# _electronics_
## 2 Satellite Network Model and Cluster  
With the application of satellite network communication and new internet technologies, satellite networks are becoming more dense, and terrestrial users may be covered by multiple satellites within a certain period. As shown in Figure 1, the satellite network architecture of this article is divided into the GEO layer, LEO layer, and terrestrial layer. The control layer of software-defined networking (SDN) [19; 20] consists of three GEO satellite constellations, which are responsible for the status collection of LEO satellites and the calculation of cache placement positions. LEO satellites are equipped with NDN routers for in-network caching and content forwarding. The terrestrial layer is composed of Earth stations and content service providers. Since the caching mechanisms in the NDN networks greatly improve the efficiency of content transmission, this paper combines the coded caching strategy and uses multiple satellites to achieve efficient content data distribution. Assuming that the storage space of the satellite node is \(C\) (for the convenience of research, the storage spaces of all satellite nodes are set to be the same in this paper). There are pieces of content in the network, which can be represented as sets \(F=\{f_{1},f_{2},\cdots,f_{N}\}\). The size of each piece of content is \(M\), which can be represented as sets \(M=\{m_{1},m_{2},\cdots,m_{N}\}\). Each content package is divided into \(k\) data blocks of equal length, which can be represented as sets \(f_{1}=\{f_{11},f_{12},\cdots,f_{k}\}\). In this paper, the maximum distance separable (MDS) code [21] is used to encode the content data package, and \(k\) equal-length data blocks can be coded into any number of coded blocks through the Vandermonde generator matrix, and stored in the satellite nodes. With MDS coding, the satellite node does not need to consider the correlation between content blocks when caching content, as long as the user is guaranteed to receive a sufficient number of coded packages, and then the original data package can be reconstructed. To simplify the management of the satellite networks and realize the cooperative distribution mechanism of the satellite clusters, this paper divides the clusters into multiple LEO satellite clusters according to the geographic locations of the satellites [22]. The cluster head selection mainly considers the connection degree of the node. The topology of the satellite networks can be viewed as an undirected graph \(G=(V,E)\), where \(V\) is the set of nodes in the networks and \(E\) is the set of links in the networks. If \(\{i,j\}\in E\), there is a bidirectional link between node \(i\) and node \(j\), which can communicate with each other. Due to the predictability and periodicity of the satellite node movement, the satellite operation period can be discretized into \(N\) sufficiently small time slices, and it is assumed that the topology of the satellite network does not change in each time slice [7]. Figure 1: Architecture of the satellite networks. The connection degree \(degree_{i}\) of node \(i\) in a period can be calculated as follows:  
\[degree_{i}=\frac{1}{N}\sum_{t=0}^{N}\sum_{j=0,j\
eq i}^{n}a_{ij}^{t} \tag{1}\]  
where \(N\) is the number of divided time slices, \(a_{ij}^{t}\) represents the degree of node \(i\) in the \(t\) time slice. If node \(i\) is connected to node \(j\) in the \(t\) time slice, there is \(a_{ij}^{t}=1\); otherwise, \(a_{ij}^{t}=0\). For satellites \(S_{i}\) and \(S_{j}\), with the latitude and longitude given, the geocentric angle \(\theta\) between the satellites is derived by  
\[\theta\ =\arccos[\sin(\varphi_{i})*\sin(\varphi_{j})+\cos(\varphi_{i})* \cos(\varphi_{j})*\cos(\lambda_{i}-\lambda_{j})] \tag{2}\]  
where \(\varphi_{i}\) and \(\lambda_{i}\) represent the latitude and longitude of satellite \(S_{i}\), and \(\varphi_{j}\) and \(\lambda_{j}\) represent the latitude and longitude of satellite \(S_{j}\).