Pixel-Based Fluid Antennas

• Pixel-based fluid antennas are electronically reconfigurable EM apertures that adapt radiation patterns via switchable pixels, eliminating the need for mechanical movement.
• They employ diverse hardware realizations—from single-feed arrays to spherical architectures—to synthesize dynamic beamforming and sensing capabilities.
• Practical implementations must balance enhanced reconfigurability with increased control complexity, addressing challenges like CSI acquisition, mutual coupling, and calibration.

Pixel-based fluid antennas are fluid antenna realizations in which a discretized radiating surface, a switchable feeding structure, or both are reconfigured electronically so that the effective radiator, aperture geometry, or excitation state can be changed without physical movement. In the current literature, the term covers electronically reconfigurable structures composed of static radiating elements whose interconnections are toggled by integrated solid-state devices such as PIN diodes or MEMS, single-feed pixel antennas whose discrete states emulate fluid-antenna ports, highly reconfigurable pixel antennas with jointly switchable aperture topology and feeding ports, pixel-based reconfigurable beamforming networks that emulate physical translation through excitation-vector switching, and spherical architectures that extend pixel-like switching to hierarchical region and element selection on a 3D aperture (Yang et al., 16 Oct 2025, Zhang et al., 2024, Han et al., 19 Jan 2026, Zhang et al., 3 Dec 2025, Cheng et al., 4 Jun 2026). Across these lines of work, pixel-based implementations are distinguished by purely electronic control, microsecond- to nanosecond-level switching, and the absence of pumps or mechanical actuators, while also inheriting nontrivial burdens in channel acquisition, control, coupling management, and calibration (Yang et al., 16 Oct 2025).

1. Conceptual foundations and relation to fluid antenna systems

Fluid antenna systems were introduced as architectures in which a single radiating element can access multiple preset ports or positions within a small aperture, with only one port active at any instant in the classical formulation. Pixel-based realizations replace physical movement of metal or liquid with electronically selected radiation states. In the 2024 pixel-based reconfigurable antenna prototype, the 12 discrete states of a single-feed radiator were treated as 12 FAS ports distributed within a half-wavelength aperture, so that “fluidity” was realized as state-dependent radiation-pattern morphing rather than motion of the radiator itself (Zhang et al., 2024).

A central statistical target is the Bessel or Clarke/Jakes spatial correlation law. For uniformly sampled ports over an aperture of size $W\lambda$, the target spatial correlation in rich scattering is

$$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$

and, in translation form,

$\rho(d) \approx J_0(2\pi d/\lambda),$

which is the correlation law that several pixel-based architectures explicitly attempt to reproduce (Zhang et al., 2024, Zhang et al., 3 Dec 2025). The PRBFN-FAS work makes the underlying equivalence explicit: under rich scattering and far-field conditions, switching the physical position of a radiator along a line is equivalent, for channel statistics, to switching the excitation current vector of a multi-port antenna (Zhang et al., 3 Dec 2025). This equivalence shifts the problem from mechanical displacement to electromagnetic state synthesis.

Later work generalizes this viewpoint beyond port emulation. Antenna coding for wireless power transfer treats the binary ON/OFF configuration of pixel switches as a beamspace control variable, thereby extending fluid-antenna ideas from position selection to direct radiation-pattern coding (Chen et al., 16 Dec 2025). The spherical fluid-antenna literature then extends pixel-based switching from 1D and 2D apertures to full 3D spatial reconfigurability by partitioning a spherical surface into electronically addressable regions and refining the activated topology within each region (Cheng et al., 4 Jun 2026). Taken together, these developments define pixel-based fluid antennas less as a single hardware topology than as a class of electronically reconfigurable EM apertures whose state space is engineered to emulate or surpass the spatial degrees of freedom of mechanically or liquid-actuated FAS.

2. Hardware realizations and architectural variants

The earliest explicit prototype in this lineage is a single-feed pixel-based reconfigurable antenna operating at 2.5 GHz. It consists of a probe-fed E-slot patch on Rogers 4003C, an upper reconfigurable pixel layer, and six RF switches implemented with MA4AGP907 PIN diodes. The reported structure provides 12 FAS ports across $1/2$ wavelength, maps 12 optimized switch states to 12 ports, and occupies $0.67\lambda \times 0.67\lambda \times 0.125\lambda$ at 2.5 GHz (Zhang et al., 2024). Its implementation emphasis is not only on pattern diversity but also on impedance matching and correlation shaping across states.

A second hardware direction is the highly reconfigurable pixel antenna. In the HRPA formulation, a half-wavelength square aperture is discretized into a $5\times 5$ pixel array on Rogers 4003C, with $M=25$ potential feeding ports and $Q=40$ loaded ports connecting adjacent pixels. Binary switch states $g_q\in\{0,1\}$ control whether a link is open or short, while a digitally controlled module connects $N$ RF chains to selected feed ports. This architecture introduces joint radiating-aperture and feeding-port reconfiguration, so the effective radiator can be altered both by changing pixel connectivity and by moving the excitation point over the grid (Han et al., 19 Jan 2026).

A third line of work relocates reconfiguration from the radiator to the feeding network. The scalable PRBFN-FAS architecture is constructed from cascaded unit cells, each comprising a 3 dB equal power divider and a pixel-based four-port reconfigurable coupler controlled by PIN diodes, with SPDT switches added in deeper stages when necessary. Two demonstrated cases emulate FAS movements of $$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$0 and $$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$1 wavelengths, using $$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$2 and $$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$3 antenna ports, respectively, and operate around 2.6 GHz over at least 5% fractional bandwidth (Zhang et al., 3 Dec 2025). In this design, each FAS state is an excitation current vector rather than a geometric radiator state.

The 3D spherical fluid antenna system generalizes the classical notion of pixels into two hierarchical layers. At the array level, the spherical surface of radius $$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$4 is divided into electronically addressable regions parameterized by azimuth $$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$5 and elevation $$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$6; activating different regions relocates the effective aperture over the sphere. At the element level, subsets of ports or pixel-level radiators within the selected region are switched to shape the effective aperture size, topology, polarization, and radiation characteristics. The paper explicitly lists liquid-metal-based elements and RF-switch-based reconfigurable pixel antennas as feasible realizations, coordinated by a backend digital controller inside the sphere through an RF-switch matrix and reconfigurable feeding network (Cheng et al., 4 Jun 2026).

A related, though mechanically actuated, branch is the electromagnetically reconfigurable fluid antenna system based on a quasi-Yagi element with six liquid-metal directors and a rear fluid-metal reflector. That work discretizes a continuously tunable fluid geometry into a finite dictionary of radiation states and uses one-hot state selection vectors in the communication model (Wang et al., 4 May 2025). This suggests a broader interpretation in which “pixel-based” may refer not only to literal metallic sub-elements but also to any finite EM state dictionary used as the control alphabet of a fluid antenna.

3. Electromagnetic modeling, state spaces, and optimization formalisms

Pixel-based fluid antennas are modeled as discrete-state EM systems whose switching variables directly perturb current paths, mutual coupling, embedded patterns, and effective apertures. In the single-feed PRA, the internal multi-port method represents the structure as one external feed and $$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$7 internal ports, with input impedance

$$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$8

and reflection coefficient

$$\rho(i,j) \approx J_0\!\left(2\pi |i-j|W/(N-1)\right),$$9

A two-step search first filters matched state sets satisfying $\rho(d) \approx J_0(2\pi d/\lambda),$0 dB and then orders $\rho(d) \approx J_0(2\pi d/\lambda),$1 states to minimize deviation from the target Bessel covariance profile (Zhang et al., 2024). In this formulation, state design is an explicitly EM-constrained covariance synthesis problem.

The HRPA literature adopts a more general network reduction. Let $\rho(d) \approx J_0(2\pi d/\lambda),$2 denote the chosen feeding-port set and $\rho(d) \approx J_0(2\pi d/\lambda),$3 the binary pixel-switch vector. The effective $\rho(d) \approx J_0(2\pi d/\lambda),$4-port seen by the activated feeds is

$\rho(d) \approx J_0(2\pi d/\lambda),$5

while coupled embedded patterns are obtained from

$\rho(d) \approx J_0(2\pi d/\lambda),$6

This model feeds directly into a CRLB-based optimization in which the codebook entries $\rho(d) \approx J_0(2\pi d/\lambda),$7 are chosen to minimize worst-case angular estimation error over prescribed sectors (Han et al., 19 Jan 2026). Here the state space is not merely a set of ports; it is the Cartesian product of feed selection and topology selection.

The spherical formulation abstracts the aperture at a higher level. For $\rho(d) \approx J_0(2\pi d/\lambda),$8 candidate elements on a sphere, the array factor is

$\rho(d) \approx J_0(2\pi d/\lambda),$9

with region activation determining the support of the sum and element-level switching refining the activated subset. The paper further frames joint region and element control using a binary region vector $1/2$0, an element-selection vector $1/2$1, an aperture-size constraint $1/2$2, and beamforming weights $1/2$3, with representative objectives such as maximizing $1/2$4 under power and support constraints (Cheng et al., 4 Jun 2026). In this setting, “pixels” become hierarchical support variables on a conformal surface.

Beamspace formulations provide an additional abstraction. In antenna-coded pixel antennas for MIMO wireless power transfer, each switch configuration $1/2$5 yields a coded radiation pattern

$1/2$6

and the singular vectors of $1/2$7 define an effective aerial degrees-of-freedom basis. The resulting beamspace channel is written as

$1/2$8

so that binary pixel states appear as beamspace coder matrices rather than directly as physical ports (Chen et al., 16 Dec 2025). This formalism makes explicit that pixel-based fluidity can be interpreted as state-dependent projection onto a low-dimensional radiation basis.

The burden created by large state spaces is evident in radio-map reconstruction. For a base station with $1/2$9 antenna modes, the multi-mode radio map is represented as a tensor

$0.67\lambda \times 0.67\lambda \times 0.125\lambda$0

and recovered from sparse measurements by combining overlapped nuclear norms with a physics regularizer based on differential gain topology maps derived from Effective Aerial Degrees-of-Freedom theory (Jia et al., 5 Feb 2026). This is not merely a mapping convenience; it formalizes the fact that practical control of pixel-based fluid antennas is inseparable from dimensionality reduction, state compression, and physics-aware priors.

4. Beamforming, sensing, and communication functionalities

A major use of pixel-based fluid antennas is arbitrary beam-pattern synthesis within a fixed aperture. The flexible beamforming framework for a 2D planar fluid antenna array models an $0.67\lambda \times 0.67\lambda \times 0.125\lambda$1 grid of selectable ports, activates only $0.67\lambda \times 0.67\lambda \times 0.125\lambda$2 ports at a time, and formulates design as the sparse regression problem

$0.67\lambda \times 0.67\lambda \times 0.125\lambda$3

The method combines an FFT-aligned far-field model, a modified orthogonal matching pursuit algorithm, and an iterative FFT-based phase retrieval procedure requiring one FFT and one inverse FFT per iteration (Xu et al., 27 Nov 2025). Within this framework, narrow beams and broad beams are both treated as sparse port-selection problems on a pixelized aperture.

Angular sensing uses the same hardware degrees of freedom differently. The HRPA work defines codebooks indexed by sensing sectors, where each codeword specifies both active feed positions and pixel connections. The resulting Fisher-information-driven design minimizes the CRLB over a target region and reports that the HRPA reduces the angle estimation error by more than 50% across the full three-dimensional sphere when compared with a conventional uniform planar array of the same size (Han et al., 19 Jan 2026). The key mechanism is not simply beam steering but the steepening of angular gradients through joint control of embedded patterns, coupling, and feed placement.

In multiuser MIMO-OFDM, pixel-based fluid antennas introduce a state-non-separable channel response problem. The measured radiation functions of the prototype are modeled by DNNs, and the composite channel under state vector $0.67\lambda \times 0.67\lambda \times 0.125\lambda$4 is approximated on an angular-delay grid as

$0.67\lambda \times 0.67\lambda \times 0.125\lambda$5

Modified orthogonal matching pursuit and turbo variational Bayesian inference are then used for channel sounding, after which predicted channels for all fluid-antenna states enable analog precoding by state selection (Guo et al., 11 Sep 2025). This pipeline shows that pixel-based fluid antennas are not only pattern-agile front ends; they require estimation procedures that explicitly incorporate radiation-state dependence.

Other communication regimes exploit the same reconfigurability with different objectives. In ambient backscatter communications, a reader equipped with a dense set of $0.67\lambda \times 0.67\lambda \times 0.125\lambda$6 preset pixel ports selects one port based on short-term measurements rather than explicit CSI. The selected cascaded gain drives the receive SNR

$0.67\lambda \times 0.67\lambda \times 0.125\lambda$7

while the backscatter device’s modulation coefficient is jointly optimized under the energy-neutrality constraint

$0.67\lambda \times 0.67\lambda \times 0.125\lambda$8

A PSO-based optimize-then-average strategy jointly chooses the port index and the reflection level (Kaveh et al., 18 Feb 2026). In MIMO wireless power transfer, alternating optimization combines quasi-Newton beamforming with Successive Exhaustive Boolean Optimization of antenna coders, using rectifier nonlinearity as the system objective rather than RF power alone (Chen et al., 16 Dec 2025).

The spherical literature further broadens the functional scope. Region switching supports concurrent multi-region transmission, blockage-adaptive aperture switching, effective-aperture reconfiguration, and high-resolution 3D aperture control; multi-region activation can serve different directions or users simultaneously, while element-level selection inside each region adjusts local topology such as annular, meridional, or contiguous-patch activations (Cheng et al., 4 Jun 2026). This suggests that, in 3D environments, the distinction between beamforming, aperture steering, and EM topology control becomes increasingly artificial.

5. Empirical performance and representative application domains

Prototype and simulation results consistently show that pixel-based fluid antennas can reproduce the matching and correlation properties required by FAS while extending functionality beyond simple port hopping. The 2024 PRA prototype reports return loss better than 10 dB for all 12 states over a bandwidth slightly above 50 MHz around 2.5 GHz, simulated covariance error $0.67\lambda \times 0.67\lambda \times 0.125\lambda$9 and measured covariance error $5\times 5$0 relative to the Bessel target, realized gain above 6.6 dBi for every state, and average total efficiency of about 80% (Zhang et al., 2024). Field measurements with a 2×2 MIMO testbed in NLOS showed up to about 30 dB variation across the 12 PRA ports for stationary underlying channels, confirming strong state-dependent diversity (Zhang et al., 2024).

The PRBFN-FAS studies show that the same statistical goal can be met through excitation synthesis. For the $5\times 5$1, $5\times 5$2, $5\times 5$3 design, measured relative errors between realized and ideal Bessel correlations are 0.051, 0.045, and 0.055 at 2.55, 2.6, and 2.65 GHz for the ideal-antenna case, with insertion loss below 1.8 dB in all 11 states. For the $5\times 5$4, $5\times 5$5, $5\times 5$6 design, the PRBFN-only correlation errors are 0.057, 0.043, and 0.037 at the same frequencies, and system-level experiments in an indoor NLoS environment showed that both users achieved SIR $5\times 5$7 dB via per-state selection (Zhang et al., 3 Dec 2025).

The 3D spherical results are comparative rather than absolute. With equal transmit power and equal number of activated elements across compared schemes, the fixed planar array gives the lowest spectral efficiency, 2D FAS achieves moderate gain, 3D SFAS with array-level reconfiguration achieves higher channel gain by selecting favorable spherical regions, and 3D SFAS with joint array-level and element-level reconfiguration achieves the highest spectral efficiency across the entire SNR range. In the two-user example of Fig. 4, single-region activation oriented toward each user provides higher directional gain, while two-region simultaneous activation forms two beams toward Users A and B with equal power allocation and concurrent coverage (Cheng et al., 4 Jun 2026).

Performance gains are also reported in more specialized tasks. The HRPA reports more than 50% reduction in angle estimation error across the full three-dimensional sphere relative to a same-size uniform planar array (Han et al., 19 Jan 2026). The physics-aware tensor reconstruction method for pixel-based fluid-antenna radio maps reports about a 4 dB gain over baselines at a 10% sampling ratio and better preservation of sharp shadowing edges under extreme sparsity (Jia et al., 5 Feb 2026). In MIMO wireless power transfer, antenna coding with pixel antennas yields up to 15 dB higher average output DC power in a 4×4 configuration than a conventional fixed-antenna system (Chen et al., 16 Dec 2025). In ambient backscatter, pixel-based FAS at the reader significantly improves achievable rate over a conventional single-antenna reader, with gains preserved under imperfect observations, stringent energy-harvesting constraints, and different pixel spacings (Kaveh et al., 18 Feb 2026).

Application domains reflect this breadth. The spherical work explicitly identifies space–air–ground integrated networks, vehicular and high-mobility communications, integrated sensing and communication, and emergency communications as natural targets for region-level and element-level reconfiguration (Cheng et al., 4 Jun 2026). The sensing-oriented HRPA is framed for ISAC (Han et al., 19 Jan 2026). Pixel-based fast switching is also highlighted as suitable for beyond-5G/6G and IoT applications requiring frequent reconfiguration, fast port selection, rapid user scheduling, and multiuser interference suppression (Yang et al., 16 Oct 2025).

6. Practical constraints, modeling caveats, and open research problems

A recurring theme is that idealized analyses overestimate achievable gains. The practical-review literature identifies four pervasive assumptions: near-instant reconfiguration, perfect channel knowledge, static or slowly varying propagation, and ideal material properties. For pixel-based antennas, the review emphasizes that finite driver latency, limited and imperfect CSI, electromagnetic coupling, and implementation constraints materially degrade gains predicted under ideal models, especially at high SNR and in rapidly varying channels (Yang et al., 16 Oct 2025). The reported imperfect-CSI study uses zero-mean complex Gaussian CSI errors with variances from 0 to 40% over SNR from $5\times 5$8 dB to 30 dB and shows that capacity degradation is minor at low SNR but substantial at high SNR (Yang et al., 16 Oct 2025).

The main trade-off is straightforward but technically consequential: more pixels increase reconfigurability, but they also increase switch count, control complexity, CSI burden, and coupling risk. This trade-off is stated explicitly in the practical-review paper, is evident in the HRPA discussion of mutual coupling and efficiency saturation when increasing the number of active feed ports, and reappears in spherical architectures as low-overhead CSI acquisition and joint region/element control become central challenges (Yang et al., 16 Oct 2025, Han et al., 19 Jan 2026, Cheng et al., 4 Jun 2026). In multiuser MIMO-OFDM, the state-non-separable channel response problem is a direct manifestation of this complexity, since the radiation function depends jointly on angle and selected state and therefore breaks standard hybrid-beamforming separability assumptions (Guo et al., 11 Sep 2025).

Hardware nonidealities remain architecture-specific. The PRA prototype attributes covariance deviations to phase errors from switch modeling and fabrication tolerances (Zhang et al., 2024). HRPA analysis notes that PIN-diode ON resistance and OFF capacitance affect the effective load matrix and radiation efficiency, and that embedded-pattern calibration and impedance characterization are essential (Han et al., 19 Jan 2026). PRBFN-FAS must control insertion loss, phase consistency across bandwidth, and multiport antenna isolation; the design therefore places switching before power amplifiers so that the switching network remains in small-signal operation (Zhang et al., 3 Dec 2025). The spherical architecture adds co-design burdens for the spherical structure, RF-switch matrix, reconfigurable feed, and multi-link integration (Cheng et al., 4 Jun 2026).

Several model restrictions are also explicit. The flexible beamforming paper assumes narrowband operation, LOS, slow fading, static channels over the control interval, unity element patterns, and coupling handled only through a minimum-spacing constraint (Xu et al., 27 Nov 2025). The HRPA sensing model assumes narrowband, far-field conditions and idealized switch states in the analytical model (Han et al., 19 Jan 2026). The radio-map reconstruction framework assumes quasi-stationary channels over the mapping time and mode-independent path loss and shadowing in the differential-gain construction (Jia et al., 5 Feb 2026). These assumptions do not invalidate the reported results, but they delimit the regime in which those results should be interpreted.

Open problems follow directly from these limitations. The practical-review paper calls for realistic stochastic or hybrid models, predictive ML, online-learning-based port selection, limited-codebook strategies, and hardware-in-the-loop trials (Yang et al., 16 Oct 2025). The spherical work highlights low-overhead CSI and beam-region management, hardware co-design, and efficient joint control and resource allocation (Cheng et al., 4 Jun 2026). The MU-MIMO-OFDM work points toward fast online estimation under mobility, joint state-set and switching-policy design, and learning-based mappings from pilots to antenna states (Guo et al., 11 Sep 2025). A plausible implication is that the most consequential research direction is no longer the demonstration of reconfigurability itself, but the co-design of EM state spaces, inference pipelines, and system-level control so that the electronic fluidity of pixel-based antennas remains usable under realistic channel dynamics and hardware constraints.