In this correspondence, we propose a movable antenna (MA)-aided multi-user hybrid beamforming scheme with a sub-connected structure, where multiple movable sub-arrays can independently change their positions within different local regions. To maximize the system sum rate, we jointly optimize the digital beamformer, analog beamformer, and positions of subarrays, under the constraints of unit modulus, finite movable regions, and power budget. Due to the non-concave/non-convex objective function/constraints, as well as the highly coupled variables, the formulated problem is challenging to solve. By employing fractional programming, we develop an alternating optimization framework to solve the problem via a combination of Lagrange multipliers, penalty method, and gradient descent. Numerical results reveal that the proposed MA-aided hybrid beamforming scheme significantly improves the sum rate compared to its fixed-position antenna (FPA) counterpart. Moreover, with sufficiently large movable regions, the proposed scheme with sub-connected MA arrays even outperforms the fully-connected FPA array.

翻译：本文提出了一种可移动天线（MA）辅助的多用户混合波束赋形方案，采用子连接结构，其中多个可移动子阵列可在不同局部区域内独立调整其位置。为最大化系统总速率，我们在单位模约束、有限移动区域约束和功率预算约束下，联合优化数字波束赋形器、模拟波束赋形器及子阵列位置。由于目标函数/约束的非凹/非凸性以及变量高度耦合，所建问题难以直接求解。通过采用分式规划，我们发展了一种基于拉格朗日乘子法、惩罚函数法和梯度下降法相结合的交替优化框架。数值结果表明，与固定位置天线（FPA）方案相比，所提MA辅助混合波束赋形方案显著提升了总速率。此外，在移动区域足够大的条件下，采用子连接MA阵列的所提方案甚至优于全连接FPA阵列。