[Paper Review] Finite-Aperture Fluid Antenna Array Design: Analysis and Algorithm

Zhentian Zhang, Kai-Kit Wong+4 more|arXiv (Cornell University)|Jan 26, 2026

Antenna Design and Optimization0 citations

TL;DR

The paper derives a closed-form CRB for finite-aperture fluid antenna arrays (FAA) unifying reconfigurable and conventional arrays, analyzes minimum port spacing under random placement, and proposes a gradient-based port-placement algorithm that reduces CRB by ~30% and AoAMSE by ~42.5%.

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 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.

Motivation & Objective

• Clarify fundamental geometric limits for FAA under fixed aperture.
• Derive a closed-form CRB that unifies reconfigurable and conventional arrays via port-location variance.
• Characterize the minimum inter-port spacing distribution under random FAA placement.
• Propose and validate a practical gradient-based FAA port-placement algorithm.
• Demonstrate performance gains over traditional ULAs in CRB and AoAMSE metrics.

Proposed method

• Model FAA with continuous port positions inside a fixed aperture and fixed boundary ports.
• Derive a closed-form CRB for angle estimation that depends on the geometric variance of port positions, via the Slepian–Bangs FIM framework.
• Derive the PDF of the minimum port spacing for random port placements within the aperture.
• Formulate a Pareto-like objective linking CRB and sidelobe suppression, and derive a gradient for port optimization.
• Propose a projected gradient-descent algorithm with edge-pinning and spacing-enforcement to optimize intermediate port locations.
• Validate analysis via Monte Carlo results and compare against ULA and discrete FAS baselines.

Experimental results

Research questions

• RQ1 How does finite aperture constrain FAA design and what is the fundamental CRB for angle estimation with FAA?
• RQ2 How does port geometry (positions) affect estimation accuracy and sidelobe behavior under fixed aperture?
• RQ3 What is the distribution of the minimum inter-port spacing under random port placement within the aperture?
• RQ4 Can a gradient-based algorithm effectively optimize continuous port placements to improve CRB and AoA sensing performance?
• RQ5 How do FAA designs compare to ULAs in CRB and AoAMSE across different M and SNR regimes?

Key findings

• A closed-form CRB is obtained: CRB(θ) = 1 / [8π^2 T · SNR · sin^2(θ) · L_geo(p)] with λ normalized, showing the dependence on geometric variance L_geo(p) = Σ(p_m − p̄)^2.
• The expected minimum spacing under random placement is E[Δ_min] = W_max / (M^2 − 1) and its PDF is f_Δ_min(δ) = M(M−1)/W_max · (1 − (M−1)δ/W_max)^{M−1} over δ ∈ [0, W_max/(M−1)].
• Maximizing L_geo(p) (placing ports near boundaries) improves CRB but increases ambiguity/false spectral peaks, highlighting a precision-vs-ambiguity trade-off.
• A gradient-based continuous-port-optimization algorithm reduces CRB by about 30% at M=11 and achieves up to ~42.5% AoAMSE reduction across SNRs.
• The proposed continuous FAA and discrete FAS (scaled MRA) outperform ULA in sensing matrix conditioning, with smaller γ_max and improved CRB results as M grows.
• The algorithm converges for various M, with modest step sizes and offline computation suitable for design-time optimization.