# Cooperative Downloading for LEO Satellite Networks: A DRL-Based Approach
## 4 Performance Evaluation  
For performance evaluation, we compare the proposed scheme, DRL-CD, with the following schemes: (1) RANDOM, where each LEO satellite makes offloading decisions randomly until it begins to contact GS, and (2) No-COOP, which does not support any ISL offloading.  
We assume that the altitude of satellite is 1150 km and consider a target area of 7800 \(\times\) 4500 \(\times\)1150 (km\({}^{3}\)) in which one GS is deployed at the center of the area as shown in Figure 4. At the beginning of each episode, we generate random orbits that intersect around GS to prevent satellites from passing through the target area without any contact. The elevation angle of GS is set to 35\({}^{\circ}\), resulting in the maximal SGL distance (denoted by \(d_{\text{th}}^{\text{SGL}}\)) of 1230 km [36]. In addition, \(d_{\text{th}}^{\text{ISL}}\) is set to 1865 km, which can be computed based on the maximum distance between two satellites that move along adjacent planes within one constellation. When the inclination of the constellation is 53\({}^{\circ}\) and the difference in the right ascension of the ascending nodes of the two satellites is 8\({}^{\circ}\), the maximum distance is 1865 km [37]. The bandwidths of SGL and ISL are set to 33 MHz in the C-band of 5.1-5.2 GHz and 16.5 MHz in the L-band of 6.2-6.5 GHz, respectively [22].  
We composed the input layer, the hidden layers, and the output layers of the DNN with 1 GAT layer, 4 FC layers, and \(|\text{L}|\) paralleled FC layers, respectively. Other simulation parameters are summarized in Table 1.  
The optimal cooperative downloading policy allows data to be distributed to satellites to fully utilize satellites' contact time and maximize the amount of downloaded data. To quantify the distribution of data that satellites initially retain, the G-fairness index is defined as  
\[\mathcal{I}(\mathbf{m})=\prod_{l\in\text{L}}\sin\left(\frac{\pi\cdot m _{l}}{2\cdot\max\left(\mathbf{m}\right)}\right), \tag{15}\]  
where \(\mathbf{m}=\{m_{l}|l\in\text{L}\}\) denotes a set of initial amounts of data that satellites retain [38]. If each LEO satellite has comparable amounts of data (i.e., the total amount of data is distributed in a balanced manner over the satellites), \(\mathcal{I}(\mathbf{m})\) is close to 1; otherwise, it is close to 0. At the beginning of every episode, the total amount of initial data is set as the sum of the maximally downloadable data of each trajectory and distributed to satellites according to \(\mathcal{I}(\mathbf{m})\).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Neurons of each hidden layer & 512 \\ \hline Neurons of each output layer & number of satellites + number of GSs \\ \hline Batch size & 128 \\ \hline Replay buffer size & 1,000,000 \\ \hline Learning rate & \(3\times 10^{-4}\) \\ \hline Discount rate & 0.99 \\ \hline Optimizer & Adam \\ \hline Target entropy & \(0.98*\log\left(\text{number of satellites}\right)\) \\ \hline Weight for offloading (\(\lambda\)) & \(-0.3\) \\ \hline Soft update cycle (\(B\)) & 2 \\ \hline Coefficient for soft update (\(\tau\)) & \(5\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters.