## 2 System Model and Configuration  
### Definition of TEF  
The satellite-to-ground data transmission of LEO EO satellites is intermittent. In the limited transmission arc segment, the high-rate data transmission is required to dump high-volume of payload data. If only pursuing high link availability, sufficient margins need to be reserved to compensate the atmospheric attenuation especially for small elevation angles, which will result in lower useful data rate and could not meet the requirement of high-rate data transmission. For a G/S of LEO EO satellites, the transmission capacity of satellite-to-ground link is measured by the total data amount that can be received correctly in the transmission arc segment of a repeat period. However, different locations of G/S will lead to different total durations of transmission arc segments. The application characteristics of CCM, VCM and ACM are different:  
1. The MCS and useful data rate of CCM are fixed in all transmission arc segments. 2. VCM can complete MCS switching at some fixed elevation angles threshold, increase the MCS and change the useful data rate with the increase of elevation angles. 3. ACM can dynamically adjust MCS according to the state of satellite-to-ground link. Even at a specific elevation, any MCS may be used. It can be considered to use the maximum MCS first, whose link availability is minimum but the useful data rate is maximum, and then select a smaller MCS in different link availability intervals with the increase of link availability. The TEF could be defined as \"the product of link availability and average useful data rate\", which clarifies the weighted average effect of link availability on the useful data rate. Beyond the time corresponding to link availability (i.e., outage period), the bit error rate (BER) does not meet the requirement and the desired remote sensing data cannot be recovered correctly. Therefore, the CCM TEF of LEO EO satellite for a single G/S is defined as:  
\[E_{\text{CCM}}=A_{\text{L}}\cdot R_{\text{b}} \tag{1}\]  
where \(A_{\text{L}}\) is the link availability and \(R_{\text{b}}\) is the useful data rate. Both parameters are related to the MCS. Then, the VCM TEF of LEO EO satellite for a single G/S is modified and defined as:  
\[E_{\text{VCM}}=A_{\text{L}}\cdot\frac{\sum\limits_{i=1}^{N}\left[\int_{t_{ \text{start}}(i)}^{t_{\text{end}}(i)}R_{\text{b}}(t)dt\right]}{\sum\limits_{i= 1}^{N}[t_{\text{end}}(i)-t_{\text{start}}(i)]} \tag{2}\]  
where \(A_{\text{L}}\) is the link availability (related to the selected initial minimum MCS), \(R_{\text{b}}(t)\) is the useful data rate (Mbps) at time \(t\), \(t_{\text{start}}(i)\) and \(t_{\text{end}}(i)\) are the start time and the end time of the \(i\)-th transmission arc segment, respectively, and \(N\) is the number of data transmission arc segments in a repeat period. Furthermore, the ACM TEF of LEO EO satellite for a single G/S is modified and defined as:  
\[E_{\text{ACM}}=\frac{\sum\limits_{i=1}^{N}\left\{\int_{t_{\text{start}}(i)}^{ t_{\text{end}}(i)}\!\!\left[A_{\text{L}}(8)\!\cdot\!R_{\text{b}}(8,t)+\sum \limits_{k=7}^{9-K}\left(A_{\text{L}}(k)-A_{\text{L}}(k+1)\right)\!\cdot\!R_{ \text{b}}(k,t)\right]\!dt\right\}}{\sum\limits_{i=1}^{N}[t_{\text{end}}(i)-t_ {\text{start}}(i)]} \tag{3}\]  
where \(R_{\text{b}}(k,t)\) is the useful data rate of the \(k\)-th MCS at time t (\(k\) = 1 for MCS 1, 2 for MCS 3, 3 for MCS 6,..., 8 for MCS 28 in this paper), \(K\) is the number of MCSs used in ACM system and \(A_{\text{L}}(k)\) is the link availability of the \(k\)-th MCS.