# Outage Performance of SWIPT-D2D-Based Hybrid Satellite-Terrestrial Networks
## 2 System Model and SWIPT-D2D Schemes
### PS-D2D Scheme  
In the PS-D2D scheme, which is shown in Figure 1, we assume that \(T\) denotes the duration of the entire transmission process, which is divided into three orthogonal phases with equal time duration.  
During the first time slot, with a time duration of \(T/3\), the satellite \(S\) broadcasts its signal \(x_{s}\) to the terrestrial nodes. Therefore, the received symbols at the terrestrial nodes can be respectively given by  
\[y_{si,ps}=\sqrt{P_{s}}h_{si}x_{s}+n_{si}, \tag{1}\]  
where \(i\in\{r,u1,u2\}\), \(h_{si}\) denotes the channel coefficient between \(S\) and the terrestrial nodes, respectively, \(n_{si}\) denotes the AWGN, respectively, and \(P_{s}\) denotes the transmit power of \(S\).  
During the second time slot, \(R\) amplifies and forwards \(y_{sr,ps}\) to \(U_{1}\); the received symbol will be  
\[y_{rul,ps}=\sqrt{P_{r}}g_{rul}\frac{y_{sr,ps}}{\sqrt{|y_{sr,ps}|}^{2}}+n_{rul}, \tag{2}\]  
where \(g_{rul}\) denotes the channel coefficient between \(R\) and \(U_{1}\), \(n_{rul}\) denotes the AWGN, and \(P_{r}\) denotes the transmit power of \(R\). After receiving \(y_{rul,ps}\), \(U_{1}\) splits the symbol into two  
Figure 1: Illustration of the PS-D2D-based HSTN model.  
portions with PS coefficient \(\rho\in(0,1)\), where the portion \(\sqrt{p}y_{rn1,ps}\) is utilized in ID and the portion \(\sqrt{1-\rho}y_{rn1,ps}\) is utilized in EH. Thus, the harvested energy at \(U_{1}\) can be given by  
\[E_{u1,ps}=\frac{\omega T(1-\rho)P_{r}|g_{rn1}|^{2}}{3}, \tag{3}\]  
where \(\omega\in(0,1)\) denotes the energy conversion efficiency. The received symbol at \(U_{1}\) can be rewritten as  
\[y_{rn1,z}=\sqrt{\rho}\left(\sqrt{P_{r}}g_{rn1}\frac{y_{sr,ps}}{\sqrt{|y_{sr, ps}|}^{2}}+n_{rn1}\right)+n_{rn1,z}, \tag{4}\]  
where \(n_{rn1,z}\) denotes the AWGN. The SNR of satellite-terrestrial direct link at \(U_{1}\) is given by  
\[\Lambda_{su1,ps}=\eta_{s}|h_{su1}|^{2}, \tag{5}\]  
where \(\eta_{s}=P_{s}/\sigma^{2}\). The SNR of the terrestrial relay link at \(U_{1}\) is given by  
\[\Lambda_{srul,ps}=\frac{\rho^{\prime}\Lambda_{sr,ps}\Lambda_{rul,ps}}{\Lambda _{sr,ps}+\rho^{\prime}\Lambda_{rul,ps}+1}, \tag{6}\]  
where \(\Lambda_{sr,ps}=\eta_{s}|h_{sr}|^{2}\), \(\Lambda_{rul,ps}=\eta_{r}|g_{rn1}|^{2}\), \(\eta_{r}=P_{r}/\sigma^{2}\), and \(\rho^{\prime}=\rho/(\rho+1)\).  
During the third time slot, \(U_{1}\) decodes and forwards the signal \(x_{u1,ps}\) to \(U_{2}\) with the harvested energy. The transmit power at \(U_{1}\) will be given by  
\[P_{u1,ps}=\frac{3E_{u1,ps}}{T}=\omega(1-\rho)P_{r}|g_{rn1}|^{2}. \tag{7}\]  
Thus, the symbol received at \(U_{2}\) is given by  
\[y_{u1u2,ps}=\sqrt{\omega(1-\rho)P_{r}|g_{rn1}|^{2}}g_{u1u2}x_{u1,ps}+n_{u1u2}, \tag{8}\]  
where \(g_{u1u2}\) denotes the channel coefficient between \(U_{1}\) and \(U_{2}\), and \(n_{u1u2}\) denotes the AWGN. The SNR of the satellite-terrestrial direct link at \(U_{2}\) is given by  
\[\Lambda_{su2,ps}=\eta_{s}|h_{su2}|^{2}. \tag{9}\]  
The SNR of the terrestrial link at \(U_{2}\) is given by  
\[\Lambda_{u1u2,ps}=\omega(1-\rho)\eta_{r}|g_{rn1}|^{2}|g_{u1u2}|^{2}. \tag{10}\]