# Secure Information Transmission with Self Jamming SWIPT
## 2 System Model
The received signals at \(R\), \(\wp\), and \(\xi\) experience additive white Gaussian noise (AWGN) modeled as a zero mean complex Gaussian random variable, and their respective AWGNs are given as \(N^{(k)}\sim\mathcal{CN}(0,\sigma_{N}^{2})\), \(W^{(k)}\sim\mathcal{CN}(0,\sigma_{W}^{2})\), and \(J^{(k)}\sim\mathcal{CN}(0,\sigma_{I}^{2})\), respectively. The system model exploits the CSI of \(H_{E2R}^{(k)}\) and \(H_{E1R}^{(k)}\), to cancel the interference of the energy signals to the information signal at \(R\). \(X_{E1}^{(k)}\) and \(X_{E2}^{(k)}\) will be precoded to equalize \(H_{E2R}^{(k)}\) and \(H_{E1R}^{(k)}\), respectively. Unlike \(R\), the eavesdropper \(\xi\) receives a highly distorted signal, which makes the decoding process difficult. In general, \(\xi\) can decode the information based on the estimated value of \(X_{E1}^{(k)}\), \(X_{E2}^{(k)}\)  
Figure 1: System model. EH, energy harvesting. Figure 2: Frame structure of the proposed system, where \(T\) and \(T_{I}\) are the time duration of a symbol and a block, respectively. \(H_{E2R}^{(k)}\), and \(H_{E1R}^{(k)}\). Furthermore, to reduce the accuracy of these estimated values at \(\xi\), the EH signal should act as AN. Similar to \(\xi\), \(\wp\) will receive the combination of all the transmitted signals as a PLNC signal. Furthermore, \(\wp\) can effectively take advantage of the PLNC signal for harvesting energy, and the received PLNC signal at \(\wp\) is given as:  
\[Y_{\wp}^{(k)}=H_{E1\wp}^{(k)}X_{E1}^{(k)}+H_{E2\wp}^{(k)}X_{E2}^{(k)}+H_{T \wp}^{(k)}X_{I}^{(k)}+W^{(k)}. \tag{2}\]  
The performance of this secure self jamming SWIPT technique is analyzed based on the secrecy rate and the bit error rate (BER). Here, three different scenarios are considered, and in all the scenarios, \(R\) and \(\xi\) are considered to have a CSI of \(\mathbf{H}_{T\xi}\) and \(\mathbf{H}_{T\xi}\), respectively. Here, both \(R\) and \(\xi\) do not have a CSI of \(\mathbf{H}_{E1R}\) and \(\mathbf{H}_{E2R}\). The assumptions behind the three scenarios are explained as follows:  
* Scenario A: \(\mathcal{T}\) has the CSI of \(\mathbf{H}_{E1R}\) and \(\mathbf{H}_{E2R}\). \(\xi\) is assumed to be far away from \(R\), and \(\xi\) does not have channel correlation. In this scenario, \(\xi\) is denoted as \(\xi(a)\), and \(R\) is denoted as \(R(a)\). * Scenario B: \(\mathcal{T}\) does not have the CSI of \(\mathbf{H}_{E1R}\) and \(\mathbf{H}_{E2R}\), and \(\mathcal{T}\) estimates \(\mathbf{H}_{E1R}\) and \(\mathbf{H}_{E2R}\). \(\xi\) is assumed to be very close to \(R\), and their channel correlation is very high. In this scenario, \(\xi\) is denoted as \(\xi(b)\), and \(R\) is denoted as \(R(b)\). * Scenario C: This scenario is similar to A where \(\mathcal{T}\) has the CSI of \(\mathbf{H}_{E1R}\) and \(\mathbf{H}_{E2R}\), but here, \(\xi\) is assumed to be very close to \(R\), and their channel correlation is very high. In this scenario, \(\xi\) is denoted as \(\xi(c)\). Based on the perfect CSI condition, \(R\) is the same in Scenario A and Scenario C.  
Then, the received signal at \(R(a)\) is given as:  
\[Y_{R(a)}^{(k)}= \begin{cases}H_{TR}^{(k)}X_{I}^{(k)}+N^{(k)};&\text{if }\mathcal{L}( \mathcal{V}^{(k)})=0,\\ H_{TR}^{(k)}X_{I}^{(k)}+N^{(k)}+H_{E1R}^{(k)}X_{E1}^{(k)}+H_{E2R}^{(k)}X_{E2}^ {(k)};&\text{otherwise},\end{cases}  \tag{3}\]  
where \(\mathcal{L}(. )\) denotes the linear subspace of a vector and \(\mathcal{V}^{(k)}=H_{E1R}^{(k)}X_{E1}^{(k)}+H_{E2R}^{(k)}X_{E2}^{(k)}\). Here, \(H_{E1R}^{(k)}X_{E1}^{(k)}\) is the additive inverse of \(H_{E2R}^{(k)}X_{E2}^{(k)}\), and this allows \(\mathcal{T}\) to nullify the interference of \(X_{E1}^{(k)}\) and \(X_{E2}^{(k)}\). To achieve \(\mathcal{L}(H_{E1R}^{(k)}X_{E1}^{(k)}+H_{E2R}^{(k)}X_{E2}^{(k)})=0\), both \(X_{E1}^{(k)}\) and \(X_{E2}^{(k)}\) should be precoded based on the CSI of the EH signals; thereby, the inference of EH signals to \(X_{I}^{(k)}\) can be reduced to a negligible level as in (3). The precoded \(X_{E1}^{(k)}\) and \(X_{E2}^{(k)}\) are given in Appendix A.1.