# Distributed-Satellite-Clusters-Based Spectrum Sensing with Two-Stage Phase Alignment
## 5 Simulation Results  
In this section, we conduct computer simulations to evaluate the performance of the proposed algorithm and confirm the validity of our analytical results. The proposed two-stage phase alignment frame is simulated under Windows system. Satellite Tool Kit (STK) and MATLAB software are used as the main development tools, and the connect module inside STK is used as the interface between them. The hardware environment includes AMD Ryzen-7-5800 and GeForce GTX 1660 Ti. A DSC system is established in STK software to obtain the dynamic distance data between satellites and that between the satellites and sensing target in the process of movement. Then, the data is output to MATLAB software to convert the changing distance into the dynamic phase. The orbit parameters are shown in Table 1. Without loss of the generality, the satellite link is subject to SR average shadowing (AS) with \((m_{s},b_{s},\Omega)\) = (10.1, 0.126, 0.835) by default ([23], Table III), and the frequency band is 14 GHz (Ku). Figure 4 illustrates the phase changes of the four concomitant satellites without phase control in 200 time slots. It can be found that the phases in the DSC system are randomly distributed. The reason for this is that the distance between each satellite and the sensing target, and the distance between satellites are constantly changing in the process of movement. Obviously, it is difficult to obtain beamforming gain if the singal-lever soft fusion is directly carried out at the master satellite. However, in Figure 5, the phases of the concomitant satellites gradually achieve synchronization from the initial random distribution with the help of the proposed RPC_TF algorithm, which proves the effectiveness of the algorithm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Semimajor Axis** & **Eccentricity** & **Inclination** & **Right Ascension** & **True** \\  & & & **Angle** & **Node** & **Anomaly** \\ \hline Master-Sat & 7058.14 km & \(6.472\times 10^{-16}\) & \(68^{\circ}\) & \(0^{\circ}\) & \(11.917^{\circ}\) \\ Concom-S1 & 7058.14 km & 0.000356 & \(68^{\circ}\) & \(1.333\times 10^{-14\circ}\) & \(237.376^{\circ}\) \\ Concom-S2 & 7058.14 km & 0.000356 & \(68^{\circ}\) & \(1.117\times 10^{-15\circ}\) & \(147.434^{\circ}\) \\ Concom-S3 & 7058.14 km & 0.000356 & \(68^{\circ}\) & \(0^{\circ}\) & \(57.246^{\circ}\) \\ Concom-S4 & 7058.14 km & 0.000356 & \(68^{\circ}\) & \(0^{\circ}\) & \(327.148^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Orbital parameters of distributed satellite clusters. Next, the average convergence speeds of the proposed RPC_TF algorithm, the directional perturbation feedback algorithm (DPA) in [21], and the modified hybrid algorithm (MHA) in [22] for the situation in which a sudden change occurs at timeslot \(t=200\) are depicted in Figure 6, where \(L=4\), \(\overline{\gamma}=0\) dB, \(\delta_{0}=\left(\frac{\pi}{5},\frac{\pi}{100}\right)\), respectively. Moreover, a maximum strength \(S_{5}^{ECC}\) based on EGC is also given for comparison. It can be found that the three algorithms can converge to \(\gamma_{ECC}\), and the error rate is less than 5%, which confirms the effectiveness of the proposed algorithm. Figure 4: The signal phase of each concomitant satellite versus timeslot without phase control. Figure 5: The signal phase of each concomitant satellite versus timeslot with RPC_TF algorithm. the rationality of using EGC for theoretical analysis. To be specific, with a relatively large initial step size, \(\delta_{0}=\frac{\overline{\gamma}}{5}\), the performance of the three algorithms is similar at the beginning, and RPC_TF is slightly faster. However, when a sudden change occurs, DPA can quickly recover and converge first, followed by RPC_TF, and MHA performs the worst. The reason for this is that DPA adopts a fixed step size and is not affected by the surrounding environment. However, the improvement in convergence speed is at the expense of performance: its convergence value is less than that of the other two algorithms.