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arxiv: 2604.22323 · v1 · submitted 2026-04-24 · 📡 eess.SP

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Fundamental Theorems on Controllability in Wave-domain Processing for Holographic MIMO

Davide Dardari
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Pith reviewed 2026-05-08 10:31 UTC · model grok-4.3

classification 📡 eess.SP
keywords controllabilitywave-domain processingholographic MIMOreconfigurable EM devicesmutual couplinggeometrydegrees of freedomdirectivity
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The pith

Reconfigurable EM devices for holographic MIMO achieve controllability when geometry and mutual coupling satisfy derived necessary and sufficient conditions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives the conditions under which wave-domain processing can be achieved by configuring passive scatterers in reconfigurable electromagnetic devices. A sympathetic reader would care because such processing promises lower complexity, energy use, and latency in future wireless systems like holographic MIMO. The theorems tie controllability directly to physical layout and interactions between elements. Numerical analysis then explores how this affects the number of elements, device size, available degrees of freedom, and beam directivity.

Core claim

The paper establishes fundamental theorems on controllability of generic reconfigurable EM devices for wave processing through dynamic configuration of passive scatterers. It derives necessary and sufficient conditions for controllability expressed as functions of geometry and mutual coupling between elements, providing a basis for design in holographic MIMO systems.

What carries the argument

The controllability conditions for reconfigurable EM devices, which determine whether dynamic configuration of passive scatterers can achieve arbitrary wave transformations based on geometry and mutual coupling.

Load-bearing premise

Controllability of the reconfigurable EM devices depends only on geometry and mutual coupling, with ideal passive scatterers free of losses, nonlinear effects, or other real-world imperfections.

What would settle it

A physical experiment showing a device whose geometry and coupling satisfy the derived conditions but cannot achieve the predicted wave transformations due to unaccounted losses or nonlinearities would disprove the theorems.

Figures

Figures reproduced from arXiv: 2604.22323 by Davide Dardari.

Figure 1
Figure 1. Figure 1: Generic reconfigurable EM device. the dynamic configuration of passive scatterers. We prove that the governing equation of the DSA satisfies the general theorem’s assumptions. Consequently, we derive a closed-form sufficient condition for controllability as a function of the di￾mension of the observation space, the number of elements, and their geometry-dependent mutual coupling. For any specific device, w… view at source ↗
Figure 3
Figure 3. Figure 3: The mapping between currents and modes in a single-input DSA. view at source ↗
Figure 4
Figure 4. Figure 4: Graphical sketch of the proof of Theorem II.1. view at source ↗
Figure 6
Figure 6. Figure 6: Numerical validation of Lemma IV.4. where ℓ = 𝑚 − 𝐿max − 1, giving a total of 𝑀 = 2𝐿max + 1 modes. In this case, since 𝐽ℓ (𝑥) ≈ 0 for |ℓ| > 𝑥, the number of well-radiating modes is approximately given by 𝑀r = 𝑀2D ≈ 2𝜅𝑎 + 1 and the directivity is 𝐷 ≈ 𝑀 𝐷vertical, being 𝐷vertical the directivity along the vertical direction. It is worth noticing that for randomly distributed dipoles the condition 𝑁 ≥ 2𝑀, wit… view at source ↗
Figure 8
Figure 8. Figure 8: Radiation pattern as a function of the number of elements for a target view at source ↗
Figure 10
Figure 10. Figure 10: Average MSE as a function of the number of elements view at source ↗
read the original abstract

Wave-domain processing is an emerging paradigm where signal processing operations are partially shifted from the digital to the electromagnetic (EM) domain. Leveraging reconfigurable EM devices, this approach aims to reduce complexity, energy consumption, and latency in next-generation wireless systems employing holographic MIMO. This paper establishes fundamental theorems on the controllability of generic reconfigurable EM devices, where wave processing is achieved through the dynamic configuration of passive scatterers. Specifically, we derive necessary and sufficient conditions for controllability as a function of geometry and mutual coupling between elements. Finally, we provide a detailed discussion and numerical results characterizing the interplay between the number of elements, physical size, degrees of freedom, and directivity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper derives necessary and sufficient conditions for controllability of generic reconfigurable EM devices used in wave-domain processing for holographic MIMO. Controllability is characterized as a function of geometry and mutual coupling between passive scatterers. The work includes a discussion and numerical results on the interplay among the number of elements, physical size, degrees of freedom, and directivity.

Significance. If the controllability theorems hold under the paper's modeling assumptions, they supply a theoretical foundation for shifting signal processing into the EM domain, which could reduce digital complexity, energy use, and latency in holographic MIMO systems. The geometry-and-coupling conditions and the numerical trade-off characterization are potentially useful for system design. The idealized lossless linear scatterer model, however, restricts immediate applicability; real devices with dissipation or nonlinearities would require additional validation.

major comments (1)
  1. [Model and Theorems sections] The necessary-and-sufficient controllability conditions rest on an idealized model of passive scatterers that are lossless, linear, and frequency-independent. This assumption is load-bearing for the central claim because the controllability matrix rank analysis and DoF count are derived directly from the resulting wave-domain operator; any material loss, dispersion, or weak nonlinearity alters that operator and can invalidate the rank conditions. The numerical results inherit the same idealization and therefore do not test robustness against omitted physics.
minor comments (2)
  1. [Numerical results] Clarify whether the mutual-coupling matrix is assumed frequency-flat or whether the controllability conditions must be re-derived at each frequency of interest.
  2. [Discussion] Add a brief statement on how the derived conditions reduce to known results for the special case of zero mutual coupling.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments. We address the major comment below and indicate planned revisions.

read point-by-point responses

  1. Referee: [Model and Theorems sections] The necessary-and-sufficient controllability conditions rest on an idealized model of passive scatterers that are lossless, linear, and frequency-independent. This assumption is load-bearing for the central claim because the controllability matrix rank analysis and DoF count are derived directly from the resulting wave-domain operator; any material loss, dispersion, or weak nonlinearity alters that operator and can invalidate the rank conditions. The numerical results inherit the same idealization and therefore do not test robustness against omitted physics.

    Authors: We agree that the controllability theorems rely on the idealized model of lossless, linear, and frequency-independent scatterers, as defined in the Model section. This modeling choice enables the closed-form derivation of the necessary and sufficient rank conditions on the wave-domain operator. The paper's scope is the fundamental characterization under these standard assumptions for theoretical analysis of wave-domain processing. We acknowledge that material losses, dispersion, or nonlinearities would modify the operator and potentially the rank results. In the revised version we will add a dedicated paragraph in the Discussion section that explicitly states the modeling assumptions, notes their implications for real devices, and outlines possible extensions to non-ideal cases. The numerical results are intended to illustrate the theoretical trade-offs (element count, size, DoF, directivity) within the stated model rather than to demonstrate robustness to omitted physics. revision: partial

Circularity Check

0 steps flagged

No circularity: controllability conditions derived from standard rank analysis on explicit EM model

full rationale

The paper derives necessary and sufficient controllability conditions directly from the wave-domain scattering model parameterized by geometry and mutual coupling. This follows the standard linear-systems controllability test (rank of the controllability matrix) applied to the idealized passive-scatterer operator. No step reduces a claimed result to a fitted parameter, self-definition, or self-citation chain; the theorems are obtained by algebraic manipulation of the given interaction matrix under the stated lossless linear assumptions. The idealization is an explicit modeling choice, not a hidden tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the controllability conditions are presented as general results derived from geometry and coupling.

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