## 2 System Model
### MRC-ZFB/MRT-SC-ZFB with FD Scenario
By applying projection matrix theory, weight vector \(\mathbf{w}_{ZF1}\) is given by  
\[\mathbf{w}_{ZF1}\!=\!\frac{\Xi^{\perp}\mathbf{h}_{BE2}}{\left\|\Xi^{\perp} \mathbf{h}_{BE2}\right\|}, \tag{11}\]  
where \(\Xi^{\perp}\!=\!\left(\mathbf{I}-\mathbf{h}_{BP}\!\left(\mathbf{h}_{BP} \mathbf{h}_{BP}^{\dagger}\right)^{-1}\mathbf{h}_{BP}^{\dagger}\right)\) is the correlation matrix with rank \(N_{B}-2\). Hence, the instantaneous SNR at the [PERSON] and the instantaneous SINR at the [PERSON] are written as  
\[\gamma_{RB,2}\!=\!\frac{P_{R}\max_{i\in N_{B}}\left\|\mathbf{h}_{RBi}\right\|^ {2}}{\sigma_{B}^{2}}, \tag{12}\]  
and  
\[\gamma_{RE,2}=\frac{P_{R}|\mathbf{h}_{RE}|^{2}}{P_{J}|\mathbf{h}_{BE2}^{ \dagger}\mathbf{w}_{ZF1}|^{2}\!+\!\sigma_{E}^{2}}. \tag{13}\]  
As mentioned before, the precoding matrix \(\mathbf{w}_{ZF}\) and \(\mathbf{w}_{ZF1}\) are designed for MRC-ZFB and MRT-SC-ZFB schemes so that the AN signal is wholly eliminated at the Bob-Relay and Bob-PU. It is clearly noted that in the MRC-ZFB/MRT-SC-ZFB with FD scenario, jamming signal is transmitted throughout the information transmission process to degrade the eavesdropping channel capacities of Alice-Eve and Relay-Eve links, and it does not interfere with the PU. However, both \(\gamma_{AR,j}\), \(\gamma_{AE,j}\), \(\gamma_{RB,j}\) and \(\gamma_{RE,j}\) are affected by the common variable RV, \(j\in\left(1,2\right)\) represent scheme 1 and scheme 2, respectively. \(G=\left|\mathbf{h}_{AP}\right|^{2}\) and \(G_{1}=\left|\mathbf{h}_{RP}\right|^{2}\) in \(P_{S}\) and \(P_{R}\). To solve this problem, we should derive the Cumulative Distribution Function (CDF) of \(\gamma_{AR,j}\) and \(\gamma_{RB,j}\), and Probability Density Function (PDF) of \(\gamma_{AE,j}\) and \(\gamma_{RE,j}\) conditioned on \(G\) and \(G_{1}\). According to RaF protocol, the SOPs of the two different phases are independent. A fundamental secrecy performance criterion in the complete Alice-Bob process is instantaneous secrecy capacity, which is represented as  
\[C_{S,k}=\max\left(C_{Bk}-C_{Ek},0\right)^{+}, \tag{14}\]  
where \(C_{Bk}\)=\(\log_{2}\left(1+\gamma_{BR}\right)\) and \(C_{Ek}\)=\(\log_{2}\left(1+\gamma_{Ek}\right)\) represent the capacities of the main channel and eavesdropping channel links, respectively, and \(k=\left\{1,2\right\}\) stands for the first phase and the second phase, respectively. For maximizing the secrecy capacity \(C_{S,k}\), the main channel need to maximize \(C_{Bk}\) and the eavesdropping channel need to minimize \(C_{Ek}\) through the number of \(N_{R}\) and \(N_{B}\) at the Relay and Bob in two different phases. Two different phases of each scenario have independent transmission processes. \(\mu=\frac{Q}{P_{t}}\), \(\epsilon=\frac{\lambda_{RB}}{\lambda_{AR}}\), \(\eta=\frac{\lambda_{BE}}{\lambda_{AE}}\), \(\overline{\gamma}_{I}=\frac{P_{t}}{\sigma_{E}^{2}}\lambda_{JE}\), \(\overline{\gamma}_{B}=\frac{P_{t}}{\sigma_{E}^{2}}\lambda_{AR}=\frac{Q}{\mu \sigma_{R}^{2}}\lambda_{AR}=\frac{P_{t}}{\sigma_{B}^{2}}\lambda_{RB}=\frac{Q}{ \epsilon\mu\sigma_{B}^{2}}\lambda_{RB}\) and \(\overline{\gamma}_{E}=\frac{P_{t}}{\sigma_{E}^{2}}\lambda_{AE}=\frac{Q}{\mu \sigma_{E}^{2}}\lambda_{AE}=\frac{P_{t}}{\eta\sigma_{E}^{2}}\lambda_{RE}=\frac {Q}{\eta\mu\sigma_{E}^{2}}\lambda_{RE}\) are defined in this paper for doing simple notational analysis.