Fluid antenna systems (FAS) enable unprecedented spatial diversity within a compact form factor by flexibly switching among high-density antenna ports. To activate this capability, channel state information (CSI) over the ports is required, which implies high estimation overhead because the number of ports is usually very large. Conventional estimation schemes tend to first estimate the CSI for a small number of ports and then infer the CSI for the remaining antenna ports by interpolation exploiting correlation characteristics. However, existing correlation-based techniques lack generalization ability, and the fundamental limits of interpolating the CSI from sparse observations remain poorly understood. This paper adopts a generative modeling framework for characterizing the channel correlation among the FAS ports that departs fundamentally from covariance-descriptive models. Specifically, we represent the spatially sampled channel as a $p$th-order autoregressive (AR) Gauss-Markov process, which provides a principled and tunable tradeoff between model complexity and approximation accuracy via the AR order. In so doing, we can characterize the limits of channel interpolation by deriving the globally optimal minimum mean-square error (MMSE) estimator and establishing a tight lower bound on the minimum number of observations required to meet a prescribed reconstruction error. To reduce the complexity of MMSE estimation, we then exploit the state-space structure due to the ${\rm AR}(p)$ model and develop a Kalman filtering/smoothing-based interpolation algorithm. The resulting method attains the optimal MMSE performance with strictly linear complexity $\mathcal{O}(N)$ with $N$ denoting the number of ports, resulting in a scalable, efficient, and theoretically grounded framework for practical FAS channel reconstruction.

翻译：流体天线系统（FAS）通过在高密度天线端口间灵活切换，在紧凑外形内实现了前所未有的空间分集能力。为激活该能力，需要获取各端口上的信道状态信息（CSI），但由于端口数量通常极为庞大，这导致极高的估计开销。传统估计方案通常先估计少量端口的CSI，再通过利用相关性特征的插值方法推断剩余天线端口的CSI。然而，现有基于相关性的技术缺乏泛化能力，且从稀疏观测中插值CSI的基本极限仍鲜有理解。本文采用生成式建模框架来刻画FAS端口间的信道相关性，该框架从根本上区别于协方差描述模型。具体而言，我们将空间采样信道表示为p阶自回归（AR）高斯-马尔可夫过程，通过AR阶数在模型复杂度与近似精度之间实现原理性且可调的权衡。藉此，我们可通过推导全局最优的最小均方误差（MMSE）估计器，并建立满足预设重构误差所需最少观测次数的紧下界，来表征信道插值的极限。为降低MMSE估计的复杂度，我们进一步利用AR(p)模型带来的状态空间结构，开发了基于卡尔曼滤波/平滑的插值算法。所提方法以严格线性的复杂度$\mathcal{O}(N)$（其中$N$表示端口数）达到最优MMSE性能，为实际的FAS信道重构提供了可扩展、高效且具有理论基础的框架。