Fluid Reconfigurable Intelligent Surface

• FRIS is a programmable metasurface that extends classical RIS by enabling dynamic spatial reconfiguration and adaptive phase/amplitude control.
• It employs techniques like movable elements, fluidic materials, and selective activation on dense grids to optimize channel response and index modulation.
• FRIS design involves trade-offs in actuation granularity and overhead, utilizing advanced optimization methods under Rayleigh and Nakagami fading models.

Fluid reconfigurable intelligent surface (FRIS) denotes a class of programmable metasurfaces that extend classical reconfigurable intelligent surfaces (RIS) by adding spatial reconfigurability to conventional electromagnetic tuning. In the FRIS literature, this additional degree of freedom is realized through switchable effective apertures, pattern-reconfigurable units, fluidic conductive materials, movable reflecting elements, or dense preset grids from which only a subset of positions is activated at a given time. Accordingly, FRIS is treated both as a geometric generalization of RIS and as a metasurface-level analogue of fluid antenna systems, with the common objective of making the effective active layout of the surface time-varying rather than fixed (Zhu et al., 21 May 2026, Khazaee et al., 30 Mar 2026, Salem et al., 24 Feb 2025).

1. Architectural concept and variants

The defining distinction between RIS and FRIS is that RIS controls the phase and, in some models, amplitude of fixed-position elements, whereas FRIS controls phase or amplitude together with the spatial layout or active region of the surface. In the broad formulation used for FRIS-assisted index modulation, the controlled resources include phase/amplitude and spatial layout, and the main role shifts from reflection control to channel adaptation through layout plus reflection (Zhu et al., 21 May 2026). In the earliest system-level formulation, the surface aperture is partitioned into non-overlapping subareas, each containing one “fluid element” whose position can change within its assigned subarea while its reflection phase remains tunable (Salem et al., 24 Feb 2025).

The literature does not enforce a single physical realization. One stream treats fluidity as actual positioning reconfigurability: elements or effective reflecting points move within a predefined aperture, sometimes under minimum-spacing constraints intended to mitigate coupling (Khazaee et al., 30 Mar 2026, Salem et al., 24 Feb 2025). Another stream adopts a “virtual fluid” interpretation in which a fixed dense 2D grid spans the aperture and only a subset of elements is turned ON at any time; the effective active geometry is then reshaped by ON/OFF selection rather than by literal mechanical motion (Kaveh et al., 29 Sep 2025, Xiao et al., 18 Mar 2025). These formulations are compatible at the modeling level because both make the set of active radiating positions time-varying.

A further specialization is FIRES, the fluid integrated reflecting and emitting surface, which combines FRIS-style spatial fluidity with simultaneous reflection and transmission. In FIRES, each fluid element occupies one of several preset positions within its own subarea, applies independent reflection and transmission phases, and operates under an energy-splitting constraint $\beta_r+\beta_t=1$; this makes FIRES a concrete STAR-capable subclass of FRIS rather than a separate concept (Ghadi et al., 19 May 2025).

2. Channel models, correlation control, and statistical characterization

Two modeling viewpoints dominate. The first is an effective-response abstraction, used especially for FRIS-assisted index modulation, in which each surface configuration $\mathcal{S}_i$ is mapped directly to an observable receiver-side response $\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$ through

$$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$

This deliberately subsumes propagation, mutual coupling, hardware distortion, and calibration into a coupling-aware response model rather than an idealized independent-element reflection matrix (Zhu et al., 21 May 2026). The second viewpoint is a cascaded-channel model in which FRIS geometry enters through a correlation matrix of the selected elements. In the exact Rayleigh analysis, a blocked BS–FRIS–UE downlink is modeled as

$$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$

with $$G_0\triangleq |\mathbf{g}_u^{\mathrm H}\mathbf{A}\mathbf{g}_f|^2$$ and $$\mathbf{A}=\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}$$ (Khazaee et al., 30 Mar 2026).

Spatial correlation is usually modeled through Jakes- or Clarke–Jakes-type kernels. For active elements at positions $\mathbf p_{i,j}$, the Rayleigh formulation uses

$$\mathbf{R}_{\mathcal S}=\Big[J_0\!\Big(\tfrac{2\pi}{\lambda_c}\|\mathbf p_{i,j}-\mathbf p_{i',j'}\|_2\Big)\Big]_{m,m'\in\mathcal S},$$

and fluidic reconfiguration is represented by choosing $\mathcal S$ so that active elements are sufficiently separated, often through a correlation-cap or sub-lattice rule (Khazaee et al., 30 Mar 2026, Khazaee et al., 7 Jul 2026). This is the central analytical mechanism by which FRIS reshapes spatial correlation: rather than merely tuning phases on a fixed dense array, it changes which correlation modes are present.

The exact statistical theory for correlated Rayleigh FRIS-assisted cascades shows that the end-to-end gain distribution can be written as a finite linear combination of $\mathcal{S}_i$0-distributions parameterized by the eigenvalues and multiplicities of $\mathcal{S}_i$1. This yields exact closed-form expressions for outage probability and ergodic capacity, and identifies fully correlated, effectively decorrelated, and intrinsically uncorrelated regimes as special cases (Khazaee et al., 30 Mar 2026). Under that single-cascade Rayleigh model, the outage-based asymptotic analysis gives diversity order $\mathcal{S}_i$2, independent of the number of active elements, the correlation structure, and the phase configuration (Khazaee et al., 30 Mar 2026). A separate Nakagami-$\mathcal{S}_i$3 analysis constructs a physically consistent correlation model at the Gaussian-cluster level, applies a weighted Cauchy–Schwarz bound to the sum-product channel, and derives strict outage lower bounds via Gamma-mixture and Meijer-$\mathcal{S}_i$4 representations; in the i.i.d. Nakagami-$\mathcal{S}_i$5 case, the resulting high-SNR behavior is driven by composite shape parameters $\mathcal{S}_i$6 and $\mathcal{S}_i$7 (Khazaee et al., 7 Jul 2026).

Alongside exact and bound-based analyses, a tractable approximation line models the equivalent FRIS gain by a Gamma random variable with parameters

$\mathcal{S}_i$8

where $\mathcal{S}_i$9 is the correlation matrix of the selected active subset. This produces closed-form approximations for the gain PDF/CDF, outage probability, and a Jensen-type upper bound on ergodic capacity (Ghadi et al., 29 May 2025). The exact Rayleigh results were introduced partly to benchmark and correct such approximation-based methods in the tails, especially for outage analysis (Khazaee et al., 30 Mar 2026).

3. Configuration spaces, actuation granularity, and optimization methods

FRIS design is intrinsically mixed discrete–continuous. The variables may include element positions, activation indicators, discrete or continuous phase shifts, and BS beamforming vectors. In the SU-SISO and MU-MISO formulations, the standard objective is rate maximization under subarea constraints and minimum inter-element spacing, with channels depending explicitly on element coordinates through LoS steering vectors and correlation matrices (Salem et al., 24 Feb 2025). For secure MISO wiretap channels, the joint design extends to AP beamforming, activated-element selection, and discrete FRIS phases, producing a mixed-integer nonlinear program that is explicitly identified as NP-hard (Zhu et al., 19 Nov 2025).

Several algorithmic families recur. Particle swarm optimization is used for position optimization in SU-SISO FRIS, for alternating position/phase/precoder design in MU-MISO FRIS, for FIRES multicast geometry design, and for FRIS-aided ambient backscatter links (Salem et al., 24 Feb 2025, Ghadi et al., 19 May 2025, Kaveh et al., 29 Sep 2025). Cross-entropy optimization is used when the dominant variables are combinatorial, notably for joint ON/OFF selection and discrete phase design over dense grids, and again inside an alternating-optimization framework for secure FRIS beamforming (Xiao et al., 18 Mar 2025, Zhu et al., 19 Nov 2025). In the secure MISO case, the beamforming subproblem reduces to a generalized Rayleigh quotient whose maximizer is the principal generalized eigenvector of $\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$0 (Zhu et al., 19 Nov 2025). A more recent beamforming-gain study formulates finite-resolution FRIS configuration through a Minkowski-geometry reformulation of the codebook superposition, converting the FRIS subproblem into a one-dimensional maximization over a directional parameter while retaining a closed-form MRT update at the BS (Jeon, 12 Feb 2026).

A recurrent practical variable is actuation granularity, defined as the smallest physical unit at which the FRIS can be reconfigured. The FRIS-assisted index-modulation study distinguishes element-level, group-level, and block-level control. Finer granularity increases the number of candidate layouts and potential spatial indices but also raises pilot overhead, control complexity, and sensitivity to coupling and hardware drift; coarser granularity reduces overhead but limits diversity (Zhu et al., 21 May 2026). This trade-off is summarized by the normalized net spatial-index throughput

$\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$1

with $\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$2 the number of response-separable codewords, $\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$3 the overhead fraction, and $\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$4 the spatial-index detection error probability. In the illustrative setting of that paper, group-level control achieves the best net throughput because it balances separability, overhead, and robustness (Zhu et al., 21 May 2026).

4. Information-bearing surface states and communication schemes

FRIS is not limited to passive channel enhancement. One major direction treats the surface configuration itself as an information-bearing symbol. In FRIS-assisted index modulation, a spatial codebook

$\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$5

maps $\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$6 bits to one FRIS configuration per reconfiguration interval, while conventional waveform modulation operates in parallel. Detection then becomes a multi-hypothesis problem over induced receiver responses: $\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$7 The central design problem is not raw layout diversity but response-domain separability, quantified by

$\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$8

The proposed codebook criterion maximizes the minimum pairwise response distance over feasible configurations, because distinct physical layouts may collapse to nearly identical receiver responses after propagation, mutual coupling, and hardware distortion (Zhu et al., 21 May 2026).

A more explicit IM realization uses FRIS to focus energy onto one of several receiver antennas, so that bits are conveyed by receiver-antenna index selection. This yields FRIS-assisted receiver spatial modulation (FRIS-RSM), where the index and a conventional symbol both carry information, and receiver spatial shift keying (FRIS-RSSK), where only the index is used. The design combines strongest-link selection over a dense FRIS candidate grid with phase alignment, supports both continuous and $\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}$9-bit phase control, and derives MGF-based unconditional pairwise error probabilities and union-bound BER expressions under double-Rayleigh cascaded fading (Zhang et al., 12 Mar 2026). To reduce detection cost, that work proposes a two-stage Top-$$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$0 list detector whose complexity scales with $$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$1 rather than the full receiver-index alphabet, approaching ML performance for moderate list sizes (Zhang et al., 12 Mar 2026).

FRIS has also been integrated into ambient backscatter communication. In the FRIS-assisted AmBC model, a backscatter tag communicates with a reader through a blocked or weak direct path, while the FRIS optimizes its element positions and ON/OFF pattern to maximize the achievable backscatter rate. Under optimal phase alignment, the effective channel magnitude reduces to a coherent sum over the active set, and PSO is used to obtain near-optimal fluid configurations. Simulations in that work show that FRIS-aided AmBC achieves higher throughput than a conventional RIS-based AmBC baseline, especially as the host aperture and the candidate-position grid become larger (Kaveh et al., 29 Sep 2025).

5. Physical-layer security and channel estimation under motion uncertainty

Physical-layer security has become a major FRIS application. In one secure downlink model, a BS communicates with Bob in the presence of Eve through a FRIS that activates only $$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$2 elements selected from a larger aperture using Bob’s CSI. Bob’s equivalent channel gain is approximated as $$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$3 with

$$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$4

while Eve’s gain is modeled as exponential with rate $$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$5. This leads to a Jensen-type upper bound on average secrecy capacity and a Meijer-$$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$6-based lower bound on secrecy outage probability (Kaveh et al., 29 Sep 2025). The same paper emphasizes that partial activation can be sufficient: selecting a properly chosen subset with $$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$7 can improve secrecy while reducing phase-control and circuitry costs (Kaveh et al., 29 Sep 2025).

A second secrecy formulation considers a MISO wiretap channel with AP beamforming, FRIS position selection over $$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$8 candidate slots, and $$\mathbf{y}=\mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)}x+\mathbf{n}.$$9-bit discrete phases. The secrecy-rate objective is

$$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$0

subject to a power constraint, binary selection variables, a cardinality constraint $$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$1, and discrete phase alphabet $$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$2. The alternating-optimization solution couples a generalized-eigenvalue beamformer with cross-entropy search over FRIS configurations and shows that random position selection already outperforms fixed-position RIS in some regimes, while optimized selection plus phase design improves further (Zhu et al., 19 Nov 2025).

A third secrecy study is particularly important for benchmarking claims about FRIS gains. It approximates the optimized end-to-end FRIS and RIS channels by Nakagami distributions fitted via maximum-likelihood estimation, then evaluates secrecy outage probability analytically. The reported conclusion is nuanced: optimizing FRIS element placement significantly improves secrecy outage over conventional RIS when the latter lacks phase adaptation, but those gains become less evident once the conventional RIS also uses optimized beamforming and phase-shift control. FRIS nonetheless maintains a clear advantage over compact RIS layouts because the compact geometry incurs stronger spatial correlation (Vega-Sánchez et al., 24 Nov 2025).

Channel estimation introduces another FRIS-specific difficulty: position uncertainty. In a multi-user uplink MISO system assisted by FRIS, the reflecting elements select effective radiating positions from a dense preset grid, and motion errors induce unknown phase terms

$$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$3

To handle this, a two-time-scale FRIS configuration protocol keeps electronic phase shifts fixed within each sub-frame while varying positions across blocks, generating a tensor structure

$$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$4

With orthogonal pilots and tensor unfolding, the resulting framework gives closed-form least-squares/Khatri–Rao estimates when motion is known, and HOSVD-based joint estimates of $$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$5, $$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$6, and $$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$7 when motion-induced phases are unknown (Magalhães et al., 15 May 2026). The reported numerical result is that ignoring motion mismatch severely degrades NMSE, whereas joint estimation largely recovers the performance of the ideal-motion benchmark (Magalhães et al., 15 May 2026).

6. Comparative interpretation, misconceptions, and research directions

A central controversy in the FRIS literature concerns the source of its gains. A fair-comparison study distinguishes two baselines: a conventional RIS with the same aperture and same number of active elements, and a compact RIS with the same number of active elements but a smaller aperture and sub-$$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$8 spacing. Its main conclusion is regime-dependent. When no beamforming or phase optimization is applied, FRIS spatial position optimization yields noticeable gains over a conventional RIS. When both FRIS and conventional RIS employ optimized beamforming and phase design over the same aperture, those gains vanish and position optimization becomes irrelevant. FRIS remains superior to compact RIS, however, because compact layouts suffer from smaller aperture and stronger spatial correlation (Vega-Sánchez et al., 24 Nov 2025). This result does not negate other FRIS papers; it narrows the conditions under which spatial flexibility itself, rather than aperture or phase control, is the decisive factor.

A second recurring misconception is that denser physical layout automatically implies more reliable spatial indexing. The response-aware FRIS-IM formulation states the opposite: many feasible layouts do not generate many reliable spatial indices, because different configurations can induce similar receiver-side responses after propagation, coupling, hardware distortion, and observation. Consequently, maximizing layout diversity alone is insufficient, and codebooks should be built around response-domain separability, training cost, and controllability (Zhu et al., 21 May 2026). A related practical lesson is that the densest control is not always best; moderate actuation granularity may outperform element-level control once overhead and robustness are included (Zhu et al., 21 May 2026).

Current open directions cluster around four themes. First, scalable low-overhead learning of response-aware or correlation-aware codebooks remains unresolved, particularly when exhaustive testing of FRIS configurations is infeasible (Zhu et al., 21 May 2026). Second, richer physics are entering the models: FIRES explicitly couples fluid positions with simultaneous reflection and transmission, while recent FRIS analyses point toward joint modeling of fluid dynamics, electromagnetic behavior, and communication performance (Ghadi et al., 19 May 2025, Zhu et al., 21 May 2026). Third, robust system design must absorb reconfiguration latency, motion errors, hardware drift, and partial CSI, rather than treating these as negligible perturbations (Magalhães et al., 15 May 2026, Zhu et al., 19 Nov 2025). Fourth, multi-user and multifunction FRIS—especially for integrated sensing and communications, scheduling, and secrecy—require codebooks and control policies that remain separable across users while respecting correlation, latency, and hardware limits (Zhu et al., 21 May 2026).

Across these strands, FRIS emerges not as a single hardware object but as a modeling and design class in which the environment’s effective geometry becomes programmable. The literature now supports exact statistical characterization in some Rayleigh settings, rigorous outage bounds in correlated Nakagami-$$y=\sqrt{P L_f L_u}\;\mathbf{g}_u^{\mathrm H}\mathbf{R}_{\mathcal S}^{1/2}\boldsymbol{\Phi}\mathbf{R}_{\mathcal S}^{1/2}\mathbf{g}_f\,x+z,$$9 fading, practical optimization procedures for dense preset grids and movable subareas, and a clearer understanding of when spatial flexibility materially changes performance relative to well-optimized fixed-geometry RIS (Khazaee et al., 30 Mar 2026, Khazaee et al., 7 Jul 2026, Vega-Sánchez et al., 24 Nov 2025).