Through adaptive antenna repositioning, the movable antenna (MA) technology enables on-demand reconfiguration of wireless channels, thereby creating an additional spatial degree of freedom in improving communication performance. This paper investigates a multiuser uplink communication system aided by MAs, where a base station (BS) equipped with multiple MAs serves multiple single-antenna users. Specifically, given that an optimized array geometry cannot guarantee rate fairness, we focus on designing antenna trajectory at the BS to maximize the minimum achievable rate among all users over a finite time period. The resulting optimization problem is fundamentally challenging to solve due to the continuous-time nature. To address it, we first examine an ideal case with infinitely fast MA movement and demonstrate that the relaxed problem can be optimally solved via the Lagrangian dual method. The obtained trajectory solution reveals that the BS should employ a finite set of MA deployment patterns, each allocated an optimal time duration. Building on this, we then study the general case with limited MA movement speed and propose a heuristic trajectory design inspired by the optimal patterns identified in the ideal scenario. Several insights are also gained by examining the simplified special case. Finally, numerical results are provided to validate the effectiveness of the proposed designs compared to competitive benchmarks.

翻译：通过自适应的天线重新定位，移动天线（MA）技术能够按需重构无线信道，从而为提升通信性能创建一个额外的空间自由度。本文研究了一种由MA辅助的多用户上行链路通信系统，其中配备多个MA的基站（BS）服务于多个单天线用户。具体而言，考虑到优化的阵列几何形状无法保证速率公平性，我们专注于在BS处设计天线轨迹，以在有限时间段内最大化所有用户中最小可达速率。由于问题的连续时间特性，所得优化问题本质上难以求解。为解决此问题，我们首先考察了MA移动速度无限快的理想情况，并证明松弛问题可通过拉格朗日对偶法得到最优解。所获得的轨迹解表明，BS应采用一组有限的MA部署模式，并为每个模式分配最优的时间持续时间。在此基础上，我们进一步研究了MA移动速度受限的一般情况，并提出了一种启发式轨迹设计，该设计受理想情况下识别出的最优模式启发。通过考察简化特例，我们还获得了一些见解。最后，提供了数值结果以验证所提设计相较于竞争基准的有效性。