# DNNs Based Computation Offloading for LEO Satellite Edge Computing
## 3 System Model
### Edge Execution  
When the users choose to offload the computing tasks to the MEC server on the LEO satellite, the users offload the computing tasks to the LEO satellite and process tasks on the edge server. Limited by the size of solar panels, we think that the available energy of LEO satellites is a very precious resource. Therefore, we consider the energy consumption of MEC server on the LEO satellite processing the tasks [32; 33; 34; 35; 36]. Due to the small size of the returned results generated by the MEC server, we do not consider the energy consumption and delay caused by the process of returning the computation results to the users [37; 38].  
We divide the total energy consumption of ground users offloading tasks to the MEC server on the LEO satellite into two parts: one part is the energy consumption \(E_{nm}^{\text{trans}}\) of transmitting the tasks to the MEC server, and the other part is the energy consumption of the MEC server on the LEO satellite processing the tasks, which is denoted as a linear function of task \(l_{nm}\). The total energy consumption of user \(n\)'s task \(m\) offloading to the MEC server is:  
\[E_{nm}^{\text{edge}}=E_{nm}^{\text{trans}}+\phi l_{nm}, \tag{4}\]  
where \(\phi\) is the weight of MEC server energy consumption.  
In this system, we define \(p_{n}\) as the transmit power of the \(n\)th user offloading the tasks. The transmission rate when user \(n\) offloads the tasks can be derived from [PERSON]'s formula as \(r_{n}=b_{n}\text{log}_{2}\Big{(}1+\frac{h_{n}p_{n}}{\sigma}\Big{)}\), where \(b_{n}\) is the bandwidth allocated to user \(n\), \(h_{n}\) is the channel gain of the channel occupied by the \(n\)th user, and \(\sigma\) is the noise power. We think that the satellite-to-ground link loss in this system is mainly free space loss.  
The transmission delay for user \(n\) to offload task \(m\) to the MEC server is as follows:  
\[T_{nm}^{\text{trans}}=\frac{l_{nm}}{r_{n}}. \tag{5}\]  
In addition, the processing delay of the MEC server is given by:  
\[T_{nm}^{\text{sat}}=\frac{l_{nm}}{f^{\text{sat}}}. \tag{6}\]  
We think that there is a MEC server in LEO satellite, and the processing rate of the MEC server is \(f^{\text{sat}}\).  
The total delay when user \(n\) offloads computing tasks to the MEC server on the LEO satellite for execution is:  
\[T_{n}^{\text{edge}}=\sum_{m=1}^{M}\big{(}T_{nm}^{\text{trans}}+T_{nm}^{\text{ sat}}\big{)}x_{nm},\forall n\in N. \tag{7}\]  
The simultaneous task transmission and MEC task execution are not considered in this paper because the focus of this paper is on the offloading decisions problem and bandwidth allocation problem [39; 40; 41; 42; 43]. In addition, in LEO satellite edge computing, if the simultaneous task transmission and MEC task execution are considered, the MEC servers need to process more tasks in one time slot, and the MEC servers will generate more energy consumption within a unit time, which will bring a great burden on the resource-constrained MEC servers on LEO satellites.  
In this paper, we assume that all computing tasks that need to be offloaded can be finished during the LEO satellite coverage time.