Active Stacked Intelligent Metasurface

• Active Stacked Intelligent Metasurface (ASIM) is a multilayer electromagnetic processor that uses active circuitry to enable tunable amplitude and phase control.
• It leverages cascaded programmable layers to perform advanced wave-domain processing, improving interference suppression and multiuser communication.
• Integration of amplifiers and AI-based optimization in ASIM addresses hardware-realism and computational challenges for enhanced performance.

Active stacked intelligent metasurface (ASIM) denotes a stacked intelligent metasurface in which the multilayer electromagnetic processor incorporates active circuitry—most commonly amplifiers—so that the stack is not restricted to passive phase manipulation but can also realize tunable amplitude control, amplification, and, in some designs, unilateral feed-forward signal flow (Yeganeh et al., 23 Aug 2025, Abrardo et al., 7 May 2026, Sheemar et al., 5 Mar 2026). Within the broader SIM literature, ASIM is the active extension of wave-domain front-end processing: electromagnetic waves are transformed as they propagate through cascaded programmable layers, and the resulting device is studied as a front-end architecture for communication, sensing, and computing, with current work emphasizing multiuser interference suppression, non-terrestrial communications, and AI-driven control (An et al., 2023, Iudice et al., 28 Jan 2026).

1. Definition, taxonomy, and scope

In the SIM hardware taxonomy, ASIM corresponds to the programmable active class. A representative survey distinguishes three hardware types: non-programmable passive SIM, programmable passive SIM, and programmable active SIM, with the active class characterized by meta-atoms that include active amplifiers and support dynamic amplitude-and-phase adjustment (Liu et al., 2024). A broader survey likewise describes programmable-active SIMs as metasurfaces whose meta-atoms include amplifiers, enabling amplitude and phase control and, in some cases, nonlinearity (Sheemar et al., 5 Mar 2026).

A recurrent misconception is to treat all stacked metasurfaces as active by default. The literature does not support that equivalence. One state-of-the-art review notes that most wireless implementations so far are nearly-passive, while active architectures have appeared more often in optical or THz implementations (Renzo, 2024). Accordingly, ASIM should be understood as a specific architectural branch of SIM research rather than a synonym for multilayer metasurfaces in general.

Another distinction concerns the relation between ASIM and earlier single-layer intelligent-surface architectures. In the LEO-satellite study, diagonal RIS is described as passive, single-layer, and diagonal; active RIS as single-layer with amplifiers; BD-RIS as single-layer with some intra-group coupling; and ASIM as multi-layer, stacked, and active, with inter- and intra-layer spatial processing optimized sequentially (Yeganeh et al., 23 Aug 2025).

Architecture	Defining property	Stated limitation or advantage
Diagonal RIS	Passive, single-layer, diagonal	Limited beamforming, weak gain/control
Active RIS	Single-layer, with amplifiers	Only one layer, limited interference suppression
BD-RIS	Some intra-group coupling	Still single-layer, spatial filtering only within groups
ASIM	Multi-layer, stacked, active	Inter- and intra-layer spatial processing, optimized sequentially

2. Physical architecture and wave-domain operation

ASIM inherits the stacked geometry of SIM while extending the per-element control space. In the LEO formulation, the signal path starts from a satellite beamforming array with $N$ elements, impinges on an ASIM with $M$ elements per metasurface and $Q$ stacked metasurfaces, and propagates through programmable inter-layer coupling matrices $\mathbf{H}^{(q)}$ and reflection/amplification matrices $\mathbf{\Phi}^{(q)}$ before radiating toward ground users (Yeganeh et al., 23 Aug 2025). Each metasurface element applies customizable gain $\rho_m^{(q)}$ and phase shift $\theta_m^{(q)}$, and the overall transfer function is written as

$$\mathbf{T} = \prod_{q=Q}^{1} \mathbf{\Phi}^{(q)} \mathbf{H}^{(q)} .$$

This construction is explicitly associated with multi-layer sequential processing in three electromagnetic spatial dimensions, increased effective channel gain, and superior inter-user interference suppression relative to single-layer alternatives (Yeganeh et al., 23 Aug 2025).

Several active architectures are mixed rather than uniformly active. In the AI-driven SDR implementation, each SIM layer can be amplitude-controlled or phase-controlled: active-control layers regulate amplitude through amplifiers, whereas passive-control layers adjust phase with constant amplitude response $\alpha_{\text{pc}} \le 1$ (Iudice et al., 28 Jan 2026). The end-to-end transformation is modeled as

$$\mathbf{G} = \mathbf{W}_1 \mathbf{T}_1 \mathbf{W}_2 \mathbf{T}_2 \cdots \mathbf{W}_{L-1} \mathbf{T}_{L-1} \mathbf{W}_L \mathbf{T}_L ,$$

with $M$0 derived from Rayleigh–Sommerfeld diffraction and $M$1 containing the per-meta-atom transmission coefficients $M$2 (Iudice et al., 28 Jan 2026).

The same paper treats back reflections as neglected and focuses on forward propagation through perfectly impedance-matched layers (Iudice et al., 28 Jan 2026). By contrast, the active unilateral formulation makes the forward character structural rather than assumptive: each unit cell comprises a receive antenna and a transmit antenna connected through a tunable, non-reciprocal two-port network, typically a phase shifter plus an amplifier (Abrardo et al., 7 May 2026). This difference is important because it changes both the achievable physical behavior and the computational structure of optimization.

Physical integration is already being specialized to platform constraints. In the LEO-satellite design, the ASIM is mounted on the backplate behind the solar panels, which is described as exploiting otherwise-unused space, adding no significant mass or obstruction to solar harvesting, and providing an Earth-facing surface for dynamic downlink beamforming (Yeganeh et al., 23 Aug 2025). The same study frames active stacking as a way to reduce the requirements on the main satellite power amplifier by distributing amplification across the metasurface (Yeganeh et al., 23 Aug 2025).

3. Electromagnetic and network-level models

Two modeling traditions dominate the ASIM literature: cascaded propagation operators and multiport network models. The cascaded view is the more compact one, in which layer responses and inter-layer propagation are multiplied in sequence; it is the natural abstraction for wave-domain beamforming and AI-based training (Yeganeh et al., 23 Aug 2025, Iudice et al., 28 Jan 2026). The multiport view is more physically explicit and is used when mutual coupling, insertion loss, return loss, and hardware non-idealities must be retained (Pettanice et al., 15 Mar 2026).

For active unilateral ASIMs, the multiport S-parameter formulation yields the end-to-end transfer

$M$3

where

$M$4

In this framework, the unit-cell interconnection is modeled as a matched, ideal unilateral two-port,

$M$5

with gain $M$6 and tunable phase $M$7 (Abrardo et al., 7 May 2026). Because only adjacent layers exchange signals and the interconnections are unilateral, the architecture admits a recursive cascade representation of the end-to-end channel and eliminates the matrix inversion that is otherwise required in reciprocal SIM formulations (Abrardo et al., 7 May 2026).

A more general multiport framework for realistic SIMs models each layer as a transmitarray of tunable two-port networks and retains full electromagnetic coupling in a global S-parameter matrix. The resulting response can be written as

$M$8

with non-isolated, layered-isolated, and weakly-coupled variants trading physical fidelity against computational cost (Pettanice et al., 15 Mar 2026). Although that paper is not restricted to active stacks, its treatment of lossy and mismatched two-port cells is directly relevant to ASIM because active operation makes non-ideal circuit behavior harder to ignore.

The surveys place these models in a broader electromagnetic-processing context. Cascaded operator models are useful for scalable optimization, whereas multiport impedance or S-parameter models are needed when reciprocity, feedback, dense coupling, and hardware realism matter (Sheemar et al., 5 Mar 2026). This suggests that ASIM modeling is not a single abstraction problem but a model-selection problem conditioned on whether the design objective is algorithmic tractability, circuit realism, or both.

4. Configuration and optimization strategies

ASIM optimization is typically joint across multiple variable blocks: surface coefficients, beamforming variables, power allocation, and, in networked settings, resource-allocation variables. In the LEO-satellite system, three optimization approaches are studied for the joint design of beamforming, ASIM configuration, and symbiotic-radio resource variables: block coordinate descent with successive convex approximation (BCD-SCA), model-assisted multi-agent constraint soft actor-critic (MA-CSAC), and multi-constraint proximal policy optimization (MCPPO) (Yeganeh et al., 23 Aug 2025). The reported qualitative behavior is differentiated rather than uniform: BCD-SCA converges fast and stably in convex scenarios without learning, MCPPO achieves rapid initial convergence with moderate stability, and MA-CSAC attains the highest long-term spectral and energy efficiency in large-scale networks (Yeganeh et al., 23 Aug 2025).

For active unilateral ASIMs, the main algorithmic advance is structural. The feed-forward cascade enables a layer-wise forward recursion for the internal transfer and a backward recursion for sensitivities, giving factorized gradients such as

$M$9

The per-iteration complexity is stated as $Q$0, compared with $Q$1 for layered reciprocal SIMs and $Q$2 for the general electromagnetic optimization case (Abrardo et al., 7 May 2026). That reduction is not a minor implementation detail: it is the principal reason active unilateral ASIMs are presented as scalable to larger stacks.

AI-native optimization has become a third line of work. In the Sionna implementation, the SIM is realized as a custom Keras layer inside a differentiable TensorFlow pipeline, and both the transmit precoder and the per-layer transmission coefficients are trained end-to-end under MSE or BER objectives (Iudice et al., 28 Jan 2026). The benchmark configuration uses $Q$3 satellite antennas, $Q$4 users, $Q$5 layers, $Q$6 meta-atoms per layer, with $Q$7 active layers and $Q$8 passive layers (Iudice et al., 28 Jan 2026). The reported outcome is that end-to-end learning outperforms model-based and baseline systems for QPSK and 16QAM at all tested SNRs, while, when only passive layers are used, data-driven and model-based approaches become similar (Iudice et al., 28 Jan 2026). This directly attributes the additional gains to the extra degrees of control enabled by active layers.

Across these optimization paradigms, a common theme is constraint handling. ASIM design is always conditioned by physical feasibility—unit-modulus restrictions for passive cells, gain limits for active cells, power budgets, and, in multi-agent control, explicit system constraints enforced through penalty or Lagrangian terms (Yeganeh et al., 23 Aug 2025, Iudice et al., 28 Jan 2026). The literature therefore treats ASIM control as constrained electromagnetic programming rather than unconstrained function approximation.

5. Principal application domains

The most explicit ASIM application in current wireless research is non-terrestrial communications. The LEO-satellite system couples an ASIM-enhanced downlink with rate-splitting multiple access for cellular users and a symbiotic radio network for IoT devices (Yeganeh et al., 23 Aug 2025). Within that framework, simulation results are reported to show ASIM outperforming active RIS and BD-RIS in spectral efficiency for a given power budget, with the advantage becoming more pronounced at higher surface powers because of layered sequential filtering and greater spatial degrees of freedom (Yeganeh et al., 23 Aug 2025). The same study formulates energy efficiency as

$Q$9

with total power accounting for satellite power amplification, ASIM amplification, and circuit and digital costs (Yeganeh et al., 23 Aug 2025).

A second application strand is software-defined and cognitive radio. The AI-driven implementation positions SIMs, including stacks with active layers, as differentiable, GPU-accelerated front ends for adaptive beamforming and dynamic reconfiguration in non-terrestrial-network propagation environments (Iudice et al., 28 Jan 2026). The paper’s emphasis is not only on performance, but also on modularity: active/passive layer masks, gain bounds, and propagation matrices are exposed as software-defined objects inside the physical-layer learning stack (Iudice et al., 28 Jan 2026).

The broader SIM literature indicates that active stacking is not confined to communications. The communications overview associates programmable active SIMs with nonlinear operations and more neural-network functions in the electromagnetic domain, including real-time image recognition (Liu et al., 2024). The SIM survey similarly states that programmable-active SIMs have been used for deep neural network emulation in the EM domain and optical computation (Sheemar et al., 5 Mar 2026). These claims concern the wider active-SIM family rather than a single wireless ASIM platform, but they indicate that the active extension is being studied as a route toward physical neural networks, not merely as a high-gain beamforming surface.

This broader context matters for interpretation. ASIM is often discussed in communication-system papers because communication metrics such as spectral efficiency and energy efficiency are immediately quantifiable. A plausible implication, however, is that the same active, multilayer, wave-domain substrate can support integrated communication, sensing, and computing when the hardware and optimization stack are co-designed for multifunctionality rather than a single link-level objective.

6. Trade-offs, limitations, and open research problems

ASIM improves controllability at the cost of a more difficult design space. The active unilateral study isolates a three-way trade-off among inter-layer spacing, active gain, and SIM size. Small spacing, stated as less than $\mathbf{H}^{(q)}$0, reduces inter-layer propagation loss but limits channel diagonalization; larger spacing improves diagonality but increases propagation loss and therefore needs active gain compensation (Abrardo et al., 7 May 2026). Increasing the number of unit cells $\mathbf{H}^{(q)}$1 boosts beamforming gain, and the paper explicitly notes that increasing either $\mathbf{H}^{(q)}$2 or $\mathbf{H}^{(q)}$3 can achieve similar performance to a point (Abrardo et al., 7 May 2026). It also states that excessive gain can introduce instability or noise, while moderate gains $\mathbf{H}^{(q)}$4 are effective (Abrardo et al., 7 May 2026).

Energy–spectral-efficiency trade-offs appear at the network level as well. In the LEO study, increasing the numbers of ASIM elements, satellite antennas, or satellite transmit power initially increases energy efficiency because throughput rises faster than power, but beyond a saturation point the power demand dominates and energy efficiency drops (Yeganeh et al., 23 Aug 2025). This is consistent with the survey-level observation that while performance often increases with depth, diminishing returns and energy/cost overheads make architectural co-design for specific use cases essential (Sheemar et al., 5 Mar 2026).

Hardware realism remains a central issue. The survey literature repeatedly identifies modeling fidelity, insertion loss, quantization, alignment, and control overhead as unresolved deployment barriers (Sheemar et al., 5 Mar 2026), while the MIMO transceiver overview notes that empirical power models for SIM and ASIM are still an open area and that the fundamental trade-offs associated with amplifiers require further exploration (An et al., 2023). The communications overview adds calibration against hardware imperfections and efficient large-scale configuration under phase quantization as practical bottlenecks (Liu et al., 2024).

A further limitation is methodological rather than physical. Rich active models can become computationally prohibitive unless the architecture itself enforces structure, as in the unilateral feed-forward formulation (Abrardo et al., 7 May 2026). Conversely, simplified cascaded models may miss coupling and circuit effects that materially change performance predictions (Pettanice et al., 15 Mar 2026). Current research therefore converges on hardware–algorithm co-design: physically consistent reduced-order models, scalable constrained optimization, and trustworthy AI control that respects passivity, stability, and task constraints (Sheemar et al., 5 Mar 2026).

Taken together, the literature presents ASIM not as a finalized platform but as an active research architecture. The established results are strongest for wave-domain front-end processing, especially in non-terrestrial communication settings, while the more ambitious vision—joint communication, sensing, and computing with active multilayer electromagnetic processors—remains conditioned on advances in modeling, calibration, scalable control, and hardware realization (Yeganeh et al., 23 Aug 2025, Sheemar et al., 5 Mar 2026).