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.

翻译：有限孔径约束使得阵列设计变得非平凡，并可能削弱经典稀疏几何结构的有效性。本文为固定孔径下的流体天线阵列设计提供了普适性指导。我们推导了一个闭式克拉美-罗界，通过显式地将费舍尔信息与端口位置的几何方差相关联，统一了传统阵列与可重构阵列。进一步获得了随机FAA布局下最小间距的闭式概率密度函数，从而为最小间距约束提供了理论下界。基于这些分析见解，我们提出了一种基于梯度的算法来优化连续端口位置。通过采用简单的梯度更新设计，优化后的FAA可实现约30%的CRB降低和42.5%的均方误差降低。