In this paper, we present a novel hemispherical antenna array (HAA) designed for high-altitude platform stations (HAPS). A significant limitation of traditional rectangular antenna arrays for HAPS is that their antenna elements are oriented downward, resulting in low gains for distant users. Cylindrical antenna arrays were introduced to mitigate this drawback; however, their antenna elements face the horizon leading to suboptimal gains for users located beneath the HAPS. To address these challenges, in this study, we introduce our HAA. An HAA's antenna elements are strategically distributed across the surface of a hemisphere to ensure that each user is directly aligned with specific antenna elements. To maximize users minimum signal-to-interference-plus-noise ratio (SINR), we formulate an optimization problem. After performing analog beamforming, we introduce an antenna selection algorithm and show that this method achieves optimality when a substantial number of antenna elements are selected for each user. Additionally, we employ the bisection method to determine the optimal power allocation for each user. Our simulation results convincingly demonstrate that the proposed HAA outperforms the conventional arrays, and provides uniform rates across the entire coverage area. With a $20~\mathrm{MHz}$ communication bandwidth, and a $50~\mathrm{dBm}$ total power, the proposed approach reaches sum rates of $14~\mathrm{Gbps}$.

翻译：本文提出了一种专为高空平台站设计的新型半球形天线阵列。传统矩形天线阵列用于高空平台站时存在一个显著缺陷：其天线单元朝下定向，导致对远端用户的增益较低。圆柱形天线阵列的引入旨在缓解此问题，但其天线单元朝向地平线方向，导致位于高空平台站正下方的用户增益欠佳。为应对这些挑战，本研究引入了我们提出的半球形天线阵列。该阵列的天线单元策略性地分布在半球表面，以确保每个用户都能与特定的天线单元直接对准。为最大化用户的最小信干噪比，我们构建了一个优化问题。在完成模拟波束成形后，我们提出了一种天线选择算法，并证明当为每个用户选择大量天线单元时，该方法能达到最优性能。此外，我们采用二分法来确定每个用户的最优功率分配。仿真结果有力地表明，所提出的半球形天线阵列优于传统阵列，并在整个覆盖区域内提供均匀的速率。在通信带宽为$20~\mathrm{MHz}$、总功率为$50~\mathrm{dBm}$的条件下，所提方法的总速率可达$14~\mathrm{Gbps}$。