## 3 A Collaborative Multi-Satellite Selection Algorithm Based on Maximum SINR  
In this section, we design a collaborative multi-satellite selection algorithm based on the maximum SINR to facilitate the gateway station to find the right satellites when collaborating on collided packets.  
In the actual ultra-dense IoT network using RA protocol, uplink packet collision and retransmission lead to channel congestion, which limits the overall capacity of the system. When network traffic surges, lots of packets are transmitted at the same time, resulting in a collision between packets due to contention for channel resources. Collisions cause packet information to be lost, and the packet loss ratio (PLR) will increase as a result. In RA protocols, because of automatic repeat requests (ARQ), lost packets will be retransmitted within a certain period of time. If the channel is still under-resourced, the retransmitted packets will add to the congestion in the network. In addition, in some RA protocols that send copies, the lost packets will be retransmitted at multiplier levels, leading to an avalanche of degradation in system performance. Therefore, a collaborative approach to eliminating collision between packets in LEO satellite IoT is necessary. Although from an end-to-end performance perspective, full-node participation in collaboration is an optimal strategy. But in the actual collaboration process, adding satellite nodes with poor parameters to the collaboration will cause both instability in the processed SINR and additionally does not meet the low-power IoT foundation requirements. Therefore, inspired by the cluster selection scheme based on large-scale fading in the literature [22], this paper designed a multi-satellite selection collaboration algorithm based on maximum SINR to reduce system complexity and overall processing power consumption.  
To better illustrate the proposed scheme, consider a scenario, as shown in Figure 2, where the scenario consists of IoT terminals 1-3 and LEO satellites A-G. The terminal simultaneously sends packets PK1-3 to LEO satellites, assuming that PK2 and PK3 collide in all LEO satellites. The satellite is responsible for receiving and forwarding packet signals to the gateway station. At the gateway station, if a packet collision is detected in the forwarding signal of one satellite node, it searches for copies in other satellites with the same form of collision. Therefore, since the collision of PK2 packets is detected in satellite A-G, they can participate in processing as collaborative nodes. However, because of the difference in channel parameters, the collaboration of some nodes may reduce the processing gain. At this point, appropriate satellite collaboration nodes A and B can be obtained by algorithm from the forwarded signals of multiple collaborative satellites according to the satellite selection strategy. Subsequently, a distributed beamforming operation is performed between the selected nodes. The corresponding received signals in the nodes are multiplied by the optimal beamforming weights, which can make a power difference between two packet signals where the collision occurs. According to the idea of packet demodulation in the power domain in non-orthogonal multiple access (NOMA), if there is a large enough power difference between collided packets, then packets can be eliminated from collision and demodulated separately.  
Figure 2: Multi-satellite selection algorithm application diagram.