Enormous Fluid Antenna Systems (E-FAS)--Part II: Channel Estimation

TL;DR

Enormous fluid antenna systems (E-FAS) exploit surface-wave routing to form a two-timescale end-to-end channel $\mathbf{h}_u=\sqrt{\beta_u}\,\mathbf{g}_u$, where $\beta_u$ is a slow routing gain and $\mathbf{g}_u\sim\mathcal{CN}(\mathbf{0},\mathbf{I}_M)$. The authors develop a pilot-based MMSE estimation framework, deriving closed-form variances for the estimate and error ($\Omega_{\hat{h},u}$ and $\Omega_{\tilde{h},u}$), and analyze both single-user and multiuser downlink performance under training overhead. They show that imperfect CSI causes SINR saturation in the single-user case and a residual-interference ceiling for multiuser ZF, with the routing gain $\beta_u$ strongly shaping estimation quality and performance ceilings. The work demonstrates that, despite CSI costs, E-FAS retains substantial gains over conventional space-wave transmission due to amplified large-scale routing gains and robustness to estimation errors, while revealing important trade-offs between pilot length, coherence time, and the number of served users.

Abstract

Enormous fluid antenna systems (E-FAS) have recently emerged as a new wireless architecture in which intelligent metasurfaces act as guided electromagnetic interfaces, enabling surface-wave (SW) propagation with much lower attenuation and more control than conventional space-wave transmission. While prior work has reported substantial power gains under perfect channel state information (CSI), the impact of practical channel acquisition on E-FAS performance remains largely unexplored. This paper presents the first comprehensive analysis of E-FAS-assisted downlink transmission under pilot-based channel estimation. We develop an estimation framework for the equivalent end-to-end channel and derive closed-form expressions for the statistics of the minimum mean-square-error (MMSE) channel estimate and its estimation error. Building on these results, we analyze both single-user and multiuser operation while explicitly accounting for the training overhead. For the single-user case, we characterize the outage probability and achievable rate with imperfect CSI, and reveal an inherent signal-to-noise ratio (SNR) saturation phenomenon caused by residual self-interference. For the multiuser case, we study zero-forcing (ZF) precoding based on imperfect channel estimates and show that the system becomes interference-limited in the high SNR regime because of residual inter-user interference. Furthermore, we quantify the trade-off between spatial multiplexing gains and pilot overhead when the number of users increases. Analytical findings are validated via Monte Carlo simulations and benchmarked against least-squares (LS) estimation and conventional non-E-FAS transmission. The results reveal that despite CSI imperfections and training costs, E-FAS retains substantial performance advantages and provides robustness enabled by its amplified large-scale channel gain.

Figures (8)

• Figure 1: Illustration of the E-FAS-assisted downlink system.
• Figure 2: NMSE versus routing gain $\beta$ for LS and MMSE estimators under different pilot SNR values.
• Figure 3: NMSE versus pilot length $\tau_p$ at $\rho_p=0$ dB for different $\beta$.
• Figure 4: Outage probability versus downlink SNR $\rho_d$ for $M=64$, $\tau_p=8$, and $\rho_p=0$ dB.
• Figure 5: Achievable single-user rate versus downlink SNR $\rho_d$ under MRT precoding with training overhead.

Theorems & Definitions (2)

• Remark 1: Mismatched MMSE Estimation
• Remark 2