Pattern-Reconfigurable Fluid RIS

• Pattern-reconfigurable FRIS is a dynamic surface that adapts its element radiation patterns or activation layout to modify its effective scattering and improve signal separability.
• It extends conventional RIS by incorporating spatial reconfigurability through techniques like switchable apertures, fluidic conductive materials, and fixed-position radiation tuning.
• The technology enhances index modulation, beamforming, and security measures while introducing challenges in hardware design and channel estimation.

Pattern-reconfigurable fluid reconfigurable intelligent surface (FRIS) denotes a class of reconfigurable intelligent surfaces in which the surface does not merely tune reflection coefficients on a fixed aperture, but reconfigures the effective scattering pattern itself through dynamic control of element radiation patterns, active regions, or spatial layout. In the narrow classification used by the FRIS overview literature, pattern-reconfigurable FRIS is the branch in which element positions remain fixed while the radiation patterns of the elements are dynamically changed; in a broader systems interpretation adopted by several recent works, the same concept also encompasses switchable apertures, pattern-reconfigurable units, fluidic conductive materials, and movable surface elements that alter the spatial layout or effective active regions seen by the incident wave (Xiao et al., 23 Sep 2025, Zhu et al., 21 May 2026). Across these formulations, the unifying idea is that FRIS adds a spatial or pattern degree of freedom beyond conventional phase-only RIS control.

1. Conceptual scope and taxonomy

Conventional RIS is consistently modeled as a surface with fixed geometry whose primary control variables are phase or phase/amplitude coefficients. FRIS extends that model by introducing spatial reconfigurability. One broad definition states that FRIS “extends conventional reconfigurable intelligent surfaces (RIS) by adding spatial reconfigurability through switchable apertures, pattern-reconfigurable units, fluidic conductive materials, or movable surface elements,” and emphasizes that the key feature is the ability to change “not only its electromagnetic response, but also the spatial layout or effective active regions seen by the incident wave” (Zhu et al., 21 May 2026). A complementary survey classifies FRIS into two main types—position-reconfigurable FRIS and pattern-reconfigurable FRIS—and defines the latter as the case where geometry stays fixed but the element radiation patterns are dynamically changed (Xiao et al., 23 Sep 2025).

These two usages are compatible but not identical. In the strict survey terminology, “pattern reconfiguration” refers to radiation-pattern adaptation at fixed element positions. In the broader systems literature, pattern reconfiguration also includes layout-state control: which regions of the surface are activated, switched, or moved, and which candidate reflecting locations are used at a given interval (Zhu et al., 21 May 2026). This broader usage is common in FRIS-assisted communication papers that do not synthesize far-field patterns explicitly but nonetheless alter the effective reflection pattern by selecting active ports or relocating reflecting points (Salem et al., 24 Feb 2025, Xiao et al., 18 Mar 2025).

FRIS modality	Reconfigured object	Representative arXiv ids
Pattern-reconfigurable FRIS	Element radiation pattern or directional gain	(Xiao et al., 23 Sep 2025)
Position-reconfigurable FRIS	Effective reflecting positions on a preset grid	(Magalhães et al., 15 May 2026, Salem et al., 24 Feb 2025)
Dense-grid activation FRIS	Active subset or aperture support pattern	(Xiao et al., 18 Mar 2025, Ghadi et al., 29 May 2025)

A recurring conceptual distinction is between the layout domain and the response domain. The FRIS-assisted index-modulation literature stresses that physically distinct layouts do not automatically produce reliably distinguishable receiver-side responses after propagation, mutual coupling, hardware distortion, and observation. This shifts the design criterion from layout diversity alone to response-domain separability (Zhu et al., 21 May 2026). That point is central to pattern-reconfigurable FRIS because it ties physical state design to detectability, estimation, and communication performance rather than to geometric variation alone.

2. Architectural realizations and physical abstractions

One influential FRIS abstraction treats the surface as a metasurface with $M$ fluid reflecting elements deployed over a total area $A$, where each element can switch among $N$ preset positions on a dense grid. In that model, the $m$-th element at training block $k$ has realized position $\mathbf{p}_{k,m}$, inducing the motion-dependent phase term

$$t_{k,m}=e^{-j\frac{2\pi}{\lambda}\|\mathbf{p}_{k,m}\|},$$

and the FRIS state across the aperture is collected as $\mathbf{t}_k=[t_{k,1},\ldots,t_{k,M}]^T$. Electronic phase control is represented separately by $\boldsymbol{\phi}_j$, so the effective element response is the Hadamard combination $\boldsymbol{\phi}_j\odot \mathbf{t}_k$ (Magalhães et al., 15 May 2026). In this formulation, pattern reconfiguration arises through joint position selection and phase tuning.

A related physical model partitions a square FRIS aperture into non-overlapping subareas, each hosting one fluid element that can change its position within the assigned region and adjust the reflected phase. The position of element $A$0 is $A$1, constrained by subarea membership and minimum spacing,

$A$2

with the position dictating the point of reflection of the incident signal in that subarea (Salem et al., 24 Feb 2025). The same work notes that the mathematical model is effectively an ideal movable point reflector, while practical realization is more plausibly associated with metamaterial-based, reconfigurable pixel, or slot-based technologies (Salem et al., 24 Feb 2025).

Another major architectural line realizes “fluidity” through dense preset candidate ports rather than literal motion. In the joint on-off selection formulation, the FRIS contains $A$3 candidate reflecting elements with spacing $A$4, only $A$5 of which are active at a time. The active subset is encoded by a selection matrix, and inactive elements are connected to matched loads (Xiao et al., 18 Mar 2025). A closely related downlink performance-analysis model uses a dense matrix of sub-elements over a surface of size $A$6, activates only $A$7 of them, and represents the active aperture through a binary orthogonal projection matrix $A$8 satisfying $A$9 (Ghadi et al., 29 May 2025).

Pattern-reconfigurable FRIS in the strict radiation-pattern sense is described more explicitly in the survey literature. There, the defining mechanism is precise control of each element’s radiation characteristics rather than position changes, and the principal implementation mechanism explicitly mentioned is a pixel-reconfigurable architecture in which the surface is discretized into pixels interconnected via hardwires or RF switches so that the electromagnetic characteristics of an element can be modified by altering local connections (Xiao et al., 23 Sep 2025). The survey also stresses that very few studies directly address the design of elements capable of dynamically reconfiguring their radiation patterns (Xiao et al., 23 Sep 2025).

3. Mathematical models and signal representations

The FRIS literature uses several abstraction levels. At the most communication-oriented level, a selected FRIS codeword $N$0 induces a receiver-side response

$N$1

where $N$2 may be a scalar channel coefficient, a multi-antenna response vector, or a feature extracted from received samples (Zhu et al., 21 May 2026). This response-domain formulation is particularly important for FRIS-assisted index modulation, where a codebook of reliably distinguishable configurations carries $N$3 bits per reconfiguration interval if the codebook contains $N$4 distinguishable states (Zhu et al., 21 May 2026).

At the cascaded-channel level, a representative uplink multi-user MISO model with FRIS-assisted reflection writes the matched-filtered pilot observation as

$N$5

where $N$6 is the UEs-to-FRIS channel, $N$7 is the FRIS-to-BS channel, $N$8 indexes sub-frame-dependent phase control, and $N$9 captures block-dependent motion-induced coefficients (Magalhães et al., 15 May 2026). This model explicitly separates the electronic and motion-driven components of FRIS reconfiguration.

Dense-grid activation models incorporate spatial correlation through a full aperture correlation matrix $m$0. In a canonical downlink representation, the equivalent FRIS-assisted channel is

$m$1

with $m$2 the phase-shift matrix and $m$3 the reduced correlation matrix induced by the active pattern (Ghadi et al., 29 May 2025). Similar selection-matrix formulations reappear in security and covert-communication models, where the selected active subset determines not only the equivalent channel but also the effective statistics seen by legitimate and adversarial receivers (Kaveh et al., 29 Sep 2025, Ghadi et al., 4 Dec 2025).

The strict pattern-reconfigurable FRIS model is path-aware rather than purely cascaded. The survey writes the received power as

$m$4

where $m$5 is the radiation-pattern gain of the $m$6-th element in the direction associated with the $m$7-th cascaded path (Xiao et al., 23 Sep 2025). In this model, pattern reconfiguration is mathematically embodied by changing the directional gain term $m$8, enabling path-aware manipulation of multipath components rather than uniform phase adjustment across a fixed pattern (Xiao et al., 23 Sep 2025).

4. Estimation, control, and optimization methodologies

Channel estimation for FRIS introduces challenges that do not appear in fixed-geometry RIS. A notable example is uplink CE under element-position uncertainty, where a two-time-scale FRIS configuration protocol is used to capture both reflection phase-shift and element-motion dynamics. By exploiting orthogonal pilot sequences and tensor modeling, the resulting estimator uses PARAFAC-based algebraic structure to obtain closed-form estimates of the user–FRIS channel, the FRIS–BS channel, and the motion-induced phase coefficients (Magalhães et al., 15 May 2026). This places FRIS estimation in a regime where configuration design and CSI acquisition are tightly coupled.

Codebook design in FRIS-assisted index modulation is framed as a response-aware problem rather than a pure layout-selection problem. The stated design rule is to select FRIS spatial codebooks according to response-domain separability rather than layout diversity alone, while actuation granularity is treated as a practical knob balancing spatial diversity, pilot overhead, coupling robustness, and hardware feasibility (Zhu et al., 21 May 2026). This design philosophy is especially relevant for pattern-reconfigurable FRIS because it ties the usefulness of a pattern state to receiver observability.

Optimization strategies vary with the FRIS abstraction. In the early performance-enhancement study, SU-SISO FRIS rate maximization is solved through particle swarm optimization, while the MU-MISO extension uses a combination of PSO, semi-definite relaxation, and minimum mean square error to jointly optimize positions, phases, and BS precoding (Salem et al., 24 Feb 2025). The dense-port discrete-phase model formulates a mixed discrete combinatorial problem over active-element selection and quantized phase shifts and addresses it through cross-entropy optimization (Xiao et al., 18 Mar 2025). Secure-communication formulations with binary activation vectors and discrete phase sets likewise employ alternating optimization combined with a generalized-eigenvalue beamforming step and a CEO-based combinatorial update for FRIS pattern and phase design (Zhu et al., 19 Nov 2025).

A more geometric line of work addresses beamforming-gain maximization by alternating between closed-form maximum-ratio-transmission at the BS and an optimal FRIS-configuration update. The key FRIS step reformulates the reflected-sum set as a Minkowski-geometry problem, leading to a one-dimensional directional search with per-port directional scoring, Top-$m$9 port selection, and optimal codeword assignment (Jeon, 12 Feb 2026). In that formulation, FRIS configuration consists of selecting which ports are active and which discrete unit-modulus codewords they apply, directly mapping pattern adaptation to a constructive phasor-sum problem (Jeon, 12 Feb 2026).

5. Communication functions and application domains

Pattern-reconfigurable FRIS has been studied as an enabling substrate for several distinct physical-layer functions. One major direction is index modulation. The FRIS-assisted IM literature treats the surface configuration index as an information carrier and develops receiver spatial modulation and receiver spatial shift keying schemes in which FRIS element-position reconfiguration changes the effective propagation response so that information bits are conveyed through receiver-antenna index selection (Zhang et al., 12 Mar 2026). The broader IM design article emphasizes that the decisive object is the receiver-observable signature induced by a configuration, not merely the physical distinctness of layouts (Zhu et al., 21 May 2026).

A second direction is beamforming and link enhancement. Early FRIS studies argue that joint control of where each reflecting element is located and what phase it applies changes the effective spatial sampling of the aperture and therefore the reflected field or beam pattern (Salem et al., 24 Feb 2025). Dense-grid activation analyses report that FRIS can substantially improve outage and ergodic-capacity metrics relative to conventional RIS by dynamically selecting optimal elements from a dense preconfigured grid (Ghadi et al., 29 May 2025). The survey’s pattern-reconfigurable case study further reports weighted-sum-rate gains over traditional RIS baselines and interprets the benefit as path-aware manipulation of multipath signals via radiation-pattern control (Xiao et al., 23 Sep 2025).

Security-oriented work has treated FRIS as a pattern-reconfigurable surface in the sense of geometry and support selection. Physical-layer security models examine secrecy outage probability and secrecy rate when a FRIS dynamically selects active reflecting positions or candidate locations from a larger set and combines that choice with phase control (Vega-Sánchez et al., 24 Nov 2025, Zhu et al., 19 Nov 2025). A related letter derives lower and upper bounds for secrecy outage probability and average secrecy capacity under spatial correlation and attributes FRIS gains to order-statistics effects, selection diversity, and the ability to choose stronger and more spatially separated elements from a larger aperture (Kaveh et al., 29 Sep 2025).

Covert communications provide another interpretation of pattern reconfiguration. In the covert FRIS model, the selected active subset $k$0 and phase matrix $k$1 jointly determine both Bob’s equivalent channel and Willie’s detection statistics, thereby shaping the reliability–covertness trade-off through active-position selection over a correlated aperture (Ghadi et al., 4 Dec 2025). This suggests that FRIS pattern control can improve legitimate reliability while simultaneously changing signal leakage to an adversary.

The survey literature also places FRIS in integrated sensing and communication, simultaneous wireless information and power transfer, mobile edge computing, and space-air-ground integrated networks. In those scenarios, the stated relevance of pattern reconfiguration lies in adaptive spatial focusing, path-aware energy synthesis, and environmental adaptability rather than in a single universal optimization target (Xiao et al., 23 Sep 2025).

6. Benchmarks, misconceptions, and open research questions

A persistent misconception is that more physical layout diversity automatically yields more useful FRIS states. The IM literature rejects that view explicitly: different feasible FRIS layouts may produce similar receiver-side responses after propagation, mutual coupling, hardware distortion, and receiver observation, causing index-detection errors. The practical consequence is that codebook quality is governed by response separability, not by layout diversity alone (Zhu et al., 21 May 2026).

A second misconception is that FRIS gains can always be attributed to spatial flexibility itself. Comparative benchmarking complicates that claim. One study designed specifically to separate position effects from aperture effects reports that spatial position optimization in FRIS provides noticeable gains over conventional RIS in the absence of phase-shift design, but that these benefits vanish when FRIS and conventional RIS employ optimal beamforming and phase-shift design over the same aperture; by contrast, FRIS continues to outperform compact RIS because the latter suffers from smaller aperture and stronger spatial correlation (Vega-Sánchez et al., 24 Nov 2025). A security-focused study reaches a closely aligned conclusion: optimizing element placement improves secrecy outage probability compared to conventional RIS without phase adaptation, but the improvement becomes less evident once conventional RIS implements optimized beamforming and phase-shift control, whereas FRIS retains a clearer advantage over compact RIS due to lower spatial correlation (Vega-Sánchez et al., 24 Nov 2025). These results do not negate FRIS utility; they refine the attribution of gain.

Hardware and control remain major open issues. The survey identifies channel estimation, hardware design, and AI-driven optimization design as primary future directions and states that the development of elements capable of dynamically reconfiguring their radiation patterns is still largely unexplored (Xiao et al., 23 Sep 2025). Several analytical papers also leave important system aspects abstracted or omitted, including switching overhead, control latency, training cost, mutual coupling beyond adopted correlation models, and exact hardware realization of the fluid mechanism (Ghadi et al., 29 May 2025, Kaveh et al., 29 Sep 2025, Ghadi et al., 4 Dec 2025).

A further open problem is methodological unification. Current FRIS research spans at least three partly overlapping notions of pattern reconfiguration: element radiation-pattern control, movable effective reflecting positions, and dense-grid active-subset selection. The literature indicates that all three can modify the effective scattering structure, but it does not yet provide a single electromagnetic-to-communication framework that links physical pattern states, channel observability, codebook separability, and robust low-overhead control across those realizations (Xiao et al., 23 Sep 2025, Zhu et al., 21 May 2026). A plausible implication is that future work on pattern-reconfigurable FRIS will need to integrate hardware-feasible pattern-state models with estimation-aware and response-aware communication design rather than treating geometry, pattern, and control as separable layers.