Sparse Fluid Antenna Systems (FAS) Overview

• Sparse Fluid Antenna Systems (FAS) are reconfigurable antenna architectures that use a large set of candidate ports but activate only a limited subset to maximize channel performance.
• They leverage sparse port activation, continuous-position design, and advanced signal processing to enhance DOA estimation and reduce RF complexity.
• Recent research integrates FAS with ISAC, sparse recovery methods, and innovative hardware prototypes, demonstrating significant performance and efficiency improvements.

Searching arXiv for papers on sparse fluid antenna systems and related FAS theory. Sparse Fluid Antenna Systems (FAS) denote a family of reconfigurable antenna architectures and signal processing models in which a large set of candidate spatial states is available, but only a small subset of positions, ports, beam states, or observations is used at a given time. In the foundational single-RF-chain model, a fluid antenna switches among $N$ ports distributed over a fixed aperture $W\lambda$ and selects the strongest channel realization, while more recent work extends the idea to continuous-position sparse arrays, sparse port activation for integrated sensing and communication (ISAC), sparse observation and interpolation over dense port grids, and hardware that realizes “virtual movement” through electronic reconfiguration rather than mechanical displacement (Wong et al., 2020, Wu et al., 19 May 2026, Wu et al., 2024).

1. Conceptual scope and defining interpretations

The canonical FAS model places a single antenna on a line segment of length $W\lambda$ with $N$ candidate ports at

$$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$

and applies ideal selection

$|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$

In this setting, a sparse FAS is naturally understood as a system that uses relatively few ports $N$, or a chosen subset of positions with larger spacing, within a fixed aperture (Wong et al., 2020).

Subsequent literature broadens the notion of sparsity. In wideband and multiuser designs, many candidate ports exist but usually only one is active at any instant, making port activation intrinsically sparse in the RF-chain sense (Hong et al., 7 Mar 2025). In survey treatments, FAS is described more generally as exposing a large state space of position- and shape-reconfigurable antenna configurations while activating only a small subset during operation, which directly connects FAS to sparse control, sparse CSI acquisition, and sparse state selection (Wu et al., 2024).

A distinct but related interpretation appears in sparse-array theory. There, a small number of fluid antennas are continuously repositioned within a deployment region $[0,D]$, and the resulting virtual array is sparse in hardware but not constrained to a half-wavelength grid. This continuous-position sparse FAS is studied as a new sparse-array class for direction-of-arrival (DOA) estimation and coarray design (Wu et al., 19 May 2026).

Taken together, the literature uses “sparse FAS” in four closely connected senses: sparse port activation, sparse physical sampling of an aperture, sparse channel or angular representations, and sparse observation of a dense port field.

2. Statistical and electromagnetic models

Across the literature, sparse FAS models are built from spatially correlated fading over closely spaced ports. In one widely used formulation, the channel at port $k$ is

$$y_k=g_k x+\eta_k,\qquad g_k\sim\mathcal{CN}(0,\sigma^2),$$

with average SNR

$W\lambda$0

and spatial correlation under Jakes’ model

$W\lambda$1

The same Bessel-function structure appears in many later FAS papers as the default correlation law for ports packed within a compact aperture (Wong et al., 2020).

For user-side FAS in unsourced massive access, the spatial correlation matrix is written as

$W\lambda$2

and the port-gain vector is generated through an eigendecomposition $W\lambda$3, followed by correlated Gaussian synthesis. Only one port is then activated at a time, typically the one with maximum channel magnitude (Xu et al., 29 Jun 2026).

A central modeling question is how to replace the exact Jakes or Clarke correlation matrix with a tractable approximation when $W\lambda$4 is large and port spacing is much smaller than $W\lambda$5. A block-diagonal spatial correlation model addresses this by partitioning the aperture into spatial coherence blocks, each represented by a dense equal-correlation submatrix, while forcing inter-block correlation to zero. For 1D apertures under Jakes’ and 3D Clarke’s models, the number of dominant eigenvalues is shown to be approximately $W\lambda$6, which formalizes the idea that dense port grids have far fewer effective degrees of freedom than raw port count suggests (Ramirez-Espinosa et al., 2024).

A different response to the same problem is generative modeling. Instead of treating the covariance matrix as purely descriptive, the port-indexed channel is represented as an $W\lambda$7 Gauss-Markov process,

$W\lambda$8

with Yule–Walker fitting to the desired low-lag spatial correlation. This produces a state-space model that supports globally optimal MMSE interpolation and Kalman filtering/smoothing with strictly linear complexity $W\lambda$9 in the number of ports (Zhang et al., 17 Apr 2026).

3. Sparse geometry beyond fixed grids

A major recent development is the treatment of sparse FAS as a continuous-position sparse-array problem rather than a discrete port-selection problem. In this formulation, $W\lambda$0 antenna positions $W\lambda$1 are optimized directly, the virtual array is defined by the set of difference coarray positions

$W\lambda$2

and the coarray degrees of freedom are bounded by the universal dual bound

$W\lambda$3

This distinguishes sparse FAS from nested, coprime, and minimum-redundancy arrays, whose positions remain tied to the half-wavelength grid (Wu et al., 19 May 2026).

Within this framework, FAS position design is studied through D-optimality and continuous experimental design. For a single source, the D-optimal design places antennas at the interval endpoints, maximizing the second central moment of the positions. For multiple sources, a Frank–Wolfe algorithm over design measures is used to maximize $W\lambda$4, where $W\lambda$5 is the Fisher information matrix (Wu et al., 19 May 2026).

The resulting asymptotics differ sharply from grid-constrained sparse arrays. The Cramér–Rao bound scales as

$W\lambda$6

for $W\lambda$7 sources, with an improvement factor

$W\lambda$8

over the best grid design. A two-stage FAS-MUSIC method combines coarray MUSIC disambiguation with full-aperture local maximum-likelihood refinement, and simulations report $W\lambda$9 lower RMSE than ULA MUSIC, while FAS with $N$0 antennas outperforms MRA with $N$1 antennas (Wu et al., 19 May 2026).

This line of work shows that sparse FAS is not only a matter of activating fewer ports. It is also a geometry-design problem in which continuous position freedom changes the attainable coarray structure, the CRB, and the relation between aperture and degrees of freedom.

4. Sparse control, estimation, and reconstruction

Sparse FAS control usually begins with port selection. In narrowband selection-combining models, the rule is simply to activate the port with maximum instantaneous magnitude. In wideband FAS-OFDM, because the physical antenna cannot change port per subcarrier, port selection is performed per subframe using a compressed metric such as average SNR,

$N$2

so that one active port is used across all subcarriers during that interval (Hong et al., 7 Mar 2025).

For ISAC, sparse activation is made explicit in the beamformer. In one formulation, a BS with $N$3 candidate FAS ports and $N$4 active antennas designs a multicast ISAC beamformer $N$5 under the cardinality constraint

$N$6

while satisfying communication and sensing SNR requirements and minimizing transmit power. A sparse-optimization, convex-approximation, and penalty-based iterative algorithm is developed for this problem, and simulations show $N$7 reductions in transmit power with guaranteed sensing and communication performance (Zou et al., 2024).

Channel estimation in sparse FAS follows two main strategies. In sparse angular-domain models, the port-space channel is approximated by

$N$8

or, in unsourced random access with a fluid receiver,

$N$9

where $$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$0 is sparse over a dictionary of candidate angles. This leads naturally to OMP- or SOMP-type recovery for activity detection, channel estimation, and angle estimation (Zhang et al., 2023, Zhou et al., 24 Apr 2025).

When sparse angular assumptions are unreliable, prior-aided stochastic-process models are used instead. The successive Bayesian reconstructor models the FAS channel as a Gaussian process over ports, chooses the next sampled port by maximum posterior variance,

$$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$1

and performs online reconstruction using the posterior mean

$$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$2

In simulations, S-BAR achieves higher estimation accuracy than existing schemes in both model-matched and model-mismatched cases (Zhang et al., 2023).

Sparse observation itself becomes a design variable in dense-port FAS. With only a subset $$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$3 of ports observed, the ideal MMSE lower bound on interpolation error is governed by the eigenvalues $$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$4 of the spatial covariance: $$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$5 which also yields a lower bound on the minimum number of observations needed for a target reconstruction error. This formalizes the intuition that dense FAS channels can often be reconstructed from a sparse training set because the effective spatial degrees of freedom are limited (Zhang et al., 17 Apr 2026).

5. Communication, sensing, and access systems

Sparse FAS has been studied across several communication regimes. In downlink short-packet NOMA, both the central user and cell-edge user employ single-RF-chain FAS receivers with $$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$6 correlated ports and max-gain selection. The resulting finite-blocklength block error rates scale with diversity order $$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$7, and the paper explicitly states that the diversity order for both users is $$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$8 (Zheng et al., 2023).

In wideband 5G NR OFDM, FAS is integrated through a port-selection matrix and average-SNR-based adaptive modulation and coding. Even with $$d_k=\left(\frac{k-1}{N-1}\right)W\lambda,\quad k=1,\dots,N,$$9 candidate ports and a small aperture $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$0, the reported BLER gain is about $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$1 dB at BLER $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$2 over a fixed-position antenna, while larger apertures and more ports produce throughput gains up to $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$3 Mbit/s versus $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$4 Mbit/s at $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$5 MHz and $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$6 dB (Hong et al., 7 Mar 2025).

For uplink unsourced integrated sensing and communication under finite blocklength, a user-side FAS is used to select one port with maximum channel gain while the BS employs a fixed ULA. The resulting framework integrates SOMP-based activity detection, MMSE channel estimation, ESPRIT AOA estimation, sparse channel refinement, and alternating SIC. Numerical results show that the FAS-aided approach significantly reduces per-user probability of error and improves angle-of-arrival accuracy; at $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$7 active users, the reported capacity gain over TDMA is $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$8 dB (Xu et al., 29 Jun 2026).

RIS-assisted multiuser transmission has also been combined with sparse or telescopic FAS. In a downlink RIS-assisted MISO model, a low-complexity grating-lobe-based telescopic FAS is proposed under sub-connected hybrid beamforming and LoS-dominant channels. This scheme relies on statistical CSI only, chooses subarray spacings in closed form from the geometric relation between main-lobe and grating-lobe directions, and provides a considerable gain over conventional fixed-position antenna systems (Chen et al., 12 Apr 2025).

These results point to a recurrent pattern. Sparse FAS improves performance not by activating many RF chains, but by exposing a rich spatial state space and then selecting, estimating, or optimizing only a small portion of it.

6. Hardware realizations, scalability, and open problems

Practical sparse FAS requires hardware that can realize many candidate states while preserving the one-port-or-few-port activation model. A pixel-based reconfigurable antenna design addresses this by realizing $|g_{\rm FAS}|=\max\{|g_1|,\dots,|g_N|\}.$9 FAS ports across $N$0 wavelength with an E-slot patch antenna, an upper reconfigurable pixel layer, and $N$1 RF switches. A prototype operating at $N$2 GHz demonstrates that the design can meet FAS requirements including port correlation with matched impedance (Zhang et al., 2024).

A more scalable architecture is the pixel-based reconfigurable beamforming network for FAS. Rather than emulating position shifts through a single reconfigurable radiator, the PRBFN-FAS uses a beamforming network to synthesize the current vectors corresponding to FAS states. Two design examples emulate equivalent physical movements of $N$3 and $N$4 wavelengths, and measurements show good matching and Bessel correlation across the desired bandwidth, with system-level experiments confirming practical viability (Zhang et al., 3 Dec 2025).

At the hardware level, current FAS implementations span liquid metal, conductive fluid in tubes with nano-pumps, metallophobic patterned surfaces, stacked 3D liquid-metal structures, water antennas, stretchable liquid-metal textiles, and pixel-based reconfigurable antennas. At the systems level, the main open issues repeatedly identified in the literature are CSI acquisition over large port sets, versatile channel modeling that captures position and shape flexibility together with operating mechanisms, robust joint beamforming and position optimization under imperfect CSI, localization, and AI-driven FAS control (Wu et al., 2024).

Several quantitative constraints recur across these studies. Sparse-array DOA designs analyze robustness to minimum spacing, mutual coupling, and finite position accuracy, with a reported position-error tolerance requirement of approximately $N$5 for less than $N$6 dB loss (Wu et al., 19 May 2026). Communication-oriented works repeatedly note that large candidate-port sets reduce pilot collisions or improve selection diversity, but only a small subset is actually activated or trained at any instant (Xu et al., 29 Jun 2026, Zhang et al., 17 Apr 2026).

A plausible implication is that sparse FAS will continue to evolve along two coupled directions. One direction is algorithmic: sparse optimization, sparse recovery, Bayesian interpolation, and geometry-aware array design. The other is hardware: electronically reconfigurable radiators and beamforming networks that can expose dense spatial state spaces while keeping the number of active RF chains, moving parts, and control variables small.