Movable Antenna Aided Robust Wireless Transmission: From Model-Based Optimization to Scalable Reinforcement Learning

This paper investigates robust joint antenna positioning and precoding for multiuser movable antenna (MA) systems under imperfect channel state information (CSI). First, we identify the mismatch between the spatial statistics of densely sampled MA channels and the discrete Fourier transform (DFT) basis used for conventional robust precoding. To address this, we develop a novel discrete prolate spheroidal sequence (DPSS)-based a posteriori channel model. By exploiting the spatial covariance structure of MA channels, this model is better suited to modeling MA channel uncertainty. Building on this model, we develop an efficient iterative algorithm for robust joint antenna positioning and precoding to maximize the expected sum rate. By transforming the coupled optimization of antenna positioning and precoding at each iteration into direct comparisons of closed-form scores, we design a low-complexity position replacement scheme that effectively reuses matrix computations across candidate sets. To further improve efficiency and scalability, we exploit the inherent tensor equivariance (TE) of the problem to develop a reinforcement learning framework. To explicitly account for channel uncertainty, we develop novel pairwise user-interaction and CSI-conditioned equivariant attention mechanisms to encode channel statistics and adaptively fuse them with the available CSI. We further introduce distance-biased spatial attention to incorporate the geometry of candidate positions into attention weighting, thereby enhancing spatial feature learning. Simulation results show that the proposed methods improve sum-rate performance while reducing online runtime under imperfect CSI. These methods also achieve near-optimal performance under perfect CSI, closely matching the exhaustive-search method. Moreover, the learning framework generalizes across different numbers of users and MAs without retraining.