## 5 Numerical Results  
In this section, analytical results demonstrate the secrecy performance of the MRC/MRT-SC and MRC-ZFB/MRT-SC-ZFB schemes in terms of the achievable SOP. A detailed investigation on the effect of various system parameters, namely the number of antennas and thresholds, i.e., \(N_{R}\), \(N_{B}\) and \(R_{S}\) is conducted. Without loss of generality, \(R_{S}=2\), \(\sigma^{2}={\sigma_{R}}^{2}={\sigma_{R}}^{2}={\sigma_{E}}^{2}=1\), \(\varepsilon=\eta=1\) and \(P_{I}=10\) dB are set, and the transmitted SNR at Alice or Relay can be derived as \(P_{I}/\sigma^{2}\). In addition, we take path loss attenuation \(g_{M,N}\) as \(g_{M,N}={d_{M,N}}^{-\omega}\), where \(d_{M,N}\) is the distance from \(M\) to \(N\) node and \(\omega\) is normalized to \(1\), and all simulation results are obtained by averaging over 300,000 independent Monte Carlo trials. The Monte Carlo simulations in all figures thoroughly coincide with the theoretical simulation curves, which verifies that the closed-form expression is derived correctly in this paper. With the high SNR, the asymptotic curve approaches the exact curve. We also verified the secrecy diversity order in the asymptotic analysis expressions by the asymptotic curve. Figures 2 and 3 illustrate the impact for different numbers of \(N_{R}\), \(N_{B}\), \(\left(N_{R},N_{B}\right)\) and \(Q\) on the SOPs of the MRC/MRT-SC and MRC-ZFB/MRT-SC-ZFB schemes, respectively. \(N_{R}=1,2,3,4\) at different \(N_{B}=3,4,5,7\). The exact curves are obtained from \(P_{out}^{MRC/MRT-SC}\left(R_{S}\right)\) and \(P_{out}^{MRC-ZFB/MRT-SC-ZFB}\left(R_{S}\right)\). Due to the strong eavesdropping ability of the eavesdropper, the MRC/MRT-SC scheme does not significantly change the system performance. It is clearly seen that the outage performance of wireless communications is proportional to the number of \(N_{R}\), \(N_{B}\) and \(\left(N_{R},N_{B}\right)\). Obviously, if the \(P_{I}/\sigma^{2}\) is higher, the outage performance of the system will be better. As shown, MRC-ZFB/MRT-SC-ZFB scheme achieves the best performance over the range of  
and the secrecy rate of the MRC-ZFB/MRT-SC-ZFB scheme gradually increases with \(P_{t}/\sigma^{2}\) before it saturates. And in this section, secrecy outage floor will appear in MRC-ZFB/MRT-SC-ZFB and MRC/MRT-SC schemes when \(P_{t}/\sigma^{2}\) increases, this is because the \(Q\) is a crucial factor influencing the secrecy performance of system and is not limited by the \(P_{t}\) of the secondary user transmitter. Additionally, when the number of \((N_{R},N_{B})\) and \(Q\) are fixed in two schemes, MRC-ZFB/MRT-SC-ZFB scheme with FD operation and beamforming with AN obviously attain better performance than MRC/MRT-SC scheme with HD operation from the perspective of enhancing the secrecy performance of wireless communications. Figure 4 shows the effect of increasing \(N_{R}\) and \(N_{B}\) on the SOP and the asymptotic expressions curves of SOP attained from (47) under the \(\overline{\tau}_{Bj}\rightarrow\infty\) and _fixed_\(\overline{\tau}_{Ej}\), respectively, where \(\overline{\tau}_{E}=10\) dB and \(\overline{\tau}_{J}=10\) dB. The parallel slope of the asymptote shows that the high SNR slope is independent of \(N_{R}\). It is worth noting that the curve converges quickly and hence the derived approximation is accurate. Furthermore, when \(N_{R}\) and \(N_{B}\) increase, the SOP will be significantly improved. Moreover, as expected, MRC/MRT-SC scheme has the lowest performance than the MRC-ZFB/MRT-SC-ZFB scheme. Thus, we see that the MRC-ZFB/MRT-SC-ZFB scheme with FD operation and beamforming with AN always outperforms than the MRC/MRT-SC scheme with HD operation, which means that transmitting jamming signals from a FD Bob through the MRC-ZFB/MRT-SC-ZFB scheme would enhance the secrecy array gain of the system compared with the MRC/MRT-SC scheme under Scenario I.  
Figure 3: Secrecy outage probability for the MRC-ZFB/MRT-SC-ZFB scheme when \(\overline{\tau}_{J}=10\) dB and different number \(N_{R}\), \(N_{B}\) and \(Q\).