Wave-Controlled Reconfigurable Intelligent Surface

Updated 6 April 2026

Wave-controlled RIS are programmable metasurfaces that dynamically manipulate electromagnetic waves using guided wave biasing for beam steering and interference suppression.
They employ low-dimensional biasing networks to reduce wiring complexity, enhancing scalability and cost-efficiency for next-generation 6G deployments.
Integration of machine learning and optimization techniques supports real-time adaptation, improving system capacity and robustness in multipath environments.

A wave-controlled reconfigurable intelligent surface (RIS) is a two-dimensional (2D) or volumetric metastructure composed of electrically tunable subwavelength elements ("unit cells") capable of dynamically shaping the reflection and/or transmission coefficients of incident electromagnetic (EM) waves. By synthesizing prescribed phase and, in some designs, amplitude profiles across its aperture, an RIS enables real-time control of wireless propagation for functions such as beam steering, focusing, null forming, channel hardening, and interference suppression. Wave-controlled architectures, in particular, exploit guided waves—such as biasing standing waves beneath the metasurface—to address hardware scalability and enable low-overhead reconfiguration, thus supporting programmable propagation environments for 6G and beyond (Huang et al., 2022, Ayanoglu et al., 2022, Itzhak et al., 2024, Itzhak et al., 11 May 2025).

1. Fundamental Principles and Architectures

The foundational principle of RIS is the manipulation of wavefronts via a programmable, finely discretized array of metallic patches, each equipped with electronically tunable components—most commonly PIN diodes or varactor diodes. Each unit cell is characterized by a complex reflection or transmission coefficient: $\Gamma_n = A_n \cdot e^{j\phi_n}$ with $A_n \in [0,1]$ and $\phi_n \in [0,2\pi)$ settable via controlled biasing (Huang et al., 2022). By programming the phase profile $\{\phi_n\}$ across the surface, one realizes functions such as:

Beam steering: imposing a linear phase gradient, $\phi_n = -k x_n \sin \theta$ , to direct energy toward angle $\theta$ ;
Focusing: programming surface phases to constructively interfere at a spatial focus;
Null forming: imposing destructive interference in selected directions to mitigate interference.

Wave-controlled RIS explicitly refers to approaches where the generation of biasing voltages required for tuning each cell is achieved not via a dense per-element wired network, but by sampling multimode guided waves—created by driving one or more transmission lines beneath the array, whose spatial field profile is decomposed into a set of basis functions across the RIS (Ayanoglu et al., 2022, Itzhak et al., 2024, Itzhak et al., 11 May 2025). This enables substantial reductions in interconnect complexity.

In advanced implementations, 3D-RIS structures support both reflection and controlled transmission, enabling holistic volumetric control in cube or polyhedral geometries for omnidirectional coverage (Wang et al., 13 Feb 2026).

2. Mathematical Models of RIS-Assisted Propagation

RIS-augmented wireless links are modeled by an effective channel characterized by the non-linear composition of the element-wise RIS response and the line-of-sight (LoS) and non-LoS paths. In the canonical SISO case: $y = \mathbf{h}_r^T \Theta \mathbf{h}_t x + n$ where $\mathbf{h}_t$ , $\mathbf{h}_r$ are the Tx–RIS and RIS–Rx channel vectors, and $\Theta = \text{diag}(e^{j\phi_1},\ldots,e^{j\phi_N})$ is the diagonal matrix of RIS-imposed phase shifts (Huang et al., 2022).

Far-field path loss for an RIS-assisted link is: $A_n \in [0,1]$ 0 with $A_n \in [0,1]$ 1 the physical area per element and $A_n \in [0,1]$ 2 the number of elements. In the far field, both Tx and Rx are at Fraunhofer distances from the RIS, and the simple phase-gradient approximation applies; in the near field, element-level phase laws must account for spherical wavefronts (Huang et al., 2022).

For multiuser scenarios, spatial multiplexing and capacity enhancement are modeled via the composite channel matrix and capacity metrics: $A_n \in [0,1]$ 3 with $A_n \in [0,1]$ 4 containing both direct and RIS-assisted links (ElMossallamy et al., 2020).

3. Wave-Controlled Hardware and Biasing Networks

Classic RIS designs require one bias/control line per element, yielding prohibitive wiring complexity for large arrays. Wave-controlled RIS overcomes this via low-dimensional bias-encoding strategies.

The dominant approach is to excite standing waves in transmission lines ("biasing TLs") beneath the meta-array. The local bias at element $A_n \in [0,1]$ 5 is then: $A_n \in [0,1]$ 6 where each $A_n \in [0,1]$ 7 indexes a guided mode. The resulting spatial envelope controls the local reflection phase $A_n \in [0,1]$ 8 (Ayanoglu et al., 2022, Itzhak et al., 2024, Itzhak et al., 11 May 2025). Only $A_n \in [0,1]$ 9 control lines are required.

Two principal biasing and sampling circuits are commonly used (Itzhak et al., 2024):

Method	Principle	Hardware Complexity
Envelope Detector	Rectifies and holds peak voltage of local TL signal	Minimal per-cell
Sample-and-Hold	Samples TL waveform at global timing signal	Common sampling bus

Enforcing cell-to-cell phase smoothness (e.g., $\phi_n \in [0,2\pi)$ 0) is necessary to stabilize beamforming and account for mutual coupling (Ayanoglu et al., 2022, Itzhak et al., 2024).

3D-RIS hardware implements volumetric coverage using multiple interconnected surfaces with subarray-based beamforming primitives, orthogonal polarizations for isolation, and PIN-diode gating for binary amplitude weighting (Wang et al., 13 Feb 2026).

4. Optimization, Machine Learning, and Control

Controllable RISs require optimization of the spatial biasing profiles to maximize communication metrics under hardware constraints. The general problem can be formulated as: $\phi_n \in [0,2\pi)$ 1 or, in multiuser settings, as maximization of sum-rate or SLNR (Ayanoglu et al., 2022, Itzhak et al., 2024, Itzhak et al., 11 May 2025):

$\phi_n \in [0,2\pi)$ 2

Machine learning, especially data-driven neural network regressors, has been used to learn the complex mapping from multimode bias amplitudes to the observed far-field pattern, bypassing the explicit EM modeling of nonlinear, coupled device responses (Itzhak et al., 11 May 2025). Training is performed on a large dataset of physically simulated (or measured) bias–pattern pairs; the resulting NN is then used as a predictive surrogate in fast optimization—typically via simulated annealing or genetic algorithms—to design bias vectors that achieve target beam, null, or multiplexing patterns efficiently.

Lookup-table schemes, prepopulated with biasing solutions for canonical beam/null cases, further accelerate real-time configuration and enable rapid adaptation to dynamic network conditions (Itzhak et al., 11 May 2025).

5. Channel Characterization and Control in Rich Scattering Environments

Wave-controlled RISs have demonstrated significant efficacy in manipulating multipath-rich propagation for both capacity and sensing.

In reverberant scenarios, the channel impulse response (CIR) is composed of numerous multipath components: $\phi_n \in [0,2\pi)$ 3 The RIS reshapes the distribution $\phi_n \in [0,2\pi)$ 4 by selectively controlling the phases $\phi_n \in [0,2\pi)$ 5, enabling both focusing (impulse-like CIR) and specific temporal scattering signatures (wave fingerprinting) (Alexandropoulos et al., 2021).

Sequential greedy algorithms, convex relaxations, and AI-aided black-box optimization are employed to maximize rate-based or localization objectives under quantization and feasible bias constraints.

Experiments demonstrate up to $\phi_n \in [0,2\pi)$ 630–40% capacity increases in convoluted multipath settings, and >98% object localization accuracy via wave-fingerprints using low-SNR measurement vectors and neural-network classifiers (Alexandropoulos et al., 2021).

6. Experimental Performance and Deployment Metrics

Empirical studies on both 2D and 3D wave-controlled RIS prototypes have documented:

SNR enhancements of 14–25 dB across near- and far-field measurement arrangements at mmWave and sub-6 GHz frequencies (Wang et al., 2023, Ratajczak et al., 2023, Wang et al., 13 Feb 2026).
EVM improvements of 6–7 dB in QPSK communication links over 24–30 GHz bands, coinciding with measured gain enhancements in both reflection and inter-surface transmission (Wang et al., 13 Feb 2026).
Directivity and sidelobe profiles closely tracking full-wave theoretical predictions, with mainlobe beam scanning up to $\phi_n \in [0,2\pi)$ 760° and sector (30°–60°) amplitude patterns realized via deliberate excitation of evanescent surface waves (Ataloglou et al., 8 Apr 2025).
Robustness to hardware constraints: Even coarse quantization (2–3 bits) at the RIS phase control level yields near-ideal beamforming within 1–3 dB penalty (Huang et al., 2022).

Power consumption is typically $\phi_n \in [0,2\pi)$ 81 W for passive/varactor architectures, enabling practical large-scale deployment (Ratajczak et al., 2023), while modern active/amplifying RISs deliver significant coverage boost for low-power relay applications (Wu et al., 2024).

7. Advanced Concepts and Future Directions

Active research directions include extension to multi-user/OFDMA operation using frequency-selective phase profiles, exploitation of AI-driven real-time control to adapt to unknown scattering environments and mobile users, co-design of RIS and digital transceivers for latency and overhead minimization, and integration of sensing and analog signal processing functionalities directly into the wave-controlled propagation medium (Alexandropoulos et al., 2021, Ayanoglu et al., 2022, Itzhak et al., 11 May 2025).

Research has also quantified the utility of RIS for channel eigenstructure manipulation in massive MIMO, enabling deterministic shaping of eigenvalue distributions via selective RIS state switching, with full-wave FDTD paradigms used for system-level optimization (Sarkar et al., 2019).

Extending from classical planar designs to 3D polyhedral and hybrid reflecting/transmitting RIS geometries vastly increases spatial coverage capabilities—approaching full-solid-angle control and enabling non-hemispherical volumetric coverage in wireless networks (Wang et al., 13 Feb 2026).

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