Low Earth orbit (LEO) satellites has brought about significant improvements in wireless communications, characterized by low latency and reduced transmission loss compared to geostationary orbit (GSO) satellites. Ultra-dense LEO satellites can serve many users by generating active beams effective to their locations. The beam placement problem is challenging but important for efficiently allocating resources with a large number of users. This paper formulates and solves a fast beam placement optimization problem for ultra-dense satellite systems to enhance the link budget with a minimum number of active beams (NABs). To achieve this goal and balance load among beams within polynomial time, we propose two algorithms for large user groups exploiting the modified K-means clustering and the graph theory. Numerical results illustrate the effectiveness of the proposals in terms of the statistical channel gain-to-noise ratio and computation time over state-of-the-art benchmarks.

翻译：与地球静止轨道（GSO）卫星相比，低地球轨道（LEO）卫星凭借其低延迟和低传输损耗的特点，为无线通信带来了显著提升。超密集的LEO卫星可通过向用户位置生成有效波束来服务大量用户。波束部署问题在存在海量用户时对高效分配资源至关重要且极具挑战性。本文针对超密集卫星系统，构建并求解了一个快速波束部署优化问题，旨在以最少的活跃波束数量（NABs）提升链路预算。为实现这一目标并在多项式时间内平衡波束间负载，我们针对大规模用户群提出了两种算法，分别利用了改进的K-means聚类和图论方法。数值仿真结果表明，相较于现有先进基准方法，所提方案在统计信道增益噪声比和计算时间方面均表现出优越性能。