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Continuous Fluid Antenna Sampling for Channel Estimation in Cell-Free Massive MIMO

Masoud Kaveh, Farshad Rostami Ghadi, Francisco Hernando-Gallego, Diego Martin, Riku Jantti, Kai-Kit Wong

TL;DR

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.

Abstract

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.

Continuous Fluid Antenna Sampling for Channel Estimation in Cell-Free Massive MIMO

TL;DR

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.

Abstract

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.
Paper Structure (22 sections, 2 theorems, 18 equations, 2 figures)

This paper contains 22 sections, 2 theorems, 18 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Network Model
  4. Continuous FA Channel Model
  5. Uplink Training and Continuous FA Sampling
  6. Pilot Transmission Model
  7. Continuous FA Sampling Interpretation
  8. position constraints
  9. LMMSE Channel Estimation via GP Regression
  10. Second-Order Statistics and Covariance Structure
  11. LMMSE Channel Estimator
  12. GP Interpretation
  13. Estimation Error and NMSE
  14. Comparison with Discrete Port-Based FA
  15. Discrete Port-Based FA Model
  16. ...and 7 more sections

Key Result

Proposition 1

Fix $\tau_p$ and assume that both continuous and discrete FA sampling satisfy the same position constraint, i.e., eq:motion_constraint and eq:motion_constraint_discrete, respectively. Then, the minimum achievable NMSE under continuous FA sampling is no larger than that of any discrete port-based sch

Figures (2)

  • Figure 1: Uplink CF-mMIMO with continuous fluid antenna sampling.
  • Figure 2: (a) CDF versus NMSE; (b) NMSE versus pilot length $\tau_p$; (c) NMSE versus FA length $\ell$; and (d) NMSE versus number of ports $Q$.

Theorems & Definitions (3)

  • Proposition 1
  • proof
  • Corollary 1