Accurate channel state information (CSI) acquisition is critical for exploiting the spatial flexibility of fluid antenna systems (FASs). However, port selection and transmission optimization require CSI over a large number of candidate port positions, making direct port-wise estimation prohibitively costly in terms of pilot overhead. This paper addresses this challenge through geometry-structured channel reconstruction, which exploits the fact that the port-domain CSI can be parameterized by a small number of dominant propagation paths. We first establish fundamental mean square error (MSE) and normalized MSE (NMSE) benchmarks for both geometry-structured and unstructured channel reconstruction, providing analytical references for evaluating the intrinsic benefit of geometric modeling in conventional antenna systems and FASs. Motivated by the strong spatial correlation induced by densely distributed fluid antenna ports, we further propose a Bayesian reconstruction framework, termed geometry-structured expectation-maximization approximate message passing (GS-EM-AMP). The proposed algorithm incorporates geometric channel structure into the EM-AMP procedure and adaptively learns unknown statistical parameters from noisy observations. Numerical results demonstrate that GS-EM-AMP achieves near-bound reconstruction accuracy while maintaining strong robustness against steering-domain correlation, thereby offering an efficient and reliable solution for large-scale CSI acquisition in FASs.

翻译：精确的信道状态信息获取对发挥液态天线系统空间灵活性至关重要。然而，端口选择与传输优化需要覆盖大量候选端口位置的信道状态信息，使得逐端口直接估计面临导频开销过大难以实施的问题。本文通过几何结构引导的信道重建应对这一挑战，该方法利用端口域信道状态信息可由少量主传播路径参数化表征的特性。我们首先建立了几何结构化与非结构化信道重建的均方误差与归一化均方误差基准，为评估传统天线系统与液态天线系统中几何建模的固有优势提供分析参考。针对液态天线端口密集分布引发的强空间相关性，进一步提出一种贝叶斯重建框架——几何结构期望最大化近似消息传递算法。该算法将几何信道结构融入EM-AMP迭代过程，能根据含噪观测自适应学习未知统计参数。数值结果表明，GS-EM-AMP在保持对导向域相关性强鲁棒性的同时实现了近理论界的重建精度，为液态天线系统大规模信道状态信息获取提供了高效可靠的解决方案。