## 5 Simulation and Results
### Different SNRs  
Performances were analyzed by using the probability of detection versus SNR. Here, let the desired global probability of false alarm at the FC be 0.01.  
Figure 8 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 best performance because there was little loss of information in it. The system with SH-DFS (a two-bit decision, M = 4) significantly outperformed the system which only used a hard decision fusion (Con/Hard). In addition, although the system with the SH-DFS had similar performance with the system that only used soft decision fusion (a two-bit decision), it was better than the system with Con/Soft because it consumed less energy according to Figure 7.  
Figure 9 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. From Figure 9, we found that the number of local sensors had a smaller influence at a low SNR than that at a high SNR. Furthermore, the probability of detection increased with the number of local sensors increasing.  
Figure 10 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. We observed that with the rise of the cluster number, the probability of detection increased.  
Figure 8: The probability of detection of four different methods versus SNR.  
Figure 9: The probability of detection of the clustered distributed system with SH-DFS at a different number of local sensors versus SNR.  
Figure 11 shows the comparison of the performances of the clustered distributed systems with SH-DFS (N = 30, M = 4, \(P_{e}\) = 0.05), where \(b\) is fixed at 2, 3, and 4. With \(b\) increasing, which means more information was transmitted, the performance of the system with SH-DFS also increased. Compared with the centralized system, we found that the performance of the system with SH-DFS was close to the performance of the centralized system when \(b\) was 3 or 4. Therefore, two-bit soft fusion or three-bit soft fusion can be applied to improve the performance of the Con/Hard, where only a one-bit decision is transmitted. At the same time, when we need to get a tradeoff between communication costs and detection performance, it is meaningless to let \(b\) (the number of bits in b-bit soft fusion) be more than 4.  
Figure 12 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 respectively. It was clear that the non-ideal communication channel had a negative influence on the clustered distributed system. It was necessary to take the non-deal communication channel into consideration.  
Figure 11: The probability of detection of the clustered distributed system with SH-DFS (\(b\) = 2, 3, 4) and the centralized system versus SNR.  
Figure 10: The probability of detection of the clustered distributed system with SH-DFS and different clusters versus SNR.