## 5 Simulation Results
Figures 11 and 12 show the impact of \(P_{f}\) on the awareness performance for the modulation set \(\theta_{1}\). As SNR improves, the findings show that the awareness performance dependency on correctly detecting the BPSK modulation scheme on \(P_{f}\) diminishes. The justification for this is that, when SNR is larger, the influence of the noise contribution becomes less noticeable, and the performance is determined mostly by the estimate error that arises from using a limited observation time. As the observation time approaches infinity, this error disappears. In principle, reducing \(P_{f}\) leads to a decrease in the barrier value, which increases the BPSK modulation scheme's efficiency as indicated in Figure 13. The distinction of the QPSK modulation scheme, on the other hand, is the inverse. As a result, \(P_{f}\) is intended to accomplish a performance compromise for BPSK and QPSK awareness. Figure 7: \(Pcc(\alpha|\alpha)\) for the modulation group of \(\theta_{1}\). Figure 8: \(Pcc(\alpha|\alpha)\) for the modulation group of \(\theta_{2}\). Figure 9: \(Pcc(\alpha|\alpha)\) for the modulation group of \(\theta_{3}\). Figure 10: \(Pcc(\alpha|\alpha)\) for the modulation group of \(\theta_{4}\). Figure 12: \(P_{cc}(\alpha=\text{QPSK}|\alpha=\text{QPSK})\) for the modulation group of \(\theta_{1}\). Figure 13: PDF of the Rayleigh RV, \(e\). For comparative purposes, Figure 14 depicts the awareness performance obtained by the proposed method in addition to that obtained by the technique described in [10; 25] for the modulation set \(\theta_{4}\). The findings reveal that the proposed method significantly outperforms the methods described in [10; 25], which are unable to deliver a suitable awareness performance even at high SNR levels. This is because the approaches described in [10; 25] are based on a DF relaying scheme in which the relay re-transmits the received frame if it is correctly decoded. Here, we recall that the DF relaying system may fail to decode the received frame at the relay due to channel circumstances, which has a detrimental impact on modulation awareness performance. Furthermore, the method presented in [25] demonstrates a performance with poor awareness due to the absence of a training preamble. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{\(K=2000\)} & \multicolumn{3}{c}{\(K=6000\)} \\ \hline  & BPSK & QPSK & \(8-\)PSK & \(64-\)QAM & & BPSK & QPSK & \(8-\)PSK & \(64-\)QAM \\ \hline BPSK & \(0.652\) & \(0.213\) & \(0.056\) & \(0.079\) & BPSK & \(0.852\) & \(0.113\) & \(0.026\) & \(0.079\) \\ \hline QPSK & \(0.21\) & \(0.585\) & \(0.156\) & \(0.049\) & QPSK & \(0.184\) & \(0.721\) & \(0.056\) & \(0.039\) \\ \hline \(8-\)PSK & \(0.058\) & \(0.28\) & \(0.551\) & \(0.111\) & \(8-\)PSK & \(0.038\) & \(0.225\) & \(0.721\) & \(0.016\) \\ \hline \(64-\)QAM & \(0.017\) & \(0.013\) & \(0.04\) & \(0.93\) & \(64-\)QAM & \(0.01\) & \(0.01\) & \(0.02\) & \(0.96\) \\ \hline \multicolumn{9}{c}{\(K=10,000\)} & \multicolumn{3}{c}{\(K=12,000\)} \\ \hline  & BPSK & QPSK & \(8-\)PSK & \(64-\)QAM & & BPSK & QPSK & \(8-\)PSK & \(64-\)QAM \\ \hline BPSK & \(0.99\) & \(0.007\) & \(0.002\) & \(0.001\) & BPSK & \(1\) & \(0\) & \(0\) & \(0\) \\ \hline QPSK & \(0.009\) & \(0.980\) & \(0.003\) & \(0.008\) & QPSK & \(0.001\) & \(0.999\) & \(0\) & \(0\) \\ \hline \(8-\)PSK & \(0.007\) & \(0.002\) & \(0.983\) & \(0.008\) & \(8-\)PSK & \(0\) & \(0.002\) & \(0.996\) & \(0.002\) \\ \hline \(64-\)QAM & \(0.009\) & \(0.002\) & \(0.002\) & \(0.987\) & \(64-\)QAM & \(0.002\) & \(0.003\) & \(0.004\) & \(0.991\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Confusion matrices at different number of received symbols, \(K\), at SNR = 15 dB. Figure 14: Awareness performance comparison with the modulation set \(\theta_{4}\). Dashed lines represent the proposed method, sold lines are used for the method of [10], and dot-dashed are used for the method of [25]. Star, square, hexagram, and circle markers refer to \(8-\)PSK, BPSK, \(64-\)QAM, and QPSK modulations, respectively.