## 3 System Model
### Channel Model  
To avoid interference among UEs, the orthogonal frequency division multiple access (OFDMA) is used, which allocates a sub-channel with the same bandwidth to each UE. The satellite-terrestrial transmission link between UEs and the satellite uses Ka band [26]. Since line-of-sight (LOS) transmission is mainly considered, the link uses the Ricean channel and takes into account free-space path loss (FSPL) and additive white Gaussian noise (AWGN). The achievable data rate of the link between UE \(i\) and the LEO satellite is  
\[r_{iS}=B_{iS}\text{log}_{2}\bigg{(}1+\frac{p_{iS}i_{\text{G}}r_{\text{H}}i_{S }}{N_{0_{iS}}}\bigg{)}, \tag{1}\]  
\(B_{iS}\) is the bandwidth of the sub-channel (Hertz), \(p_{i}\) is the transmitting power of UE \(i\) (Watt), \(g_{i}\) is the transmitting antenna gain of UE \(i\), \(G_{\text{r}}\) is the receiving antenna gain of the LEO satellite, \(H_{iS}\) is the channel gain of the link, and \(N_{0_{iS}}\) is the noise power of the link. \(G_{\text{r}}\approx\left(4D_{\text{RA}}f_{\text{u}}/\,c\right)^{2}\), \(D_{\text{RA}}\) is the diameter of the LEO satellite receiving antenna (meter) [27], and \(f_{\text{u}}\) is the carrier frequency of the uplink (Hertz). \(H_{iS}=\left(h_{iS}\right)^{2}\), channel coefficient  
Figure 1: Network model. \(h_{i,S}=\rho_{i,S}/\sqrt{L_{i,S}^{t}}\), \(\rho_{i,S}\) is the Ricean stochastic variable, \(L_{i,S}^{t}\) is FSPL, \(L_{i,S}^{t}=\left(4\pi d_{i,S}f_{\text{u}}/c\right)^{2}\), \(c\) is the speed of light (meter per second), \(d_{i,S}\) is the distance between UE \(i\) and the LEO satellite (meter). As shown in Figure 2, \(d_{i,S}=\sqrt{\left(R_{\text{e}}\right)^{2}+\left(R_{\text{e}}+h_{\text{s}} \right)^{2}-2R_{\text{e}}\left(R_{\text{e}}+h_{\text{s}}\right)\cos\theta_{ \text{ec}}}\), where \(R_{\text{e}}\) is the earth radius, \(h_{\text{s}}\) is the orbital height of the LEO satellite, and \(\theta_{\text{ec}}\) is the geocentric angle corresponding to the area covered by the LEO satellite. \(\theta_{\text{ec}}=\arccos[R_{\text{e}}\cos\theta_{\text{u}}/\left(R_{\text{e }}+h_{\text{s}}\right)]-\theta_{\text{u}}\), \(\theta_{\text{u}}\) is the elevation angle between UE \(i\) on the ground and the LEO satellite in space [28]. The satellite-terrestrial transmission link between the LEO satellite and the gateway uses Ka band [26]. Since LOS transmission is mainly considered, the link uses the Ricean channel and considers FSPL and AWGN. The achievable data rate of the link between the LEO satellite and the gateway is  
\[r_{\text{S,G}}=B_{\text{S,G}}\text{log}_{2}\left(1+\frac{PG_{\text{t}}G_{\text {g}}H_{\text{S,G}}}{N_{0_{\text{S,G}}}}\right), \tag{2}\]  
\(B_{\text{S,G}}\) is the bandwidth of the sub-channel (Hertz), \(P\) is the transmitting power of the LEO satellite (Watt), \(G_{\text{t}}\) is the transmitting antenna gain of the LEO satellite, \(G_{\text{g}}\) is the receiving antenna gain of the gateway, \(H_{\text{S,G}}\) is the channel gain of the link, \(N_{0_{\text{S,G}}}\) is the noise power of the link. \(G_{\text{t}}\approx\left(4D_{\text{TA}}f_{\text{d}}/c\right)^{2}\), \(D_{\text{TA}}\) is the diameter of the LEO satellite transmitting antenna (meter) [27], and \(f_{\text{d}}\) is the carrier frequency of the downlink (Hertz). Similarly, \(G_{\text{g}}\approx\left(4D_{\text{g}}f_{\text{d}}/c\right)^{2}\), \(D_{\text{g}}\) is the diameter of the gateway satellite antenna (meter). \(H_{\text{S,G}}=\left(h_{\text{S,G}}\right)^{2}\), channel coefficient \(h_{\text{S,G}}=\rho_{\text{S,G}}/\sqrt{L_{\text{S,G}}^{t}}\), \(\rho_{\text{S,G}}\) is the Ricean stochastic variable, \(L_{\text{S,G}}^{t}\) is FSPL, \(L_{\text{S,G}}^{t}=\left(4\pi d_{\text{S,G}}f_{\text{d}}/c\right)^{2}\), \(d_{\text{S,G}}\) is the distance between the LEO satellite and the gateway (meter).