# Distributed Satellite Relay Cooperative Communication with Optimized Signal Space Dimension
## 1 Introduction  
With the development of new high-resolution remote sensors that need to deal with massive amounts of information, requirements for the data transmission rate of new earth observation satellites, data relay satellites and space communication network nodes are becoming higher and higher [1; 2; 3; 4; 5]. When remote sensing satellites conduct observations and communications, due to the long transmission distance of electromagnetic waves, it is inevitable that large deep space free space losses will occur due to factors such as space radiation, solar wind and corona. Insufficient observational resources and limited capacity are one of the main factors affecting the acquisition of remote sensing satellite images. In order to improve the image acquisition capability and timeliness of remote sensing satellites, high-orbit satellites are used for data relay to increase spectral efficiency and transmission reliability. At present, there are more and more networked satellite projects either in orbit or planned for launch in the field of remote sensing, and the scale is getting bigger and bigger. In order to meet the fundamental requirements of satellite nodes, it is necessary to build a more intelligent constellation system. Space-based networks are an important part of intelligent constellations. They have a unique location advantage and can provide continuous service with seamless coverage around the world. Space information transmission based on satellite cooperation has the advantages of long communication distance, large capacity, and flexibility. However, large delay and high bit error rate (BER) make the space information transmission based on satellite cooperation less reliable. This has become the key problem that needs to be solved in space communication. In view of these problems, most of the existing research has used the traditional relay cooperation methods of Amplify and Forward (AF) andDecode and Forward (DF). For near-earth satellite communication networks, [6] selected the relay node whose received signal-to-noise ratio is higher than the set threshold as cooperative relay, and gave the interrupt probability expression and system performance simulation results under AF and DF cooperation modes respectively. Based on DF cooperative satellite communication, [7] adopted the maximum ratio combining (MRC) and selective diversity combining (SDC) methods with the objective of minimizing outage probability. Reference [8], based on AF cooperative satellite communication, transmitted the received source satellite signal to the ground destination node with multiple antennas through beamforming vector amplification. The destination node adopted MRC method to receive signals. The average symbol error rate under different modulation modes and different antenna numbers was simulated and analyzed. Network coding technology was used in the scenario of multi-beam satellite cooperative communication and the minimum transmission time was obtained by comprehensively considering the load per beam and channel conditions [9; 10; 11]. The results show that the system throughput has been greatly improved after the introduction of network coding. In the future, the space earth cooperative communication network will include not only satellite nodes in the traditional space segment, but also high-altitude platforms (HAPs), unmanned aerial vehicles (UAVs) and other space nodes in the adjacent space. This is a complex communication network with wide coverage, large capacity, strong time-variances and is multi-level. At present, the existing satellite network topology control strategies can be divided into three categories, the first of which is virtual node policy [12]. The basic idea of this is to use the concept of satellite logical location to form a virtual network covering the whole world. Each node in the network is a virtual node, which is served by the nearest satellite. This strategy regards the satellite network as a fixed topology to shield the movement of satellites.