Numerical simulations are presented in this section to compare the proposed scheme with the proposed adaptive scheme with Alice-aided AN beamforming (without relying on Charlie), the Non-CJ-NOMA scheme in [

19] and the CJ-OMA scheme (only for LU1) in [

21]. We adopt the basic setting

${N}_{a}=4$,

${N}_{c}=4$,

$M=4$,

$\epsilon =0.01$,

${P}_{c}=10$ dB,

${\Vert {\mathbf{h}}_{a1}\Vert}^{2}=10$ dB,

${\Vert {\mathbf{h}}_{a2}\Vert}^{2}=5$ dB, and

${R}_{th}=2$ bit/s/Hz. Note that the aforementioned second scheme is named the Alice-aided scheme, in which AN beamforming is exploited by Alice but not Charlie, and Alice allocates

${P}_{c}$ to generate AN for fairness. Here, all the simulation results are averaged over 200 channel realizations.

Figure 2 and

Figure 3 compare the secrecy rates and the transmission rates at LU2 achieved by different schemes, respectively. It can be shown that the proposed scheme suffers an inevitable loss of secrecy performance for providing service to LU2 by the NOMA principle compared with the CJ-OMA scheme. From

Figure 2, obviously, the secrecy rate of the proposed scheme outperforms the Non-CJ-NOMA scheme, especially when

${P}_{a}<-3$ dB and

${a}_{1}^{U}<0$. This is mainly due to the fact that the proposed scheme consists of adaptive strategy adjustment while the NON-CJ-NOMA scheme fails to work in this case. In addition, we can observe from

Figure 2 that, thanks to the external jamming signal from Charlie for anti eavesdropping, a much higher secrecy rate can be achieved by the proposed scheme against the Alice-aided scheme when

${P}_{a}\ge 0$ dB. Specifically, when

${P}_{a}<-3$ dB, the desired QoS constraint at LU2 can not be satisfied, Alice stops serving LU2 and the CJ scheme in [

21] is carried out. When

${P}_{a}\ge -2$ dB, Alice begins to provide service to Rx2 by NOMA principle, and the

${R}_{s}$ at LU1 first decreases to zero when

${P}_{a}=-2$ dB then increases as

${P}_{a}$ increases. Similar results are provided by the adaptive Alice-aided scheme that the QoS requirement at LU2 can not be met when

${P}_{a}<-8$ dB, and in this case Alice only provides service to LU1 by adopting the CJ scheme in [

21]. Then, the secrecy rate decreases to zero when

${P}_{a}=8$ dB due to the transmit strategy adjustment, and Alice begins to serve both LU1 and LU2 simultaneously when

${P}_{a}\ge -8$ dB.

Figure 3 validates the effectiveness of the proposed power allocation strategy that, as

${P}_{a}$ increases from −3 dB to 19 dB,

${a}_{1}^{*}$ is set to be

${a}_{1}^{U}$ and

${R}_{2}$ remains at

${R}_{th}$. Compared with the Non-CJ scheme, when the required QoS at LU2 is satisfied, more power could be allocated to LU1 thanks to the jamming signals generated by Charlie in the proposed scheme. In addition, although both the proposed scheme and the Alice-aided scheme consist of adaptive power allocation adjustment, it can be observed that the first scheme outperforms the second one in a wide range of

${P}_{a}$. The reason is that, compared to the Alice-aided scheme, in the systems exploiting the proposed scheme, the SOP constraint can be satisfied much more easily with the aid of external jamming from Charlie, thus more power could be allocated to serve both LU1 and LU2.

Figure 4 and

Figure 5 demonstrate the effective sum rate and the effective EE performance of all the four schemes, respectively. As shown in

Figure 4 and

Figure 5, we observe that significantly higher performance of both effective sum rate and effective EE can be achieved by the proposed scheme in a wide range of the total transmit power. Specifically, it can be observed from

Figure 5 that there exists a close match between the curves of the proposed scheme and the Alice-aided scheme. This observation indicates that though introducing a cooperative jammer in our considered systems may lead to higher total power consumption, a relatively sufficient effective EE can be achieved by the proposed scheme.