Continuous Fluid Antenna System

• Continuous Fluid Antenna System is a model where an antenna moves continuously within a bounded region to optimize SIR, surpassing discrete fluid-antenna designs.
• CFAS employs continuous random-field analysis to model spatial fading and interference, using metrics like level crossing rate and outage CDF to assess performance.
• Recent research extends CFAS into trajectory optimization and practical electromagnetic designs, enhancing throughput and energy efficiency in communications and sensing.

Continuous Fluid Antenna System (CFAS) denotes the continuous-position generalization of the fluid antenna paradigm: instead of switching a single RF chain among a finite set of preset ports, the radiating element is modeled as being able to move to any point in a bounded region, so the received channel, interference, and resulting SIR or SNR become continuous stochastic processes over space (Psomas et al., 2023). In this sense, CFAS is both a physical idealization of liquid or movable antennas and a performance benchmark for discretized fluid-antenna systems. Recent work has developed CFAS along three main axes: continuous random-field analysis of spatial fading and interference (Psomas et al., 2023), dimensional high-SNR scaling laws for 1D, 2D, and 3D search regions (Smith et al., 12 Mar 2026), and continuous-time or continuous-position optimization frameworks for communications and sensing (Yang et al., 27 Mar 2026).

1. Definition and relation to discrete fluid antenna systems

The earliest analytical fluid-antenna literature was formulated as a discrete-position selection problem. In “Fluid Antenna Systems” (Wong et al., 2020), a single receive antenna with one RF chain switches among $N$ preset positions on a line segment of length $W\lambda$, and the selected SNR is the maximum over the candidate positions. “Performance Limits of Fluid Antenna Systems” (Wong et al., 2020) retained the same basic structure and studied ergodic capacity, a lower bound on capacity, and second-order statistics through LCR and AFD. These works established the central intuition that a compact movable aperture can harvest substantial spatial diversity even when candidate locations are strongly correlated.

CFAS differs in the treatment of position. “Continuous Fluid Antenna Systems: Modeling and Analysis” (Psomas et al., 2023) makes the liquid position a continuous variable $t\in[0,T]$, motivated by the observation that the liquid conductor does not jump among a finite set of predefined ports but can move to any point inside the holder. The continuous model is therefore the natural upper benchmark for discrete fluid antenna systems: if a discrete system samples only finitely many candidate positions, a CFAS can choose the best point anywhere on the interval and can capture maxima that lie between ports. The same paper states that CFAS outperforms its discrete counterpart and provides the performance limits of FA-based systems, with the advantage especially visible “in particular for medium to large threshold values” in the comparison against a 10-port DFAS (Psomas et al., 2023).

Survey-style work on FAS broadens the interpretation further. “Fluid Antenna Systems Enabling 6G: Principles, Applications, and Research Directions” (Wu et al., 2024) does not use the term CFAS explicitly, but it repeatedly describes FAS as giving access to a signal “function” defined very finely in spatial domain and refers to a “nearly continuous switchable area for radiators.” That framing is consistent with treating CFAS as the continuous-position and, in some works, continuous-shape limit of FAS rather than merely a dense discrete-port model.

2. Continuous random-field formulation and core performance metrics

The canonical analytical CFAS model is a downlink point-to-point link with one conventional transmit antenna, one linear fluid antenna at the receiver, and $N$ cochannel interferers. The received signal at position $t$ is modeled as

$$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$

with $g(t)\sim\mathcal{CN}(0,\beta_0)$, $h_i(t)\sim\mathcal{CN}(0,\beta_I)$, unit-power desired and interfering symbols, and AWGN $n(t)$ of variance $\sigma^2$ (Psomas et al., 2023). In the interference-limited regime, thermal noise is neglected relative to interference, and the position-dependent SIR becomes

$W\lambda$0

The defining CFAS statistic is the supremum over the continuous movement region,

$W\lambda$1

which represents the strongest SIR achievable by ideal continuous repositioning (Psomas et al., 2023). The analysis proceeds by treating $W\lambda$2 as a continuous random process over space rather than a finite collection of port values. Spatial correlation is explicit: under two-dimensional isotropic scattering,

$W\lambda$3

and more generally the local form

$W\lambda$4

is used, with $W\lambda$5 under Jakes’ model (Psomas et al., 2023).

The main analytical tool is the level crossing rate of the continuous SIR process. For the interference-limited Rayleigh model, the closed-form result is

$W\lambda$6

which quantifies how often the SIR process crosses a threshold $W\lambda$7 per unit antenna length (Psomas et al., 2023). The average fade duration then follows from

$W\lambda$8

These second-order statistics are then used to bound the outage CDF of the supremum: $W\lambda$9

This formulation establishes several characteristic CFAS facts. If $t\in[0,T]$0 is very small, the supremum CDF approaches the pointwise SIR CDF, so there is effectively no selection gain. As $t\in[0,T]$1 increases, the receiver explores a larger spatial region and outage decreases. The same paper also shows that a 3D isotropic correlation model $t\in[0,T]$2 increases autocorrelation relative to the 2D Jakes case and therefore reduces the benefit of spatial exploration (Psomas et al., 2023).

3. Dimensional scaling laws and Ricean extensions

A major development beyond the original 1D continuous-holder model is the study of CFAS over 1D, 2D, and 3D continuous search regions under Rayleigh fading. “Dimensional Scaling Laws for Continuous Fluid Antenna Systems” (Smith et al., 12 Mar 2026) defines the received SNR at location $t\in[0,T]$3 as

$t\in[0,T]$4

with the CFAS choosing

$t\in[0,T]$5

The paper focuses on the high-SNR probability

$t\in[0,T]$6

or equivalently the upper-tail probability of the supremum of a $t\in[0,T]$7 random field over $t\in[0,T]$8.

For a 1D region $t\in[0,T]$9, the asymptotically exact high-threshold approximation is

$N$0

where $N$1 and $N$2 is the derivative variance implied by the local correlation curvature (Smith et al., 12 Mar 2026). In higher dimensions, the same expected Euler characteristic machinery yields closed forms in which the dominant geometric term is proportional to length in 1D, area in 2D, and volume in 3D. For equal side lengths $N$3, the paper states the approximation

$N$4

so each additional dimension contributes an approximately multiplicative high-tail gain (Smith et al., 12 Mar 2026). Under Jakes correlation, $N$5, and for $N$6, $N$7, the paper gives

$N$8

meaning that every extra dimension gives about a tenfold increase in the probability of exceeding the high-SNR threshold.

The same work also studies aperture geometry under fixed area or volume budgets. For a 2D rectangle with area constraint $N$9 and side limits $t$0, $t$1, the optimal shape for asymptotic HSP is

$t$2

and for a 3D cuboid with volume constraint $t$3 and $t$4, the optimum is

$t$5

Thus, under the stated high-threshold asymptotics, elongated admissible regions outperform compact square or cube-like shapes (Smith et al., 12 Mar 2026).

Ricean environments change the picture materially. “High SNR Probabilities of Continuous Fluid Antenna Systems in Ricean Environments” (Inwood et al., 14 Aug 2025) models the channel as a LoS plus correlated NLoS field,

$t$6

and studies the high-SNR probability of the supremum of the resulting non-central $t$7 field. In 1D, the approximation becomes

$t$8

with analogous 2D and 3D formulas involving $t$9, $$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$0, and $$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$1 (Inwood et al., 14 Aug 2025). The paper emphasizes that stronger LoS reduces the spatial fluctuations on which CFAS relies. In the reported 3D case with $$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$2, the HSP drops from about $$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$3 at $$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$4 to about $$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$5 at $$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$6, and matching a Rayleigh CFAS HSP in Ricean fading can require large aperture inflation, with reported 2D area ratios $$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$7 ranging from around $$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$8–$$y(t)=g(t)x_0+\sum_{i=1}^{N} h_i(t)x_i+n(t),\qquad 0\le t\le T,$$9 at $g(t)\sim\mathcal{CN}(0,\beta_0)$0 to around $g(t)\sim\mathcal{CN}(0,\beta_0)$1–$g(t)\sim\mathcal{CN}(0,\beta_0)$2 at $g(t)\sim\mathcal{CN}(0,\beta_0)$3 depending on the reference Rayleigh side length (Inwood et al., 14 Aug 2025). A common misconception is therefore incorrect: a stronger LoS component does not necessarily increase the benefit of continuous spatial mobility.

4. Continuous-position and continuous-trajectory optimization

Once the antenna position is treated as a continuous variable, CFAS naturally becomes an optimization problem rather than only a performance-limit model. “Antenna Elements’ Trajectory Optimization for Throughput Maximization in Continuous-Trajectory Fluid Antenna-Aided Wireless Communications” (Yang et al., 27 Mar 2026) introduces the continuous-trajectory fluid antenna (CTFA), in which each antenna element moves continuously over time inside a prescribed 2D region under velocity and acceleration constraints. The optimization variables are the trajectories $g(t)\sim\mathcal{CN}(0,\beta_0)$4, $g(t)\sim\mathcal{CN}(0,\beta_0)$5 and the transmit covariance $g(t)\sim\mathcal{CN}(0,\beta_0)$6, with throughput

$g(t)\sim\mathcal{CN}(0,\beta_0)$7

The paper discretizes time, then solves the resulting non-convex problem using block coordinate descent, majorization-minimization, and WMMSE. In the reported results, the proposed CTFA achieves $g(t)\sim\mathcal{CN}(0,\beta_0)$8 bits/Hz in the $g(t)\sim\mathcal{CN}(0,\beta_0)$9 case and $h_i(t)\sim\mathcal{CN}(0,\beta_I)$0 bits/Hz in the $h_i(t)\sim\mathcal{CN}(0,\beta_I)$1 case, corresponding to gains of $h_i(t)\sim\mathcal{CN}(0,\beta_I)$2 and $h_i(t)\sim\mathcal{CN}(0,\beta_I)$3 over fixed-position antenna benchmarks, respectively (Yang et al., 27 Mar 2026). The conceptual point is that continuous antenna motion cannot be reduced to independent per-slot position choices once kinematic feasibility is imposed.

Continuous spatial optimization also appears in networked settings. “Fluid Antenna System Meets Low-Resolution ADCs in Energy-Efficient Cell-Free Massive MIMO” (Qian et al., 27 May 2026) treats each user-side antenna position as a continuous 2D variable

$h_i(t)\sim\mathcal{CN}(0,\beta_I)$4

and jointly optimizes transmit powers, continuous positions, and AP ADC resolutions for energy efficiency. The framework uses Dinkelbach fractional programming for power control and accelerated projected gradient ascent for both continuous positions and relaxed bit allocations. The reported results show that fluid antennas outperform fixed-position antennas by about $h_i(t)\sim\mathcal{CN}(0,\beta_I)$5 EE across the equal-resolution ADC range, that increasing the normalized movement side length from $h_i(t)\sim\mathcal{CN}(0,\beta_I)$6 to $h_i(t)\sim\mathcal{CN}(0,\beta_I)$7 gives about $h_i(t)\sim\mathcal{CN}(0,\beta_I)$8 EE gain, and that full joint optimization yields $h_i(t)\sim\mathcal{CN}(0,\beta_I)$9–$n(t)$0 EE gain over the unoptimized baseline depending on the number of APs (Qian et al., 27 May 2026).

Sensing-oriented CFAS formulations follow the same logic. “UAV-Enabled Fluid Antenna Systems for Multi-Target Wireless Sensing over LAWCNs” (Zhang et al., 26 Sep 2025) jointly optimizes UAV trajectory, continuous transmit and receive antenna coordinates within $n(t)$1, and transmit covariance to minimize average CRB for multi-target estimation. The simplified reciprocal-CRB objective makes explicit that transmit geometry, receive geometry, and platform motion all appear as coupled design variables. This suggests that in sensing and ISAC settings, CFAS is best viewed as manifold optimization: continuous antenna coordinates alter the steering vectors themselves, not merely the beamforming weights.

5. Electromagnetic interpretation and hardware realizations

A distinct strand of the literature interprets fluid antennas not only as movable points in a fading field but as continuously reconfigurable electromagnetic objects. “Fluid Antennas: Reshaping Intrinsic Properties for Flexible Radiation Characteristics in Intelligent Wireless Networks” (Lu et al., 6 Jan 2025) develops a unified eigenmode-based model in which variable occupied space, boundary conditions, feed schemes, and eigenmode parity define the fluid-antenna state. In the paper’s spectral expansion, the current distribution is expressed as a superposition of resonant eigenmodes over a variable domain, and the antenna’s continuous adaptability lies in the ability to reshape geometry, feed location, and excited modal family. The dipole example

$n(t)$2

illustrates how even and odd modal parity produce different radiation patterns and therefore an additional degree of freedom for beam and null control (Lu et al., 6 Jan 2025). In this interpretation, CFAS is not only continuous position selection over a fixed field; it can also be continuous movement over an electromagnetic modal manifold.

Implementation-oriented survey work identifies several hardware classes: liquid metal in microchannels, conductive fluid in tube-like containers with digitally controlled nano-pumps, metallophobic-surface designs, water antennas, and pixel-based reconfigurable antennas. The same survey states that CSI acquisition becomes difficult when FAS has a “nearly continuous switchable area for radiators,” which is precisely the CFAS control problem in practical form (Wu et al., 2024).

A concrete mmWave realization appears in “Design and Implementation of mmWave Surface Wave Enabled Fluid Antennas and Experimental Results for Fluid Antenna Multiple Access” (Shen et al., 2024). The single-channel fluid antenna (SCFA) and double-channel fluid antenna (DCFA) use Galinstan radiators inside microfluidic channels above a Rogers 5880 substrate with a surface-wave launcher. For the SCFA, the reported continuous motion range of the radiator is

$n(t)$3

which is about one free-space wavelength at $n(t)$4 GHz; the measurements themselves sample this continuum at discrete positions. In the 5G millimeter-wave bands $n(t)$5–$n(t)$6 GHz, the prototypes can vary their gain up to an averaged value of $n(t)$7 dBi, and in 4-user FAMA the DCFA reduces outage probability by $n(t)$8 and increases the multiplexing gain to $n(t)$9 compared with a static omnidirectional antenna (Shen et al., 2024). The result is not a strict continuous-aperture experiment in the random-field-theoretic sense, but it is a strong quasi-continuous physical realization of the CFAS principle.

6. Applications, caveats, and unresolved problems

CFAS ideas now appear across UAV links, wideband OFDM, cell-free networks, low-resolution front ends, and sensing, but many system papers remain fundamentally discretized approximations rather than native continuous-position theories. “Fluid Antenna System-Enabled UAV-to-Ground Communications” (Zhu et al., 21 Nov 2025), for example, studies a ground receiver with an $\sigma^2$0-port FAS over a linear aperture of length $\sigma^2$1 and one RF chain, selecting the port that maximizes SNR under a UAV double-shadowing channel. The paper does not formulate a continuum maximization; instead, it adopts the eigenvalue-based approximation of Zhao and Slock, replacing the correlated $\sigma^2$2-port problem by $\sigma^2$3 independent eigen-branches and deriving the diversity order

$\sigma^2$4

Its strongest CFAS-relevant conclusion is that effective spatial rank, not raw port count, governs diversity. At fixed $\sigma^2$5, increasing $\sigma^2$6 from $\sigma^2$7 to $\sigma^2$8 may yield only marginal gain because the reported effective rank saturates from $\sigma^2$9 to $W\lambda$00 (Zhu et al., 21 Nov 2025). This directly corrects another common misconception: finer spatial sampling of the same compact region does not indefinitely create new diversity.

A similar caution applies to wideband and network-level studies. “Fluid Antenna System Empowering 5G NR” (Hong et al., 7 Mar 2025) treats FAS in OFDM by selecting a single port for an entire frequency-time grid, while “Cell-free Fluid Antenna Multiple Access Networks” (Han et al., 29 Apr 2025) studies user-side port selection in a distributed downlink with MRT beamforming. Both are important for deployment-oriented analysis, but both remain discrete-port approximations to CFAS rather than continuous field optimization.

The practical obstacle course is now well characterized. “Fluid Antenna Systems under Channel Uncertainty and Hardware Impairments: Trends, Challenges, and Future Research Directions” (Pakravan et al., 30 Jan 2026) formulates the ideal control law as

$W\lambda$01

and then shows how estimation error

$W\lambda$02

and temporal evolution

$W\lambda$03

undermine that idealization. The same survey emphasizes fluid response delay, RF nonlinearity, insertion loss, impedance mismatch, port coupling, positioning inaccuracies, and the need for continuous-space CSI reconstruction, robust optimization, and learning-based control (Pakravan et al., 30 Jan 2026). These caveats are not peripheral. They define the difference between CFAS as a continuous random-field benchmark and CFAS as a deployable technology.

The resulting research agenda is specific. A mature CFAS theory still requires continuous-position spatio-temporal channel models beyond isotropic toy correlations, tighter characterization of the supremum distribution outside asymptotic upper tails, delay-aware control laws that account for mechanical dynamics, joint electromagnetic-fluid-channel co-design, and experimental validation of continuous rather than densely discretized operation. What existing work already makes clear is the central design rule: CFAS gains come from creating more effectively independent spatial opportunities within the admissible region, whether by longer apertures, lower correlation, higher-dimensional movement, richer scattering, or continuously optimized trajectories.