## 5 Simulation and Results
### Different Probabilities of the Desired Global False Alarm at the FC  
Performances were analyzed by using the probability of detection versus the global desired probability of false alarm at the FC. Here, let SNR be 10 dB.  
Figure 13 shows the comparison of the performances of the distributed systems with the conventional hard decision, SH-DFS, the conventional soft decision, and of the centralized system. Here, let the number of local sensors be 30. We found that the centralized system had the optimal performance. The system with SH-DFS (a two-bit decision, M = 4) significantly outperformed the system which only used hard decision fusion (Con/Hard). In addition, the system with the SH-DFS had a similar performance with the system that only used soft decision fusion (a two-bit decision).  
Figure 14 shows the comparison of the performances of the clustered distributed systems with SH-DFS (M = 4, \(b\) = 2, \(P_{e}\) = 0.05), but with a different number of local sensors. The number of local sensors was fixed at 5, 15, 25, and 35. It was clear that given the same SNR and the global desired probability of false alarm at the FC, the probability of detection increased along with the increase in the number of local sensors. Furthermore, it was also clear that given the same SNR and the number of local sensors, the probability of detection increased along with the increase of the global desired probability of false alarm at the FC.  
Figure 14: The probability of detection of the clustered distributed system with SH-DFS at a different number of local sensors versus the global desired probability of false alarm at the FC.  
Figure 13: The probability of detection of four different methods versus the global desired probability of false alarm at the FC.  
Figure 15 shows the comparison of the performances of the clustered distributed systems with SH-DFS (N = 30, \(b\) = 2, \(P_{e}\) = 0.05), but with a different number of clusters. With the rise of the cluster number, the probability of detection was increased. However, for the system with 30 local sensors, when the cluster number changed from 2 to 4, its probability of detection had a more significant improvement than that when the cluster number changed from 4 to 8.  
Figure 16 shows the comparison of the performances of the clustered distributed systems with SH-DFS (N = 30, M = 4, \(P_{e}\) = 0.05), where \(b\) was fixed at 2, 3, and 4. When \(b\) increased, the performance of the system with SH-DFS also increased because more information was transmitted and fused to make a global final decision. In addition, we found that the performance of the system with SH-DFS was close to the performance of the centralized system with the increase of \(b\). The system could achieve a probability of detection of about 0.8 when the probability of false alarm was fixed at 0.1.  
Figure 17 shows the comparison of the performances of the clustered distributed systems with SH-DFS (N = 30, M = 4, \(b\) = 2), where \(P_{e}\) = 0 and \(P_{e}\) = 0.05. It was clear that the non-ideal communication channel had a negative influence on the clustered distributed system.  
Figure 16: The probability of detection of the clustered distributed system with SH-DFS (\(b\) = 2, 3, 4) and the centralized system versus the global desired probability of false alarm at the FC.  
Figure 15: The probability of detection of the clustered distributed system with SH-DFS at a different cluster number versus the global desired probability of false alarm at the FC.