# Distributed Satellite Relay Cooperative Communication with Optimized Signal Space Dimension
## 1 Introduction
Secondly, there is the coverage division method [13]. The basic idea is to divide the earth's surface into several cells at equal intervals. Due to the rotation of the earth and the movement of satellites, each satellite adopting this strategy needs to update the topology information of the network. Before transmitting data, the source satellite needs to calculate the corresponding destination satellite according to the geographical coordinates of the destination node. Finally, there is virtual topology policy [14; 15; 16; 17; 18]. The basic idea is to divide a system cycle into several time slices with the change of inter satellite link occurring only at the end time point of each time slice. The future space communication network has the inherent characteristics of complex structure, dynamic topology and unstable transmission quality. The first classification of satellite network topology control strategy faces the problems of long delay, high bit error rate and low connectivity of spatial information transmission. A reliable and effective spatial information cooperative transmission and routing scheme should be designed and proposed. Space interference is one of the main modes of cooperative communication interference among satellite nodes. Space interference mainly includes near-satellite interference and adjacent channel interference. With the rapid development of satellite communication, there are more and more synchronous orbit satellites. Satellite spacing has been reduced from about five degrees to about two and a half degrees now, which will inevitably lead to near satellite interference. The disturbed signal exceeds the coverage of the original signal and is easy to be doped with the signals of its near satellites. This leads to a sharp decline in the performance of the transmission signal [19; 20; 21; 22]. Adjacent channel interference is mainly caused by the overlap between the node carrier frequency allocation and the frequency bands of adjacent signal when there is not enough protection bandwidth. Alternatively, it may happen when the carrier spectrum characteristics of satellite nodes do not meet requirements, resulting in high noise bottom or sidelobe [23; 24; 25]. With the propagation characteristics of electromagnetic waves, satellite cooperative nodes share limited spectrum resources. Since wireless electromagnetic waves are omnidirectional broadcast transmissions, signals transmitted at the same time in the same frequency band will inevitably produce common channel interference (CCI). Although CCIis not a new concept, the characteristics of CCI in a multiple input multiple output (MIMO) environment are different from those of traditional single input single output (SISO). MIMO not only provides spatial degrees of freedom (DoF), but also greatly increases the difficulty and complexity of anti-jamming algorithms. The reception and demodulation of the satellite cooperative node is essentially to decompose the superimposed signal and design a signal structure that can be encoded at the physical layer. Designing the key method is important to realize cooperative transmission. The interference in the satellite cooperative network has a unified transmission system and a unified performance evaluation system, so it can share resources and cooperate with each other in the physical layer. Using the unique broadcast characteristics of wireless communication and the superposition of signal electromagnetic waves, physical layer network coding can multiply the throughput of wireless relay networks without requiring additional resources. This paper studies the theory and method of interference utilization based on physical layer network coding. The signals of different nodes are superimposed over the air. Self-interference cancellation is performed at the receiving node to improve spectrum utilization. The main contributions of this paper are as follows:  
1. Joint design of signal spatial structure optimization and superposition signal separation method.