## 3 System Model
### Channel Model  
In order to avoid the interference among IoT devices, orthogonal frequency division multiple access (OFDMA) technology is used. Subcarriers with equal bandwidth are allocated to IoT devices. The satellite-terrestrial transmission links between IoT devices and the local satellite use the Ka band [27] and have high communication rates. Since the line-of-sight (LOS) transmission is mainly considered in the link, the Rice channel is used. Free-space path loss (FSPL) and additive white Gaussian noise (AWGN) are taken into consideration. The achievable data rate of the link between IoT device \(i\) and the local satellite is:  
\[r_{i,1}=B_{i,1}\text{log}_{2}\bigg{(}1+\frac{p_{i}g_{i}H_{i,1}}{N_{0,1}}\bigg{)}, \tag{1}\]  
where \(B_{i,1}\) is the subchannel bandwidth, \(p_{i}\) is the transmission power of IoT device \(i\), \(g_{i}\) is the antenna gain of IoT device \(i\), \(H_{i,1}\) is the channel gain of the link, and \(N_{0,i}\) is the noise power of the link. \(H_{i,1}=(h_{i,1})^{2}\), where the channel coefficient \(h_{i,1}=\rho_{i,1}/(L_{i,1}^{\text{f}})^{1/2}\), \(\rho_{i,1}\) is the independent identically distributed Rice stochastic variable with a unit variance, \(L_{i,1}^{\text{f}}\) is FSPL, \(L_{i,1}^{\text{f}}=(4\pi d_{i,1}f/c)^{2}\), \(c\) is the light velocity (meter per second), \(d_{i,1}\) is the distance between IoT device \(i\) and the local satellite (meter), and \(f\) is the carrier frequency (hertz). \(d_{i,1}^{\text{min}}=h_{\text{s}}\), as Figure 2 depicted, \(d_{i,1}^{\text{max}}=[\left(R_{\text{e}}\right)^{2}+\left(R_{\text{e}}+h_{ \text{s}}\right)^{2}-2R_{\text{e}}(R_{\text{e}}+h_{\text{s}})\cos\theta_{\text {ec}}]^{1/2}\), where \(R_{\text{e}}\) is the earth radius, \(h_{\text{s}}\) is the LEO satellite orbit altitude, and \(\theta_{\text{ec}}\) is the covering geometric angle. \(\theta_{\text{ec}}=\arccos\left[R_{\text{e}}\cos\theta_{\text{u}}^{\text{min} }/\left(R_{\text{e}}+h_{\text{s}}\right)\right]-\theta_{\text{u}}^{\text{min }}\), \(\theta_{\text{u}}^{\text{min}}\) is the minimum elevation angle of the IoT devices on the ground to the satellite [30].  
Figure 1: Network model.  
The ISLs between the local satellite and neighboring satellites use the Ka band [31], FSPL and AWGN are taken into account. The achievable data rate of the link between the local satellite and neighboring satellite \(j,j\in\mathcal{M}\) is:  
\[r_{1,j}=B_{1,j}\text{log}_{2}\bigg{(}1+\frac{PGH_{1,j}}{N_{0_{1,j}}}\bigg{)}, \tag{2}\]  
where \(B_{1,j}\) is the subchannel bandwidth, \(P\) is the transmission power of the local satellite, \(G\) is the antenna gain of the local satellite, \(H_{1,j}\) is the channel gain of the link, and \(N_{0_{1,j}}\) is the noise power of the link. \(G\approx\left(4D_{\text{TA}}f/c\right)^{2}\), and \(D_{\text{TA}}\) is the diameter of the local satellite's transmitting antenna [31]. \(H_{1,j}=\left(h_{1,j}\right)^{2}\), where the channel coefficient \(h_{1,j}=1/(L_{1,j}^{\text{f}})^{1/2}\), \(L_{1,j}^{\text{f}}\) is FSPL, \(L_{1,j}^{\text{f}}=\left(4\pi l_{1,j}f/c\right)^{2}\), and \(l_{1,j}\) is the distance between the local satellite and neighboring satellite \(j\) (meter).  
Normally, each satellite has four neighboring satellites, two in the same orbit and the other two in the left and right orbits. The distance between the local satellite and the neighboring satellite in the same orbit is \(l_{1,j}=\sqrt{2}R\sqrt{1-\cos\left(360^{\circ}/\right)/}\), where \(R\) is the orbital radius, \(R=h_{\text{s}}+R_{\text{e}}\), and \(J\) is the number of satellites in each orbit. The distance between the local satellite and the neighboring satellite in different orbits is \(l_{1,j}=\omega\cos(lat)\), \(\omega=\sqrt{2}R\sqrt{1-\cos\left(360^{\circ}/21\right)}\), where \(lat\) is the latitude where the ISL of the current satellite locate, and \(I\) is the number of orbits of satellite constellation [32].