In this letter, we develop a continuous fluid antenna (FA) framework for uplink channel estimation in cell-free massive multiple-input and multiple-output (CF-mMIMO) systems. By modeling the wireless channel as a spatially correlated Gaussian random field, channel estimation is formulated as a Gaussian process (GP) regression problem with motion-constrained spatial sampling. Closed-form expressions for the linear minimum mean squared error (LMMSE) estimator and the corresponding estimation error are derived. A fundamental comparison with discrete port-based architectures is established under identical position constraints, showing that continuous FA sampling achieves equal or lower estimation error for any finite pilot budget, with strict improvement for non-degenerate spatial correlation models. Numerical results validate the analysis and show the performance gains of continuous FA sampling over discrete baselines.

翻译：本文针对无蜂窝大规模多输入多输出（CF-mMIMO）系统的上行链路信道估计，提出了一种连续流体天线（FA）框架。通过将无线信道建模为空间相关的高斯随机场，信道估计被表述为具有运动约束空间采样的高斯过程（GP）回归问题。文中推导了线性最小均方误差（LMMSE）估计器的闭式表达式及其对应的估计误差。在相同位置约束下，与基于离散端口的架构进行了基本比较，结果表明：对于任何有限的导频资源，连续FA采样均能实现相等或更低的估计误差；在非退化空间相关模型下，其性能具有严格提升。数值结果验证了理论分析，并展示了连续FA采样相较于离散基线的性能增益。