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.
@article{arxiv.2602.16459,
title = {Continuous Fluid Antenna Sampling for Channel Estimation in Cell-Free Massive MIMO},
author = {Masoud Kaveh and Farshad Rostami Ghadi and Francisco Hernando-Gallego and Diego Martin and Riku Jantti and Kai-Kit Wong},
journal= {arXiv preprint arXiv:2602.16459},
year = {2026}
}