Finite-Aperture Fluid Antenna Array Design: Analysis and Algorithm

Finite-aperture constraints complicate array design and can degrade classical sparse geometries. This letter offers universal guidance for fluid antenna array (FAA) design under a fixed aperture. We derive a closed-form Cramér-Rao bound (CRB) unifying conventional and reconfigurable arrays by linking Fisher information to the geometric variance of port locations, and obtain a closed-form PDF of the minimum spacing under random FAA placement, yielding a principled lower bound for the minimum-spacing constraint. Based on these insights, we propose a gradient-based algorithm to optimize continuous port locations. The optimized FAA achieves about a 30% CRB reduction and a 42.5% reduction in mean-squared error.