## 5 Simulation Results  
Computer simulations have been conducted in order to evaluate how well the proposed method works. The settings of the system are as follows, unless otherwise specified: the number of symbols that are transmitted in each frame is equal to K = 10,000, and the likelihood of a false alert is set at \(P_{f}=0.01\). In each of the wireless links, the discrete time channel impulse response was constructed using \(L=5\) channel coefficients. The channel impulse responses have power delay profiles with exponential decay as [30; 34]  
\[\sigma_{hj}^{2}(l)=X_{hj}\exp(-l/9), \tag{21}\]  
where \(l=0,\cdots,4\), \(h\in\{S,R\}\), \(j\in\{R,D\}\). \(X_{hj}\) is computed in order to account for the effect of path-loss on the awareness performance as  
\[X_{hj}=\left(\frac{w_{SD}}{w_{hj}}\right)^{\rho}, \tag{22}\]  
where \(\rho\) refers to the path-loss exponent, \(w_{hj}\) is the distance between terminals \(h\) and \(j\), and nodes \(S\) and \(D\) are separated by a distance denoted by \(w_{SD}\). For the purposes of the simulations, we set \(\rho=3.4\), \(w_{SD}=1\), \(w_{SR}=0.43\) and \(w_{RD}=0.56\). It is critical to remember that all distances have been calibrated to \(w_{SD}\). The probability of proper awareness,\(P_{cc}(\alpha=\zeta|\xi)\), is employed as a quality criterion for the proposed method, where \(\zeta\) is one of modulation options. There are four different sets of modulation forms that are looked at as follows. \(\theta_{1}=\{\text{BPSK, QPSK}\}\), \(\theta_{2}=\{\text{BPSK, QPSK, 8 - PSK}\}\), \(\theta_{3}=\{\text{QPSK, 16 - PSK, 16 - QAM}\}\), and \(\theta_{4}=\{\text{BPSK, QAM, 8 - PSK, 64 - QAM}\}\). It is important to note that the proposed method is general in the sense that it can be applied to any number of modulation schemes as long as there are correlation functions that show spikes for some modulation schemes but not for others. There are a total of one thousand Monte Carlo attempts. It is worth noting that we only use the cross-correlation functions that are needed for the modulation of interest. The function \(F_{1}\) is employed for the set \(\theta_{1}\); the functions \(F_{1}\) and \(F_{2}\) are used for the set \(\theta_{2}\); the functions \(F_{2}\) and \(F_{3}\) are used for the set \(\theta_{3}\); and the functions \(F_{1}\), \(F_{2}\) and \(F_{3}\) are utilized for the set \(\theta_{4}\). For example, the AMA for \(\theta_{4}\) was performed in the following manner. The proposed statistical test on the function \(F_{1}\) distinguishes BPSK modulation from other modulation techniques. The presence of BPSK is marked by the appearance of spikes, while the lack of spikes indicates the presence of other modulation schemes. Then, using the proposed statistical test on the function \(F_{2}\), we distinguish the \(8-\)PSK modulation scheme from the QPSK and \(64-\)QAM schemes. The absence of spikes indicates \(8-\)PSK modulation systems, but the presence of spikes indicates QPSK or \(64-\)QAM modulation schemes. Finally, we apply the proposed statistical test on the function \(F_{3}\) to classify between the QPSK and \(64-\)QAM modulation schemes. In this case, the loss of spikes implies the \(64-\)QAM modulation scheme, but the presence of spikes shows the QPSK modulation scheme. Figures 7-10 depict the awareness performance for the modulation groups \(\theta_{1}\), \(\theta_{2}\), \(\theta_{3}\) and \(\theta_{4}\), respectively, as a function of SNR. The results indicate that the awareness performance of QPSK, \(8-\)PSK, \(16-\)PSK and \(8-\)PSK shown in Figures 7-10, respectively, are not impacted in any way by the SNR values. This is as a result of the fact that their performance is determined by the probability of a false alarm, which was planned to be \(0.01\). On the other hand, the other modulation choices exhibit significant improvements in performance as the SNR value rises. This is due to the fact that as the SNR levels are increased, the spike detection performance is strengthened.