Wave-Controlled RIS Architecture

• Wave-controlled RIS architecture is an advanced electromagnetic metasurface system that adaptively manipulates incident waves through distributed biasing and control strategies.
• It employs modal decomposition, biasing transmission lines, and beyond-diagonal networks to achieve agile beamforming, dynamic nulling, and robust ISAC applications.
• The architecture significantly reduces control wiring and optimization variables, enabling scalable, low-complexity solutions for next-generation wireless and sensing systems.

A wave-controlled reconfigurable intelligent surface (RIS) architecture is an advanced class of electromagnetic surfaces designed to adaptively and efficiently manipulate incident electromagnetic fields to optimize wireless propagation. In distinction to conventional per-element-controlled RIS, wave-controlled RIS architectures employ physically distributed control and excitation mechanisms (such as biasing transmission lines, standing wave modulations, or beyond-diagonal inter-element networks) to engineer the metasurface’s phase and amplitude response with dramatic reductions in hardware complexity and significant improvements in system-level performance. These architectures are pivotal for the scalability, control bandwidth, and fine-grained wave manipulation required in emerging wireless, sensing, and integrated communication systems.

1. Physical and Circuit-Level Principles

Wave-controlled RIS architectures depart from the standard "diagonal" control model—where each metasurface element is connected to a dedicated bias line or control circuit—by utilizing distributed or group-level control mechanisms. A prototypical implementation leverages biasing transmission lines (BTLs) beneath the RIS to carry biasing standing waves (BSWs), from which each element samples its control voltage (Itzhak et al., 3 Sep 2024, Ayanoglu et al., 2022, Itzhak et al., 11 May 2025, Saavedra-Melo et al., 8 Sep 2025). The local reflection phase of each RIS element, modulated via varactors or PIN diodes, is collectively determined by the spatial voltage profile of the BSW superposition: $$w(x,t) = W_0 + \sum_{n=1}^N W_n \sin\left(\frac{n\pi (x + L_\text{left})}{L_\text{tot}}\right) \sin(n\omega_b t)$$ where $W_n$ are modal amplitudes, $N$ is the number of modes, $x$ is element position, and $\omega_b$ is the modulation frequency. Rectifier or sample-and-hold circuits locally convert this periodic profile into a DC bias suitable for varactor actuation.

Advanced circuit models incorporate SPICE-based nonlinear varactor modeling, mutual coupling between elements (local periodicity assumptions, impedance network embeddings), and realistic losses in all relevant components (Itzhak et al., 3 Sep 2024, Saavedra-Melo et al., 8 Sep 2025). This yields a reflection coefficient for each element: $$\phi_m = \frac{Z_{\mathrm{RIS},m} - Z_0}{Z_{\mathrm{RIS},m} + Z_0}$$ with $Z_{\mathrm{RIS},m}$ a function of varactor bias $V_m$ modulated by the local BSW envelope.

In "beyond-diagonal" (BD)-RIS, element-level modulation is replaced or augmented by sparse or global interconnection networks—such as stem- or cluster-connected graphs—allowing energy exchange and nontrivial scattering patterns via off-diagonal admittance control in the RIS circuit's susceptance matrix (Zhou et al., 22 Sep 2025, Zhou et al., 17 Oct 2025). The scattering matrix $\Theta$ is no longer diagonal, but given by: $\Theta = (I + jZ_0B)^{-1}(I - jZ_0B)$ where $B$ is a symmetric, structured susceptance matrix representing both direct and interconnected admittance paths.

2. Control Strategies, System Modeling, and Optimization

Wave-controlled architectures require system-level modeling techniques that account for the collective effect of physically coupled control degrees of freedom—substantially reducing the dimension of the optimization space relative to element-wise approaches. This is achieved via:

• Modal decomposition: Only a few ($N \ll M$) BSW modes are controlled, providing $N$ degrees of freedom for phase profile synthesis (Itzhak et al., 3 Sep 2024, Ayanoglu et al., 2022).
• Group-level constraints: Cluster- or stem-connected BD-RIS impose block-diagonal or tree-structured sparsity in the susceptance matrix, enabling trade-offs between achievable scattering diversity and hardware simplicity (Zhou et al., 22 Sep 2025).
• Physical circuit constraints: Envelope detectors and sample-and-hold circuits for standing wave sampling impose nonlinearity (min, max, or absolute-value operations) on the biasing strategy, which affects achievable pattern synthesis and must be incorporated into the system model (Itzhak et al., 3 Sep 2024, Saavedra-Melo et al., 8 Sep 2025).

Optimization strategies include:

• Least squares (LS), weighted LS, or simulated annealing (SA) over mode weights $W_n$ to match target SNR or SLNR patterns at the users, including the formation of beams, nulls, or more complex patterning (Itzhak et al., 3 Sep 2024, Itzhak et al., 11 May 2025).
• Structure-oriented symmetric unitary projection for BD-RIS to find a feasible susceptance/scattering matrix under architectural constraints (Zhou et al., 22 Sep 2025).
• Data-driven modeling, where a neural network is trained to learn the (nonlinear, potentially black-box) mapping from BSW parameters to RIS radiation patterns using sampled data, enabling subsequent gradient-free optimization (e.g., via genetic algorithms and SA) for rapid configuration (Itzhak et al., 11 May 2025).
• Machine learning for architecture discovery: GNN-based frameworks are employed to jointly select optimal interconnection topologies and tune element admittances in non-ideal BD-RIS for near-optimal performance under circuit, quantization, or mutual coupling constraints (Zhou et al., 17 Oct 2025).

3. Resource Efficiency, Scaling, and Hardware Complexity

A primary motivation for adopting wave-controlled RIS architectures is the dramatic reduction in control wiring, component count, and optimization overhead relative to traditional single-connected implementations:

Parameter	Per-Element Control	Wave-Controlled / Modal	BD-RIS (Cluster/Stem)
# Control Wires	$M$	$N \ll M$ (modes)	$Q, Q_G \sim \mathcal{O}(M)$
Optimization Variables	$M$	$N$	$\sim Q^2$ or $G \cdot Q_G^2$
Scalability	Poor (rapidly rises)	Good	Tunable

Individual control scales poorly ($M$ per $M$-element array), whereas modal/Beyond-Diagonal designs scale linearly or quadratically in the reduced parameter set (e.g., $N$ biasing modes, number of stems/groups). Experimentally validated prototypes have confirmed control via as few as one standing wave mode, achieving single-beam broadside steering, with more modes enabling multiple beams or nulls (Saavedra-Melo et al., 8 Sep 2025).

The wave-controlled approach also significantly reduces signaling from baseband controller to the RIS—only the mode coefficients or nonzero elements of $B$ need be communicated, rather than the full vector of $M$ phase shifts (Itzhak et al., 3 Sep 2024, Ayanoglu et al., 2022).

4. Applications, Performance, and Experimental Insights

Wave-controlled RIS systems have demonstrated practical advantages in a spectrum of applications:

• Beamforming and coverage shaping: Modal control enables agile beam steering, 3D spot beam creation, vortex beam (OAM) modulation for secure or interference-robust transmission, and dynamic nulling, all with rapid response times in digital architectures (Zhao et al., 28 Jul 2024, Saavedra-Melo et al., 8 Sep 2025).
• Resource allocation and multi-user support: When combined with RRA (reconfigurable reflect-arrays) or NOMA at the transmitter, wave-controlled RIS delivers near-FDAA performance (in sum rate or reliability) with orders-of-magnitude reduced hardware complexity (Zhou et al., 2019, Kota et al., 7 Feb 2024).
• Integrated Sensing and Communications (ISAC): Joint radar-communication beampattern synthesis via RIS achieves high detection probabilities and transmission rates with a few active sources, optimized in space and frequency (Grossi et al., 8 Jul 2025, Liu et al., 2021).
• Dynamic propagation pathwriting: Fluid-metal-based reconfigurable surfaces allow programmable guided surface wave pathways with dynamically configurable bends and junctions, maintaining low path loss in complex topologies (Chu et al., 2023).
• Multi-RIS, trajectory-aware control: LSTM-powered control frameworks can proactively toggle RIS ON/OFF to maximize SINR in dense, mobile environments while suppressing interference, leveraging trajectory prediction and codebook-based configuration (Wang et al., 27 May 2025).
• Hardware-aware deployment: Liquid crystal–based wave-controlled RIS designs enable cost-effective and energy-efficient realization of ultra-large arrays, with statistical modeling and optimized phase-shift scheduling mitigating the effects of slow response times (Delbari et al., 11 Apr 2025).

Measured and simulated results consistently show that with careful mode selection, biasing circuit design, and control policy, wave-controlled RIS can replicate the ideal phase profile’s performance under realistic hardware constraints, with only minor SNR or ESR losses relative to full per-element control (Itzhak et al., 3 Sep 2024, Saavedra-Melo et al., 8 Sep 2025). Trade-offs are evident: for envelope detector-based biasing, spurious ghost beams may appear due to the nonlinearity, which is avoided in sample-and-hold-based systems.

5. Advanced Architectural Innovations: Beyond-Diagonal and Learning-Based RIS

The frontiers of wave-controlled RIS architecture are marked by beyond-diagonal (BD)-RIS and learning-driven topology optimization:

• Stem- and cluster-connected BD-RIS: These generalize the control topology, distributing interconnections that enable amplitude as well as phase control, vastly expanding achievable scattering matrices without incurring the full cost of a completely dense network (Zhou et al., 22 Sep 2025). The associated design problem is solved by structure-oriented symmetric unitary projection, yielding optimal or near-optimal wave control constrained to feasible circuit complexity.
• Data-driven and learning-based optimization: Deployments under non-ideal conditions (mutual coupling, quantization, loss) leverage learning-based two-tier frameworks (architecture generator with STE, GNN-based performance optimizer) to jointly discover near-optimal hardware graphs and element settings, delivering strong performance-complexity tradeoffs validated in simulation across both SISO and MU-MIMO regimes (Zhou et al., 17 Oct 2025). This strategy is imperative as global search is computationally prohibitive; targeted learning approaches are able to avoid poor local optima and adapt the RIS design to practical deployment limits.

6. Implications for Next-Generation Wireless Systems

Wave-controlled RIS architectures provide a transformative lever in the system design for 6G and beyond:

• Scalability and complexity management: Distributing control using modal, group, or interconnect networks circumvents wiring, control, and hardware scaling bottlenecks inherent in large intelligent surfaces.
• Dynamism and reconfigurability: Advanced architectures support (sub-)millisecond reconfiguration times, dynamic coverage adaptation, and robust operation in mobile, interference-laden, or energy-constrained scenarios.
• Application breadth: The versatility demonstrated—real-time adaptive beamforming, radar/communication co-design, physical-layer security, and interference-aware network optimization—positions wave-controlled RIS as a foundational technology for wireless, radar, and sensing systems in smart radio environments.
• Open technical pathways: Further research is called for in the design of more linear unit cells, joint hardware-software control for multi-modal surfaces, decentralized learning control in large networks, and integration of dynamic group/BD-RIS in architecture-aware protocol stacks.

In summary, wave-controlled RIS architectures synthesize advances in distributed hardware control, circuit modeling, system optimization, and network-level intelligence, yielding metasurfaces poised for practical deployment in large-scale, high-performance, and dynamically reconfigurable wireless systems.