## 5 Simulations Results  
To evaluate the efficiency and the robustness of the proposed detection method, we generate Receiver Operating Characteristic (ROC) curves using Monte Carlo simulations [54, 55]. The parameters defined in Table 1 are used with different kinds of communication signals, such as 64-QAM, 16-QAM, BPSK, and 4-ASK.  
In order to compare the theoretical and experimental performance of the RAD, we generated \(P_{d}\) versus SNR performance curves. Figure 8 shows these performance curves. The theoretical curves were generated by Equation (50) and the experimental curves according to the Monte Carlo simulations. It can be clearly observed that the theoretical results match the simulated ones. From the theoretical and experimental curves, reliable detection is possible as soon as \(SNR\geq-12\) dB with \(P_{d}\geq 0.95\) and \(P_{fa}=0.05\).  
The Receiver Operating Characteristic curves for different \(SNR\) values can be viewed in Figure 9. Here, the RAD is applied on a 16-QAM signal, and the observation time is 31.25 ms. For \(\text{SNR}~{}=~{}-14\) dB and \(P_{fa}~{}=~{}0.1\), the RAD detects the presence of a communication signal with \(P_{d}=0.76\), but for \(\text{SNR}=-13\) dB, \(P_{d}=0.9\). The detector proves itself powerful as soon as the \(\text{SNR}\geq-12\) dB, since the detection probability \(P_{d}=0.95\) with a very low value of \(P_{fa}=0.05\); see Figure 9.  
Another advantage of the proposed detector is its robustness against any type of classical modulations, such as QAM, PSK, and ASK; see Figure 10, where the ROC curves for 4-ASK, BPSK, and 64-QAM sign  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Entity** & **Parameters** & **Value** \\ \hline \multirow{3}{*}{PU’s signal} & Sampling frequency \(F_{e}\) & 128 kHz \\  & Symbol rate & 16 Bd \\  & Bandwidth of Interest B & 24 kHz \\ \hline \multirow{3}{*}{SU’s Detector} & Observation time & 15.6 ms \\  & Sampling Frequency & 128 KHz \\ \hline \multirow{2}{*}{Embedding parameters} & Dimension \(m\) & 16 \\  & time delay \(\tau\) & 6 \\ \hline Transmission Channel & Noise Model & AWGN \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
Figure 8: Theoretical and experimental probability of detection for RAD versus SNR.  
Figure 10: Robust RQA detector insensitivity versus classical modulation techniques.  
Figure 9: Receiver Operating Characteristic for \(16-QAM\) signal.  
The performance of RAD increases with the number of samples \(N\). Figure 11 depicts this performance evolution based on \(N\) in a Gaussian channel where \(\text{SNR}=~{}-12\) dB. We notice that for \(P_{fa}=0.1\), the RAD detects the communication signal with \(P_{d}=0.5\) when \(N=500\) samples, with \(P_{d}=0.8\) when \(N=1000\) samples, and with \(P_{d}=0.97\) when \(N=2000\) samples.  
By comparing RAD with two other blind spectrum sensing algorithms, Energy Detection (ED) [56] and Cyclostationary Features Detector (CFD) [57, 58], and according to the results presented in Figures 12 and 13, we notice the superiority of the RAD to ED and CFD in a Gaussian channel. For example, for the \(SNR=-12\) dB and \(P_{fa}=0.05\), the RAD detects the signal with \(P_{d}~{}=~{}0.95\), whereas the probability of detection for the ED is only \(P_{d}~{}=~{}0.67\) (see Figure 12). Figure 13 shows that the RAD is able to detect the communication signal in very weak low SNR conditions. For \(-12\) dB \(\leqslant\) SNR \(\leqslant-10\) dB, the RAD detects the presence of a communication signal with \(P_{d}\geqslant 0.95\) for \(P_{fa}=0.05\). ED achieves RAD performance only when SNR \(\geqslant-10\) dB, and CFD works correctly when SNR \(\geqslant-7\) dB with \(P_{d}~{}\geqslant~{}0.97\).  
Figure 11: Receiver Operating Characteristic of the RAD model based on the number of observed samples in a Gaussian channel with \(SNR=-12\) dB.  
Figure 12: ROC performance: ED vs RAD. The RAD is superior to ED.