## 4 LEO Satellite Mega-Constellation Network Caching Policy
### Caching Policy Based on RF  
Due to the dynamic characteristics of the satellite nodes, the content required by the CARF needs to be able to describe both satellite nodes' location and content properties. Thus, the policy is analyzed in terms of both the satellite nodes and content dimensions. The satellite node dimension is utilized to represent the load status of a satellite node during different time intervals. Therefore, we give the definitions of the cache rate and the cache replacement rate. Definition 1: The cache rate is defined as the load rate during the unfilled phase of the cache load for satellite nodes, and the cache rate is given by:  
\[CR=\frac{\sum_{c=1}^{L}CS_{c}}{CZ}, \tag{10}\]  
where \(CS_{c}\) is the size of the cached contents, \(L\) represents the amount of cached content \(c\) within unit time, and \(CZ\) represents the cache capacity of the satellite node \(i\). Definition 2: The cache replacement rate is given by:  
\[RR=\frac{\sum_{c=1}^{L}RS_{c}}{CZ}, \tag{11}\]  
where \(RS_{c}\) is the replaced content size, \(\overline{L}\) represents how many replaced content \(c\) within unit time. The replacement rate is used to define the operating state of the satellite nodes' cache capacity during the full load phase. If the network is in a stable status and the cache space of some satellite nodes is occupied, the cache replacement rate can describe the load and cache status of the satellite nodes effectively, which reflects the timeliness of different contents at the satellite nodes [58]. Content popularity goes through a dynamic process of rising, peaking, and finally decaying in popularity [46]. Content popularity is also affected by location and request rate [46]. Thus, even with the same content, the popularity may not be the same on different satellite nodes. In terms of content dimension, the temporal relevance and spatial correlation of popularity are discussed here. In terms of temporal relevance, popularity describes the dynamic trend in the number of content requests. From a spatial association perspective, viscosity is adopted to define matching relationships between the content of different popularity and satellite nodes at different locations. Now, we give the definitions of the content popularity, the content request weight, and the cache viscosity. Definition 3: The content popularity is given by:  
\[CP=\frac{RN}{\sum_{c=1}^{L}TR_{c}}, \tag{12}\]  
where \(RN\) is how much content \(c\) requests within unit time according to the PIT table, \(L\) represents how much content \(c\), and \(\sum_{c=1}^{L}TR_{c}\) represents the total number of requests in the satellite node \(i\) within a unit of time. Definition 4: The content request weight is given by:  
\[RW=\log\frac{\mathbb{N}}{\mathbb{M}^{\prime}}, \tag{13}\]  
where \(\mathbb{M}\) represents how many satellite nodes send the requested content \(c\), and \(\mathbb{N}\) indicates the total number of satellite nodes. \(\log\mathbb{N}/\mathbb{M}\) represents a global factor of all satellite nodes and performs the relative importance of requested content \(c\) to all satellite nodes, without considering any specificsatellite nodes. The value becomes smaller when more satellite nodes send the same content, meaning that there is less correlation between the request and the satellite nodes. RW is proportional to the popularity of the content on the satellite nodes and inversely proportional to the number of requesting satellite nodes in the whole network._  
The matching relationship value checks whether the content \(c\) matches the satellite node \(i\) and is defined as follows:  
**Definition 5**.