# Covert Communication for Integrated Satellite-Terrestrial Relay Networks with Cooperative Jamming
## 4 Numerical Simulation Results  
Numerical simulation results are given for exploring the impact of the system parameters on the covert performance of the ISTRN there. In our simulation, we set the \(P_{sum}=1\) W, the noise power \(\sigma^{2}=-20\) dB and the required transmission rate \(R_{SB}=1\) bps/Hz. Moreover, the system parameters are shown in Table 1[35], and Table 2 gives a series of parameters based on the SR fading channel [36]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Type of satellite & GEO \\ Carrier frequency & \(f=2\) GHz \\
3 dB angle & \(\theta_{3 dB}=0.8^{\circ}\) \\ Maximum beam gain & \(G_{\text{MS}}=48\) dB \\ Antenna gain & \(G_{\text{R}/E}=4\) dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The system parameters. Figure 2 plots the PDE versus \(\eta\) with diverse detection thresholds, where \(\
u=\
u_{opt}\), \(\
u=2\sigma^{2}\) and \(\
u=4\sigma^{2}\) under ILS. Clearly, when \(\
u=\
u_{opt}\), the eavesdropper can minimize its PDE. Moreover, it is clear that the rise of \(P_{R}\) may create more randomness and can better hide source signals, which causes a larger detection error probability at \(E\). Furthermore, when \(\eta\to 0\), \(P_{e}\) approaches 1. In addition, it should be noted that there is an upper limit to the \(\eta\). Figure 3 shows the PDE with optimal detection thresholds versus \(\eta\) under different shadowing types. Compared with the above, this illustrates that, with the worsening of channel shadowing, \(P_{e}\) increases continuously. This is because the \(E\) is interfered by not only the \(R\) but also the channel uncertainty. Additionally, the value interval of \(\eta\) varies with the change of fading type, which verifies Formula (25). For the jamming performance, the above two figures show a similar pattern--namely, as the jamming power decreases, the jamming performance gradually weakens, and the eavesdropper is able to detect the presence of legitimate communications increasingly accurately. Therefore, in order to ensure system covertness, sufficiently high jamming power is necessary. However, higher jamming power is not better. Excessive jamming power can produce more pronounced jamming noise at the receiver, which is not conducive to effectively achieving covert communication. Thus, how to balance the relationship between the transmission power and jamming power is the key to strengthening the jamming performance. \begin{table}
\begin{tabular}{c c} \hline \hline
**Shadowing Type** & **Parameter Value** \\ \hline Frequent heavy shadowing (FHS) & \(\{m,b,\Omega\}=\{1,0.063,0.0007\}\) \\ Average shadowing (AS) & \(\{m,b,\Omega\}=\{5,0.251,0.279\}\) \\ Infrequent light shadowing (ILS) & \(\{m,b,\Omega\}=\{10,0.158,1.29\}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The channel parameters. Figure 2: PDE versus \(\eta\) under different detection thresholds. Figure 4 depicts the \(R_{c}\) versus \(\varepsilon\) for diverse \(P_{sum}\), which shows the effectiveness of the proposed scheme by us. It should be noted that, when \(\varepsilon\) continues rising, \(R_{c}\) increases first and then stabilizes, which implies that, as the value of \(\varepsilon\) rises, the requirement for covertness decreases, allowing higher communication rates. Moreover, when \(\varepsilon\) is small, the global optimum power allocation factor varies with its increase, which enables the \(R_{c}\) to increase. However, as \(\varepsilon\) continues to rise, the optimal \(R_{c}\) and global \(\eta_{opt}\) will be unchanged. We list the \(\eta_{opt}\) when \(R_{c}\) reaches the stable maximum value. Furthermore, it should be noted that the worse channel shadowing contributes to the rise of \(\eta_{opt}\) but also inevitably causes the decrease of \(R_{c}\). Lastly, we can see that, as \(P_{sum}\) increases, the effective covert rate improves significantly. Figure 4: The maximum \(R_{c}\) versus covertness requirement \(\varepsilon\) for different values of the total transmission power.