Finite-Aperture Fluid Antenna Array Design: Analysis and Algorithm

TL;DR

This paper introduces a comprehensive analysis and a gradient-based optimization algorithm for finite-aperture fluid antenna arrays, improving estimation accuracy and minimum spacing constraints.

Contribution

It derives a unified CRB and minimum spacing distribution for FAA design, and proposes an optimization method for port placement.

Findings

Achieved approximately 30% reduction in CRB.

Reduced mean-squared error by about 42.5%.

Provided analytical bounds for FAA design constraints.

Abstract

Finite-aperture constraints render array design nontrivial and can undermine the effectiveness of classical sparse geometries. This letter provides universal guidance for fluid antenna array (FAA) design under a fixed aperture. We derive a closed-form Cram\'er--Rao bound (CRB) that unifies conventional and reconfigurable arrays by explicitly linking the Fisher information to the geometric variance of port locations. We further obtain a closed-form probability density function of the minimum spacing under random FAA placement, which yields a principled lower bound for the minimum-spacing constraint. Building upon these analytical insights, we then propose a gradient-based algorithm to optimize continuous port locations. Utilizing a simple gradient update design, the optimized FAA can achieve about a $30\%$ CRB reduction and a $42.5\%$ reduction in mean-squared error.