The availability of satellite communication systems is extremely limited by atmospheric impairments, such as rain (for radio frequencies) and cloud coverage (for optical frequencies). A solution to this problem is the site diversity technique, where a network of geographically distributed ground stations (GSs) can ensure, with high probability, that at least one GS is available for connection to the satellite at each time period. However, the installation of redundant GSs induces unnecessary additional costs for the network operator. In this context, we study an optimization problem that minimizes the number of required GSs, subject to availability constraints. First, the problem is transformed into a binary-integer-linear-programming (BILP) problem, which is proven to be NP-hard. Subsequently, we design a branch-and-bound (B&B) algorithm, with global-optimization guarantee, based on the linear-programming (LP) relaxation and a greedy method as well. Finally, numerical results show that the proposed algorithm significantly outperforms state-of-the-art methods, and has low complexity in the average case.

中文翻译：

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具有站点多样性的卫星系统地面站的全局优化选择

卫星通信系统的可用性受到大气损害的极大限制，例如雨（无线电频率）和云覆盖（光频率）。该问题的一种解决方案是站点分集技术，其中地理分布的地面站 (GS) 网络可以确保在每个时间段内至少有一个 GS 可用于连接到卫星。然而，冗余 GS 的安装会给网络运营商带来不必要的额外成本。在这种情况下，我们研究了一个优化问题，该问题在可用性约束下最小化所需 GS 的数量。首先，将问题转化为二进制整数线性规划 (BILP) 问题，该问题已被证明是 NP 难的。随后，我们设计了一个分支定界（B&B）算法，具有全局优化保证，基于线性规划（LP）松弛和贪婪方法。最后，数值结果表明，所提出的算法明显优于最先进的方法，并且在平均情况下具有低复杂度。