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REVIEW 3 major objections 6 minor 1 cited by

Covering Underwater Shadow Zones using Acoustic Reconfigurable Intelligent Surfaces

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Acoustic smart surfaces can fill underwater shadow zones, lifting coverage from under 20% to nearly 100%.

desk verdict A new and plausible use of acoustic RIS for shadow-zone coverage, but the near-100% coverage claim rests on equating the RIS to an independent source, which is exactly what needs proving. read the letter →

arxiv 2501.02256 v1 pith:ZHMGM7CK submitted 2025-01-04 cs.NI

Longfei Zhao , Jingbo Tan , Jintao Wang , Ian F. Akyildiz , Zhi Sun This is my paper · ORCID
classification cs.NI
keywords underwateracousticcommunicationshadowzonereconfigurableintelligentsurfacesoundspeedprofilerayacousticsbeamformingcoverageoptimizationdeep-seaandshallow-seanetworks
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that underwater acoustic shadow zones—regions tens of kilometres wide where sound bends away and no signal arrives—can be actively filled rather than passively avoided. The proposed tool is an acoustic Reconfigurable Intelligent Surface (aRIS): a panel of piezoelectric elements that absorbs an incoming sound wave and re-radiates it with a controlled phase, steering energy into the shadow zone. The paper develops a ray-acoustics model of shadow zones, proves a deep-sea deployment rule (place the aRIS at the sound-channel axis) and a shallow-sea rule (place it as deep as possible), supplies a hardware design validated in pool tests, and reports Bellhop simulations in which coverage rises from under 20% without the aRIS to nearly 100% with it. The significance, if the claims hold, is that a single controllable reflector could provide seamless connectivity for underwater networks in dynamic oceans.

What carries the argument

The load-bearing object is the geometric shadow-zone model built from ray acoustics: with a depth-dependent sound speed $c(z)$, each ray's horizontal range $r(z)$ is an integral over grazing angle, and the coverage set is the region between the envelopes $r_{\min}(z)$ and $r_{\max}(z)$. In deep water this yields the V-shaped convergence-zone pattern; the aRIS is then equated to a point source positioned at its deployment depth, and Theorem 1 compares the maximum horizontal span $r_{\max}$ of rays that graze the sea surface. The second machinery element is the aRIS unit itself: two piezoelectric elements in a 'first absorb, then radiate' configuration that together allow phase-controlled reflection and high-gain beamforming, which the paper validates with a two-element pool test showing roughly 3 dB of gain.

What would settle it

Measure, in Bellhop or at sea, the received energy in a shadow zone for aRIS deployments at several depths (including the axis) using a realistic finite-aperture aRIS model that respects the actual incident field from the primary source; if an off-axis depth yields equal or larger coverage area than the axis under that model, the theorem's deployment rule fails. A simpler check: compute the coverage sets from the full acoustic field (not the point-source equivalence) and compare the $r_{\max}$ at each depth.

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Extended reading notes

Core claim

The central claim is that an underwater region whose geometry makes it unreachable to direct rays can be covered by placing an acoustic RIS so that it re-radiates incident energy into that region, and that in a deep-sea sound channel the unique optimal depth for this re-radiation is the sound-channel axis, where sound speed is minimal. The paper expresses this as Theorem 1: comparing the horizontal span of the surface-tangent ray emitted from the aRIS depth, the span is largest when the aRIS sits at the axis, and since the coverage area is monotone in that span, the axis depth maximises coverage. For shallow seas, the paper treats rays as circular arcs under a linear sound-speed gradient and formulates an optimisation for the aRIS depth, concluding that the seabed position yields the longest coverage distance because it creates the largest reflection grazing angles.

Load-bearing premise

The proof that the sound-channel axis is the best depth treats the aRIS as if it were an ideal point source that receives enough energy from the primary source to re-radiate with the same wavefront, and it identifies maximum coverage with the single widest surface-tangent ray span.

Editorial extensions

If this is right

  • If the deep-sea rule is correct, a single pair of aRIS units placed symmetrically at the sound-channel axis can eliminate the first shadow zone, something no increase in source level accomplishes.
  • In shallow seas, placing the aRIS at the seabed roughly halves the number of units needed to cover a 10 km shadow zone compared with non-optimal depths (about 10 vs 20 units).
  • The viability of the two-element 'absorb-then-radiate' unit in pool tests suggests the aRIS does not need simultaneous send/receive piezoelectric operation, lowering the hardware barrier.
  • Dynamic-platform compensation (phase correction for displacement and rotation) is claimed to restore coverage with ~99% RMSE reduction for translation and ~80% for rotation, supporting robustness claims.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the source-equivalence assumption at the heart of Theorem 1 is relaxed, the optimal depth could shift: at the axis the incident intensity from a distant source is lower than at shallower depths, so a real aRIS may need more surface area than the paper's unit-count analysis suggests.
  • The coverage metric used (fraction of grid points above a transmission-loss threshold) does not directly measure bit error rate or data rate; a testable extension would quantify whether the redirected energy actually supports demodulation in the shadow zone.
  • The claim that energy coverage reaches 'almost 100%' is demonstrated for a single environmental snapshot; a natural extension is to sweep seasonal sound-speed-profile variations and count how often the fixed deployment rule remains near-optimal.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes using acoustic Reconfigurable Intelligent Surfaces (aRIS) to actively fill underwater acoustic shadow zones, which are regions of severe signal loss caused by sound-speed refraction. The authors analytically model shadow zones in deep-sea and shallow-sea environments, prove a deep-sea optimal deployment rule (sound channel axis), formulate a shallow-sea placement optimization, redesign a piezoelectric-based aRIS hardware with a 'first absorb, then radiate' unit, validate the hardware in a pool test, and use Bellhop ray-tracing simulations to claim that without aRIS coverage is below 20% while with optimal aRIS deployment coverage approaches nearly 100%.

Significance. If the coverage claims are validated, the work would represent a meaningful advance over the current passive shadow-zone-avoidance paradigm in underwater acoustic networking, with a concrete hardware prototype and a plausible deployment strategy. The pool-test measurement of a two-element beamforming gain near the theoretical 3 dB is a useful practical data point. However, the central performance claim rests on an ideal-source assumption that is shared by both the analytical proof and the numerical validation; the physical energy-capture problem is not addressed. The paper is therefore potentially significant but requires more rigorous proof and a physically grounded simulation before its headline results can be accepted.

major comments (3)
  1. [§IV-A, Theorem 1] The proof equates the aRIS to a source and then compares only the horizontal span rmax of the surface-tangent ray (Eqs. (15)-(17)). However, the coverage area defined in Eq. (3) is determined at each depth by the difference rmax(z) - rmin(z), and the total coverage area in Eq. (6) integrates this difference. The statement in the proof that 'a larger V-shaped span implies a greater rmax - rmin at each depth' is asserted without derivation. As written, Theorem 1 proves only that the sound channel axis maximizes a single ray's horizontal span, not that it maximizes the full coverage area. Please provide a proof that the depth maximizing the boundary span also maximizes the integral of rmax(z) - rmin(z) over the region of interest, or revise the theorem statement to match what is actually established.
  2. [§V-A and §IV-A] The Bellhop validation appears to model the aRIS as an independent source placed at the sound channel axis, which is exactly the same assumption used in the proof of Theorem 1. This does not independently validate the physical premise that a finite-gain aRIS, which must first absorb and amplify the incident field from the 200-m source, can reradiate enough energy at 2100-m depth to behave like the source in the simulation. The pool test in §III-B demonstrates only short-range beam steering with two elements and does not measure end-to-end capture-and-reradiate gain or the achievable source level at long range. Please add an explicit link-budget analysis (incident transmission loss at the aRIS, array gain for N elements, amplifier power constraints) and, if possible, a Bellhop configuration in which the aRIS is modeled as a receiver-amplifier-radiator with a finite gain derived from this budget, rather than as an independent source. Without this, the 'nearly 100%' coverage claim is conditional on an unvalidated assumption.
  3. [§V-A, Fig. 10] The abstract and conclusions state that optimal aRIS deployment 'achieves nearly 100% energy coverage,' but the left panel of Fig. 10 indicates that this occurs only at the highest transmission-loss threshold considered (150 dB). At lower thresholds, the covered proportion is evidently smaller. Please report the coverage proportion at each threshold and state the corresponding source level and range assumptions, or explicitly qualify the 'nearly 100%' claim as applying only to the highest threshold simulated. The current wording overgeneralizes the simulation result.
minor comments (6)
  1. [§IV-A, after Eq. (17)] The sentence 'which proves (13)' should refer to (12), the theorem's coverage gain definition, rather than to (13), which defines the coverage efficiency η.
  2. [§VI-A] The opening sentence 'Sec. V-A models these impacts' appears to refer to Section VI-A, not Section V-A; please correct the cross-reference.
  3. [§III-A] The 'first absorb, then radiate' unit is described as containing amplifiers and phase shifters, yet the text contrasts it with amplify-and-forward relays by saying it 'reflects incident waves immediately through the intrinsic piezoelectric effect without needing signal receiving, processing, and re-transmitting modules.' This is internally confusing, since absorption, amplification, and phase-shifting constitute a receive-process-transmit chain. Please clarify the intended distinction from an AF relay, and specify the power source for the amplifiers.
  4. [§V-A] The simulation setup (frequency, source level, number of Bellhop rays, array size of the aRIS, and the threshold for 'coverage') is only partially specified. Please provide a table of the simulation parameters so that the results are reproducible.
  5. [§V-A and §V-B] The calculations of the 'required number of aRIS units' (e.g., approximately 10 units for 10 km in shallow water) are described only qualitatively. Please include the formula or algorithm used to obtain these numbers.
  6. [§I] The claim of 'first time in the literature' for active shadow zone coverage is strong; please provide a more nuanced comparison with prior work on underwater relays and node placement to support this novelty statement.

Circularity Check

1 steps flagged · score 4.0 of 10

Deep-sea coverage claim is partially circular: the optimality proof equates aRIS to a point source and the Bellhop validation inherits that equivalence, so the near-100% coverage result is conditional on the source-equivalence assumption rather than independently established.

  1. self definitional [Section IV-A, Theorem 1 proof, and Section V-A deep-sea Bellhop validation]
    ""Here, we equate an aRIS to a source, and thus the coverage realized by the aRIS can be analyzed based on the established coverage model." "Deploying two aRIS units symmetrically at the sound channel axis depth (2100 m) (left side of Fig. 9) effectively redirects energy into shadow zones by utilizing convergence zones.""

    The analytical theorem defines the coverage produced by an aRIS as the coverage of an ideal point source, so the 'optimal aRIS deployment' result is a statement about source placement. The Bellhop validation then evaluates aRIS deployment with the same source-equivalence assumption (the aRIS units redirect energy exactly as sources in the convergence zones); it does not independently simulate the finite-gain 'first absorb, then radiate' capture from the 200-m primary source. The near-100% deep-sea coverage therefore follows by construction from the assumed equivalence rather than from an independent test of the aRIS hardware/physics. The pool test validates only two-element beam steering, not the source-level equivalence needed for the coverage claim.

full rationale

The paper contains one significant instance of assumption-as-validation. Theorem 1 explicitly equates an aRIS to a source, and the deep-sea Bellhop validation appears to inherit that equation by modeling the aRIS units as sources at the tested depths. Consequently, the 'optimal aRIS deployment' and the resulting near-100% coverage claim are conditional on the source-equivalence assumption; the pool test shows only that two piezoelectric elements can steer a reflected beam, and the required-gain analysis in Sec. V-A calculates how many units would be needed but does not validate that the incident field at the array supports the assumed re-radiated level. This makes the central coverage prediction partially circular. Separately, in Theorem 1 the coverage gain is defined through the rmax ratio while Eq. (3) defines coverage area with rmax minus rmin; the proof asserts a larger rmax implies a larger area, which is an unproven identification rather than a circular reduction. Self-citations [13], [15], and [22] support the aRIS hardware concept but are not the load-bearing step; the load-bearing issue is the source-equivalence shared between the derivation and the simulation. Overall score 4: partial circularity with some independent content (Bellhop ray tracing, pool tests, required-gain calculations).

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities; it reuses the aRIS concept from prior work. Its contributions rest on standard ocean-acoustics models and a simplifying assumption that the aRIS acts as an independent source. The hardware design contains an unresolved contradiction about active signal processing, and the shallow-sea model relies on a linear SSP approximation.

assumptions (5)
  • domain assumption Sound speed varies only with depth (1D SSP).
    Section II states that horizontal variations in sound speed are relatively small compared to depth variation, which is standard but may be invalid in coastal areas with strong fronts or eddies.
  • domain assumption The deep-sea ocean can be modeled by the Munk profile with given parameter values.
    Equation (1) uses epsilon = 0.00737, z0 = 2100 m, zs = 1300 m, which are standard literature values, not fitted in this paper.
  • ad hoc to paper The aRIS can be modeled as an ideal point source for coverage analysis.
    The proof of Theorem 1 in Section IV-A begins 'Here, we equate an aRIS to a source,' which is a strong simplification that may not hold because the aRIS receives and reflects energy from a primary source rather than radiating independently.
  • domain assumption Rays in shallow water can be approximated as circular arcs due to linear SSP gradient.
    Section IV-B uses a linear sound speed approximation and models rays as circular arcs, citing prior work, but this is a coarse approximation that may not capture thermocline behavior.
  • ad hoc to paper The 'first absorb, then radiate' two-element unit achieves high beamforming gain without active signal processing.
    Section III-A describes amplifiers and phase shifters that process the received signal, yet later claims the aRIS reflects 'without needing signal receiving, processing, and re-transmitting modules.' This unresolved contradiction is needed for the hardware feasibility claim.

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Cite this review

Pith. "Pith review of Covering Underwater Shadow Zones using Acoustic Reconfigurable Intelligent Surfaces." pith.science (2026). https://pith.science/paper/ZHMGM7CK

@misc{pith2026250102256,
  author       = {Pith},
  title        = {Pith review of: Covering Underwater Shadow Zones using Acoustic Reconfigurable Intelligent Surfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZHMGM7CK}},
  note         = {Machine review of arXiv:2501.02256}
}
read the original abstract

To better explore the oceans, seamless communication coverage of the vast 3D underwater space is desired. Unlike terrestrial networks using radio signals, underwater acoustic communications face a unique challenge: nodes in underwater shadow zones cannot connect to the network, even within the line of sight. These shadow zones can extend for tens of kilometers, causing communication nodes to disconnect. Existing efforts focus on passive avoidance of shadow zones, but this strategy cannot ensure seamless coverage in dynamic ocean environments. This paper addresses the shadow zone problem by utilizing acoustic Reconfigurable Intelligent Surfaces (RIS) to actively control the underwater channel. Shadow zones are analytically modeled, and optimal RIS deployment strategies are developed for both deep-sea and shallow-sea environments. The acoustic RIS is redesigned considering practical engineering limitations and validated through pool tests. Bellhop-based simulations show that without RIS deployment, coverage is limited to less than 20%, regardless of source strength. However, with optimal RIS deployment, energy coverage can reach almost 100%.

Figures

Figures reproduced from arXiv: 2501.02256 by the authors.

Figure 1
Figure 1. Underwater acoustic communication network coverage. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Standard ocean sound speed profile and layered structure (left); Deep-sea V-shaped coverage pattern (right). Sound rays [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Shallow-sea surface waveguide. B. Shallow-Sea Shadow Zone Model In shallow-sea environments, the surface mixed layer with a positive sound speed gradient forms an upper channel boundary. The critical grazing angle θm satisfies Snell’s law: cos θm c0 = 1 ch , (8) where c0 is the sound speed at the source depth, and ch is the sound speed at the surface mixed layer depth. Sound rays emitted at angles larger than θm for… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: Illustration of the underwater acoustic RIS hardware. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Wet-end setup of the RIS experiment. The beam pattern measured during the experiments is shown on the right side of [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Pool Tests experiment setup (left); Measured beam pattern of the reflected acoustic waves (right). [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Shallow Sea RIS coverage. Specifically, the coverage distance r can be expressed based on the circular arcs approximation of the sound ray as r ≜ |zRIS − h| tan θreflect 2  + |D − h| tan θD 2 , (19) where zRIS is the aRIS depth, h is the surface waveguide depth, D is…
Figure 8
Figure 8. Figure 8: Standard Munk deep-sea sound speed profile model (left); Deep-sea coverage model showing V-shaped structure (right). [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 9
Figure 9. Figure 9: Deep-Sea Acoustic Dual RIS Array Optimal Coverage(left);Deep-Sea Acoustic Dual RIS Array Non-optimal [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Comparison of Proportions of Grid Points with TL Threshold (Without and With RIS) (left); Required Number of RIS [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]
Figure 11
Figure 11. Figure 11: Standard shallow-sea sound speed profile model(left); Shallow-sea coverage model (right). [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: Coverage Proportion vs. RIS Placement Depth in Shallow Sea (left); Number of RIS Units Required to Cover a 10 [PITH_FULL_IMAGE:figures/full_fig_p024_12.png]
Figure 13
Figure 13. Figure 13: Energy Distribution with RIS Coverage(left); Multi-Hop Relay Approach with Multiple RIS (right). [PITH_FULL_IMAGE:figures/full_fig_p025_13.png]
Figure 14
Figure 14. Figure 14: Impact of displacements and rotation on underwater acoustic RIS: (a) Vertical displacement, (b) Horizontal displacement, [PITH_FULL_IMAGE:figures/full_fig_p027_14.png]
Figure 15
Figure 15. Figure 15: Vertical Displacement Phase Correction over Time (left); Vertical RMSE Comparison Before and After Correction [PITH_FULL_IMAGE:figures/full_fig_p028_15.png]
Figure 16
Figure 16. Figure 16: Horizontal Displacement Phase Correction over Time (left); Horizontal RMSE Comparison Before and After Correction [PITH_FULL_IMAGE:figures/full_fig_p029_16.png]
Figure 17
Figure 17. Figure 17: Phase deviation due to random rotation and correction over time (left); Rotation RMSE Comparison Before and After [PITH_FULL_IMAGE:figures/full_fig_p029_17.png]

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Forward citations

Cited by 1 Pith paper

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    A trajectory-prediction-based RIS on/off control scheme is proposed to mitigate interference, with simulations claiming SINR gains over always-on and spectrum-learning baselines.

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.