Multiple RISs: Architectures & Signal Models

• Multiple RISs are programmable electromagnetic surfaces deployed in parallel, serial, or networked configurations to create enhanced reflective paths for communication, localization, and sensing.
• They exploit both configurational and spatial diversity, enabling cascaded and distributed signal processing through well-defined channel, physics-based, and hardware models.
• Experimental and simulation studies show that multi-RIS systems can boost signal strength, data rates, and positioning accuracy while raising challenges in channel estimation and interference management.

Multiple reconfigurable intelligent surfaces (RISs) are wireless environments in which two or more programmable electromagnetic surfaces are jointly deployed to manipulate propagation for communication, localization, and sensing. In contrast to a single RIS, a multi-RIS system can exploit both configurational diversity—through distinct phase profiles on each surface—and spatial diversity—through distinct viewpoints, path lengths, and angular signatures across surfaces. The literature covers several non-equivalent realizations of this idea: parallel independent RISs that create multiple reflected links, serial or double-RIS cascades, one-RIS-per-cell multi-cell networks, multiple single-RF-chain RISs for localization, and tightly integrated multi-face structures that act as a cooperative multi-aperture node (Yildirim et al., 2019, Katsanos et al., 2022, Alexandropoulos et al., 2022, Wang et al., 2024, Wang et al., 13 Feb 2026).

1. Architectural forms and operating paradigms

The term “multiple RISs” does not denote a single architecture. One recurring topology is the parallel deployment, where several spatially separated RISs create independent reflected paths from a transmitter to a receiver. Another is the serial or double-RIS topology, where the signal follows a path such as $$\text{S} \rightarrow \text{RIS}_1 \rightarrow \text{RIS}_2 \rightarrow \text{D}$$. A third is the networked topology, exemplified by one RIS per BS in a multi-cell OFDM system, where each surface improves its serving link but also affects inter-cell interference. A fourth is the RIS-centric sensing topology, where RISs are treated as the primary sensing apertures rather than as communication auxiliaries, and unknown sources are inferred from reflected measurements (Yildirim et al., 2019, Katsanos et al., 2022, Wang et al., 2024).

Architecture	Defining feature	Representative source
Parallel independent RISs	Multiple S–RIS–D paths reflected simultaneously	(Yildirim et al., 2019)
Serial/double RISs	Cascaded reflections through two surfaces	(Yildirim et al., 2019)
One-RIS-per-BS multi-cell network	Each BS controls a separate RIS in OFDM	(Katsanos et al., 2022)
RIS-centric sensor network	RISs serve as sensing devices using configurational diversity	(Wang et al., 2024)
Multiple single-RF-chain RISs	Each RIS emulates receive beams over time and sends scalar measurements to a controller	(Alexandropoulos et al., 2022)

These architectures imply different control and observability assumptions. In the multi-cell communication model, each BS controls only its associated RIS, yet every RIS contributes to desired links and to interference at non-associated UEs. In the single-RF-chain localization model, all RISs are attached to a common controller that programs phase profiles, collects scalar measurements, performs angle estimation at each RIS, and fuses them for position estimation. In backward sensing, multiple RISs play the role of a distributed programmable lens: a single RIS can identify directions of arrival, whereas several RISs provide the spatial diversity required to localize multiple sources (Katsanos et al., 2022, Alexandropoulos et al., 2022, Wang et al., 2024).

A related but distinct line replaces spatially separated panels with a tightly integrated multi-face structure. The cube-based 3D-RIS consists of six cooperative RIS faces with shared internal routing, so that one illuminated face can either reflect locally or transfer energy to a neighboring face for reradiation. This is not a distributed deployment, but it functions as a physically integrated multi-RIS node with six coordinated apertures (Wang et al., 13 Feb 2026).

2. Signal, channel, and operator models

A central abstraction in the multi-RIS literature is that the end-to-end channel is either a sum of cascaded terms or a product of cascaded terms, depending on topology. In RIS-centric sensing with a discretized scene, the canonical linear model is

$\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$

where $\mathbf{E}$ is the discretized source-strength field and $\mathbf{H}$ is the sensing operator induced by RIS geometry, element locations, and phase configurations. With $K$ RISs, one mode stacks measurements from separate receivers at each RIS, while another aggregates all RIS reflections at a single receiver; both reduce to the same linear inverse form with differently structured $\mathbf{H}$ (Wang et al., 2024).

In communication-oriented multi-RIS MIMO, the effective channel is typically written as a direct path plus a sum of RIS-assisted links. For active multi-RIS OFDM MIMO, the per-subcarrier received signal is modeled as

$$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$

so the multi-RIS effect appears through the superposition $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$. In the point-to-point learning framework, the same structure appears in scalar form,

$$y=\left(\sum_{m=1}^{M}\mathbf{g}_m\boldsymbol{\Phi}_m\mathbf{h}_m+h_0\right)s+n.$$

These models formalize the fact that multiple RISs create multiple controllable branches of a common link (Chen et al., 21 May 2025, Alexandropoulos et al., 2020).

Serial or cooperative two-RIS models introduce explicit multiplicative cascades. In the double self-sustainable RIS system, the effective channel seen by user $k$ is the sum of three terms: $\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$0 corresponding to BS–RIS1–user, BS–RIS2–user, and BS–RIS1–RIS2–user paths. The same paper couples these communication channels to energy-harvesting constraints at both RISs, making the amplitudes $\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$1 optimization variables rather than fixed passive coefficients (Wang et al., 2024).

At the element level, the literature spans several hardware abstractions. One wideband multi-cell model treats each element as a Lorentzian resonator with frequency-selective reflection coefficient

$\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$2

which couples all OFDM subcarriers through a small set of physical parameters. Another line assumes ideal unit-modulus phase control. Experimental active multi-RIS work instead factors each RIS matrix as $\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$3, with $\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$4 the fixed LNA gain and $\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$5 a quantized diagonal phase matrix (Katsanos et al., 2022, Chen et al., 21 May 2025).

This suggests a useful classification: some multi-RIS models are field-superposition models; others are serial-cascade models; and still others are physics-constrained hardware models that couple angle, frequency, and power consumption. The distinction matters because identifiability, optimization, and performance scaling differ sharply across these classes.

3. Localization and sensing with multiple RISs

One of the clearest motivations for multiple RISs is that they resolve geometric ambiguities that a single RIS cannot. In RIS-centric backward sensing, a single RIS in the far field can estimate directions of arrival by using configurational diversity across phase patterns. However, localization of multiple simultaneous sources requires multiple RISs because each RIS primarily provides angular information, and several viewpoints are needed to intersect rays in space and disambiguate source pairing (Wang et al., 2024).

The mathematical formulation in backward sensing is an inverse problem over a discretized region of interest. For localization, the region is divided into voxels and the unknown vector $\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$6 stores source strengths. Each RIS contributes a block of measurements, and the stacked system is

$\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$7

A key theoretical result is a rank bound for the sensing operator. If each RIS $\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$8 has $\mathbf{S}=\mathbf{H}\mathbf{E}+\mathbf{n},$9 elements and $\mathbf{E}$0 measurements, then in the stacked-receiver mode

$\mathbf{E}$1

This links recoverable scene dimension to the total number of RIS elements and measurements, and shows that increasing snapshots alone cannot overcome an insufficient total aperture (Wang et al., 2024).

The single-RF-chain localization framework reaches a similar conclusion from a different direction. Each RIS uses time-varying phase profiles $\mathbf{E}$2 to emulate receive beams and produce one scalar measurement per slot,

$\mathbf{E}$3

Angle estimation at each RIS is posed as a beamspace compressed-sensing problem and solved with OMP. Position estimation then proceeds in two stages: a least-squares line intersection initializer,

$\mathbf{E}$4

followed by a maximum-likelihood refinement weighted by per-RIS AoA error covariance matrices $\mathbf{E}$5. The Fisher information for position is additive across RISs,

$\mathbf{E}$6

which makes explicit that multiple RISs reduce the position error bound through geometric diversity (Alexandropoulos et al., 2022).

The measurement data support these analytical conclusions. In the two-RIS single-RF-chain prototype, the DoA from the left RIS is around $\mathbf{E}$7 in simulation and $\mathbf{E}$8 in measurement, while the right RIS gives around $\mathbf{E}$9 in simulation and $\mathbf{H}$0 in measurement, with errors within $\mathbf{H}$1. Joint reconstruction over a $\mathbf{H}$2 grid shows a clear peak at the true source location. In the backward-sensing prototype with two RISs and one USRP receiver, magnitude-only measurements are handled through reweighted Wirtinger flow, and the multi-RIS configuration localizes a source from scalar magnitude data (Alexandropoulos et al., 2022, Wang et al., 2024).

4. Multi-RIS communications: optimization, interference, and control

In communication systems, multiple RISs primarily enlarge the design space of beamforming, power control, and network coordination. The multi-cell OFDM formulation with one RIS per BS is representative. On subcarrier $\mathbf{H}$3, the effective self-channel of user $\mathbf{H}$4 is

$\mathbf{H}$5

while every non-serving BS $\mathbf{H}$6 also creates a cross-channel

$\mathbf{H}$7

The resulting sum-rate maximization is jointly nonconvex in BS power allocation and all RIS Lorentzian parameters. The proposed solution is a distributed successive concave approximation in which each BS–RIS–UE triplet optimizes a local surrogate and exchanges interference prices with neighboring cells. This formalizes a core multi-RIS feature: each RIS is simultaneously a link enhancer and an interference shaper (Katsanos et al., 2022).

A different control viewpoint is offered by supervised phase configuration learning. For $\mathbf{H}$8 RISs assisting a single communication pair, the effective channel

$\mathbf{H}$9

induces a large discrete phase-configuration problem. To reduce dimensionality, the work groups RIS elements into $K$0 phase-sharing groups and trains multi-layer perceptrons using either position values or instantaneous channel coefficients. The paper studies centralized learning, individual RIS learning, and their federation, and reports that all NN-based schemes achieve at least $K$1 of the optimal rate on average across the tested setups, while individual NNs at RISs perform very close to centralized control (Alexandropoulos et al., 2020).

The self-sustainable double-RIS model adds yet another optimization layer: the surfaces must harvest enough power to sustain their circuitry and active reflection amplitudes. The resulting power-minimization problem jointly optimizes BS beamforming, RIS phase shifts, common amplitude coefficients, and the double-RIS cascade. A block coordinate descent framework alternates among BS beamforming, RIS1 phases, RIS2 phases, and closed-form amplitude updates derived from the energy-harvesting constraints. In the reported setup with total elements fixed at 100, the required BS transmit power is minimized when $K$2, indicating that balanced element allocation is preferred in that particular self-sustainable two-RIS geometry (Wang et al., 2024).

Active multi-RIS field tests show that control objectives need not be purely power-centric. In a commercial 5G MIMO network, a codebook-based beamforming scheme optimizes RISs over angular codebooks rather than explicit CSI. Under the same measurement budget, the two-RIS configuration with $K$3 angular separation yields RI $K$4 and maximum throughput $K$5 bps, whereas the single “big” RIS configuration yields RI $K$6 and maximum throughput $K$7 bps. The reported gain is up to $K$8, despite the fact that the multi-RIS case has lower SINR than the single-RIS case. The mechanism is channel-rank diversification rather than pure link-budget enhancement (Chen et al., 21 May 2025).

5. Performance laws, deployment planning, and experimental evidence

Several papers derive or validate scaling laws for multi-RIS systems. In indoor simultaneous transmission over multiple independent RISs, the error probability is dominated by the square of the total number of reflecting elements $K$9, so from a pure error-performance viewpoint $\mathbf{H}$0 small RISs can be comparable to one large RIS with $\mathbf{H}$1 elements when path losses are similar. In the outdoor double-RIS serial system, the low-SNR BER scales as

$\mathbf{H}$2

which the paper attributes to a virtual $\mathbf{H}$3 MIMO effect between the two RISs. The same study also introduces max-SNR RIS selection for indoor and outdoor settings, activating only the best RIS or the best RIS pair instead of all surfaces simultaneously (Yildirim et al., 2019).

Deployment planning cannot be reduced to element counts alone. The RISE-6G scenario paper introduces two planning notions. The Area of Influence (AroI) is the region where RIS-induced gain in received power exceeds a threshold, illustrated with a $\mathbf{H}$4 dB criterion. The Bandwidth of Influence (BoI) is the frequency range over which a reflectarray significantly affects incident signals; a reflectarray optimized at $\mathbf{H}$5 GHz is reported to strongly reflect signals across a band of $\mathbf{H}$6 GHz. Both notions imply that in dense multi-RIS deployments, influence regions may overlap in space and frequency, creating both opportunities for cooperation and risks of unintended interference (Alexandropoulos et al., 2022).

Field trials reinforce these planning considerations. In real-world multi-hop Wi-Fi 6 experiments with two RISs, the farthest point $\mathbf{H}$7 improves from $\mathbf{H}$8 dBm to $\mathbf{H}$9 dBm in signal strength, the data rate rises from $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$0 to $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$1 Mbps, jitter falls from $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$2 to $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$3 ms, and packet loss drops from $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$4 to $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$5. In a two-hop RIS-assisted commercial 5G underground parking deployment, the average RSRP over the garage improves from $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$6 to $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$7 dBm, downlink speed from $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$8 to $$\mathbf{y}=\left(\mathbf{H}_{\rm d}+\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell\right)\sqrt{P_{\rm t}}\,\mathbf{x} +\sum_{\ell=1}^{L}\mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{z}_\ell+\mathbf{v},$$9 Mbps, and uplink speed from $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$0 to $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$1 Mbps (Xiong et al., 2023).

The same study also provides a cautionary result for long RIS relay chains. In an anechoic chamber, the 1-hop, 2-hop, 3-hop, and 4-hop chains yield $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$2, $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$3, $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$4, and $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$5 dBm, respectively, showing that while RIS gains can create links where none existed, cumulative path loss still dominates as hops increase. A related observation is that replacing the third RIS by a much larger quad-RIS adds only $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$6 dB when the incident power at that stage is already weak. This suggests that later surfaces in long cascades often act more as coverage extenders than as major SNR contributors (Xiong et al., 2023).

6. Related architectures, physical-layer platforms, and open problems

Multiple RIS research increasingly overlaps with broader notions of multifunctional and three-dimensional intelligent surfaces. A notable comparator is STAR-RIS, where each element simultaneously transmits and reflects. Under the paper’s asymptotic analysis, a STAR-RIS with $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$7 elements achieves diversity order $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$8 on both sides of the surface, whereas splitting the aperture into transmitting-only and reflecting-only sub-surfaces reduces the per-side diversity orders. This is not a multi-RIS deployment in the spatial sense, but it addresses a similar objective—extending controllable coverage beyond a single reflective half-space (Xu et al., 2021).

Another related direction is the cube-based 3D-RIS, which tightly integrates six cooperative RIS faces. Each face covers an angular range from $$\sum_{\ell} \mathbf{G}_\ell \mathbf{\Phi}_\ell \mathbf{F}_\ell$$9 to $$y=\left(\sum_{m=1}^{M}\mathbf{g}_m\boldsymbol{\Phi}_m\mathbf{h}_m+h_0\right)s+n.$$0, and inter-face routing enables neighboring-surface transmission. The measured prototype reports gain enhancement of $$y=\left(\sum_{m=1}^{M}\mathbf{g}_m\boldsymbol{\Phi}_m\mathbf{h}_m+h_0\right)s+n.$$1 dB for reflection and $$y=\left(\sum_{m=1}^{M}\mathbf{g}_m\boldsymbol{\Phi}_m\mathbf{h}_m+h_0\right)s+n.$$2 dB for transmission to the neighboring surface, together with a $$y=\left(\sum_{m=1}^{M}\mathbf{g}_m\boldsymbol{\Phi}_m\mathbf{h}_m+h_0\right)s+n.$$3-$$y=\left(\sum_{m=1}^{M}\mathbf{g}_m\boldsymbol{\Phi}_m\mathbf{h}_m+h_0\right)s+n.$$4 dB improvement in error vector magnitude for both reflection and neighboring-surface transmission scenarios. This suggests that some multi-RIS functions can be realized not only by spatially distributing panels, but also by physically integrating multiple apertures into a single node (Wang et al., 13 Feb 2026).

The physical-layer modeling burden of such systems has motivated dedicated simulation platforms. One open platform based on OpenEMS simulates electromagnetic coupling between RIS pairs by treating one RIS as active and the other as passive, extracting port-to-port S-parameters and enabling verifiable channel-model generation for multi-RIS deployments such as V2X and cybersecurity schemes. The existence of such platforms underscores that multiple RISs are not well captured by purely abstract fading models when inter-surface coupling, resonance, and geometry matter (Papadopoulos et al., 2022).

Open problems recur across the literature. Large-scale networks with many RISs require new spatial models because conventional stochastic geometry often ignores reflections; multi-RIS systems instead need models where reflection, blockage, and refraction are explicit state variables. Joint channel estimation and configuration remain difficult because passive RISs have limited sensing and control capability, and the overhead grows with the number of surfaces and their elements. The RISE-6G scenarios identify AroI and BoI as planning challenges, while communication-theoretic surveys emphasize the need to rethink channel models, optimization formulations, and performance limits when the wireless environment itself becomes programmable (Alexandropoulos et al., 2022, Basar et al., 2019).

A plausible implication is that the subject has already moved beyond the question of whether multiple RISs can help. The technically harder question is how to allocate functionality across surfaces—communication enhancement, localization, sensing, secrecy, harvesting, amplification, or routing—while respecting geometry, hardware constraints, and control overhead. Across the cited works, multi-RIS systems appear less as a single technology than as a family of programmable multi-aperture infrastructures whose behavior is governed jointly by electromagnetics, inference, and network optimization.