## 2 System Model  
Figure 1 shows a multi-user mixed RF/FSO system based on the optimal user interference. The system contains a multi-user source node \(\mathcal{S}_{\text{i}}(\text{i}\in\{1,\dots,M\})\), a single-input-and-single-output relay (R), a legitimate destination receiving user with a single receive antenna (D) and an illegal eavesdropper (E). The RF link experiences the Rayleigh fading distribution and the FSO link experiences the \(\mathcal{F}\) fading distribution. The source node adopts the SWIPT technology and multi-user scheduling scheme and is equipped with an energy harvesting device. The source node utilizes the optimal user to transmit jamming signals to the illegal eavesdropper. Figure 2 is a schematic diagram of the time slot switching protocol for SWIPT, where \(\rho\) and T are the time switching factor and the time period of the time slot switching protocol, respectively. The relay device first transmits the RF energy signal to the source node multi-user in the first time slot \(\rho T\) and the multi-user source node equipped with the energy harvesting device recognizes the received energy signal and stores it [19]. In the remaining time slot \((1-\rho)T\), the optimal user of the source node transmits interference signals to the eavesdropper, and the relay receives signals sent by other users of the source node with the EGC technology. Figure 1: A multi-user mixed RF/FSO system based on optimal user interference. In the energy harvesting phase, the relay node R sends a radio signal \(\mathrm{x}_{RS_{i}}\) with a power of \(P_{R}\), which is transmitted to each user \(S_{\mathrm{i}}\) at the transmitter through the channel of \(RS_{\mathrm{i}}\). The RF energy signal received by each user \(S_{\mathrm{i}}\) on the source node can be expressed as follows [20]:  
\[\mathrm{y}_{RS_{i}}=\frac{1}{\sqrt{d^{\tau}{}_{RS_{i}}}}\sqrt{P_{R}}h_{RS_{i}}x _{RS_{i}}+n_{S_{i}} \tag{1}\]  
where \(P_{R}\) and \(\mathrm{x}_{RS_{i}}\) are the transmitted power and normalized signal of the relay node, respectively, \(h_{RS_{i}}\) is the channel coefficient between the users of the relay R and the source node, \(\mathrm{d}_{RS_{i}}\) represents the distance between R and \(S_{\mathrm{i}}\), \(\tau\) is the path loss index, and \(\mathrm{n}_{S_{i}}\) represents the additive white Gaussian noise with zero mean and variance \(\sigma_{RS_{\mathrm{i}}}\) at each user. According to (1), it can be gathered from [21] that when noise influence is ignored, the energy stored by each user can be expressed as  
\[E_{S_{\mathrm{i}}}=\rho\eta\left|\frac{1}{\sqrt{d^{\tau}{}_{RS_{i}}}}\sqrt{P_ {R}}h_{RS_{i}}\right|^{2}T \tag{2}\]  
where \(\eta\) is the energy conversion efficiency of the source node corresponding to the conversion of the RF signal into direct current (DC). Defining the optimal user as \(S_{J}\), the RF signal received by it from the relay can be expressed as  
\[\mathrm{y}_{RS_{J}}=\frac{1}{\sqrt{d^{\tau}{}_{RS_{J}}}}\sqrt{P_{R}}h_{RS_{j}}x _{RS_{j}}+n_{S_{J}} \tag{3}\]  
where \(\mathrm{h}_{RS_{J}}\) and \(\mathrm{d}_{RS_{J}}\) denote the channel coefficient between the relay R and the optimal user \(S_{J}\), respectively, and \(\mathrm{n}_{S_{J}}\) denotes the additive white Gaussian noise with zero mean and variance \(\sigma_{RS_{J}}\) at the optimal user. The energy received by the optimal user \(S_{J}\) is expressed as [22]  
\[E_{S_{\mathrm{J}}}=\rho\eta\left|\frac{1}{\sqrt{d^{\tau}{}_{RS_{J}}}}\sqrt{P_ {R}}h_{RS_{J}}\right|^{2}T \tag{4}\]  
The signal received by the relay after EGC is expressed as follows:  
\[\mathrm{y}_{S_{G}R}=\frac{1}{2}\frac{\left(\sum\limits_{i=1:\
eq J}^{M}y_{S_{ i}}\right)^{2}}{\sum\limits_{i=1:\
eq J}^{M}N_{i}} \tag{5}\]  
where \(\mathrm{y}_{S_{i}}\) and \(N_{i}\) denote the SNR and additive white Gaussian noise at each branch, respectively. As the optimal user at the source node has multiple RF transmit antennas, it generates a matrix \(W_{J}\) with an orthogonal basis of null space \(N_{S_{J}}(N_{S_{J}}-1)\) using the artificial interference generation method in [23].