# Secure Information Transmission with Self Jamming SWIPT
## 2 System Model  
The MIMO system model is shown in Figure 1. It is composed of three transmitting antennas and two receiving antennas, with a dedicated transmitting antenna and a receiving antenna for information transmission, denoted as \(\mathcal{T}\) and \(R\), respectively. The other two transmitting antennas, \(E1\) and \(E2\), are used for energy transmission, and the rectenna \(\wp\) is used to harvest energy from the physical layer network coded (PLNC) signal. The eavesdropper is denoted as \(\xi\). It is assumed that \(E1\), \(E2\), and \(\mathcal{T}\) are not spatially correlated. In Figure 1, based on the location of \(\xi\), if \(\xi\) is very close to \(R\), \(\xi\) is considered to have high channel correlation with \(R\)[16]. The system adopts the quadrature amplitude modulation (QAM) signal over the Rayleigh frequency selective fading channel by using SC-FDMA for simultaneously transferring information from \(\mathcal{T}\) and the high energy signal from \(E1\) and \(E2\) to both \(R\) and \(\wp\). The frequency domain signals transmitted from \(\mathcal{T}\), \(E1\), and \(E2\) are denoted as \(X_{I}^{(k)}\), \(X_{E1}^{(k)}\), and \(X_{E2}^{(k)}\), respectively, where \(k\) represents the index of the symbol with \(k=0,1,...,K\) and \(K\) is the total number of symbols in the respective signal stream. The frame structure of \(\mathbf{X}_{I}\), \(\mathbf{X}_{E1}\), and \(\mathbf{X}_{E2}\) is illustrated in Figure 2, where the time duration per symbol, block duration, and total time for all the blocks are denoted as \(T\), \(T_{I}\), and \(T_{I}L\), respectively. A frame consists of \(L\) signal blocks where each signal block contains \(N\) symbols. The signal blocks are denoted as \(l\), where \(l=0,1,...,L\). We assume that \(X_{I}^{(k)}\), \(X_{E1}^{(k)}\), and \(X_{E2}^{(k)}\) are transmitted with perfect time synchronization and in equal block size. The following system of equations is considered for a single block, and therefore, we set \(l=1\). \(S_{E1}\), \(S_{E2}\), and \(S_{I}\) are the unamplified versions of \(\mathbf{X}_{E1}\), \(\mathbf{X}_{E2}\), and \(\mathbf{X}_{I}\), respectively, and the power amplification levels of energy symbols and information symbols are at different levels. \(P_{E1}\), \(P_{E2}\), and \(P_{I}\) denote the transmit powers of \(\mathbf{X}_{E1}\), \(\mathbf{X}_{E2}\), and \(\mathbf{X}_{I}\), respectively. For the sake of simplicity, without loss of generality, we assume that \(P_{E1}=P_{E2}\). The relationship between the power levels of energy and information symbols is given as:  
\[ \begin{split} X_{I}^{(k)}=S_{I}^{(k)}P_{I};\;\;X_{E1}^{(k)}=S_{E1 }^{(k)}P_{E1};\;\;X_{E2}^{(k)}=S_{E2}^{(k)}P_{E2};\\ \beta=\frac{2P_{E1}}{P_{I}},\end{split}  \tag{1}\]  
where \(\beta\) is the ratio between the transmit power of the energy and information signal. Throughout this paper, the channel coefficient for the channel link between two nodes, i.e., for example, nodes \(\mathcal{T}\) and \(R\), is denoted as \(H_{TR}^{(k)}\), where \(k\) represents the index of channel coefficient with respect to the transmitted symbol in the signal stream. Then, \(H_{TR}^{(k)}\) is characterized as \(H_{TR}^{(k)}\sim\mathcal{CN}(0,\sigma_{H,TR}^{2})\), and its channel gain is given as \(|(H_{TR}^{(k)})^{2}|\sim\mathrm{Exp}\{\sigma_{H,TR}^{2}\}\), where \(\sigma_{H,TR}^{2}\) is the variance of \(H_{TR}^{(k)}\). Since all the channel links between the nodes are Rayleigh frequency selective fading channels, they follow similar notation and channel characterization as \(H_{TR}^{(k)}\). Similarly, the channel coefficients corresponding to the channel link between \(E1\) and \(R\), \(E2\) and \(R\), \(\mathcal{T}\) and \(\wp\), \(E1\) and \(\wp\), \(E2\) and \(\wp\), \(\mathcal{T}\) and \(\xi\), \(E1\) and \(\xi\), and \(E2\) and \(\xi\) are denoted as \(H_{E1R}^{(k)}\), \(H_{E2R}^{(k)}\), \(H_{Tq}^{(k)}\), \(H_{E1p}^{(k)}\), \(H_{E2p}^{(k)}\), \(H_{Tq}^{(k)}\), \(H_{E1q}^{(k)}\), and \(H_{E2p}^{(k)}\), respectively.