# Cooperative Spectrum Sensing Based on Convolutional Neural Networks
## 5 Simulations and Discussion  
In this section, the test results of the proposed CNN-based CSS scheme are presented and discussed. First of all, the detection probability and false alarm probability of the proposed schemes under the test set are given, where the SNR varies from \(-\)8 dB to 5 dB with an SNR step of 1 dB. Then, the sensing performance of the proposed scheme is compared with the AND rule, the OR rule and the MV rule.  
Figures 6 and 7, respectively, provide the detection probability comparisons and the false alarm probability comparisons among the proposed CNN-based CSS schemes. From Figure 6, the detection probabilities of the three CNN-based CSS schemes are all above 0.9, which indicates a stronger ability to protect the PU for the proposed schemes. In addition, the detection probability improves from LeNet to VGG-16. Based on the analysis in Section 4.2, the detection probability of the proposed CNN-based CSS schemes is gradually improved with the rise in the network depth. This indicates that the network depth helps with the feature acquisition of the primary signal and the sensing performance is at a high level in return. In Figure 7, the false alarm probability of the proposed CNN-based CSS schemes is always below 0.1, even below 0.05 for AlexNet and VGG-16, which indicates that the proposed schemes can keep the throughput of the cognitive system at a high level. In addition, the false alarm probability decreases gradually from LeNet to VGG-16. The same conclusion can be obtained from the detection probability--that the network depth contributes to decreasing the false alarm probability.  
Figure 6: The detection probability comparisons of the CNN-based CSS schemes.  
As a supplement, the influence of the sensing node on the sensing performance is exhibited in Figure 9 based on the proposed AlexNet network-based CSS scheme, where the sensing node varies from 5 to 8 and from 8 to 10. From Figure 9, the sensing performance of the AlexNet network-based CSS scheme increases with the rise in the sensing node, which indicates that the sensing performance of the proposed CSS scheme is positively correlated with the sensing node.  
Note that the receiver operator characteristic curve (ROC) is widely considered to exhibit the performance of SS, where the X axis denotes the false alarm probability and the Y axis denotes the detection probability. In the simulations, the false alarm is fixed as 0-1 with a step of 0.1, where the corresponding detection probability is obtained by the mathematical statistics. The slope changes greatly at a false alarm rate of 0.1 because the false alarm probability jumps with the step of 0.1. Specifically, the false alarm probability is 0 at first, while it will jump to 0.1 at the next moment for all the considered CSS schemes. As a result, all these plots show a similar pattern.  
To further evaluate the performance of the proposed CNN-based CSS schemes, the average computation time is analyzed in Figure 10. Note that the computation time denotes the processing time of a picture through the CNN network, where the CNN network is trained in advance. In the simulations, many tests are conducted and the average computation time denotes the average value of the processing time for a picture. From Figure 9, the average computation time of the LeNet network-based CSS scheme is the lowest, while the average computation time of the VGG-16 network-based CSS scheme is the highest. This means that the sensing accuracy of the VGG-16 network-based CSS scheme is at the expense of the system overhead. As a result, the selection of the appropriate CNN-based CSS scheme depends on the system requirement of the sensing accuracy and the sensing speed.  
Figure 9: The influence of sensing node on the sensing performance.