The fluid antenna system (FAS) has emerged as a disruptive technology for future wireless networks, offering unprecedented degrees of freedom (DoF) through the dynamic configuration of antennas in response to propagation environment variations. The integration of fluid antennas (FAs) with multiuser multiple-input multiple-output (MU-MIMO) networks promises substantial weighted sum rate (WSR) gains via joint beamforming and FA position optimization. However, the joint design is challenging due to the strong coupling between beamforming matrices and antenna positions. To address the challenge, we propose a novel block coordinate ascent (BCA)-based method in FA-assisted MU-MIMO networks. Specifically, we first employ matrix fractional programming techniques to reformulate the original complex problem into a more tractable form. Then, we solve the reformulated problem following the BCA principle, where we develop a low-complexity majorization maximization algorithm capable of optimizing all FA positions simultaneously. To further reduce the computational, storage, and interconnection costs, we propose a decentralized implementation for our proposed algorithm by utilizing the decentralized baseband processing (DBP) architecture. Simulation results demonstrate that with our proposed algorithm, the FA-assisted MU-MIMO system achieves up to a 47% WSR improvement over conventional MIMO networks equipped with fixed-position antennas. Moreover, the decentralized implementation reduces computation time by approximately 70% and has similar performance compared with the centralized implementation.

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