## 4 Case II: Active Eavesdropper
### Security Gap Performance  
Considering the same assumptions that have been made for background noises and propagation channels in the case of a passive eavesdropper in Section 3.6, it is also possible to simplify the notations and to denote in general the self-jamming power-to-noise ratio as \(\rho_{SI}\) for both self-jamming \((\rho_{AE})\) and jamming \((\rho_{EA})\) channels. Since, in these conditions, we have \(\rho_{SI}=\rho_{AE}=\rho_{EA}\), adapting for practical applications, we also set  
Figure 21: \(BER_{E}\) versus \(SNR_{E}\), \(\rho_{AE}=30\) dB in case of an active eavesdropper: (**a**) Blind without feedback; (**b**) Semi-blind without feedback.  
Figure 20: \(BER_{E}\) versus \(SNR_{E}\), \(\rho_{EE}=30\) dB in case of an active eavesdropper: (**a**) Blind without feedback; (**b**) Semi-blind without feedback.  
and \(BER_{E,min}=0.5\) for the maximum and minimum average errors that user A and user E can obtain, respectively. According to the results in Figures 19 and 20, in order to achieve \(BER_{A,max}=10^{-5}\) and \(BER_{E,min}=0.5\), the minimum SNR at the legitimate user A, \(SNR_{A,min}\), and the maximum SNR at the eavesdropper user E, \(SNR_{E,max}\), can be pointed out for different values of the general self-jamming power-to-noise ratio (\(\rho_{SI}\)) and for different decoding schemes at user A and user E. Then, the security gap \(S_{g}\) is calculated based on \(SNR_{A,min}\) and \(SNR_{E,max}\) and summarized in Tables 4 and 5 when using the blind scheme without feedback and the semi-blind scheme without feedback at user E, respectively.  
Figure 22 shows the comparison of the security gap \(S_{g}\) with the various values of the general self-jamming power-to-noise ratio, \(\rho_{SJ}\), between the application of the blind feedback scheme and the semi-blind feedback scheme on the decoding side of user A. It indicates that the increase in the self-jamming power-to-noise ratio \(\rho_{Sj}\) leads to a decrease in the security gap \(S_{g}\) for all cases. The proposed semi-blind feedback scheme also allows for reducing the security gap \(S_{g}\) from about 5 to 7 dB compared to the blind feedback scheme, regardless of the use of the blind or semi-blind scheme without feedback in user E. Therefore, it can keep the security gap as small as possible, which is the most important factor in PLS. Furthermore, the \(SNR_{A}\) of user A is reduced when performing channel estimation or decoding the message using the semi-blind feedback scheme, compared to the blind feedback scheme, which means that the system not only guarantees the security factor but also improves power consumption.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(\rho_{SJ}\)} & \multicolumn{2}{c}{**Blimd without Feedback at User E**} & \multicolumn{2}{c}{**Blimd Feedback at User A**} & \multicolumn{2}{c}{**Semi-Blind Feedback at User A**} \\ \cline{2-6}  & \(SNR_{E,max}\) & \(SNR_{A,min}\) & \(S_{g}\) & \(SNR_{A,min}\) & \(S_{g}\) \\ \hline
0 & 10.7 & 24.9 & 14.2 & 19.9 & 9.2 \\
5 & 12.8 & 25.7 & 12.9 & 20.3 & 7.5 \\
10 & 15.4 & 26.3 & 10.9 & 21 & 5.6 \\
15 & 17.5 & 26.8 & 9.3 & 21.5 & 4 \\
20 & 19.9 & 27.6 & 7.7 & 22 & 2.1 \\
25 & 22.2 & 28.5 & 6.3 & 22.3 & 0.1 \\
30 & 25.6 & 29.8 & 4.2 & 22.8 & \(-2.8\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The security gap when applying the blind scheme without feedback at user E.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(\rho_{SJ}\)} & \multicolumn{2}{c}{**Semi-Blind without Feedback at User E**} & \multicolumn{2}{c}{**Blimd Feedback at User A**} & \multicolumn{2}{c}{**Semi-Blind Feedback at User A**} \\ \cline{2-6}  & \(SNR_{E,max}\) & \(SNR_{A,min}\) & \(S_{g}\) & \(SNR_{A,min}\) & \(S_{g}\) \\ \hline
0 & 6.2 & 24.9 & 18.7 & 19.9 & 13.7 \\
5 & 8.2 & 25.7 & 17.5 & 20.3 & 12.1 \\
10 & 10.8 & 26.3 & 15.5 & 21 & 10.2 \\
15 & 13.4 & 26.8 & 13.4 & 21.