## 2 System Model  
We consider an HSTS, where a satellite communicates with a destination node at the ground with the help of a relay node located at the ground, as shown in Figure 1. Therefore, there is no direct connection between the satellite and destination node. The overall communication is divided into two orthogonal phases. In the first phase, the satellite transmits its signal to the relay. At the relay, the received signal in the presence of a single dominant interferer will be:  
\[y_{1}=h_{1}x+h_{3}y+n_{1} \tag{1}\]  
where \(h_{1}\) is the channel gain between the satellite and the relay; \(x\) is the satellite's transmitted symbol with \(E_{s}\) power; \(h_{3}\) is the channel gain between the interferer and the relay; \(y\) is the interferer's transmitted symbol with \(E_{i}\) power; \(n_{1}\) is the zero-mean additive white Gaussian noise (AWGN) at the relay with \(\sigma_{1}^{2}\) variance. In the second phase, the relay multiplies the received signal \(y_{1}\) with a fixed gain \(G>0\) and forwards the amplified signal to the destination. The received signal at the destination, by using Equation (1), is given by:  
\[y_{2}=Gh_{2}(h_{1}x+h_{3}y+n_{1})+n_{2} \tag{2}\]  
where \(h_{2}\) is the channel gain between the relay and the destination and \(n_{2}\) is the zero-mean AWGN at the destination with \(\sigma_{2}^{2}\) variance. The satellite-relay link is assumed to follow the shadowed Rice fading channel with the following probability density function (PDF) [21]:  
\[f_{|h_{1}|^{2}}(x)=\alpha_{1}e^{-\beta_{1}x}{}_{1}F_{1}(m_{1};1;\delta_{1}x),(x \geq 0) \tag{3}\]  
where \(\alpha_{1}=\frac{1}{2b_{1}}\left(\frac{2b_{1}m_{1}}{2b_{1}m_{1}+\Omega_{1}} \right)^{m_{1}}\), \(\delta_{1}=\frac{\Omega_{1}}{2b_{1}(2b_{1}m_{1}+\Omega_{1})}\), \(\delta_{1}=\frac{1}{2b_{1}}\)\(\Omega_{1}\) is the average power of the LOS component, \(2b_{1}\) is the average power of the multipath component, \({}_{1}F_{1}(a;b;z)\) is the confluent hypergeometric function [23] and \(0\leq m_{1}\leq\infty\) is the Nakagami parameter. The relay-destination channel is assumed to follow the Nakagami-\(m\) distribution; hence, \(|h_{2}|^{2}\) follows the Gamma distribution [6] as:  
\[f_{|h_{2}|^{2}}(x)=\lambda_{2}x^{m_{2}-1}e^{-\epsilon_{2}x},(x\geq 0) \tag{4}\]  
where \(\lambda_{2}=\frac{m_{2}^{m_{2}}}{\Omega_{2}^{m_{2}}\Gamma(m_{2})}\), \(\epsilon_{2}=\frac{m_{2}}{\Omega_{2}}\); and \(\frac{1}{2}\leq m_{2}\leq\infty\) and \(\Omega_{2}\) denote the shape and scale parameters, respectively, of the relay-destination channel. The interferer-relay channel is also assumed to follow the Nakagami-\(m\) distribution; hence, \(|h_{3}|^{2}\) follows the Gamma distribution [6] as:  
\[f_{|h_{3}|^{2}}(x)=\lambda_{3}x^{m_{3}-1}e^{-\epsilon_{3}x},(x\geq 0) \tag{5}\]  
where \(\lambda_{3}=\frac{m_{3}^{m_{3}}}{\Omega_{3}^{m_{3}}\Gamma(m_{3})}\), \(\epsilon_{3}=\frac{m_{3}}{\Omega_{3}}\); and \(\frac{1}{2}\leq m_{3}\leq\infty\) and \(\Omega_{3}\) denote the shape and scale parameters, respectively, of the interferer-relay channel. Here, we comment on the choice of the selected channel models for different links, i.e., the shadowed Rice and the Nakagami-\(m\). The satellite-relay link (satellite-to-terrestrial wireless communication channel) is assumed to follow the shadowed Rice model, which is an example of the LMS channel, while the relay-destination link (terrestrial wireless communication channel) and interferer-relay link (terrestrial wireless communication channel) are assumed to follow the Nakagami-\(m\) model. The satellite-to-terrestrial propagation channels are inherently different from the terrestrial propagation channels because of the differences in the following underlying properties of the wireless channels: multipath fading (diffraction, reflection and scattering of the transmitted signal), LOS obstruction, path loss and shadowing. The above listed factors affect the signal level, while the channel additionally causes temporal dispersion and the Doppler shifts.