# Distributed-Satellite-Clusters-Based Spectrum Sensing with Two-Stage Phase Alignment
## 5 Simulation Results
When it is a relatively small size \(\delta_{0}=\frac{\overline{\gamma}}{100}\), the performances of RPC_TF and MHA are similar, and DPA is the worst in the initial stage.With the sudden change in environment, the proposed RPC_TF can recover rapidly, and only needs 95 time slots to reach 98% of the optimal value, while MHA requires less than 95% until 200 time slots; moreover, the convergence speed becomes slower and slower, which indicates that the proposed algorithm has faster convergence speed and stronger stability. Next, we focus on the sensing performance of the proposed SS_DSC. Figure 7 illustrates the impact of satellite fading and the satellite number on the \(P_{d}\) (equivalently probability of miss detection \(P_{m}=1-P_{d}\) ) versus the false alarm probability, where number of sensing samples Num = 20, \(L\) = (3, 5), respectively. In addition, the satellite link follows the infrequent light shadowing (ILS) fading (\(m_{s}\) = 20, \(b_{s}\) = 0.158, \(\Omega\) = 1.29), average shadowing (AS) fading (\(m_{s}\) = 10, \(b_{s}\)= 0.126, \(\Omega\) = 0.835), or frequent heavy shadowing (FHS) fading (\(m_{s}\) = 1, \(b_{s}\) = 0.063, \(\Omega\) = 0.0007). As we see, an excellent agreement between the Monte-Carlo simulation and analytical results is achieved, which validates the derived closed-form expressions of the \(P_{d}\). It is also clear that the sensing performance of \(L\) = 5 is better than that of \(L\) = 3 under equal conditions, demonstrating the benefits of employing more satellites in SS_DSC. Moreover, the \(P_{m}\) for both the \(L\) = 5 and \(L\) = 3 clusters of ILS fading are lower than those of AS fading and FHS fading. This is because when the fading is serious, the average \(\gamma\) of satellites is lower; thus, the \(P_{m}\) is higher. Figure 6: Comparison of the average convergence speeds of three algorithms for the situation in which a sudden change occurs at timeslot \(t=200\), where \(L\) = 4, \(\overline{\gamma}\) = 0 dB, \(\delta_{0}=\left(\frac{\overline{\gamma}}{5},\frac{\overline{\gamma}}{100}\right)\), respectively. In the case of the number of sampling points \(Num\) = 40, \(P_{f}\) = 0.1, Figure 8 depicts \(P_{d}\) for the proposed SS_DSC, RLRT, GLRT, ERD and OR algorithms versus SNR. It can be observed that the proposed SS_DSC is superior to other algorithms. Even when \(L\) drops to 3, it still performs best in several methods in the region of \(\gamma<\) -5, which shows the great potential of our proposed algorithm in the region of low SNR. Figure 9 shows the receiver-operating-characteristic (ROC) curves of the five different algorithms where \(L\) = 5, the SNR \(\gamma\) = -10 dB and \(Num\) = 20. It is observed that the proposed SS_DSC outperforms other estimators, where the \(P_{d}\) is 16.5% higher than that of RLRT at \(P_{f}\) = 0.1. Even when the number of cooperative satellites \(L\) is reduced to 3, it is better than the traditional ERD, OR and GLRT methods, and the performance is improved by 36%, 41% and 74% at \(P_{f}\) = 0.1, respectively. The reason for this is that the SS_DSC performs  
Figure 8: The probability of detection \(P_{d}\) versus SNR for different algorithms when \(Num\) = 40 and \(P_{f}\) = 0.1. Figure 7: The probability of miss detection \(P_{m}\) versus the false alarm probability \(P_{f}\) for different shadowed-Rician fading values. in-phase superposition after beamforming and retains the effective information of each sensing satellite as much as possible. However, the SS_DSC algorithm requires some time for phase alignment before spectrum sensing, while others do not. Therefore, it is necessary to flexibly select different sensing methods according to the needs of the scene. SS_DSC is suitable for the accurate sensing of some specific important targets, although it requires a higher implementation complexity. However, the SS_DSC has requirements for time synchronization between satellites, and Figure 10 shows the impact of time synchronization accuracy on cooperative SNR.