Movable Intelligent Surface (MIS)

• Movable Intelligent Surface (MIS) is an advanced reconfigurable system that dynamically adjusts both spatial geometry and electromagnetic response for improved wireless performance.
• MIS architectures include ME-RIS, dual-layer designs, semi-passive sensing, flexible metasurfaces, 6D movable configurations, and Spider RIS, each offering unique mechanical control strategies.
• Optimization and channel estimation in MIS integrate continuous geometric variables with discrete motion, achieving measurable gains such as up to 20% rate improvements and over 3 dB channel gains.

Searching arXiv for recent MIS papers and closely related architectures. arXiv search query: "Movable Intelligent Surface RIS movable metasurface channel estimation sensing 2025 2026". Movable Intelligent Surface (MIS) denotes an intelligent surface whose geometry is controllable in addition to, or instead of, its electromagnetic response. In the recent literature, the term spans several non-identical but related architectures: movable-element reconfigurable intelligent surfaces (ME-RIS) whose passive elements move within prescribed regions; two-layer transmissive metasurfaces whose beam patterns are switched by sliding a smaller static-phase layer across a larger one; semi-passive IRSs with movable active sensors; flexible intelligent metasurfaces whose elements move along the surface normal and thereby morph the surface shape; six-dimensional movable metasurfaces with element translation and global yaw-pitch-roll rotation; and movable panels such as Spider RIS. Across these variants, the unifying idea is that propagation control is no longer restricted to fixed geometry and phase-only adaptation, but is extended to spatial reconfiguration of elements, sub-surfaces, or whole panels (Zheng et al., 2024, Hokmabadi et al., 13 Jan 2026, Peng et al., 24 Nov 2025, Hu et al., 8 Oct 2025, Shen, 20 Oct 2025, Yildirim et al., 2024).

1. Architectural taxonomy

MIS is not a single hardware form. The literature distinguishes at least six recurrent realizations.

Architecture	Movable component	Primary control variables
ME-RIS	Individual passive RIS elements	2D element positions and phase shifts
Dual-layer MIS/MRIS	A smaller stacked sub-surface	Static phases and overlap position
Semi-passive sensing MIS	Active sensors on an IRS aperture	Group sensor positions
FIM	Element displacements normal to the surface	Surface shape and phase shifts
6DMM	3D element positions and whole-panel rotation	Positions, yaw-pitch-roll, phase shifts
Spider RIS	Entire RIS panel on a 2D platform	Panel position and phase shifts

In the ME-RIS formulation, each RIS element has two degrees of freedom: phase reconfigurability and spatial mobility. The $n$-th element is located at $\mathbf{r}_n = [x_n,y_n]^T$, and the element position matrix is

$$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$

while the phase profile is

$$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$

The paper explicitly describes this as “dual reconfigurability in space and phase” (Hokmabadi et al., 13 Jan 2026).

A second major family uses two closely stacked transmissive metasurfaces. A large fixed layer, usually denoted MS1 or S1, carries static phases, while a smaller MS2 or S2 slides over it. Different overlap positions induce different composite phase maps and therefore different beam patterns. The overlap is represented by a binary selection matrix and padding vector,

$$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$

and the effective composite phase is

$$\boldsymbol{v}_u = \bar{\boldsymbol{\theta}}_u \odot \boldsymbol{\phi}.$$

In this formulation, “position selection” is equivalent to beam-pattern scheduling, and dynamic beamforming is achieved with static phase shifts and mechanical reconfigurability (Zheng et al., 2024, Zheng et al., 21 Nov 2025, Zhuang et al., 23 Dec 2025, Zheng et al., 19 Sep 2025, Alcantara et al., 29 May 2026).

A third line of work concerns semi-passive sensing surfaces. Here the passive IRS aperture is fixed, but a set of active sensors integrated on the surface can move as groups on a 1D segment of length $D$. The surface thus becomes an intelligent aperture with movable sampling points rather than a fully movable passive array (Peng et al., 24 Nov 2025).

Flexible and high-dimensional movable surfaces broaden the concept further. Flexible intelligent metasurfaces model per-element normal displacement through a deformation vector

$\mathbf{d} = [d_1,\ldots,d_N]^T,$

and the effective steering vector becomes

$$\mathbf{a}(\theta,\phi,\mathbf{d}) = \mathbf{a}_{\text{upa}}(\theta,\phi)\odot \mathbf{a}_d(\theta,\phi,\mathbf{d}),$$

with

$$\mathbf{a}_d(\theta,\phi,\mathbf{d}) = e^{j\kappa \mathbf{d}\cos\theta\cos\phi}.$$

The 6D movable metasurface extends mobility to 3D element translation and global yaw-pitch-roll rotation via

$\mathbf{r}_n = [x_n,y_n]^T$0

Spider RIS, by contrast, moves the entire RIS together with all of its elements on a two-dimensional ceiling or wall platform (Hu et al., 8 Oct 2025, Shen, 20 Oct 2025, Yildirim et al., 2024).

2. Geometry, channel, and signal representations

The common mathematical feature of MIS models is that geometric variables enter the channel explicitly. In ME-RIS-aided full-duplex MISO, the BS itself may also employ movable antennas, with transmit and receive position matrices

$\mathbf{r}_n = [x_n,y_n]^T$1

All movable elements are subject to box constraints and minimum spacing constraints such as

$\mathbf{r}_n = [x_n,y_n]^T$2

typically with $\mathbf{r}_n = [x_n,y_n]^T$3 (Hokmabadi et al., 13 Jan 2026).

For communication links, the effective channel combines direct and RIS-mediated terms. In the full-duplex downlink,

$\mathbf{r}_n = [x_n,y_n]^T$4

and in the uplink,

$\mathbf{r}_n = [x_n,y_n]^T$5

The resulting SINRs are

$\mathbf{r}_n = [x_n,y_n]^T$6

$\mathbf{r}_n = [x_n,y_n]^T$7

with

$\mathbf{r}_n = [x_n,y_n]^T$8

The movable geometry affects $\mathbf{r}_n = [x_n,y_n]^T$9, and related cascaded channels (Hokmabadi et al., 13 Jan 2026).

A compact representation of position-dependent channels is the field-response model

$$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$0

where transmit and receive field-response matrices encode phases that vary linearly with element positions inside small movement regions. The BS–RIS channel becomes

$$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$1

This formalism is central when geometry is a variable because path gain magnitudes and angles are treated as approximately constant, while phases vary with position (Hokmabadi et al., 13 Jan 2026).

In sliding MIS and MRIS models, geometry is encoded combinatorially rather than continuously. A position index $$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$2 or $$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$3 determines which MS2 elements overlap which MS1 elements, through $$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$4 or $$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$5. The equivalent phase vector induced by the movable layer is then lifted to the fixed aperture, and the resulting beam pattern is indexed by the overlap position itself (Zheng et al., 2024, Zheng et al., 21 Nov 2025, Zhuang et al., 23 Dec 2025, Alcantara et al., 29 May 2026).

For sensing-oriented MIS, geometry also appears directly in statistical limits. In the semi-passive IRS with group movable sensors, the steering vector depends on sensor positions $$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$6,

$$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$7

and the resulting CRB under optimal beamforming and IRS phases is

$$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$8

The inverse proportionality to $$\mathbf{R} = [\mathbf{r}_1,\ldots,\mathbf{r}_N] \in \mathbb{R}^{2\times N},$$9 makes the effect of movable sensing points explicit (Peng et al., 24 Nov 2025).

3. Optimization and inference methods

MIS optimization problems are typically mixed continuous-discrete, non-convex, and strongly coupled. In the full-duplex MA-BS plus ME-RIS architecture, the joint design variables are

$$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$0

and the objective is

$$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$1

subject to BS power, uplink power, QoS, unit-modulus, box, and spacing constraints. The proposed solver uses alternating optimization, semidefinite relaxation for beamforming, sequential rank-one constraint relaxation, a closed-form generalized-eigenvector combiner, bisection for uplink power, and successive convex approximation with trust regions for phase and position optimization (Hokmabadi et al., 13 Jan 2026).

Sliding MIS with static phase shifts leads to a different optimization structure. For fairness, the minimum-user-throughput problem is handled by a penalty method, block coordinate descent, and successive convex approximation. For throughput maximization, the variables $$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$2, $$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$3, and the relaxed scheduling matrix are placed on a product manifold and optimized by a Riemannian conjugate-gradient method. A related element-wise mobility “performance ceiling” problem also uses penalty-assisted manifold optimization (Zheng et al., 21 Nov 2025).

Wireless sensing with MIS adopts a max-min worst-case SINR design. The formulation jointly optimizes MIS phase shifts and schedules MS2’s position, and the mixed-integer non-convex problem is solved by a Riemannian Augmented Lagrangian Method. The same work also derives a heuristic beam-steering construction in which MS1 uses a quadratic phase profile and MS2 uses the sign-reversed profile, so that beam steering is realized by displacement laws for $$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$4 (Zheng et al., 19 Sep 2025).

Several architectures admit more specialized solvers. The semi-passive sensing MIS yields a closed-form optimal sensor placement: the movable sensors should be arranged as two tightly packed subarrays at the two ends of the movement region, with a symmetric variant when the number of groups is odd. Flexible intelligent metasurfaces use PSO and multi-interval gradient descent in SISO, and alternating optimization in MISO. The 6D movable metasurface employs cross-entropy optimization over beamforming vectors, phase shifts, element positions, and rotation angles. Spider RIS combines angular-based hybrid beamforming with PSO over RIS position and phase shifts. Robust secure MRIS-assisted ISAC uses alternating optimization, convex bounds for Eve uncertainty, the S-procedure, and penalty dual decomposition (Peng et al., 24 Nov 2025, Hu et al., 8 Oct 2025, Shen, 20 Oct 2025, Yildirim et al., 2024, Zhuang et al., 23 Dec 2025).

Channel estimation for MIS introduces a distinct signal-processing viewpoint. A dual-layer transmissive MIS with discrete positions produces a fourth-order PARAFAC tensor

$$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$5

with decomposition

$$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$6

A trilinear alternating least-squares receiver estimates the UT–MIS channel, MIS–BS channel, and unknown movable-layer response without prior calibration of the movable layer. The identifiability conditions include

$$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$7

This suggests that motion can serve not only as a propagation control variable but also as a structured training dimension (Alcantara et al., 29 May 2026).

4. Communication performance and deployment gains

Reported gains are architecture-dependent, but a consistent pattern is that mobility is most effective when it adds geometric freedom that fixed surfaces cannot realize.

Setting	Reported outcome	Source
MA-BS + ME-RIS, full-duplex MISO, $$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$8	About 18% sum-rate improvement over FA-BS + FE-RIS	(Hokmabadi et al., 13 Jan 2026)
MA-BS + ME-RIS, $$\boldsymbol{\Phi} = \operatorname{diag}(\theta_1,\ldots,\theta_N),\quad \theta_n = e^{j\vartheta_n},\ |\theta_n|=1.$$9 dBm	About 15% improvement vs fixed architecture	(Hokmabadi et al., 13 Jan 2026)
MA-BS + ME-RIS, $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$0	DL improves by ≈ 20% and UL by ≈ 12% vs fully fixed	(Hokmabadi et al., 13 Jan 2026)
FIM, $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$1	More than 3 dB channel gain over rigid RIS	(Hu et al., 8 Oct 2025)
Block-level and element-wise MIS	Element-wise MIS can recover about 60% of the gap between block-level MIS and dynamic RIS	(Zheng et al., 21 Nov 2025)
MRIS-assisted ISAC	1.51 bps/Hz minimum secrecy rate vs 0.44 bps/Hz for SRIS	(Zhuang et al., 23 Dec 2025)

In the full-duplex 6G MISO study, the fully movable configuration improves with RIS size, outperforms fixed-geometry baselines across residual self-interference and BS power settings, and shows that mobility is especially valuable in interference-limited regimes. The uplink remains more vulnerable to residual self-interference, but movable antennas and RIS elements can jointly strengthen desired links and suppress both self-interference and inter-user interference (Hokmabadi et al., 13 Jan 2026).

The static-phase dual-layer MIS line addresses a different cost-performance point. It is explicitly positioned between dynamic RIS, with dense control circuitry and continuous power consumption, and single-layer static surfaces, which are low cost but support only one beam pattern. Simulations show that even a tiny MS2 such as $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$2 significantly improves minimum rate over a single static surface, that moderate MS2 size can maximize throughput when the total number of elements is fixed, and that manifold-based designs run much faster than BCD-SCA or PSO while achieving similar or slightly better throughput (Zheng et al., 21 Nov 2025).

Surface-shape mobility produces a different gain mechanism. In flexible intelligent metasurfaces, the deformation vector changes the array response so that each element can locally exploit multipath. The resulting channel gain increases with the number of paths, and the performance saturates beyond a moderate morphing range because the objective is periodic in the displacement variables. This suggests that large mechanical strokes are not required to realize most of the available gain (Hu et al., 8 Oct 2025).

Other related movable-surface realizations point in the same direction. In the 6D movable metasurface, joint optimization of element positions, rotation angles, phase shifts, and NOMA beamforming improves sum rate relative to static RIS, partially movable structures, and alternative multiple-access schemes. In Spider RIS, moving the whole RIS on a two-dimensional platform and optimizing its phase shifts increases signal quality and achievable rate in obstructive mmWave environments (Shen, 20 Oct 2025, Yildirim et al., 2024).

5. Sensing, channel estimation, and ISAC

MIS research has developed especially rapidly in sensing and ISAC because movement directly enlarges virtual aperture, changes sampling geometry, and permits adaptive beam reconfiguration without dense RF chains.

For semi-passive IRS sensing, the central analytical result is that the DoA CRB is inversely proportional to the variance of sensor positions on the surface: $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$3 The optimal group-based placement therefore pushes sensor groups toward the two ends of the movement region. The CRB decreases with transmit power $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$4, number of BS antennas $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$5, number of passive elements $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$6, movement region $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$7, and number of groups $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$8, while it increases with the minimum spacing $$\bar{\boldsymbol{\theta}}_u = \boldsymbol{S}_u\boldsymbol{\theta} + \boldsymbol{e}_u,$$9 and scales as $$\boldsymbol{v}_u = \bar{\boldsymbol{\theta}}_u \odot \boldsymbol{\phi}.$$0. Relative to a fixed-position uniform array, the movable-sensor scheme yields a lower CRB; at $$\boldsymbol{v}_u = \bar{\boldsymbol{\theta}}_u \odot \boldsymbol{\phi}.$$1, the MS-versus-FP CRB gap is approximately 0.64 dB, and MUSIC spectra show narrower main lobes and more accurate peaks (Peng et al., 24 Nov 2025).

The dual-layer MIS sensing architecture develops a multi-hop echo model with multi-target interference and formulates a worst-case sensing SINR maximization. The RALM-based design significantly outperforms the closed-form beam-steering design and reveals a gain-diversity trade-off: a larger movable sub-surface increases overlap and beam gain but reduces the number of distinct beam patterns, whereas a smaller movable sub-surface increases diversity but weakens aperture gain. The paper reports that a moderate MS2 size gives the best worst-case SINR (Zheng et al., 19 Sep 2025).

In robust secure ISAC, the movable-RIS architecture combines a large fixed sub-surface and a smaller movable sub-surface that slides on precision tracks. The system jointly optimizes transmit beamforming, artificial noise, MRIS phases, and the relative position of the two sub-surfaces under imperfect sensing of potential eavesdroppers. A notable result is that secrecy performance is often maximized when only a small number of elements are allocated to the movable sub-surface; performance as a function of movable-surface size is unimodal, and two-dimensional motion outperforms one-dimensional motion because it improves beam control in both azimuth and elevation (Zhuang et al., 23 Dec 2025).

Channel estimation adds an estimation-theoretic layer to the MIS concept. The tensor model in MIS-assisted uplink MIMO shows that increasing the number of training slots $$\boldsymbol{v}_u = \bar{\boldsymbol{\theta}}_u \odot \boldsymbol{\phi}.$$2 improves the NMSE of the estimated movable-layer response $$\boldsymbol{v}_u = \bar{\boldsymbol{\theta}}_u \odot \boldsymbol{\phi}.$$3 and the reconstructed cascaded channel. Once $$\boldsymbol{v}_u = \bar{\boldsymbol{\theta}}_u \odot \boldsymbol{\phi}.$$4 crosses an identifiability threshold, the cascaded-channel NMSE drops sharply; beyond that point, improvements become more modest and are limited mainly by noise and residual algorithmic error (Alcantara et al., 29 May 2026).

The broader ISAC perspective is that MA–IRS synergy can create a “reconfigurable airspace.” One reported example shows that a configuration with only 4 movable antennas and 2 IRSs achieves the same coverage strength as 8 fixed-position antennas without IRS, and joint MA–IRS design under a sensing beam-pattern MSE constraint yields a distinctly higher sum rate than MA-only or IRS-only baselines (Wang et al., 13 Nov 2025).

6. Practical constraints, misconceptions, and open directions

A recurrent misconception is that MIS always means element-wise motion of every metasurface cell. The literature is broader. ME-RIS moves individual passive elements in two dimensions; dual-layer MIS and MRIS move a whole sub-surface; Spider RIS moves an entire panel; semi-passive sensing MIS moves only active sensors integrated on a fixed IRS; and flexible metasurfaces move elements only along the normal direction. This diversity matters because the control overhead, mechanical complexity, and optimization structure differ substantially across these architectures (Hokmabadi et al., 13 Jan 2026, Zheng et al., 2024, Peng et al., 24 Nov 2025, Hu et al., 8 Oct 2025, Yildirim et al., 2024).

A second misconception is that intelligent surfaces must rely on fast per-element electronic tuning. Several MIS architectures are explicitly designed to avoid that requirement. Static-phase dual-layer MIS, MRIS, and the sensing-oriented MIS replace element-wise electronic tuning with mechanical motion of a pre-phased secondary layer, targeting quasi-static environments such as industrial Internet-of-things, smart agriculture, warehouses, smart homes, parking lots, and utility infrastructure monitoring. Conversely, other MIS variants keep both geometric and electromagnetic reconfigurability, as in ME-RIS, FIM, and 6DMM (Zheng et al., 21 Nov 2025, Zheng et al., 19 Sep 2025, Zhuang et al., 23 Dec 2025, Hokmabadi et al., 13 Jan 2026, Hu et al., 8 Oct 2025, Shen, 20 Oct 2025).

The current literature also shares strong simplifying assumptions. Typical models assume quasi-static channels during optimization, perfect CSI, exact position control, and ideal or near-ideal hardware. Movement often occurs over only a few wavelengths, which preserves far-field or plane-wave assumptions in the relevant subproblems. Common limitations include narrowband signaling, single-user or small-user settings, continuous movement models even when implementation would be discrete, no explicit motion latency, and no mutual coupling beyond minimum-spacing constraints (Hokmabadi et al., 13 Jan 2026, Peng et al., 24 Nov 2025, Alcantara et al., 29 May 2026, Hu et al., 8 Oct 2025).

Hardware realizations are beginning to appear, but they remain specialized. Reported mechanisms include sliding rails, stepper motors, MEMS-like actuators, precision sliding tracks, Lorentz-force control, and photoactuator arrays. Flexible metasurfaces are described as having deformation response times on the order of milliseconds, and the Spider RIS concept explicitly assumes motors or other mechanical systems integrated into the platform. These facts suggest practical feasibility, but also indicate that MIS control is naturally slower than the symbol-level adaptation typical of digitally reconfigurable RISs (Hu et al., 8 Oct 2025, Zhuang et al., 23 Dec 2025, Yildirim et al., 2024).

Open directions are correspondingly clear in the literature: robust design under CSI and position uncertainty, discrete-position and latency-aware models, wideband or OFDM formulations, multi-user and multi-target extensions, hybrid electronic-mechanical architectures, learning-based mechanical control, and broader 2D or 3D movement models. A plausible implication is that MIS will remain a heterogeneous research area rather than converging quickly to a single canonical architecture: some applications favor fully movable radio environments with joint antenna and surface mobility, while others favor quasi-static, low-power, mechanically reconfigurable surfaces with static phases and finite beam codebooks (Alcantara et al., 29 May 2026, Zheng et al., 21 Nov 2025, Zheng et al., 19 Sep 2025, Zhuang et al., 23 Dec 2025, Hu et al., 8 Oct 2025, Hokmabadi et al., 13 Jan 2026).