Flexible Intelligent Metasurfaces

• Flexible intelligent metasurfaces (FIMs) are morphable electromagnetic surfaces that dynamically adjust their physical geometry to optimize wave propagation.
• They employ both passive and active morphing mechanisms, offering spatial degrees of freedom beyond conventional phase and amplitude tuning.
• FIMs enhance system performance—improving channel capacity, diversity gain, and power efficiency—while introducing trade-offs in complexity and reliability.

Flexible intelligent metasurfaces (FIMs) are morphable electromagnetic surfaces that dynamically adjust their physical geometry to influence the radiation and propagation of electromagnetic waves. In the recent metasurface literature, they are positioned after two-dimensional reconfigurable intelligent surfaces (RIS) and three-dimensional stacked intelligent metasurfaces (SIM): RIS makes the electromagnetic boundary programmable, SIM makes wave-domain processing programmable, and FIM makes the geometry itself programmable. This added geometric control introduces a spatial degree of freedom beyond phase and amplitude tuning, so aperture shape, curvature, and inter-element spacing become design variables in wireless communication, sensing, and integrated sensing and communication (ISAC) systems (An et al., 2024, Magbool et al., 12 Mar 2026).

1. Definition, scope, and taxonomy

A defining property of an FIM is that the surface shape itself can be changed, rather than only the electromagnetic response on a fixed rigid plane. Conventional metasurfaces are described as flat and rigid, whereas FIMs use flexible substrates or active morphing mechanisms so that the surface can conform to, or actively deform into, different three-dimensional shapes. In this sense, FIMs are a broader class of reconfigurable wireless hardware in which mechanical flexibility and electromagnetic programmability are jointly available (An et al., 2024, Magbool et al., 12 Mar 2026).

The literature consistently separates FIMs into passive and active morphing forms. Passive morphing FIMs are flexible conformal surfaces that are bent, wrapped, stretched, or mounted on curved objects; their electromagnetic properties change because of the geometry, but the shape is not actively reconfigured in real time after fabrication. Active morphing FIMs, by contrast, change shape on demand in response to external control signals. Reported active implementations include carbon-nanotube electrodes embedded in elastomer sheets, liquid-metal networks in flexible materials, filamentary metal meshes actuated by Lorentz forces under currents in a static magnetic field, ionic actuator matrices, liquid-metal microfluidic platforms, Lorentz-force actuated FIMs, and soft electro-mechanical designs (An et al., 2024, Magbool et al., 12 Mar 2026).

A second, conceptually important taxonomy concerns how flexibility is realized relative to other intelligent metasurfaces. Compared with movable antennas, which reposition individual radiators, and rotational arrays, which reorient the whole aperture, FIMs reshape the surface continuously and can provide sub-wavelength geometric control across the entire aperture. In the stacked-metasurface literature, this broader FIM vision also includes architectures such as the flexible intelligent layered metasurface (FILM), in which shape reconfiguration alters near-field inter-layer propagation, and stacked flexible intelligent metasurfaces (SFIMs), in which every layer is deformable (Magbool et al., 12 Mar 2026, Niu et al., 11 Mar 2026, Magbool et al., 2 Nov 2025).

Paradigm	Structure	Primary programmability
RIS	Fixed 2D surface	EM response on a flat surface
SIM	Fixed 3D stacked architecture	Wave-domain processing through layered transmission
FIM	Morphable 3D surface	Physical geometry, and in many cases EM response as well

2. Physical realizations and system integration

Reported FIM hardware spans conformal flexible sheets, stretchable surfaces, and mechanically reconfigurable robotic morphing surfaces. Passive implementations use stretchable metasurfaces, conformal dielectric metasurfaces, and substrate-compliant meta-atom arrays with materials such as PDMS, elastomeric polymers, polyimide, and soft polymers. These are attractive because they are simple and low power, and can preserve reasonable electromagnetic performance under bending, but their geometry is usually static during operation. Active platforms add embedded actuation and support what has been termed software-defined aperture shaping, at the cost of increased complexity, power overhead, sealing and reliability concerns, thermal issues, and actuator fatigue (Magbool et al., 12 Mar 2026).

The hardware literature also identifies concrete trade-offs among morphing mechanisms. Passive stretching or compression has the lowest complexity and no shape-control power cost, but no on-demand reconfiguration. Conformal dielectric surfaces integrate easily on curved hosts, but remain static during operation. Active liquid-metal systems offer fine-grained three-dimensional control but introduce fabrication and reliability challenges. Lorentz-force actuation provides fast programmable deformation with higher power and control burden. Soft electro-mechanical actuation is precise and repeatable, but scaling and fatigue remain concerns. A recently developed shape-morphable FIM is specifically noted as being able to transform into many target three-dimensional configurations within milliseconds (An et al., 2024, Magbool et al., 12 Mar 2026).

Integration roles are correspondingly broad. An FIM can itself act as a transmitter or receiver; it can serve as a hybrid layer in front of a conventional transmitter or receiver; and it can operate as a reconfigurable reflector analogous to a RIS, but with an added mechanical adaptation layer. The surveyed deployment scenarios include base stations, transceiver arrays, indoor curtains, outdoor clothing, parachutes, balloons, and hot-air balloons, which indicates that FIMs are being studied not merely as array abstractions but as candidates for conformal, wearable, airborne, and infrastructure-integrated wireless platforms (An et al., 2024, Magbool et al., 12 Mar 2026).

Morphing can also be organized according to control timescale. The literature distinguishes real-time morphing, where the shape follows the instantaneous channel; pre-optimized static morphing, where the geometry is designed from long-term statistics and then fixed; and hybrid morphing, where a statistical baseline shape is established and only limited real-time adjustments are made. The hybrid strategy is described as the most practical compromise because it reduces control and feedback burden without fully sacrificing adaptability (Magbool et al., 12 Mar 2026).

3. Geometric channel models and optimization structure

Most communication-oriented FIM models start from a nominal uniform planar array and allow each element to move along the surface-normal direction. In a representative downlink MISO model, the $n$-th element is at $\boldsymbol{p}_n=[x_n,y_n,z_n]^T$, with $x_n$ and $z_n$ fixed by the planar layout and $y_n$ constrained by a morphing range. The steering vector is then

$$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$

so the channel depends explicitly on the surface shape through the $y_n$ coordinates (An et al., 23 Feb 2025).

For point-to-point MIMO, both transmit and receive FIMs may be deformable. The channel is then written as a sum of rank-one path contributions whose steering vectors are modified by morphing-induced phase factors. In one formulation, the FIM-aided MIMO channel is denoted $\mathbf{H}(\boldsymbol{\zeta},\boldsymbol{\xi})$, where $\boldsymbol{\zeta}$ and $\boldsymbol{\xi}$ are the transmit and receive deformation profiles, and the capacity objective becomes

$\boldsymbol{p}_n=[x_n,y_n,z_n]^T$0

under a total transmit power constraint and elementwise morphing-range constraints. This formalizes the central FIM premise that array geometry itself is an optimization variable (An et al., 23 Feb 2025).

Under statistical CSI, the geometry dependence appears through the shape-dependent spatial correlation matrix. For isotropic scattering, the normalized FIM correlation matrix is derived in closed form as

$\boldsymbol{p}_n=[x_n,y_n,z_n]^T$1

where $\boldsymbol{p}_n=[x_n,y_n,z_n]^T$2 depends on the morphing vector $\boldsymbol{p}_n=[x_n,y_n,z_n]^T$3. This means morphing changes not only instantaneous steering vectors but also channel statistics, MMSE estimation quality, and the effective interference structure in long-term-rate optimization (Kumar et al., 28 Dec 2025).

The associated optimization problems are uniformly non-convex because beamforming, phase control, and geometry are tightly coupled. The literature therefore relies on alternating or block-coordinate schemes. Representative examples include total downlink power minimization subject to user SINR and morphing constraints, solved by alternating beamformer updates and shape updates; MIMO capacity maximization by joint optimization of transmit covariance and transmit/receive FIM shapes via block coordinate descent; and multicell weighted sum-rate maximization through joint optimization of beamforming, phase shifts, and surface shape using a weighted minimum mean square error reformulation, Riemannian conjugate gradient for phase shifts, and projected gradient descent for morphing (An et al., 23 Feb 2025, An et al., 23 Feb 2025, Hu et al., 5 Jun 2026).

4. Communication performance and architectural roles

The communication literature treats FIMs as a new physical-layer mechanism for diversity gain, eigenchannel conditioning, interference suppression, and power reduction. In correlated Rayleigh fading, the diversity gain is reported to increase logarithmically with the morphing range. An FIM with morphing range $\boldsymbol{p}_n=[x_n,y_n,z_n]^T$4 can boost diversity gain by about $\boldsymbol{p}_n=[x_n,y_n,z_n]^T$5 dB, while achieving $\boldsymbol{p}_n=[x_n,y_n,z_n]^T$6 dB diversity gain may require a morphing range of $\boldsymbol{p}_n=[x_n,y_n,z_n]^T$7. In point-to-point MIMO, weak eigenchannels are enhanced by more than $\boldsymbol{p}_n=[x_n,y_n,z_n]^T$8 dB with a morphing range of $\boldsymbol{p}_n=[x_n,y_n,z_n]^T$9 relative to rigid arrays, and increasing the morphing range to $x_n$0 yields an additional improvement of about $x_n$1 dB. Under some setups, joint transmit and receive shape optimization can double the MIMO channel capacity (An et al., 2024, An et al., 23 Feb 2025).

In multiuser downlink communication, the canonical result is power reduction at fixed QoS. For a base station equipped with an FIM transmitting to multiple single-antenna users, joint optimization of beamforming and the FIM surface shape yields about $x_n$2 dB lower transmit power than a conventional rigid 2D array at a given data rate. In a separate comparison, a capacity of $x_n$3 bit/s/Hz is achieved with $x_n$4 dBm transmit power using FIMs, whereas a rigid array requires $x_n$5 dBm for the same capacity; another cited study reports that the inherent selection gain of FIMs can nearly halve the required transmit power for multi-user communication under the same rate constraints (An et al., 23 Feb 2025, Magbool et al., 12 Mar 2026).

Reflective and transmissive architectures both appear in the literature, and they clarify a recurring misconception: mechanical movement is not merely auxiliary to phase control. In a SISO FIM architecture that supports both element movement (EM) and passive beamforming (PBF), the PBF-only mode is reported to be less effective than the EM-only mode in enhancing received signal strength. In a multi-element, multi-path scenario, EM-only improves the received signal power by $x_n$6 compared to PBF-only, while the joint EM-PBF mode performs best overall. In transmissive FIM models, optimizing phase shifts for a tentative shape reduces the high-dimensional problem to one-dimensional shape subproblems, and more than $x_n$7 dB channel-gain improvement over rigid baselines is reported in the corresponding scenarios (Yang et al., 14 Mar 2025, Hu et al., 8 Oct 2025).

The rate gains persist under more system-level assumptions. In a multicell MU-MISO network with an FIM at the cell boundary, joint optimization of beamforming, phase shifts, and surface shape provides about $x_n$8 weighted sum-rate improvement over a rigid RIS benchmark; in a $x_n$9-cell/$z_n$0-user example, edge-user rates improve from about $z_n$1 bit/s/Hz with RIS to about $z_n$2 bit/s/Hz with FIM. Under statistical CSI, FIM gains are strongest when channels are spatially correlated: at $z_n$3 dBm and $z_n$4 dBm, average sum spectral efficiency improves by about $z_n$5 for $z_n$6 and about $z_n$7 for $z_n$8, while the gain diminishes when the channels are weakly correlated (Hu et al., 5 Jun 2026, Kumar et al., 28 Dec 2025).

5. Sensing, ISAC, and high-mobility operation

FIMs are also studied as adaptive sensing apertures. In multi-target wireless sensing, the metric of interest is often the cumulated probing power at target locations, optimized jointly over transmit covariance and FIM shape under per-antenna power and morphing constraints. For a $z_n$9 transmitting FIM at $y_n$0 GHz with three targets, FIM-MIMO achieves the highest cumulated probing power among rigid and flexible phased-array and MIMO benchmarks. At $y_n$1, the reported gains are about $y_n$2 for phased-array mode and about $y_n$3 for MIMO mode relative to rigid arrays, with convergence typically within $y_n$4 BCD iterations (Teng et al., 29 Jun 2025).

Surveyed sensing case studies emphasize that this is not only a beam-steering effect. A cited FIM-based sensing system improves received sensing power by $y_n$5 relative to a rigid-array system, and a configuration with $y_n$6 radiating elements and morphing range $y_n$7 can illuminate three distinct target angles, whereas the rigid array effectively illuminates only two. The same survey argues that FIM-based ISAC designs can achieve a better Pareto front than rigid systems because shape control provides an additional degree of freedom for communication-sensing resource allocation (Magbool et al., 12 Mar 2026).

The ISAC optimization literature makes this geometric role explicit through Cramér-Rao-bound minimization. In one formulation, both the transmit and receive FIMs are modeled as flexible arrays whose element positions along the $y_n$8-axis are bounded. The sensing metric is the angle-parameter CRB derived from a Fisher information matrix that depends on beamforming and on the transmit and receive steering vectors. Joint optimization of the beamforming matrix, transmit FIM shape, and receive FIM shape under power, QoS, and shape constraints reduces CRB relative to rigid arrays, with joint transmit-and-receive shaping outperforming transmit-only and receive-only shaping. A related formulation uses a deep deterministic policy gradient actor-critic algorithm with a constraint-aware reward to minimize the CRB while satisfying QoS constraints (Zhang et al., 23 Jan 2026, Wang et al., 1 Jul 2026).

High-mobility operation extends the same idea into doubly-dispersive channels. A FIM-parameterized doubly-dispersive MIMO channel model has been proposed for OFDM, OTFS, and AFDM waveforms, in which the channel depends on delay-Doppler parameters and on the FIM geometry vectors at the transmitter and receiver. In the reported simulations, moving from no FIM to a randomly tuned FIM yields about $y_n$9 dB achievable-rate gain, and optimization of the FIM shape adds another $$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$0 dB. MUSIC-based sensing results further show that optimized FIMs produce strong peaks at the true scatterer locations, whereas no-FIM baselines can give incorrect peaks and poor localization (Ranasinghe et al., 24 Jul 2025).

6. Channel estimation, learning-based control, and open problems

Continuous deformation makes CSI acquisition a central bottleneck. The core difficulty is that channel estimation must be carried out over a continuous space rather than a fixed finite-dimensional array geometry. Proposed tools include compressed sensing, space-alternating generalized expectation maximization, and shape-aware estimation protocols. The survey literature also notes that for fast-changing channels with short coherence time, ergodic optimization across coherence blocks may be preferable to instantaneous shape adaptation (An et al., 2024).

Model-based estimation frameworks reflect this geometry dependence. For dual-FIM MIMO, one approach uses a split single-time-scale training protocol: first the receiver morphs while the transmitter remains fixed, then the transmitter morphs while the receiver remains fixed. The resulting tensor observations admit PARAFAC decompositions, and a two-phase alternating least squares estimator recovers common transmit and receive steering matrices together with per-slot morphing-dependent factors. The per-iteration complexity is reported as

$$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$1

and numerical results show that larger morphing range improves recoverability because it increases phase diversity (Romano et al., 28 May 2026).

Sparse-recovery approaches instead optimize the training geometries. In an uplink FIM-enhanced communication system, the orthogonal matching pursuit pipeline is customized by minimizing the column coherence of the measurement matrix over the morphing variables, using a Davidon-Fletcher-Powell quasi-Newton method under morphing-range constraints. For $$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$2, $$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$3, $$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$4, and $$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$5, the reported gains include a $$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$6 dB NMSE reduction versus a rigid UPA at $$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$7 and uplink SNR $$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$8 dB, a $$\boldsymbol{a}(\boldsymbol{y},\phi,\theta) = \left[ 1,\dots,e^{j\kappa(x_n\sin\theta\cos\phi+y_n\sin\theta\sin\phi+z_n\cos\theta)},\dots \right]^T, \quad \kappa=\frac{2\pi}{\lambda},$$9 dB NMSE reduction at $y_n$0, rapid coherence stabilization in about $y_n$1 iterations, and about $y_n$2 dB downlink SNR gain over UPA when $y_n$3 using estimated CSI (Jiang et al., 31 Mar 2026).

Learning-based methods have been proposed to move beyond explicit channel priors. In a downlink multi-user mmWave system with an FIM transmitter, channel estimation has been formulated as learning the continuous operator that maps pilot-shape measurements and a target deformation to the target channel response. Model-based baselines include nearest-neighbor interpolation, KNN-based local linear interpolation, kernel ridge regression, and OMP with deformation-set design guided by mutual coherence. A Fourier neural operator (FNO) and a hierarchical FNO (H-FNO) are then used to learn the continuous mapping in function space. The H-FNO is reported to outperform model-based baselines in estimation accuracy and pilot efficiency, generalize to larger arrays such as $y_n$4 to $y_n$5 without retraining, and learn an anisotropic spatial filter adapted to the physical geometry of the FIM (Xiao et al., 1 Aug 2025).

The outstanding open problems are hardware-system co-design problems rather than purely algorithmic gaps. Repeatedly cited issues include energy consumption, the absence of experimentally validated power-consumption models for surface morphing, morphing speed relative to channel coherence time, mechanical reliability, fatigue, control complexity, calibration error, quantized morphing levels, losses, non-ideal phase responses, sealing and leakage in liquid-metal systems, thermal issues in electromechanical actuation, and the durability of conformal materials in practical deployments. This suggests that the decisive question for FIMs is not whether geometry is a useful degree of freedom—the literature already shows that it is—but how to coordinate geometry control, electromagnetic design, CSI acquisition, and actuation constraints at network timescales (Magbool et al., 12 Mar 2026, An et al., 2024).