## 2 Signal Model  
In view of the increasing number of non-geostationary satellite orbit (NGSO) constellation systems in the current space, there are more and more satellite networks with the same frequency band and adjacent orbits in use. The problem of co-frequency interference between NGSO constellation systems and between NGSO constellation systems and traditional geostationary satellite orbit (GSO) constellation systems is becoming increasingly serious. According to the transmission channel information of the satellite network, the precoding matrix of the transmitter matching characteristic channel is designed using the interference coordination technology in wireless communication. This is one of the important means to alleviate the problem of co-frequency interference in low earth orbit satellite networks. According to the different types of new services, intelligent satellite networks can consider two different types of messages in multichannel relay channels: unicast and multicast messages. Unicast messages are used for dedicated users, which means that all other users treat this unicast message as an interference signal. On the other hand, a multicast message is used for a group of users, and it is received by all other users of the group. The unicast information sent by users to specific users is defined as a private signal, and the multicast information sent by users to specific groups is defined as a common signal. Each user tries to send both unicast (private) signals and multicast (common) signals to the other users in the multiple access channel (MAC) phase and decodes both of the signals in the broadcast channel (BC) phase. Figure 1 shows the intelligent satellite network transmission model. The channel model includes \(K\) user nodes and a relay node, where each user node is equipped with \(M\) antennas and the relay node is equipped with \(N\) antennas. Assume that all nodes are in half duplex mode, and complete channel statement information (CSI) can be obtained. There is no direct link between different user nodes, and each user node sends a unicast message to the other \(K-1\) user nodes through the relay node. That is, each user sends information to two other users using the relay node. In the multiple access channel, the user node adopts interference alignment technology. In the broadcast  
Figure 1: Intelligent constellation multi-source information collaboration. channel, the relay node uses interference cancellation beamforming technology based on analog network coding to broadcast information to each user through Amplify Forward (AF). Reference [40] proved that the maximum degrees of freedom (DoF) of a MIMO-Y channel is \(K(K-1)\) when the number of antennas \(M_{i}(i\in\{1,\cdots,K\})\) of user node \(i\) and the number of antennas \(N\) of a relay node satisfy \(M_{i}\geq K-1\), \(N\geq K(K-1)/2\) and \(N<\min\{M_{i}+M_{j},\forall i\
eq j\}\) conditions. In the MAC phase, user \(i\) sends two independent signals \(s^{[j,i]},j\
eq i\in\{1,2,3\}\) to the other two users. In order to eliminate the interference between co-channel users, the precoding vector \(\mathbf{v}^{[j,i]}\) is designed by using interference alignment. Assume that the elements satisfy the complex Gaussian independent identically distributed matrices \(\mathbf{A}_{1}\) and \(\mathbf{A}_{2}\), whose size is \(N\times M\). Judging whether there is intersection subspace in the space stretched by two matrix column vectors is the precondition of precoding design to realize the alignment of interactive signals to the same signal dimension.