## 4 Application Trends  
### Analysis and Prediction of Frequency-Usage Behavior Based on Spectrum Knowledge Graph  
The long propagation distance and high propagation delay between the satellites and the ground results in the lagging of spectrum sensing results. Facing the demand for resource control of LEO constellations, the issue of obtaining the future spectrum \"state\" and \"posture\" in advance must be considered sufficiently. Spectrum knowledge graph has the capability of knowledge reasoning [27]. It makes it possible to bypass drawn-out searches and focus on the ideal answer for prompt decision-making. Therefore, the prediction of frequency-usage behavior can be achieved with the help of the spectrum knowledge graph. By mining the evolutionary characteristics of spectrum resources, the frequency behavior of frequency-usage devices could be analyzed so as to reason about the possible frequency-usage posture at future moments. However, there are numerous N-to-1 relationships in the spectrum knowledge graph, which makes calculating directly less effective. Knowledge representation learning can be applied to achieve the prediction of spectrum posture. In this approach, the entities and relationships in the spectrum knowledge graph are mapped to the continuous vector space through the training model [28], which can enhance the efficiency of data processing and computing. As shown in Figure 8, in the case of frequency prediction, the information of the 2 nd January has been aggregated into the spectrum knowledge graph in the form of triples, such as (\(\mathrm{q_{m,n}}\), Bandwidths, 703.12), (\(\mathrm{q_{m,n}}\), Timels, 02/01), (\(\mathrm{q_{m,n}}\), FrequencyIs, \(\mathrm{f_{2}}\)), (\(\mathrm{q_{m,n}}\), BelongTo, A), etc. The knowledge of the 7 th of January can be modelled as the partial triples such as (\(\mathrm{q_{ij}}\), Timels, 07/01), (\(\mathrm{q_{ij}}\), BelongTo, A), (\(\mathrm{q_{ij}}\), FrequencyIs,? ), etc. Figure 7: The local detail of spectrum knowledge graph. (**a**) The knowledge of spectrum sensing domain. (**b**) The knowledge of LEO satellite domain. Considering the complexity and variability of the electromagnetic environment and the high dynamics of satellites, it is necessary to use the model with a simple structure and computational efficiency for spectrum posture prediction. The TransR [29] model can be deployed to achieve the prediction of spectrum posture. The principle of TransR model is shown in Figure 9. In the TransR model, for each triple \(\{\mathrm{H},\mathrm{R},\mathrm{A}\}\), the entity embedding is set to \(\mathrm{H},\mathrm{A}\in\mathrm{R}^{\mathrm{k}}\) and the relationship embedding is set to \(\mathrm{R}\in\mathrm{R}^{\mathrm{d}}\). Note that the dimensions of entity embedding and relationship embedding are not necessarily the same, i.e., \(\mathrm{k}\
eq\mathrm{d}\). For each relationship \(\mathrm{R}\), a projection matrix \(\mathrm{M}_{\mathrm{r}}\in\mathrm{R}^{\mathrm{k}\times\mathrm{d}}\) is set up, which projects entities from the entity space to the relationship space. Using the projection matrix, the projection vector of the entity can be defined as:  
\[\mathrm{H}_{\mathrm{r}}=\mathrm{HM}_{\mathrm{r}} \tag{1}\]  
\[\mathrm{A}_{\mathrm{r}}=\mathrm{AM}_{\mathrm{r}} \tag{2}\]  
That is, for a triple \(\{\mathrm{H},\mathrm{R},\mathrm{A}\}\), it needs to be satisfied:  
\[\mathrm{d}(\mathrm{H},\mathrm{R},\mathrm{A})=\Bigl{|}\Bigl{|}\mathrm{H}_{ \mathrm{r}}+\mathrm{R}-\mathrm{A}_{\mathrm{r}}\Bigr{|}\Bigr{|}_{2}^{2}=\Bigl{|} \Bigl{|}\mathrm{HM}_{\mathrm{r}}+\mathrm{R}-\mathrm{AM}_{\mathrm{r}}\Bigr{|} \Bigr{|}_{2}^{2}\approx 0 \tag{3}\]  
Then, the spectrum posture prediction problem is transformed into the link prediction problem of the triple \((\mathrm{q}_{ij},\) FrequencyIs,?). All entities under the corresponding category are used as candidates to compute the score function, and the one with the highest score is determined as the predicted result.