Finite-Aperture Fluid Antenna Array Design: Analysis and Algorithm
For antenna array designers, this work offers analytical tools and an optimization algorithm to improve performance under finite-aperture constraints.
The paper provides universal guidance for fluid antenna array design under a fixed aperture, deriving closed-form Cramér-Rao bound and probability density function for minimum spacing. The proposed gradient-based algorithm achieves about 30% CRB reduction and 42.5% reduction in mean-squared error.
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 Cramér--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.