## 4 Numerical Results
Channel vectors \(\mathbf{e}_{m}\) from the SU-Tx to the \(m\)-th EH user were generated by following the aforementioned procedure, with the directions \(\phi_{\text{EH},1}\) and \(\phi_{\text{EH},2}\) pointed out in Table 2. Moreover, channels vectors \(\mathbf{h}_{k}\) and \(\mathbf{h}_{e\upsilon}\) follow Rayleigh fading with an attenuation equal to \(L_{o}\left(d_{\text{PU},k}^{-\alpha}\right)\) and the distances from the SU-Tx to SUs, EH users, PUs, and the eavesdropper are defined in Table 2.  
Furthermore, the proposed model can be adapted to several scenarios since we do not consider a fixed number of users. Instead we assume that there exist \(L\) SUs and \(M\) EH receivers. It is worth highlighting that the proposed approach is valid for other channel model because in a real deployment the inputs are channel state information (CSI), which can be obtained by a feedback process between the transmitter and the users and by cooperation between the primary and secondary network. The simulation results in this section are the average over several independent channel realizations, where the Rayleigh fading component of the channel vectors varies in each channel realization. Please note that new beamforming vectors and PS ratios should be obtained each time the channel conditions changes, which is not the best solution in fast time-varying channels because of the computational complexity of solving the optimization problem. First, we investigated the results for problem (11) by using the SDR technique. Furthermore, we compared the results with the SDMA scheme, ZF technique and with the scheme without using AN. Figure 2 shows AN power, \(\left\|\mathbf{f}\right\|^{2}\) according to the minimum SINR required at the SUs when minimum EH requirements of the SUs and EH users are given as \(\psi_{l}=\xi_{m}=-25\ dBm\) and \(\psi_{l}=\xi_{m}=-30\ dBm\), respectively. We observed that the radiated AN power is decreased as the minimum required SINR increases, because the SU-Tx needs to allocate more power to satisfy the SINR constraint while reducing the available power for the artificial noise. In addition, the proposed scheme based on the NOMA technique outperforms the SDMA method and ZF scheme for two considered cases of minimum EH. The improvement from the NOMA technique is due to the ability to decode part of the interference from other messages via the SIC procedure, which allows an increase in the achievable SINR at the SUs while reducing the required transmit power to satisfy the minimum SINR constraint. Subsequently, the NOMA technique can provide a high level of PLS, because the interference with the eavesdropper increases as the AN power increases, which makes it difficult for the eavesdropper to decode the SU's messages. The SDMA method outperforms the ZF scheme because ZF nulls the interference from other SU's and EH's messages at the \(l\)-th SU which permits an increase of the SINR but affects the harvested energy. Subsequently, the ZF scheme harvests lower energy than that harvested by the SDMA approach, which makes that the SU-Tx increases the transmission power to satisfy the EH constraint while reducing the available power to allocate to the AN. Figure 3 illustrates the SSR achieved with the proposed approach and with the scheme without AN, according to the minimum SINR and minimum EH requirements, with maximum permissible interference with the PUs equal to \(\phi_{\text{PU}}=-60\ dBm\). From Figure 3, we can observe the benefit of the proposed approach with AN on increasing the achievable SSR, because AN can effectively generate interference with the eavesdropper while the beamforming technique minimizes that interference at the SUs. We note that the SSR grows as the minimum SINR increases, and this trend coincides with previous research [13; 14] because the achievable transmission rate at the SUs increases. In addition, the SSR reduces as the minimum EH requirement increases because more power needs to be allocated to satisfy the EH requirements while reducing the available power for AN.