Geo-Temporal EM-AMP for CSI Acquisition in FAS-Assisted Grant-Free Random Access with a Mobile Receiver

Receiver mobility complicates channel state information (CSI) acquisition in fluid antenna system (FAS)-assisted grant-free random access (GFRA), because user activity and multi-port channels evolve across pilot frames. Existing FAS acquisition methods are mainly frame-wise, while temporal recovery schemes do not directly combine receiver geometry with Doppler information. This article proposes geo-temporal expectation-maximization approximate message passing (GT-EM-AMP), which transfers posterior information between frames and refines the channel prior using receiver trajectory, effective Doppler, and coarse geometry. The proposed recursion preserves the low-complexity structure of EM-AMP while introducing only limited additional state updates. Simulations over an SNR range from −14 to 8 dB show that GT-EM-AMP achieves lower channel-estimation error and a favorable activity-detection tradeoff relative to static, temporal-only, geometry-only, and greedy baselines. Ablation, robustness, mobility, scalability, and statistical evaluations characterize the operating range of GT-EM-AMP and show that its activity-detection advantage depends on the SNR regime. GT-EM-AMP introduces modest runtime and memory overhead relative to static EM-AMP. The evaluation focuses on short acquisition windows with coarse geometry information under a Jakes-type temporal model.