# Reliable and Energy-Efficient LEO Satellite Communication with IR-HARQ via Power Allocation
## 2 Preliminaries
### Link Transmission Characteristics between the LEO Satellite and the Ground User
The attenuation caused by rain can be obtained using the following steps. Firstly, the specific attenuation \(\gamma_{R}\) can be calculated according to [27]:  
\[\gamma_{R}=k_{r}R_{w}{}^{\alpha_{r}}, \tag{5}\]  
where \(R_{w}\) is the rainfall rate of the location, \(k_{r}\) and \(\alpha_{r}\) are the frequency-dependent coefficients provided in [27]. Then, the rain attenuation can be expressed as [28]:  
\[\left(A_{r}\right)_{dB}=\gamma_{R}L_{E}, \tag{6}\]  
where \(L_{E}\) is the effective path length and related to the elevation angle \(\varphi\). It can be calculated according to [28]. Similarly, we call \(R_{w}\) the characteristic parameter of the rain. The total attenuation caused by weather can be expressed as:  
\[\left(A_{t}\right)_{dB}=\left(A_{g}\right)_{dB}+\left(A_{c}\right)_{dB}+ \left(A_{r}\right)_{dB}, \tag{7}\]  
From the above analysis, it can be seen that the weather attenuation is related to the frequency \(f\), elevation angle \(\varphi\), and the characteristic parameter of the specific weather. According to [31], we can write the link equation between the LEO satellite and the ground user as:  
\[\left(C/N\right)_{dB}=\left(EIRP\right)_{dBW}+\left(\frac{G_{r}}{T}\right)_{ dB/K}-\left(k\right)_{dBI/K}-\left(B_{n}\right)_{dBHz}-\left(L_{fs}\right)_{ dB}-\left(L_{o}\right)_{dB}, \tag{8}\]  
where \(C/N\) is the carrier to noise ratio, \(G_{r}\) is the receive antenna gain, \(T\) is the receive noise temperature, \(k\) is [PERSON]'s constant, and \(B_{n}\) is the carrier bandwidth. \(L_{o}\) is other transmission loss. Here, it is assumed that \(L_{o}\) only includes the weather attenuation, that is, \(L_{o}=A_{t}\). The term \(\left(EIRP\right)_{dBW}=\left(P_{t}\right)_{dBW}+\left(G_{t}\right)_{dBi}\) (dB), where \(P_{t}\) is the transmission power and \(G_{t}\) is the transmit antenna gain. Note that the values of \(C/N\) and SNR are equal when carrier suppressed modulation methods such as Binary Phase Shift Keying (BPSK) are adopted. Based on the above analysis, we use the STK to simulate the large scale-fading between the LEO satellite and the ground user with a time interval of 5 s. The relevant parameters of LEO satellite orbit are shown in Table 2. The location of the ground user is \(116^{\circ}59^{\prime}\) E, \(40^{\circ}3^{\prime}\) N. The system operates in Ka-band with \(f=25\) GHz. The values of \((EIRP)_{dBW}\) and \((G/T)_{dB/K}\) are 40 dBW and 20 dB/K, respectively. In addition, BPSK is adopted as the modulation mode and the C/N is equal to the value of the received SNR. As shown in Figure 2, the LEO satellite suffers from highly variable channel conditions. While working around the horizon area, the LEO satellite usually achieves a poor \(C/N\) and the value grows larger as the satellite moves towards the ground user. We assume the characteristic parameter of the specific weather is fixed in a LEO communication window and the weather attenuation is only related to the elevation angle \(\varphi\). It is worth noting that the large-scale fading of satellites can be obtained in advance before information transmission [32]. On the one hand, the flight trajectory of the satellite is known to both the ground user and the satellite; hence, the satellite can obtain the real-time distance and the elevation angle. On the other hand, the characteristic parameters of the specific weather can be obtained from a local weather station. Therefore, the satellite can calculate the large-scale fading by (2)-(8) and estimate the value of \(C/N\). Even without the above assumptions, we can obtain the statistics of the current channel through the feedback of the receiver. This is also used in DVB-S2 standards where a 1 s updating time is considered achievable [33]. In addition, the characteristic parameters of the specific weather change slowly. An experimental result of a satellite link reported that the average fade slope estimated from a Ku-band satellite system was 0.24 dB/second and the maximum fade slope corresponding to heavy rain events at Ka-band does not exceed 0.5 dB/second [34].