## 3 Transmission Scenarios
### Ur-Mcjtdt Scenario  
Note that the UR-MCJST scenario described in Section 3.1 requires weak interference for the NE to exist. It is hence rational to derive an interference-free scenario. More specifically, in the time-division-based UR-MCJITD scenario, each of the selected CJs is allocated a time-bandwidth fraction of \(\frac{1-\alpha}{N}\), for an interference-free transmission during the third phase. In this interference-free UR-MCJITD scenario, NE will always exist. In a similar fashion to the UR-MCJST scenario, each jammer in this case will emit a noise signal during the initial \(\alpha/2\) period. This behavior of the jammers remains consistent across both scenarios. Then, the relay node will transmit during the second \(\alpha/2\) duration as shown in Figure 2. The remaining \((1-\alpha)\) time-bandwidth fraction will then be divided for all \(N\) selected CJs, where each CJ can enjoy an interference-free allocation of \(\frac{1-\alpha}{N}\) during the third phase. The power ratio \(\beta\) for the UR-MCJITD scenario can be calculated as:  
\[\tilde{\beta}=\frac{\bar{\mathbb{E}}[Y^{2}_{\{CJ_{i_{1}},\frac{1-\alpha}{N}\} }]}{\bar{\mathbb{E}}[Y^{2}_{\{CJ_{i_{2}},\frac{1-\alpha}{N}\}}]}\, \tag{25}\]  
where the mean power used by the \(i\)th jammer for transmitting the jamming signal in the first phase and consequently its own information in the third phase will be denoted by \(\bar{\mathbb{E}}[Y^{2}_{CJ_{i_{1}},\frac{1}{2}}]\) and \(\bar{\mathbb{E}}[Y^{2}_{CJ_{i_{2}},\frac{1-\alpha}{N}}]\), respectively. These represent the power levels associated with the jamming signal and the CJ's own data transmission during the respective phases. The total power utilized by the \(S\) represented as \(P_{s}\) will be similar to (2). However, the transmission power for the \(i\)th CJ is given by:  
\[\tilde{P}_{CJ_{i}} = \frac{1}{K}\sum_{t_{1}=1}^{\left\lfloor\frac{\alpha}{N}\right \rfloor}\bar{\mathbb{E}}[Y^{2}_{\{CJ_{i_{2}},\frac{1}{N}\}}]+ \tag{26}\] \[\frac{1}{K}\sum_{t_{2}=\left\lfloor\frac{\alpha}{N}\right\rfloor }^{\left\lfloor\frac{\alpha(+\frac{1-\alpha}{N}\alpha)}{N}\right\rfloor}\bar{ \mathbb{E}}[Y^{2}_{\{CJ_{i_{2}},\frac{1-\alpha}{N}\}}]\] \[= \frac{\alpha}{2}\bar{\mathbb{E}}[Y^{2}_{\{CJ_{i_{1}},\frac{1}{2} \}}]+\frac{1-\alpha}{N}\bar{\mathbb{E}}[Y^{2}_{\{CJ_{i_{2}},\frac{1}{N}\}}].\]  
By integrating the power ratio \(\tilde{\beta}\) from Equation (25) into Equation (26), we obtain:  
\[\bar{\mathbb{E}}[Y^{2}_{\{CJ_{i_{1}},\frac{1}{2}\}}]=\kappa_{2}\tilde{P}_{CJ_ {i}}\, \tag{27}\]where \(\kappa_{2}=\frac{\tilde{\beta}}{\frac{\alpha\kappa}{2}+\frac{1-\kappa}{N}}\) and  
\[\tilde{\mathbb{E}}[Y^{2}_{\{CJ_{i,3},\frac{1-\kappa}{N}\}}]=\frac{N\kappa_{2}}{ \tilde{\beta}}\tilde{P}_{CJ_{i}}. \tag{28}\]  
The SNR at \(D\) and \(R\) are similar to those given by (14) and (15), except that \(\kappa_{2}\) is used instead of \(\kappa_{1}\), i.e., they are given by:  
\[\gamma_{D}=\frac{\frac{2}{\tilde{\kappa}}\gamma_{sd}\gamma_{sr}+\gamma_{sd} \kappa_{2}\sum_{i\in\mathcal{J}}\gamma_{CJ_{i}r}+\gamma_{rd}\gamma_{sr}+\gamma _{sd}}{\frac{\alpha}{2}\gamma_{rd}+\gamma_{sr}+\frac{\alpha}{2}\kappa_{2}\sum_ {i\in\mathcal{J}}\gamma_{CJ_{i}r}+\frac{\alpha}{2}} \tag{29}\]  
and  
\[\tilde{\gamma}_{R;CJ_{i}}=\frac{\gamma_{sr}}{\frac{\alpha}{2}\kappa_{2}\sum_ {i\in\mathcal{J}}\tilde{\gamma}_{CJ_{i}r}+\frac{\alpha}{2}}\, \tag{30}\]  
respectively. Based on these SNR values, the achievable rates \(R_{D}\) and \(R_{R}\) as well as the secrecy rate \(\bar{R}_{s}\), can be computed from (16), (17) and (18), respectively.