# A Robust Method Based on Deep Learning for Compressive Spectrum Sensing
## 5 Experiment Results
### Joint CSS Method  
To compare the performance of different algorithms, the joint performance of the reconstruction and WSS algorithms is evaluated. BEISTA-Net+BSWSS-Net denotes that  
Figure 13: ROC curves when \(\text{SNR}=-4\) dB in NR dataset and \(\mu_{NR}\in(0,0.5]\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Algorithm** & **\# of FLOPs** & **\# Learnable** & **Execution Time** & **Video Memory** \\  & & & **Parameters** & **(ms)** & **Usage (MB)** \\ \hline \multirow{4}{*}{NR dataset} & DeepSense & \(1.7\times 10^{6}\) & \(8.6\times 10^{4}\) & 0.39 & 1.44 \\  & ParallelCNN & \(1.2\times 10^{6}\) & \(4.3\times 10^{5}\) & 0.56 & 1.82 \\  & CNNWSS-Net & \(1.6\times 10^{6}\) & \(3.1\times 10^{5}\) & 0.50 & 1.40 \\  & BSWSS-Net & \(6.3\times 10^{5}\) & \(3.0\times 10^{5}\) & 0.38 & 1.28 \\ \hline \multirow{4}{*}{TVWS dataset} & DeepSense & \(1.8\times 10^{6}\) & \(1.0\times 10^{5}\) & 0.40 & 1.59 \\  & ParallelCNN & \(1.1\times 10^{6}\) & \(4.4\times 10^{5}\) & 0.58 & 1.85 \\ \cline{1-1}  & CNNWSS-Net & \(1.6\times 10^{6}\) & \(3.2\times 10^{5}\) & 0.52 & 1.43 \\ \cline{1-1}  & BSWSS-Net & \(6.4\times 10^{5}\) & \(3.1\times 10^{5}\) & 0.38 & 1.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Complexity analysis of different WSS algorithms. BEISTA-Net is employed for reconstructing signals, and BSWSS-Net is employed for WSS. ISTA-Net+DeepSense [21] denotes that ISTA-Net is employed for reconstructing signals, and DeepSense is employed for WSS. CSS-Net [18] denotes that ISTADR-Net is employed for reconstructing signals and CNNWSS-Net is employed for WSS. R-ADMM [13] +ParallelCNN [22] denotes that R-ADMM is employed for reconstructing signals and ParallelCNN is employed for WSS. We evaluate the performance in the TVWS dataset, with \(\mu_{TVWS}\in(0,0.5]~{}P=8\) and \(L=16\). The effect of SNR on the CSS algorithms is studied. Figure 14a illustrates the \(P_{\mathbf{d}}\) versus SNR at \(P_{\mathbf{f}}=0.1\), Figure 14b illustrates the \(P_{\mathbf{f}}\) versus SNR at \(P_{\mathbf{d}}=0.9\). As SNR increases, the performance of all four algorithms progressively improves. Notably, when SNR increases from \(-10\) dB to \(10\) dB, the performance of BEISTA-Net+BSWSS-Net joint algorithm consistently surpasses that of the other three algorithms. When SNR \(>1\) dB, the detection probability can meet the requirement of \(P_{\mathbf{d}}>0.9\), while \(P_{\mathbf{f}}<0.1\). Compared to standalone WSS algorithms, the performance of CSS algorithms is slightly worse. This is because the reconstruction algorithm introduces some reconstruction errors, which affects the overall accuracy. The aforementioned experimental results demonstrate that the proposed BEISTA-Net+BSWSS-Net joint algorithm maintains robust detection performance under varying SNR conditions. Next, the influence of signal sparsity levels on detection performance is investigated. Figure 15a illustrates the \(P_{\mathbf{d}}\) versus sparsity level at \(P_{\mathbf{f}}=0.1\), Figure 15b illustrates the \(P_{\mathbf{f}}\) versus sparsity level at \(P_{\mathbf{d}}=0.9\). As the sparsity level increases, the detection probabilities of the four joint algorithms decrease, while the false alarm probabilities rise. This phenomenon occurs because, with higher sparsity levels, the number of users contained in the signal increases, leading to greater signal complexity and, consequently, higher detection difficulty. Under the same sparsity level, the BEISTA-Net+BSWSS-Net joint algorithm achieves the highest detection probability and the lowest false alarm probability. Specifically, when the sparsity level is \(0.05\), the detection probability of the BEISTA-Net+BSWSS-Net joint algorithm is approximately \(1\), and the false alarm probability is nearly \(0\). When the sparsity level  
Figure 14: TVWS dataset with \(\mu_{TVWS}\in(0,0.5]\), \(P=8\), \(L=16\). **(a)**\(P_{\mathbf{d}}\) versus SNR (dB) of BEISTA-Net+BSWSS-Net, ISTA-Net+DeepSense, CSS-Net, and R-ADMM+ParallelCNN when \(P_{\mathbf{f}}~{}=~{}0.1\).