This paper considers a downlink satellite communication system where a satellite cluster, i.e., a satellite swarm consisting of one leader and multiple follower satellites, serves a ground terminal. The satellites in the cluster form either a linear or circular formation moving in a group and cooperatively send their signals by maximum ratio transmission precoding. We first conduct a coordinate transformation to effectively capture the relative positions of satellites in the cluster. Next, we derive an exact expression for the orbital configuration-dependent outage probability under the Nakagami fading by using the distribution of the sum of independent Gamma random variables. In addition, we obtain a simpler approximated expression for the outage probability with the help of second-order moment-matching. We also analyze asymptotic behavior in the high signal-to-noise ratio regime and the diversity order of the outage performance. Finally, we verify the analytical results through Monte Carlo simulations. Our analytical results provide the performance of satellite cluster-based communication systems based on specific orbital configurations, which can be used to design reliable satellite clusters in terms of cluster size, formation, and orbits.

翻译：本文研究了一种下行卫星通信系统，其中卫星簇（即由一个主卫星和多个从卫星组成的卫星群）服务于一个地面终端。簇内卫星形成直线或圆形编队集体移动，并通过最大比传输预编码协同发送信号。我们首先进行坐标变换以有效捕捉簇内卫星的相对位置。接着，利用独立伽马随机变量之和的分布，推导出Nakagami衰落条件下基于轨道构型的中断概率精确表达式。此外，借助二阶矩匹配方法，获得了中断概率的简化近似表达式。我们还分析了高信噪比条件下的渐近行为及中断性能的分集阶数。最后，通过蒙特卡洛仿真验证了分析结果。我们的分析结果提供了基于特定轨道构型的卫星簇通信系统性能，可用于从簇规模、编队和轨道方面设计可靠的卫星簇。