# Beam-Hopping-Based Resource Allocation in Integrated Satellite-Terrestrial Networks
## 2 System Model
### Spectrum Sharing Scheme in Istn  
As mentioned in Section 1, EZ-based spectrum sharing schemes have been widely used to limit the CCI and ensure the isolation between satellite beams and terrestrial BSs in the ISTN. However, the conventional static EZ is inapplicable to the low Earth orbit (LEO) or medium Earth orbit (MEO) satellite systems with high mobility, and the oversized EZ may reduce the available resources of the terrestrial systems and degrade the spectrum efficiency [10].  
Considering the high flexibility of BH technology, dynamical protection zones can be constructed to avoid inter-system CCI and improve the reusability of the frequency resources. In each time slot, protection zones are only constructed around the satellite terminals served by the spot beams. Except for these served satellite terminals, the satellite terminals do not need to be protected since they will not receive the downlink signals from the satellite in this time slot. This means that the protection zones change dynamically in different time slots, and the terrestrial BSs that can perform transmission also change accordingly.  
Define \(d_{pro}^{st}\) as the inter-system protection distance between the satellite terminal and the terrestrial BS working in the same time slot. Assuming that the \(i\)-th satellite terminal (\(i\in\mathcal{N}_{sat}\)) is served by the satellite system in the time slot \(t\in\Gamma\), the terrestrial BS in the \(j\)-th terrestrial system (\(j\in\mathcal{N}_{ter}\)) cannot perform transmission if it is located in the protection zone of the \(i\)-th satellite terminal, i.e., the distance \(d_{i,j}^{st}\) between the \(j\)-th terrestrial BS and the \(i\)-th satellite terminal is less than \(d_{pro}^{st}\). From another perspective, if the \(j\)-th terrestrial BS is allowed to perform transmission in the time slot \(t\), there is no served satellite terminal within a distance of \(d_{pro}^{st}\) around the terrestrial BS. To avoid inter-system CCI, the size of the EZ is generally larger than the size of the satellite beam [10]. Therefore, the minimum protection distance in the BH-based spectrum sharing scheme should be the coverage radius of the spot beam corresponding to the 3 dB beam width.  
Corresponding to the BH-based spectrum sharing scheme, the procedure for resource allocation in the ISTN can be described as follows.  
First, the NCC collects the locations and the transmission capacity requirements of all the satellite terminals and terrestrial BSs. To ensure security, the accuracy of the location information and the capacity requirements can be properly reduced through the fuzzification process, and the security mechanisms and encryption schemes can be adopted to achieve secure transmission.  
Based on the acquired information, the NCC allocates the time slots in a BH time window to the satellite terminals and the terrestrial BSs according to the capacity requirements. Let \(x_{i,t}\in\{0,1\}\) and \(y_{j,t}\in\{0,1\}\) indicate whether the time slot \(t\in\Gamma\) is allocated to the \(i\)-th satellite terminal (\(i\in\mathcal{N}_{sat}\)) and the \(j\)-th terrestrial BS (\(j\in\mathcal{N}_{ter}\)), respectively. If the time slot \(t\) is allocated to both the \(i\)-th satellite terminal and the \(j\)-th terrestrial BS, i.e., \(x_{i,t}=y_{j,t}=1\), the distance \(d_{i,j}^{st}\) between them should be larger than or equal to \(d_{pro}^{st}\).  
Then, the resource allocation results are transmitted to the satellite and the terrestrial BSs. Specifically, the resource allocation results for the satellite system indicate the satellite terminals served by the spot beams in each time slot, while the results for each terrestrial system indicate the time slots allowed for transmission in a BH time window.  
After receiving the resource allocation results, the satellite provides services to the corresponding satellite terminals in each time slot, and the terrestrial BSs perform the downlink transmission in the allocated time slots.