This letter investigates the weighted sum rate (WSR) maximization problem in movable antenna (MA)-enhanced multiuser MIMO systems, where both the base station (BS) and users are equipped with MAs. The main contributions include formulating the WSR maximization problem and transforming it into a more tractable weighted sum mean-square error (WMMSE) problem suitable for MAs. The block coordinate descent (BCD) method is employed to optimize all variables alternately, with a planar movement mode used to achieve a low-complexity closed-form solution for optimizing antenna positions. Numerical results show that MA-enhanced systems outperform conventional systems, with the planar movement mode reducing computational complexity by about 30% at a slight performance cost. The system model considers a multiuser downlink wireless communication system where MAs at the BS and users can be adjusted to exploit spatial diversity gain. The channel response depends on the position vectors of the MAs, and the signal received at each user is modeled based on the channel vector and noise. A field-response-based channel model is introduced, where the signal propagation phase difference is calculated based on the positions of the MAs and the channel paths. The WSR maximization problem is formulated with transmit beamformers and antenna positions as variables, subject to transmit power constraints and minimum inter-MA distance. To reduce complexity, the WMMSE algorithm is used for beamformer design, and the majorization-minimization (MM) algorithm is applied for MA position optimization. The planar movement mode restricts each MA to a specified area, enabling a closed-form solution for antenna position optimization. The BCD method decomposes the optimization problem into blocks, optimizing beamformers and antenna positions iteratively. The transmit beamformer design uses the WMMSE algorithm, while the MA position design at the BS and users is optimized using MM techniques. The planar movement mode significantly reduces computational complexity by limiting MA movement to a planar area, achieving faster convergence and lower complexity compared to the general movement mode. Numerical results demonstrate that the MA-enhanced system outperforms conventional systems, with the planar movement mode achieving close performance to the general movement mode while reducing computational complexity. The proposed algorithm is convergent and efficient, with complexity analysis showing that the planar movement mode has lower complexity than the general movement mode. The results confirm the potential of MAs in enhancing wireless communication systems.This letter investigates the weighted sum rate (WSR) maximization problem in movable antenna (MA)-enhanced multiuser MIMO systems, where both the base station (BS) and users are equipped with MAs. The main contributions include formulating the WSR maximization problem and transforming it into a more tractable weighted sum mean-square error (WMMSE) problem suitable for MAs. The block coordinate descent (BCD) method is employed to optimize all variables alternately, with a planar movement mode used to achieve a low-complexity closed-form solution for optimizing antenna positions. Numerical results show that MA-enhanced systems outperform conventional systems, with the planar movement mode reducing computational complexity by about 30% at a slight performance cost. The system model considers a multiuser downlink wireless communication system where MAs at the BS and users can be adjusted to exploit spatial diversity gain. The channel response depends on the position vectors of the MAs, and the signal received at each user is modeled based on the channel vector and noise. A field-response-based channel model is introduced, where the signal propagation phase difference is calculated based on the positions of the MAs and the channel paths. The WSR maximization problem is formulated with transmit beamformers and antenna positions as variables, subject to transmit power constraints and minimum inter-MA distance. To reduce complexity, the WMMSE algorithm is used for beamformer design, and the majorization-minimization (MM) algorithm is applied for MA position optimization. The planar movement mode restricts each MA to a specified area, enabling a closed-form solution for antenna position optimization. The BCD method decomposes the optimization problem into blocks, optimizing beamformers and antenna positions iteratively. The transmit beamformer design uses the WMMSE algorithm, while the MA position design at the BS and users is optimized using MM techniques. The planar movement mode significantly reduces computational complexity by limiting MA movement to a planar area, achieving faster convergence and lower complexity compared to the general movement mode. Numerical results demonstrate that the MA-enhanced system outperforms conventional systems, with the planar movement mode achieving close performance to the general movement mode while reducing computational complexity. The proposed algorithm is convergent and efficient, with complexity analysis showing that the planar movement mode has lower complexity than the general movement mode. The results confirm the potential of MAs in enhancing wireless communication systems.