# 1-D Convolutional Neural Network-Based Models for Cooperative Spectrum Sensing
## 5 Simulation Results and Discussion
### Performance Evaluation  
The simulations were conducted on an NVIDIA Tesla T4 with 16 GB of GDDR6 memory and 3072 CUDA cores, with the TensorFlow framework. To demonstrate the effectiveness of our proposed cooperative spectrum detection methods based on deep neural networks, we present detailed simulation results. Our evaluation of the detection performance includes analyzing the receiver operating characteristic (ROC) curve, detection probability (\(P_{d}\)) versus signal-to-noise ratio (SNR) and online detection time. Furthermore, we compare the performance of our methods with two existing state-of-the-art methods: the maximum eigenvalue detector [24] and the hierarchical cooperative LSTM method proposed by [17].The first one was implemented as in [24], computing the sample covariance matrix starting from all the samples in a sensing period and then computing the maximum eigenvalue \(\lambda_{max}\) of this sample covariance matrix and, finally, performing the decision according to the relation \(\lambda_{max}>\gamma\sigma_{w}^{2}\), where \(\sigma_{w}^{2}\) is the variance of all the noise samples and \(\gamma\) is theoretically derived to meet the \(P_{fa}\) requirement. The second one uses a hierarchical cooperative LSTM network to process the covariance matrices (CMs) generated by the sensing data of each SU through an end-to-end CNN LSTM. To ensure a fair comparison, we employ the default hyper-parameter settings for each existing model as reported in the literature. The trained models were evaluated using separate SNR values to assess their performance under specific conditions. This approach allowed for a more focused examination \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter Settings** & **Parameter Description** & **Layer Name** \\ \hline CNN module & (Activation: ReLU) & \\ Input & (\(256\times 1\)) & \\ Kernel number and size & (\(40\), \(9\)) & Conv \(1\), \(2\) \\ Pool size & \(2\) & MaxPool \\ \hline LSTM module & Unit number: \(64\) & LSTM layer \(1\) \\ BiLSTM module & Unit number: \(64\) & BiLSTM layer \(1\) \\ \hline Cooperative LSTM & Unit number: \(64\) & CLSTM layer \(1\) \\ Cooperative MLP & Unit number: \(128\), \(64\), \(2\) & MLP layer \(1\), \(2\), \(3\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model hyper-parameters. of the model's effectiveness in handling individual SNR levels, providing insights into its capability to generalize and perform well across varying signal-to-noise scenarios during testing. Therefore, while the training set aimed for a comprehensive adaptation, the test set focused on evaluating the model's performance under specific SNR conditions. Specifically, to evaluate the ROC curves, we fixed the SNR at \(-14\) dB, while, when we evaluated the results in terms of the probability of detection when varying the SNR, we considered the latter in the range from \(-20\) dB to \(-10\) dB with a step of \(1\) dB and we fixed at \(0.1\) the probability of false alarms. The ROC curve presented in Figure 7 illustrates the performance of the proposed deep neural network techniques compared to existing methods under the \(-14\) dB SNR condition. It is evident that all DL-based detectors outperformed the conventional SS detector. This outcome is expected due to the ability of deep neural networks to learn intricate patterns from input signals, surpassing the capabilities of traditional statistical signal processing techniques in capturing such complexities. For instance, at a false alarm probability of \(0.1\), the CNN_BLSTM_MLP detector achieves a detection probability of \(69\%\), followed by the CNN_LSTM_MLP detector at \(67\%\) and the CNN_LSTM and cooperative LSTM detectors at \(63\%\) and \(60\%\), respectively. To further assess the overall detection performance and compare the models comprehensively, we calculated the area under the curve (AUC) values.