Sparse Fluid Antenna Arrays: Continuous Position Design Beyond Classical DOF Limits

TL;DR

This paper introduces a continuous-position fluid antenna array design that surpasses classical limits in DOA estimation by unlocking linear DOF growth, improved CRB scaling, and robust source tracking methods.

Contribution

It establishes the theoretical foundations of sparse fluid antenna systems with continuous positioning, enabling significant DOF and accuracy improvements over traditional grid-based arrays.

Findings

FAS-optimized positions approach the universal dual DOF bound, growing linearly with D/λ.

CRB scales as O(1/D^{2L}), a substantial improvement over grid designs.

FAS-MUSIC achieves 17.5× lower RMSE than ULA MUSIC and outperforms MRA with fewer antennas.

Abstract

Fluid antenna system (FAS), which continuously repositions a single physical element across a deployment region $[0, D]$, breaks this limit by freeing antenna positions from the discrete grid entirely. This paper establishes the theoretical foundations of sparse FAS design for direction-of-arrival (DOA) estimation and shows that continuous position freedom unlocks three compounding advantages over the classical designs. \emph{First}, we derive a universal dual DOF bound and prove that FAS-optimized positions can approach it, growing the DOF linearly with $D/\lambda$ , where $\lambda$ is the signal wavelength, rather than saturating at $O(N^2)$. \emph{Second}, the CRB scales as $O(1/D^{2L})$ for $L$ sources, a $(D/(N^2 d_0))^{2L}$ improvement over the best grid design, with $d_0 = \lambda/2$ and D-optimal positions admitting closed-form solution for single sources and efficient Frank-Wolfe algorithm for multiple sources. \emph{Third}, we propose a two-stage FAS-MUSIC approach that combines coarray MUSIC disambiguation with full-aperture local maximum likelihood (ML) refinement to track the CRB, overcoming the grating-lobe ambiguity inherent in large-aperture non-uniform arrays. Robustness to minimum spacing constraints, mutual coupling, and finite position accuracy is also analyzed. Extensive simulations show that FAS-MUSIC achieves $17.5\times$ lower root mean squared error (RMSE) than uniform linear array (ULA) MUSIC and that FAS with $4$ antennas outperforms MRA with $8$ antennas, gains that are unattainable by any grid-constrained design.