Finite-Aperture Fluid Antenna Array Design: Analysis and Algorithm

2026-01-26

AI Summary

This study addresses the challenge of designing sparse arrays under fixed aperture constraints, where conventional approaches struggle to balance performance and physical feasibility. Focusing on fluid antenna array (FAA) layout within a limited aperture, this work derives—for the first time—a closed-form Cramér–Rao bound (CRB) that unifies both traditional and reconfigurable array paradigms, and explicitly links the CRB to the geometric variance of port locations. Furthermore, it establishes the probability density function for the minimum inter-port spacing in random FAA configurations and its theoretical lower bound. Leveraging Fisher information analysis and probabilistic modeling, the authors propose a gradient-based optimization method for continuous port placement. Experimental results demonstrate that the optimized FAA achieves approximately a 30% reduction in CRB and a 42.5% decrease in mean squared error.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Applications

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• finite-aperture
• fluid antenna array
• array design
• minimum spacing
• Cramér-Rao bound

Innovation

• fluid antenna array
• Cramér–Rao bound
• finite aperture
• gradient-based optimization
• minimum spacing constraint