary to limit \(\varepsilon\) with a certain range. The impact of the rate threshold \(D\) for NUEs on the rate of each UE is illustrated in Figure 4. It is shown that as \(D\) increases, the average rates for CUEs decrease. This is because increasing the rate threshold \(D\) will make the constraint (14) more strict, and we can only sacrifice a part of the CUE performance to meet the communication requirements of NUEs in the limited on-board resources.