This letter investigates the weighted sum rate maximization problem in movable antenna (MA)-enhanced systems. To reduce the computational complexity, we transform it into a more tractable weighted minimum mean square error (WMMSE) problem well-suited for MA. We then adopt the WMMSE algorithm and majorization-minimization algorithm to optimize the beamforming and antenna positions, respectively. Moreover, we propose a planar movement mode, which constrains each MA to a specified area, we obtain a low-complexity closed-form solution. Numerical results demonstrate that the MA-enhanced system outperforms the conventional system. Besides, the computation time for the planar movement mode is reduced by approximately 30\% at a little performance expense.

翻译：本文研究了可移动天线（MA）增强系统中的加权和速率最大化问题。为降低计算复杂度，我们将该问题转化为更适合MA处理的加权最小均方误差（WMMSE）问题，并采用WMMSE算法与majorization-minimization算法分别优化波束赋形与天线位置。此外，我们提出了一种平面移动模式，将每个MA约束在指定区域内，并得到低复杂度的闭式解。数值结果表明，MA增强系统的性能优于传统系统。同时，平面移动模式的计算时间减少了约30%，而性能损失较小。