## 3 A Collaborative Multi-Satellite Selection Algorithm Based on Maximum SINR
### Proposed Satellite Selection Strategy
 \tag{24}\]

Furthermore, for RA protocols, the throughput \(T(G)\) under a particular load \(G\) is directly related to PLR \(PLR^{Niter}(G,N_{cp},N_{sl})\). The algorithm proposed in this paper consists of iterations and binary search, with a time complexity of approximately O(nlog\({}_{2}\)n). Therefore, the throughput of this scheme can be expressed as follows:

\[T(G)=G\cdot(1-PLR^{Niter}(G,N_{cp},N_{sl})) \tag{25}\]

## 5 Simulation and Analysis

In this section, we simulate the performance of the proposed multi-satellite selection algorithm based on maximum SINR and the performance of the SC-ACRDA scheme using this algorithm. A comparison is also made with the conventional scheme under the same conditions. The simulations are based on the Matlab platform and take the Monte-Carlo approach. In addition, the platform used in the experiment is AMD Ryzen 7 [EMAIL_ADDRESS] GHz, GPU is RTX 2070S and memory is 16.00 GB. The specific parameters of the simulation are shown in Table 1:

### Performance of Multi-Satellite Selection Algorithm Based on Maximum SINR

Figure 6 compares the SINR performance of the four collaboration scenarios. In Figure 6, the all-node optimal collaboration curve is the theoretical best performance for all forwarded signals selected and processed. The power-constrained random selection curve represents the performance obtained by randomly selecting nodes for beamforming of the forwarded signal under the processing power constraint. The full power random selection curve represents the performance obtained by selecting the maximum processing power \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline LEO constellation & OneWeb \\ Maximum number of visible satellites & 16 \\ Number of transmitting sources & 200 \\ Number of virtual frames & 2 \\ Virtual frame length & 100 slots \\ Packet arrival rate \(\lambda\) & [0.00:0.05:2.00] \\ Channel coding rate \(\rho\) & 1/3 \\ Modulation indices \(M\) & 4 \\ Maximum number of iterations \(N_{iter}\) & 10 \\ Collided packet demodulation threshold & 7 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. for all nodes for the forwarding signal. The light blue diamond curve is the performance curve obtained by beamforming with node selection for this scheme. The graph shows that the proposed scheme improves the SINR of collided packets by a factor of 3-4 compared to the power-constrained random selection scheme. For example, with a node count of 10, the SINR when the proposed scheme is adopted is 12.73 dB, which is 3.25 times higher than the power-constrained random selection scheme with SINR = 3.91 dB. At the same time, a similar performance improvement to the power-constrained random selection scheme can be achieved at a much smaller power consumption compared to the full-power random selection scheme. Therefore, the proposed scheme can improve the SINR of the collided packet signal more effectively and increase the probability of the collided packet meeting the demodulation threshold than the random selection scheme. In addition, the proposed scheme consumes less power in the case of handling power constraints, making it more suitable for ultra-dense network scenarios where low power consumption is the norm. ### Performance of SC-ACRDA

This section simulates and analyses the throughput and PLR curves for SC-ACRDA2 (packets with one-time domain copy), SC-ACRDA3 (packets with two-time domain copies) and other schemes with the corresponding number of copies (for schemes that do not send copies the corresponding number of receivers is increased). Figure 7 shows the throughput comparison of SC-ACRDA2, SC-ACRDA3 and other benchmark schemes. Due to the multi-satellite selection beamforming algorithm, the expected SINR, which cannot reach the demodulation threshold in the original ACRDA scheme is increased. Enables some of these packets to be demodulated. After these packets are demodulated successfully, other packets that collide with the copies can also be demodulated due to the SIC mechanism.