## 2 System Model and Formulation
### Formulations
By substituting (1) into (20) and (4) into (21), we obtain SINR at device \(D_{n}\) for \(n\in N\) when the device \(D_{n}\), respectively, decoded the data symbol \(x_{i}\), where \(i=\{N,\ldots,n\}\), as follows:  
\[EH_{S,R_{1}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{1}},\]1 \[EH_{S,R_{1}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{1}},\]2  
where expression (22) is used for IoT device \(D_{n}\) (\(n>1\) and \(n\leq N\)) while IoT device \(D_{1}\) has to adopt, respectively, expressions (22) first and then (23) to decode its own message \(x_{1}\). Similarly, the device \(D_{n}\) in the even transmission block also adopted the SIC mechanism to decode its own message \(x_{n}\). SINR obtained at device \(D_{n}\) for \(n\in N\) when the device \(D_{n}\), respectively, decoded the data symbol \(x_{i}\), where \(i=\{N,\ldots,n\}\), as follows:  
\[EH_{S,R_{1}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{1}},\]3 \[EH_{S,R_{1}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{1}},\]4  
where expression (24) is used for IoT device \(D_{n}\) (\(n>1\) and \(n\leq N\)) while IoT device \(D_{1}\) has to adopt, respectively, expressions (24) first and then (25) to decode its own message \(x_{1}\). The instantaneous bit-rate threshold is reachable when the IoT device \(D_{n}\) decodes the data symbols \(x_{i}=\{x_{N},\ldots,x_{n}\}\) in odd and even transmission blocks, respectively, as follows:  
\[EH_{S,R_{1}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{1}},\]5 \[EH_{S,R_{1}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{1}},\]6The minimum of the achievable bit-rate threshold reached at device \(D_{n}\) (\(n\in N\)) in odd and even transmission blocks, respectively, as follows:  
\[EH_{S,R_{1}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{1}},\]7  
\[EH_{S,R_{1}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{1}},\]8  
It is the presence of the eavesdropper \(E\) as shown in \[EH_{S,R_{1}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{1}},\]9 The eavesdropper \(E\) eavesdrops the IoT devices by wiretapping channel \(h_{R_{1},E}\) for odd transmission block time period \(T^{(odd)}\) or wiretapping channel \(h_{R_{2},E}\) for even transmission block time period \(T^{(even)}\). To combat eavesdropper \(E\), this study adopted the rest relay as a friendly jammer. Please note that the selected IoT relay and the rest IoT relay in the odd transmission block time period \(T^{(odd)}\) are IoT relays \(R_{1}\) and \(R_{2}\), respectively. This study proposes the IoT relay \(R_{2}\) uses the EH as given by (2) to transmit jamming signals to the eavesdropper \(E\). Simultaneously, the eavesdropper \(E\) receives the wiretapping signal from the IoT relay \(R_{1}\) and the jamming signal from the rest IoT relay \(R_{2}\) in the second time slot \(T_{2}^{(odd)}\). In contrast, the selected IoT relay and the rest IoT relay in the even transmission block time period \(T^{(even)}\) are IoT relays \(R_{2}\) and \(R_{1}\), respectively. Similarly, the IoT relay \(R_{2}\) forwards signal using EH as given by (4) while IoT relay \(R_{1}\) uses the EH as given by (3) to transmit the jamming signal to eavesdropper \(E\). The eavesdropper \(E\) receives simultaneously the wiretapping signal from the IoT relay \(R_{2}\) and the jamming signal from the rest IoT relay \(R_{1}\) in the second time slot \(T_{2}^{(even)}\). In odd or even transmission blocks, the received signal at eavesdropper \(E\) is expressed as follows:  
\[EH_{S,R_{2}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{2}}, \tag{4}\]0 \[EH_{S,R_{2}}^{T_{(even)}^{(even)}} =\eta\lambda_{R_{2}}P\sigma_{S,R_{2}}, \tag{4}\]1  
where \(n_{E}\) is AWGN at eavesdropper \(E\) with \(n_{E}\sim CN(0,N_{0})\), \(\delta\) is status of jamming signal. If \(\delta=0\), the rest IoT relay did not transmit the jamming signal. If \(\delta=1\), the rest IoT relay transmitted the jamming signal fully by EH as (2) or (4).