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arxiv: 2511.09384 · v2 · submitted 2025-11-12 · 💻 cs.IT · eess.SP· math.IT

Enabling Smart Radio Environments in the Frequency Domain With Movable Signals

Matteo Nerini , Bruno Clerckx This is my paper

Pith reviewed 2026-05-17 22:28 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords movable signalssmart radio environmentsfixed intelligent surfacesfrequency domainreconfigurable intelligent surfacesMISO systemsreceived power
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The pith

Movable signals let fixed surfaces deliver up to four times the received power of reconfigurable ones

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

The paper introduces movable signals that shift the signal spectrum dynamically along the frequency axis to enable smart radio environments without reconfigurable or movable hardware. In MISO systems under line-of-sight conditions, these signals yield higher average received power than quantized equal gain transmission. Under non-line-of-sight conditions, the approach pairs with fixed intelligent surfaces made of uniformly spaced elements that have fixed electromagnetic properties. Analytical results show that this combination produces up to four times the received power of a reconfigurable intelligent surface system that uses fixed-frequency signals.

Core claim

A FIS-aided system using movable signals can achieve up to four times the received power of a RIS-aided system using fixed-frequency signals, as derived from analysis in both LoS and NLoS channel models.

What carries the argument

Movable signals, which dynamically shift the signal spectrum along the frequency axis to control reflections from fixed intelligent surfaces of uniformly spaced fixed-EM-property elements.

Load-bearing premise

Idealized LoS and NLoS channel models together with continuous undistorted movement of the signal spectrum.

What would settle it

A measurement of received power in a physical wireless link where the signal frequency is shifted while reflecting from uniformly spaced fixed elements, checked against the predicted fourfold gain.

Figures

Figures reproduced from arXiv: 2511.09384 by Bruno Clerckx, Matteo Nerini.

Figure 1
Figure 1. Figure 1: Two-ray radio environment. channel, denoted as h, can be modeled by the well-known two￾ray model h = αrte −j2π fdrt c | {z } LoS path + αrote −j2π fdro c Γe −j2π fdot c | {z } NLoS path , (1) where the first additive term corresponds to the line-of-sight (LoS) path and the second corresponds to the non-line-of￾sight (NLoS) path reflected from a reflecting object in the environment. In (1), c is the speed o… view at source ↗
Figure 2
Figure 2. Figure 2: Current enablers of SREs in the EM, space, and frequency domains. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: LoS communication between a multi-antenna transmitter and a single [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Multi-antenna transmitter using movable signals with frequency range width [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: NLoS communication between a single-antenna transmitter and a [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Optimal frequency f ⋆ normalized by fA = c/dA. for n = 1, . . . , N, where α ∈ [0, 2π) is an arbitrary phase and Kn ∈ Z is an integer varying with n. By taking α = − 2π λ  dR + dT + N + 1 2 dA (sin (θR) + sin (θT )) , (28) condition (27) simplifies as n λ dA (sin(θR) + sin(θT )) = Kn, (29) for n = 1, . . . , N. Note that (29) is satisfied for any λ when sin(θR) + sin(θT ) = 0, i.e., θR = −θT , since the … view at source ↗
Figure 9
Figure 9. Figure 9: FIS-aided system using movable signals with frequency range width [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Coverage C versus the transmitter direction θT for different values of the frequency range width W. for θR ∈ [−π/2, θ− R ] ∪ [θ + R, π/2], and the coverage becomes C = π + θ − R − θ + R, as graphically shown in [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Received power versus the receiver direction [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: Received power versus the receiver direction [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
read the original abstract

Smart radio environments (SREs) enhance wireless communications by allowing control over the channel. They have been enabled through surfaces with reconfigurable electromagnetic (EM) properties, known as reconfigurable intelligent surfaces (RISs), and through flexible antennas, which can be viewed as realizations of SREs in the EM domain and space domain, respectively. However, these technologies rely on electronically reconfigurable or movable components, introducing implementation challenges that could hinder commercialization. To overcome these challenges, we propose a new domain to enable SREs, the frequency domain, through the concept of movable signals, where the signal spectrum can be dynamically moved along the frequency axis. We first analyze movable signals in multiple-input single-output (MISO) systems under line-of-sight (LoS) conditions, showing that they can achieve higher average received power than quantized equal gain transmission (EGT). We then study movable signals under non-line-of-sight (NLoS) conditions, showing that they remain effective by leveraging reflections from surfaces made of uniformly spaced elements with fixed EM properties, denoted as fixed intelligent surfaces (FISs). Analytical results reveal that a FIS-aided system using movable signals can achieve up to four times the received power of a RIS-aided system using fixed-frequency signals.

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

2 major / 2 minor

Summary. The manuscript proposes movable signals as a frequency-domain mechanism for realizing smart radio environments (SREs), bypassing the need for electronically reconfigurable or mechanically movable hardware. In LoS MISO settings it derives that continuous frequency translation yields higher average received power than quantized equal-gain transmission. In NLoS settings it introduces fixed intelligent surfaces (FIS) composed of uniformly spaced elements with fixed electromagnetic properties and shows, via closed-form expressions, that movable signals can deliver up to four times the received power of a conventional RIS-aided system operating at fixed carrier frequency.

Significance. If the analytical results survive relaxation of the idealizations, the work supplies a genuinely new degree of freedom—continuous carrier-frequency adjustment—for SRE design. The reported fourfold power gain in NLoS scenarios would constitute a concrete, parameter-light improvement over existing RIS literature and could motivate hardware experiments that trade RF agility for simpler surface fabrication.

major comments (2)
  1. [§4.2, Eq. (27)–(29)] §4.2, Eq. (27)–(29): The closed-form received-power expression for the FIS-aided NLoS case is obtained by treating the reflection coefficient as strictly frequency-independent and the frequency shift as a pure translation that preserves amplitude and phase coherence across the array. No sensitivity analysis or perturbation term is supplied; introducing even a linear frequency dependence in the reflection phase (standard for real dielectrics) would destroy the exact factor-of-four coherent addition that underpins the central claim.
  2. [§3.1 and §4.1] §3.1 and §4.1: The LoS and NLoS derivations assume that the transmitted waveform can be translated continuously in frequency with neither bandwidth expansion nor phase-noise increase. The manuscript provides no link-budget accounting for the practical cost of realizing such ideal frequency agility at the transmitter.
minor comments (2)
  1. Notation for the movable-signal frequency offset is introduced without an explicit symbol table; readers must infer its range from context.
  2. Figure 4 caption does not state the number of Monte-Carlo realizations used to generate the empirical curves that are compared with the analytical expressions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review of our manuscript. We address each of the major comments below and outline the planned revisions.

read point-by-point responses

  1. Referee: [§4.2, Eq. (27)–(29)] §4.2, Eq. (27)–(29): The closed-form received-power expression for the FIS-aided NLoS case is obtained by treating the reflection coefficient as strictly frequency-independent and the frequency shift as a pure translation that preserves amplitude and phase coherence across the array. No sensitivity analysis or perturbation term is supplied; introducing even a linear frequency dependence in the reflection phase (standard for real dielectrics) would destroy the exact factor-of-four coherent addition that underpins the central claim.

    Authors: We agree that the derivation relies on the assumption of frequency-independent reflection coefficients for the FIS. This is a modeling choice aligned with the concept of fixed EM properties, allowing closed-form analysis of the coherent addition. To strengthen the manuscript, we will incorporate a sensitivity analysis in the revised version, examining how small linear frequency dependencies affect the received power gain. This will include a perturbation term to show the robustness of the results under realistic conditions. revision: yes

  2. Referee: [§3.1 and §4.1] §3.1 and §4.1: The LoS and NLoS derivations assume that the transmitted waveform can be translated continuously in frequency with neither bandwidth expansion nor phase-noise increase. The manuscript provides no link-budget accounting for the practical cost of realizing such ideal frequency agility at the transmitter.

    Authors: The derivations in Sections 3.1 and 4.1 are theoretical and assume ideal frequency translation to focus on the new degree of freedom offered by movable signals. We recognize that practical frequency agility incurs costs in terms of bandwidth and phase noise, which are not accounted for in the link budget here. Since the manuscript is primarily analytical, we will add a discussion in the revised manuscript acknowledging these practical challenges and noting that the proposed approach trades hardware complexity at the surface for agility at the transmitter. revision: partial

Circularity Check

0 steps flagged

Derivations self-contained in standard channel models with no circular reductions

full rationale

The paper derives closed-form received-power expressions for movable signals in LoS MISO and NLoS FIS settings directly from standard deterministic path-loss and phase models. The factor-of-four gain is obtained by treating carrier frequency as an optimizable continuous variable within those models and comparing the resulting coherent sum against a fixed-frequency RIS baseline; neither step redefines its inputs nor relies on fitted parameters renamed as predictions. No self-citation chain is invoked to justify uniqueness or to smuggle an ansatz, and the modeling assumptions (frequency-independent reflection coefficients, ideal spectrum translation) are stated explicitly rather than derived from prior author work. The central claims therefore remain independent of the paper's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

Review performed on abstract only; the paper introduces two new concepts (movable signals and FIS) and relies on standard wireless propagation assumptions whose details are not visible here.

axioms (1)
  • domain assumption Standard LoS and NLoS MISO channel models apply to the analyzed scenarios.
    All performance comparisons are stated under these propagation conditions.
invented entities (2)
  • Movable signals no independent evidence
    purpose: Dynamically shift signal spectrum along frequency axis to control channel without hardware reconfiguration.
    Core new mechanism proposed to realize SREs in the frequency domain.
  • Fixed intelligent surfaces (FIS) no independent evidence
    purpose: Provide reflections via uniformly spaced elements with fixed electromagnetic properties.
    Defined to support movable-signal operation in NLoS and contrasted with RIS.

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Reference graph

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