## 6 Results and Discussion
### Convolutional Neural Network-Based Cooperative Spectrum Sensing  
The proposed CBCSS for the two-state classification problem was implemented using the Neural Network Toolbox in Matlab (R2017a, The MathWorks Inc., Natick, MA, USA, 2017). Unless presented otherwise, the simulation parameters were as listed in Table 2. The average SNR of the sensed channel, \(\gamma_{i}\), that was used for training the CNN ranged from \(-16\) dB to \(-6\) dB. Furthermore, the number of training samples for each SNR was 2000. In this work, we consider three different performance metrics: probability of detection \(P_{d}\), probability of false alarm \(P_{f}\), and sensing error \(P_{e}\). The total number of time slots for testing the performance of the proposed CBCSS was 10,000. Furthermore, the process was performed 10 times to get average values for \(P_{d}\), \(P_{f}\), and \(P_{e}\). The first two parameters are calculated by using Equations (1) and (2), whereas sensing error is defined as the sum of the probability of false alarm (\(P_{f}\)) and the probability of missed detection (\(1-P_{d}\)), as follows:  
\[P_{e}=P_{f}+(1-P_{d}). \tag{28}\]  
In Figures 7 and 8, we compare the performance of the proposed CBCSS with those of the conventional half-voting fusion rule for cooperative spectrum sensing, the local sensing result based on the energy detection method from one of the \(K=10\) secondary users, and the Chair-Varshney fusion rule. \begin{table}
\begin{tabular}{c l c} \hline \hline
**Symbol** & **Description** & **Value** \\ \hline \(K\) & The number of secondary users & 10 \\ \(N_{i}\) & The number of sensing samples collected by each secondary user & 300 \\ \(\gamma_{i}\) & Average signal-to-noise ratio (SNR) of the sensed channel that was used for & \(-16\) to \(-6\) \\  & training the CNN (dB) & \\ \(P_{A\bar{A}}\), \(P_{\bar{A}\bar{A}}\) & Probability of the primary user’s state transition from \(A\) to \(\bar{A}\), and vice versa & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters for the convolutional neural network (CNN) -based cooperative spectrum sensing (CBCSS) scheme. Regarding the half-voting rule, the fusion center makes a global decision based on the local sensing data. Specifically, the FC decides that the PU is active (\(A\)) if at least half of \(K\) SUs report the decision \(D_{i}=1\). With respect to the energy detection method, the local decision from SU1 was obtained for comparison. Under the Chair-Varshney rule, the detection statistics are expressed as the weighted sum of the local decisions; and the weights are functions of detection probability and false alarm [40]. The Chair-Varshney rule is the optimal decision fusion rule but requires a prior knowledge of the PU's activities and the local sensing performance of the secondary users. From the figures, we can confirm that the proposed CBCSS outperforms other conventional methods, except for the Chair-Varshney optimal fusion rule, in terms of detection probability and sensing error. We can also see that with an increment in the average SNR, the probability of detection increases while the probability of false alarm and the sensing error decrease. This is because the effect of AWGN on the local decisions, and thus the training accuracy, decreases as SNR increases. Accordingly, larger sensed channel SNRs at the SUs provide better detection performance and fewer false alarms. Although the probability of false alarm with the proposed scheme is a little higher than with the half-voting and the Chair-Varshney rules, the total sensing error of the proposed CBCSS almost reaches to that of the Chair-Varshney optimal fusion rule and is lower than those of conventional methods. In Figures 9 and 10, we examine the effect of the number of secondary users, \(K\), on the performance of the proposed CBCSS. To verify this, we evaluated the output results from three distinct CNNs  
Figure 8: Sensing error according to average SNRs for different sensing schemes.