Six-dimensional movable antenna (6DMA) is an effective approach to improve wireless network capacity by adjusting the 3D positions and 3D rotations of distributed antenna surfaces based on the users' spatial distribution and statistical channel information. Although continuously positioning/rotating 6DMA surfaces can achieve the greatest flexibility and thus the highest capacity improvement, it is difficult to implement due to the discrete movement constraints of practical stepper motors. Thus, in this paper, we consider a 6DMA-aided base station (BS) with only a finite number of possible discrete positions and rotations for the 6DMA surfaces. We aim to maximize the average network capacity for random numbers of users at random locations by jointly optimizing the 3D positions and 3D rotations of multiple 6DMA surfaces at the BS subject to discrete movement constraints. In particular, we consider the practical cases with and without statistical channel knowledge of the users, and propose corresponding offline and online optimization algorithms, by leveraging the Monte Carlo and conditional sample mean (CSM) methods, respectively. Simulation results verify the effectiveness of our proposed offline and online algorithms for discrete position/rotation optimization of 6DMA surfaces as compared to various benchmark schemes with fixed-position antennas (FPAs) and 6DMAs with limited movability. It is shown that 6DMA-BS can significantly enhance wireless network capacity, even under discrete position/rotation constraints, by exploiting the spatial distribution characteristics of the users.

翻译：六维可移动天线（6DMA）是一种通过根据用户空间分布和统计信道信息调整分布式天线面的三维位置与三维旋转，从而提升无线网络容量的有效方法。尽管连续定位/旋转6DMA面可实现最大灵活性从而获得最高容量增益，但由于实际步进电机的离散运动约束，该方案实现困难。为此，本文考虑仅在有限离散位置和旋转状态下工作的6DMA辅助基站（BS），旨在通过联合优化基站处多个6DMA面的三维位置与三维旋转（受离散运动约束），最大化随机位置随机数量用户的平均网络容量。特别地，我们分别考虑用户统计信道信息已知与未知的两种实际场景，并利用蒙特卡洛方法和条件样本均值（CSM）方法提出相应的离线与在线优化算法。仿真结果验证了所提出的离散位置/旋转优化算法相较于固定位置天线（FPA）和有限可移动性6DMA等基准方案的性能优势。研究表明，即使面对离散位置/旋转约束，6DMA-BS仍能通过利用用户空间分布特性显著提升无线网络容量。