# Performance Analysis of Two-Way Satellite-Terrestrial Relay Network with SWIPT
## 2 System Model and Selective PNC  
As shown in Figure 1, we consider a SWIPT enabled two-way DF satellite-terrestrial network, with a satellite source node (\(S_{1}\)) and an energy-constrained user source node (\(S_{2}\)) at ground exchange information with the assistance of a mobile terminal relay node (\(R\)) situated at the ground. Both the SPNC protocol and PS scheme are employed in the two-way satellite-terrestrial network. We assume the satellite source node, user source node, and mobile terminal relay node have a single antenna and operate in half-duplex mode. Therefore, there is no direct link between the satellite source node and the user source node. In the proposed network, non-identical, independent, and reciprocal fading channels are assumed. The satellite-mobile terminal link is modeled as Shadowed-Rician fading channel. The mobile terminal can receive the signal from the line of sight (LOS) and the signal from other paths. The destination-mobile terminal link is modeled as Rayleigh fading channel, which is a multipath scene. In Figure 1, \(g\) and \(h\) denote fading channel coefficients of links \(S_{1}\)--\(R\) (or \(R\)--\(S_{1}\)) and \(S_{2}\)--\(R\) (or \(R\)--\(S_{2}\)), respectively. Hence, \(g\) is the independent and identically distributed Shadowed-Rician random variable (RV), and \(h\) is the independent and identically distributed Rayleigh RV. Specifically, channel state information (CSI) is only available on the receiver side. It takes two time slots for the communication. Let \(T\) be the duration of the entire transmission block, divided into two time slots with a time proportion factor \(\beta\in(0,1)\). During the first time slot of duration \(\beta T\), the satellite or the user simultaneously transmits the signals \(s_{1}\) or \(s_{2}\) to the mobile terminal with the transmit power \(P_{1}\) or \(P_{2}\), respectively, and the received signal at the relay is  
\[r_{1}=h\sqrt{P_{1}}s_{1}+g\sqrt{P_{2}}s_{2}+n_{1} \tag{1}\]  
where the additive noise \(n_{1}\) indicates the complex Gaussian noise with zero mean and variance \(W\sigma^{2}\); \(W\) denotes the system bandwidth; \(h\) is the channel coefficient between \(S_{1}\) and \(R\); \(g\) is the channel coefficient between \(R\) and \(S_{2}\). The transmit signals are generated corresponding to the messages \(m_{1}\) and \(m_{2}\) from \(S_{1}\) and \(S_{2}\), respectively. Assume that the BPSK signaling is employed by both \(S_{1}\) and \(S_{2}\). The BPSK mapping follows \(s_{i}=1\)-\(2m_{i}\) for \(i=1\), \(2\). After receiving, decision making is according to the maximum likelihood (ML) detection rule; the message \(\hat{m}\) is equal to \(0\) if  
\[ \begin{array}{c}\sum\limits_{\hat{m}=0}\exp\big{[}\big{|}r_{1}-h\sqrt{P_{1} }s_{1}(m_{1})-g\sqrt{P_{2}}s_{2}(m_{2})\big{|}\big{]}\\ \hskip 14.226378 pt>\sum\limits_{\hat{m}=1}\exp\big{[}\big{|}r_{1}-h\sqrt{P_{1} }s_{1}(m_{1})-g\sqrt{P_{2}}s_{2}(m_{2})\big{|}\big{]}\end{array}  \tag{2}\]  
or \(\hat{m}=1\) otherwise, where \(\hat{m}=m_{1}\oplus m_{2}\). During the second time slot of duration \((1-\beta)T\), \(R\) broadcasts \(s_{R}\) to \(S_{1}\) and \(S_{2}\) with the transmit power \(P_{R}\), which follows the function \(s_{R}=1\)-\(2\hat{m}\). The received signal at \(S_{1}\) and \(S_{2}\) can be expressed as \(y_{1}=h\sqrt{P_{1}}s_{R}+n_{2}\) and \(y_{2}=g\sqrt{P_{1}}s_{R}+n_{3}\), respectively, where the additive noise \(n_{2}\) and \(n_{3}\) indicate the complex Gaussian noise with zero mean and variance \(W\sigma^{2}\). After receiving signal \(y_{2}\) from \(R\), \(S_{2}\) splits it into two parts with ratio \(\rho\), where the portion \(\sqrt{\rho}y_{2}\) is used for information decoding and the remaining \(\sqrt{1-\rho}y_{2}\) for  
Figure 1: Illustration of the system model. RF energy harvesting.