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.
@article{arxiv.2601.18471,
title = {Finite-Aperture Fluid Antenna Array Design: Analysis and Algorithm},
author = {Zhentian Zhang and Kai-Kit Wong and Hao Jiang and Farshad Rostami Ghadi and Hyundong Shin and Yangyang Zhang},
journal= {arXiv preprint arXiv:2601.18471},
year = {2026}
}