# Optical Wireless Fronthaul-Enhanced High-Throughput FC-AE-1553 Space Networks
## 3 System Model of Optical Wireless Fronthaul-Enhanced Hybrid Space Network
### Network Performance Evaluation Metrics  
The terminals within a hybrid network, along with their behavior and relationships, can be accurately depicted using a graph, \(G=(V,E)\). In this representation, the elements of the set \(V\) represent the nodes of the network, whereas the elements within the set \(E\) correspond to the edges connecting these nodes. Specifically, the interconnections between node \(i\) and node \(j\) are appropriately represented by an edge \((i,j)\in E\). Matrix \(A=\left(a_{ij}\right)_{n\times n}\) is the adjacency matrix of \(G\), indicating the connection relationship of the whole network. \[A=\left[ \begin{array}{ccc}a_{11}&\cdots&a_{1n}\\ \vdots&\ddots&\vdots\\ a_{n1}&\cdots&a_{nm}\end{array} \right] \tag{1}\]  
\(n\) denotes the number of \(G\) nodes \(|V|\), and \(a_{ij}\) denotes the connection relationship between node \(i\) and node \(j\). \[a_{ij}=\left\{ \begin{array}{ccc}1,&\
u_{i}\
u_{j}\in E\\ 0,&else\end{array} \right. \tag{2}\]  
Matrix \(B\) denotes the effective bandwidth of every connection. \[G.Edge.Bandwidth=B=\left[ \begin{array}{ccc}b_{11}&\cdots&b_{1n}\\ \vdots&\ddots&\vdots\\ b_{n1}&\cdots&b_{nm}\end{array} \right] \tag{3}\]  
Figure 6: Timeline of HSN schedule. The access network has two parallel timelines, namely the FC transmission timeline and the LiFi transmission timeline. Matrix \(C\) denotes the average latency of every connection. \[G.Edge.Latency=C=\left[ \begin{array}{ccc}c_{11}&\cdots&c_{1n}\\ \vdots&\ddots&\vdots\\ c_{n1}&\cdots&c_{nn}\end{array} \right] \tag{4}\]  
Matrix \(D\) denotes the packet-loss ratio of every connection. \[G.Edge.Loss=D=\left[ \begin{array}{ccc}d_{11}&\cdots&d_{1n}\\ \vdots&\ddots&\vdots\\ d_{n1}&\cdots&d_{nn}\end{array} \right] \tag{5}\]  
Matrices \(A\), \(B\), \(C\), and \(D\) denote the basic network parameters. When the value of \(a_{ij}\) is 1, the relevant parameters of the other three matrices also take effect. These matrices can assist in configuring, monitoring, and updating the dynamic network data results. Due to the shared software and hardware integrated platform environment in this hybrid network, the network terminals serve as both the FC-AE-1553 and Li-Fi terminals and the node sets of FC-AE-1553 (\(V_{fc}\)) and those of Li-Fi (\(V_{lif:i}\)) are identical. However, it is important to note that the physical connectivity and network transmission behavior of the wired FC-AE-1553 network differ from those of the Li-Fi network. As a result, the edge sets, \(E_{fc}\) and \(E_{lif:i}\), of the FC and Li-Fi networks are independent, encompassing distinct connectivity and edge properties. When selecting a physical channel for traffic transmission, a comprehensive evaluation of the performance parameters of the FC and Li-Fi network topologies can guide the decision-making process. Different application requirements and strategies will lead to varying weight coefficients for each edge parameter. For the connection between \(i\) and \(j\), the comprehensive evaluation score equation for channel choosing is shown below. \(\alpha_{ij}\) denotes the weight of the effective bandwidth, \(\beta_{ij}\) denotes the weight of the average latency, and \(\gamma_{ij}\) denotes the weight of the packet-loss ratio. These three weight factors are decided by the traffic type. The network factors \(b_{ij}\), \(c_{ij}\), and \(d_{ij}\) are decided by the FC-AE-1553 and Li-Fi network parameters. In addition, normalization of the network bandwidth, delay, and packet loss is required to ensure that the weights evaluated for different network parameters are only affected by the weighting factors of the services. \[S_{ij}=\alpha_{ij}b_{ij}-\beta_{ij}c_{ij}-\gamma_{ij}d_{ij} \tag{6}\]  
The purpose of proposing the comprehensive evaluation formula is to select the optimal physical channel for different transmissions while taking into account both the transmission characteristics and the dynamic operation of the network.