# Dynamic Divide Grouping Non-Orthogonal Multiple Access in Terrestrial-Satellite Integrated Network
## 3 System Modeling  
### System Model  
The NOMA model of the terrestrial-satellite integrated network is shown in Figure 1, in which BSs and one satellite serve the ground users cooperatively. The low Earth orbit (LEO) satellite is consisted of \(L\) beam, and each beam is equipped with \(M\) antennas. Each BS is equipped with \(N\) antennas for uplink transmission and can serve users within its coverage radius. In this scenario, we consider that the \(I\) BSs distribute within the coverage of the satellite, and each user can be served either by the corresponding BS or by the satellite. All nodes in the proposed model are also assumed to equip with a single antenna for simplicity. In the TSINs, the NOMA scheme is implemented for multiuser transmission, which can simultaneously serve multiple users with distinct channel conditions reusing the entire bandwidth. As the complexity of multi-user signal detection in NOMA system increases rapidly with the increase of the number of users, and the total system capacity decreases with the increase of the number of users [15], considering both the system load and implementation complexity, the single carrier time-frequency resources are reused for two users to perform NOMA. In the uplink, inter-cell interference comes from all the users in other cells sharing the same subband, as shown in Figure 1. When modeling inter-cell interference, we assume the system is fully loaded and all the cells perform a 2-user uplink NOMA with the same power control scheme. According to the dynamic user pairing scheme, the locations of two users that form a NOMA group in each cell are selected among UEs associated to that cell. For instance, there are \(N\) users in a single cell and we can select two out of N users in this cell to form a NOMA group on the sub-band under consideration. One of these two users is treated as U1, and the other one is treated as \(U2\). The locations of uses in each cell follows the homogeneous Poisson point process with a intensity \(\lambda_{u}\)[39]. In the uplink, a receiver BS or satellite normally has much more capable hardware and advanced algorithms than a UE, so a perfect SIC is assumed at BSs or satellites. Considering that the total power limit can effectively manage inter-group interference, the total power limit of satellite user group \(J\) is \(P_{S,IJ}\), the power control factor of near user and far user in group \(J\) is \(\rho_{S,IJ}^{(1)}\) and \(\rho_{S,IJ}^{(2)}\), respectively, \(\rho_{S,IJ}^{(1)}+\rho_{S,IJ}^{(2)}=1\). The bandwidth allocated each group \(J\) of satellite is \(r_{s,IJ}\), and the channel gain between two satellite users (near user and far user) within group \(J\) is represented as \(H_{S,IJ}^{(1)}\) and \(H_{S,IJ}^{(2)}\), \(H_{S,IJ}^{(1)}>H_{S,IJ}^{(2)}\), respectively. Similarly, the bandwidth allocated each group \(J\) in the BS user is defined as \(r_{B,i,J}\), \(H_{B,i,J}^{(1)}\) and \(H_{B,i,J}^{(2)}\) represent channel gain between two BS users in group \(J\), respectively, \(H_{B,i,J}^{(1)}>H_{B,i,J}^{(2)}\). \(P_{B,i,J}\) denotes the total power limit of BS user group, the power control factor of BS near user and far user is \(\rho_{B,i,J}^{(1)}\) and \(\rho_{B,i,J}^{(2)}\), \(\rho_{B,i,J}^{(1)}+\rho_{B,i,J}^{(2)}=1\). \(n\) is the additive white Gaussian noise, which obeys the power spectral density \(N_{0}\). Generally, in current communication networks, BS-based terrestrial communication is more efficient and cheaper than the satellite communication. Thus, in the TSINs, we prefer to maximize the utilization of the BSs, and the satellite will act as the complement to provide service for these users that cannot be served by the BSs. By means of beamforming and NOMA, each BS can provide service for \(2N\) users within its coverage radius, including N near users and N far users. We assume that the total number of users is \(2N+k_{i}\), \(i=\{1,2...,I\}\), where \(2N\) users are connected to BS, \(k_{i}(k_{i}\leq 2M)\) users will access satellite in this paper.