Finite-Aperture Planar Fluid Antenna Array

2026-05-21

AI Summary

This study addresses the impact of geometric diversity in planar fluid antenna arrays under finite apertures on channel estimation performance. The authors develop an analytical framework to investigate the statistical properties of minimum inter-port spacing in random layouts and its inherent trade-off with spatial ambiguity. Leveraging stochastic geometry, Cramér–Rao bound analysis, and eigenstructure characterization of associated matrices, they demonstrate that the expected minimum spacing scales as 𝒪(M⁻¹). A geometric inertia matrix is introduced to quantify joint elevation–azimuth estimation accuracy, whose trace and determinant are theoretically shown to be independent of azimuth angle. Furthermore, placing ports near aperture boundaries enhances estimation precision but exacerbates sidelobe-induced ambiguity, thereby establishing—for the first time—a quantitative relationship among array geometry, estimation performance, and ambiguity effects.

Abstract

Fluid antenna systems (FASs) are emerging as a reconfigurable-aperture technology that expands physical-layer design beyond fixed, rigid antenna geometries. While the \emph{fading diversity} of FASs -- which exploits spatial channel fluctuations for signal enhancement and interference avoidance -- has been widely studied, the \emph{geometry diversity} created by reconfigurable port placement remains far less understood, particularly for planar architectures under finite-aperture constraints. This paper develops a systematic analytical framework for finite-aperture planar fluid antenna arrays (FAAs). First, we derive a closed-form characterization of the minimum inter-port distance under uniform random placement over a rectangular aperture and show that it follows a Rayleigh law. Its mean scales as $\mathcal{O}(M^{-1})$, in sharp contrast to the $\mathcal{O}(M^{-2})$ behavior in the linear case in which $M$ represents the number of candidate ports, revealing a fundamentally more favorable packing geometry in two dimensions. Secondly, we establish a universal Cramér-Rao bound (CRB) for joint elevation-azimuth estimation, governed by a $2\times 2$ \emph{geometric inertia matrix} whose determinant and eigenstructure fully capture the role of port placement in estimation precision. We further prove that both the trace and determinant of this matrix are invariant to the azimuth look direction. Third, we uncover an intrinsic \emph{precision--ambiguity trade-off}: maximizing the geometric determinant to minimize the CRB drives ports toward the aperture boundary, but simultaneously increases sidelobe-induced spatial ambiguity.

Problem

• fluid antenna array
• geometry diversity
• finite aperture
• Cramér-Rao bound
• spatial ambiguity

Innovation

• fluid antenna array
• geometry diversity
• Cramér-Rao bound
• geometric inertia matrix
• precision–ambiguity trade-off