## 5 Simulation and Analysis
### The Analysis of the Compensated Denoising Module  
To compare the effect of the compensated denoising module, two groups are set up in this section. One is processed by the compensated denoising module (CD-MWC) and the other is the unprocessed (MWC). The signal reconstructed through the MWC system is \(z(t)\), and the reconstructed signal obtained by the CD-MWC is \(z(t)\). We will analyze \(z(t)\) and \(\tilde{z}(t)\) in terms of different metrics to derive the performance gains from our scheme. Figure 4 shows the root-mean-square error (RMSE) comparison plot of \(z(t)\) and \(\tilde{z}(t)\). RMSE is the difference in amplitude between the recovered signal and \(x(t)\). The smaller RMSE represents that the recovered signal is closer to \(x(t)\). Figure 4 compares the cases with the number of sampling channels 30 and 50, respectively. At a sampling channel number of 30, the RMSE of \(\tilde{z}(t)\) decreases by an average of 13.52% compared to that of \(z(t)\) at different SNRs. In the case of 50 sampling channels, the RMSE of \(\tilde{z}(t)\) decreased by 7.8% on average compared to \(z(t)\) for different SNRs. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Meaning** & **Value** \\ \hline \(f_{NYQ}\) & Nyquist sampling frequency & 10 GHz \\ \(f_{p}\) & mixing function frequency & \(f_{NYQ}/195\) \\ \(f_{s}\) & actual sampling frequency & \(f_{NYQ}/195\) \\ \(M\) & Number of times \(p_{i}(t)\) & 195 \\  & changes in each period & \\ \(ChannelNum\) & Number of sampling channels & 30/50 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MWC system parameter setting table. The correlation coefficients of \(z(t)\) and \(\tilde{z}(t)\) are illustrated in Figure 5. Correlation coefficients are used to measure the difference between signals in their trends of variation. As shown in Figure 5, there is a significant improvement in the correlation coefficient of \(\tilde{z}(t)\) as compared to \(z(t)\). Especially when the channel is 30, the correlation coefficient of \(\tilde{z}(t)\) is increased by 36.4% on average compared with \(z(t)\) at different SNRs. The RMSE and the correlation coefficient reflect the consistency of the two signals in macro and micro terms, respectively. Figures 4 and 5 directly demonstrate the performance gain from the compensated denoising module at the signal level. At high SNRs, adaptive threshold denoising can preserve signal features better and reduce the possibility of excessive denoising. At low SNRs, the compensating denoising module not only denoises to a maximum extent but also minimizes the impact of distortion on subsequent reconstruction. Therefore, for the optimized system, the noise in the sampled signal is suppressed while the useful signal features are enhanced. These changes lead to an improvement in system performance. From Figure 6, it can be seen that the support set false alarm rate \(F_{p}\) is \(z(t)\) and \(\tilde{z}(t)\). A false alarm is a situation that incorrectly determines an element that does not belong to the support set. In this paper, we calculate the \(F_{p}\) for each experiment separately and take the average result as the final false alarm rate. The \(F_{p}\) can reflect the accuracy of spectrum sensing. In Figure 6, compared to the unprocessed one, there is a clear decreasing trend in the recovery false alarm rate of the support set after the dynamic flexible process. Compensated denoising helps support set choices to some extent. However, the compensated denoising process does not change the support set selection criteria of the OMP algorithm, so \(F_{p}\) is not significantly improved. To further improve the performance of the system, it is necessary to optimize the reconstruction algorithm. Figure 4: Root-mean-square errors of recovered signals at different SNRs. Figure 5: Correlation coefficients of recovered signals at different SNRs. The BER from the information level measures the impact of denoising compensation modules on communication accuracy.