## 3 A Collaborative Multi-Satellite Selection Algorithm Based on Maximum SINR
### Proposed Satellite Selection Strategy
Therefore, after the packet has been demodulated, the location of copies can be found from the demodulated information. Figure 4: Basic flowchart of the SC-ACRDA scheme. (2) Packet reconstruction: Once the location of the copies is obtained, the packet in time domain can be reconstructed directly at the corresponding location of copies using the bit information of the already demodulated packet. For copies in the spatial domain in other signals, the gateway station performs an autocorrelation check of the RM sequence. If a correlation peak appears after the autocorrelation, the packet can be reconstructed at the location of the correlation peak. The packet reconstruction will eliminate the effect of the packet at the corresponding location. (3) Iterative interference cancellation: When a packet copy is eliminated, new collision-free packets may be generated, so another round of iterations is performed to eliminate more packets until the maximum number of iterations. B. If the packet collided:

(1) User detection and channel estimation based on RM sequences: For collision packets, due to the nested structure of the subsequences of second-order RM sequences, the matrix-vector pairs and CSI estimates of the collided packets can also be obtained by iterative RM sequence detection algorithms. CSI estimates can be further processed by LS channel estimators to obtain more accurate CSI. The matrix-vector pairs correspond one-to-one with the user information and can be used to determine whether the packet is a spatial domain copy. (2) A collaborative multi-satellite selection algorithm based on maximum SINR: Once the packet signal identity information is obtained, the gateway station searches for the node where the packet collision occurred based on the identity information. All nodes obtained by searching can be collaborative node sets. The iterative binary search algorithm is performed on the set of collaborative nodes to obtain the optimal parameter \(\gamma\). By substituting the optimal parameter \(\gamma\) into the proposed satellite selection algorithm, the optimal weight vector **W** can be obtained. The specific algorithm is given in Section 3. The corresponding node of the non-zero component of **W** is the set of optimal collaborative nodes. By using the optimal collaborative node set for distributed beamforming, the power difference can be generated between the collided packets. If the power difference is greater than the set threshold, the packet can be demodulated successfully. The processing process after successfully demodulating is the same as that of uncollided packets. To better illustrate the processing of packets, we give an example here. As shown in Figure 5, it is assumed that the gateway station receives four forwarding signals from satellites A-D. For these forward signals, since none of the first packets PK1 collided, they can be demodulated directly when processed. Moreover, subsequent copies of PK1 are eliminated as the preamble of PK1 contains the offset of its copy. After (1) processing, only collided PK2 and PK3 remain in the forwarding signal. Since collisions also occur between copies of PK2 and PK3, these packets are deadlocked and cannot be processed according to the ACRDA demodulation strategy. As the preamble of PK2 in the forwarding signal can all be detected, the packet can be identified as PK2 based on the RM sequence characteristics. Satellites A-D all contain collided PK2, so they can be used as collaborative nodes for satellite selection. The (2) processing is satellite selection and distributed beamforming. It is assumed that satellites A and B are the optimal collaborative set after selection, and packets meet the demodulation threshold after distributed beamforming. Therefore, PK2, PK3 and their copies will be able to be demodulated after (2) processing. The (3) processing is the reconstruction of the packet and the elimination of copies.