Two-Timescale Deep-Unfolding for Joint Optimization of Antenna Position and Beamforming in Movable-Antenna Arrays

In this study, we explore a downlink multiuser multiple-input multiple-output (MU-MIMO) system with movable antennas (MA). Our objective is to jointly optimize the MA positions and beamforming to maximize system sum-rate. Due to hardware limitations that make real-time MA position adjustments impractical, we propose a two-timescale optimization scheme. In this scheme, the antenna position vector (APV) is update based on long-term channel statistics at the beginning of each coherence time block, while the beamforming matrix is optimized based on short-term information in each subsequent time slot within the same block. We develop an efficient stochastic successive convex approximation (SSCA)-based algorithm for joint APV and beamforming design. Additionally, in order to improve performance and reduce computational complexity, we propose a deep-unfolding neural network (NN) that preserves the structure of SSCA-based algorithm while incorporating a nonlinear activation function and trainable parameters based on first-order Taylor approximations for matrix inversion. Meanwhile, projection operators are designed to ensure compliance with the design constraints. Simulation results show that the twotimescale algorithm improves sum-rate compared to conventional MIMO systems with uniform linear arrays (ULA), and the deepunfolding NN outperforms the SSCA-based algorithm.