# Analysis of Grating Lobe Effects on GEO DSC Distributed Antennas
## 1 Introduction  
The antenna is the core device of satellite communication payloads, and traditional single antenna transceiver systems face limitations with restricted frequency band resources. Higher antenna performance can only be achieved by increasing the physical aperture, amplifier power limit, or efficiency [1; 2]. In this context, distributed antennas provide higher gain, narrower beamwidths, and lower transmittance costs. In recent years, the rapid development of satellite communication systems has led to increasing demands for the frequency, polarization, and reconfigurability of antenna direction maps [3; 4]. Distributed antennas have emerged as an important way to enhance the performance of satellite antennas by allowing the addition or removal of nodes according to communication needs to achieve antenna reconfigurability [5]. By utilizing spatial dimension resources, distributed antennas can increase transmission reliability and rates without adding bandwidth or transmission power, meeting the demand for high-speed, efficient, and stable satellite communications. Distributed antennas can be dispersed flexibly on different satellite locations to improve signal coverage and communication quality, obtain higher resolution and anti-interference capability, and have good application prospects in satellite communication, navigation, and antenna arrays [6; 7]. Projects such as SpaceX's Starlink, T-Mobile's 5G Multiple Input Multiple Output (MIMO) satellite network, and Intelsat's Enhanced Performance andInteractive Capabilities Next Generation (EpicNG) satellite network have all involved considering equipping with distributed antennas. However, when considering the long distances between satellites, the use of distributed antennas can result in the generation of a significant number of grating lobes after beamforming, leading to a decrease in gain and dispersion of radiated energy. Additionally, due to the involvement of multiple antennas in distributed antenna systems, there are significant difficulties in data processing and combination. Therefore, distributed antenna systems still face technical and practical challenges. To address the issue of long distances between satellites, the concept of DSC has emerged as a promising solution [8; 9]. The typical architecture of the DSC encompasses the F6 (Future, Fast, Flexible, Fractionated, Free-Flying) Program, a space-based group, and GRACE [10]. DSC has revolutionized the traditional approach to using satellites. Instead of relying on large, heavy satellites, DSC uses multiple small, lightweight satellites that are placed in close proximity to each other and independently distributed in GEO or LEO orbits. DSC uses multi-star co-orbital control, high-speed networking, and cooperative processing technologies to integrate various resources to perform specific tasks together and achieve high-capacity, high-speed data network transmission and exchange in space [11]. DSC addresses two major issues in satellite communication. Firstly, DSC can overcome the limited capacity of single satellite platforms and low antenna gain by utilizing multiple small satellites that work together to increase network capacity and improve antenna gain. Secondly, the distance between DSC satellites is much smaller than traditional satellite communication satellites, which can reduce synchronization errors and interference. This helps to mitigate the difficulty of antenna synchronization and signal quality degradation caused by the distance between satellites. As a result, DSC brings a new perspective to the design and application of satellite-based distributed antennas. DSC antennas utilize multi-star coordination to achieve multi-signal collaboration and distributed beamforming, providing high accuracy, performance, and reliability [12]. However, the realization of star-borne distributed antennas will face some difficult problems.