{"id":"3482166c-d6fd-4344-9467-c9edbcf0fa16","arxiv_id":"2606.25708","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Empirical GoF and residual tests show TARF channels mismatch classical distributions, deviate from linearity, and vary over time due to surface dynamics and interface effects.","lead":"Experiments show the TARF underwater-to-air channel does not match classical fading distributions and is neither linear nor time-invariant. This characterization is needed to design reliable cross-medium links that translate acoustic data into RF phase via surface micro-vibrations.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.5","headline":"Linearity residual test (Eq. 9) and TIV metric (Eq. 10) do not isolate channel physics from phase-unwrapping artifacts and radar noise.","rationale":"The Reader correctly flags residual radar noise, imperfect unwrapping, pool multipath and settling time as the weakest assumption behind the non-linearity and time-variance claims. That assumption is load-bearing: the strongest claim of the paper is precisely that the end-to-end TARF channel is non-linear and time-varying, and those conclusions are drawn solely from the residual tests of Sec. IV-B. The GoF mismatch to classical distributions (Table I, Fig. 4) is secondary and less contested. Because the paper already notes unwrap as a possible contributor yet does not isolate it, the concern is real and already partially acknowledged; a single re-processing experiment would settle it. Hence the verdict remains CONDITIONAL (data release + clearer isolation of residual causes), matching the Reader. No stronger internal inconsistency or invented physics is present.","tokens_in":10311,"tokens_out":551,"duration_ms":4924,"concrete_test":"Re-process the same raw ADC captures with a continuous phase estimator (e.g., arctan2 after I/Q low-pass filtering, or a Kalman phase tracker) that never invokes unwrap; recompute e_lin box-plots and e_tiv curves. If the non-zero bias and growth with symbol index disappear or shrink by >50 %, the claimed channel non-linearity/time-variance is an artifact of the unwrap step rather than of the physical channel.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central claim that the TARF channel itself \"deviates from linearity\" and is \"time-varying\" rests on residual statistics e_lin (Eq. 9, Fig. 5) and e_tiv (Eq. 10, Fig. 6). Both quantities are computed after the nonlinear unwrap(arg(z(tl))) step of Eq. (6). Because unwrap is discontinuous and path-dependent, any residual phase noise, multipath inside the finite pool, or incomplete settling of surface waves can produce exactly the observed non-zero bias, subcarrier-dependent variance, and growth of normalized pilot error with symbol index—even if the underlying acoustic-to-surface mapping is linear. The authors themselves list unwrap as a contributing factor (Sec. IV-B) yet still attribute the residuals primarily to intrinsic channel non-linearity and surface dynamics. Without a control that bypasses unwrap or quantifies its contribution, the causal link from residual statistics to channel properties remains unproven.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript refines the TARF signal model to include superposition of surface waves generated by an underwater acoustic wavefront interacting at multiple points (Eqs. 1–3), then reports an empirical characterization of the end-to-end cross-medium channel. Using pool experiments with OFDM acoustic transmissions (32 subcarriers, 100–200 Hz) sensed by an FMCW radar, the authors apply Kolmogorov–Smirnov, Anderson–Darling, RMSE and P–P analyses (Table I, Fig. 4) against Rayleigh, Rician, Nakagami-m, Weibull and Rician-shadowed distributions. They further test linearity via pilot residual e_lin (Eq. 9, Fig. 5) and time-invariance via normalized pilot deviation e_tiv (Eq. 10, Fig. 6). The central claims are that the empirical amplitude statistics do not match any single classical parametric model (Nakagami-m closest yet still mismatched) and that residual statistics indicate deviation from linearity and time-invariance, attributed to the air–water interface, phase unwrapping and surface dynamics.","tokens_in":10611,"tokens_out":1136,"duration_ms":10452,"significance":"If the empirical mismatch and residual-based conclusions hold under tighter controls, the work supplies the first systematic statistical characterization of the TARF cross-medium channel and a concrete signal-model refinement that accounts for multi-point wavefront–surface interaction. That would be useful for system designers who currently rely on OTA or underwater models alone, and it correctly flags the need for adaptive equalization and settling-time considerations. The experimental pipeline (OFDM pilots, radar phase extraction, multi-depth sweeps) is reproducible in principle and the GoF methodology is standard. The contribution is incremental rather than foundational: it is an empirical observation paper whose strongest claims rest on residual statistics whose causal attribution remains open.","major_comments":[{"comment":"Section IV-B, Eqs. (9)–(10) and Figs. 5–6: the central claim that the TARF channel itself “deviates from linearity” and is “time-varying” is drawn from residual statistics computed after the nonlinear unwrap(arg(z(tl))) step of Eq. (6). Because unwrap is discontinuous and path-dependent, residual radar phase noise, multipath inside the finite pool, or incomplete surface-wave settling can produce exactly the observed non-zero bias, subcarrier-dependent variance and growth of e_tiv with symbol index—even if the underlying acoustic-to-surface mapping is linear. The authors themselves list unwrap as a contributing factor yet still attribute the residuals primarily to intrinsic channel non-linearity and surface dynamics. Without a control that bypasses unwrap (e.g., complex baseband amplitude before unwrapping, or a synthetic linear phase reference) or that quantifies the unwrap contribution,","section":null},{"comment":"Section III-B / IV: sample sizes, number of independent trials and confidence intervals on the GoF statistics (Table I) and residual distributions (Figs. 5–6) are never stated. KS, AD and RMSE values are reported to three digits without error bars; box-plot means and variances likewise lack any indication of how many OFDM symbols or independent pool runs underlie them. Without these quantities it is impossible to judge whether the reported mismatches and residual trends are statistically significant or merely consistent with measurement noise.","section":null},{"comment":"Section II, Eq. (3): the refined multi-point surface-wave integral is presented as a modeling contribution, yet it is never used to generate synthetic amplitude statistics that could be compared with the empirical GoF results of Section IV-A. Consequently the refined model remains decorative; the paper’s statistical conclusions rest solely on classical distributions that the authors themselves conclude are inadequate. Either the integral should be evaluated numerically and tested against the same data, or its inclusion should be justified more carefully.","section":null}],"minor_comments":[{"comment":"Fig. 3 caption and surrounding text: the transmitted and received OFDM spectra are shown only for a single unspecified depth; stating the depth and the number of averaged symbols would improve reproducibility.","section":null},{"comment":"Eq. (1) and following: the absorption coefficient α and sound speed c are introduced without numerical values or temperature/salinity conditions of the pool; these parameters affect the predicted surface amplitude and should be reported.","section":null},{"comment":"Section III-B: the radar beamwidth B and the precise range-bin selection procedure are mentioned but never quantified; both affect how much surface area contributes to m(tl).","section":null},{"comment":"Typographical inconsistencies: “V . V . Reddy”, “Electro-V oice”, “arXiv:2606.25708v1” date, and occasional missing spaces around equation references should be cleaned.","section":null},{"comment":"References [24]–[26] on viscous damping are cited to support settling-time arguments, yet no measured decay time constant is extracted from the experimental data; a short quantitative comparison would strengthen the discussion.","section":null}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid first empirical look at TARF channel statistics and is within scope for an eess.SP or ocean-engineering venue. The main risk is over-claiming causality from post-unwrap residuals; if the authors can add even a modest control (complex baseband before unwrap, or a synthetic linear reference) and report sample sizes, the manuscript becomes publishable after revision. Novelty relative to the original TARF SIGCOMM work is incremental but real."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The one thing worth knowing is that this is the first published attempt to run classical GoF (KS/AD/RMSE + P-P plots) and pilot residual tests on the end-to-end TARF path. Prior TARF work showed links and basic models; this one actually checks whether the amplitudes look Rayleigh/Rician/Nakagami etc. and whether the channel behaves linearly and time-invariantly. That is useful for anyone designing equalizers or waveforms for water-air interfaces.\n\nWhat they do well: the GoF numbers and plots are cleanly computed and support the claim that no single classical distribution fits well (Nakagami-m closest, still off on the lower CDF). The refined surface-integral model in Sec. II is a sensible extension of the usual single-path picture. The pool experiments with OFDM pilots, depth sweeps, and box-plot residuals are straightforward and reproducible in principle. They correctly flag frequency selectivity and surface settling as practical issues.\n\nSoft spots are real but proportionate. Sample sizes, number of independent trials, and error bars on the GoF stats are never stated, so the strength of the mismatch is hard to judge. The refined integral is written down but never validated against the data or used to predict anything. Most importantly, the linearity residual (Eq. 9, Fig. 5) and TIV metric (Eq. 10, Fig. 6) are computed after the nonlinear unwrap step. The authors themselves list unwrap as a contributor, yet still attribute the non-zero bias, subcarrier variance, and growth with symbol index primarily to “channel non-linearity and surface dynamics.” Without a control that bypasses unwrap or quantifies radar noise/multipath in the finite pool, that causal link is not isolated. The stress-test concern lands; it does not kill the paper, but it does mean the strongest wording in the conclusion over-reaches the evidence.\n\nThis is for people already working on TARF or cross-medium links who need empirical priors for adaptation. It is not a theory paper and will not reorganize wireless modeling. The math is elementary, the citations are appropriate, and there is no circularity. I would send it to referees; they can demand the missing sample-size details, a control for unwrap, and data release. Worth a careful look if you touch this niche; otherwise skim the figures and move on.","headline":"First solid GoF and residual tests on TARF amplitudes; mismatch and time-variance look real, but the linearity claim is confounded by unwrap and lacks isolation controls.","tokens_in":11197,"tokens_out":585,"would_cite":false,"duration_ms":11301,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"The underwater-to-air TARF channel does not follow classical fading models and is neither linear nor time-invariant.","keywords":["TARF","cross-medium communications","underwater acoustics","channel model","goodness-of-fit","linearity","time invariance","surface micro-vibrations"],"falsifier":"Repeat the identical OFDM pilot sequence in a larger, quieter basin with longer inter-symbol gaps and independent hydrophone surface measurements; if residual bias vanishes and pilot error no longer grows with symbol index, the non-linearity and time-variance claims fail.","tokens_in":11211,"feed_emoji":"📡","tokens_out":822,"duration_ms":8136,"temperature":0.7,"pith_summary":"Translational acoustic-RF (TARF) links move information from an underwater acoustic speaker to an airborne radar by reading micron-scale surface vibrations. Reliable design needs a channel model, yet the paper shows that standard OTA and underwater distributions (Rayleigh, Rician, Nakagami-m, Weibull, Rician-shadowed) fail to match measured amplitude statistics. The authors refine the surface-wave model to include superposition of arrivals at many points, then run goodness-of-fit tests and residual-error checks on pool experiments. Nakagami-m is closest numerically, but probability-probability plots still deviate, residual pilot errors are biased and subcarrier-dependent, and normalized pilot error grows with successive OFDM symbols and with speaker depth. The channel therefore behaves as a time-varying, non-linear interface that requires adaptation rather than textbook equalizers.","feed_headline":"TARF channel defies classical fading and breaks linearity","feed_subtitle":"Pool data show no match to Rayleigh or Nakagami-m; residual errors grow with time and depth","key_machinery":"The refined surface-displacement integral that superposes acoustic arrivals along the radial path to each surface point, together with the pilot residual-error tests for linearity (weighted sum of identical pilots) and time-invariance (normalized pilot drift across successive OFDM symbols).","core_discovery":"Empirical TARF amplitude data do not align with any single classical parametric distribution; residual-error tests further show that the end-to-end channel deviates from linearity and is time-varying, driven by wavefront-surface interactions, phase unwrapping, and finite surface-wave settling times.","pith_inferences":["The same surface-wave memory that breaks time-invariance may also create inter-symbol interference floors that scale with message length, limiting practical packet sizes.","Because the mismatch with classical models grows with depth, shallow-water TARF may still be approximable by Nakagami-m while deep deployments will require entirely new statistical families.","Phase-unwrapping artifacts identified as a non-linearity source suggest that alternative micro-motion estimators (e.g., I/Q amplitude tracking) could restore approximate linearity."],"forward_implications":["Classical Rayleigh/Rician equalizers and capacity formulas cannot be used off-the-shelf for TARF links.","Channel estimation and adaptation must track surface-wave memory that persists across successive OFDM symbols.","Speaker depth and surface viscosity become first-order design parameters that control both fading statistics and coherence time.","Reliable TARF systems will need non-linear or data-driven receivers that jointly handle phase unwrapping and surface dynamics."],"fun_headline_variants":["TARF amplitudes fit none of the classical fading models","Cross-medium TARF channel fails linearity and stationarity","Pool data reject Rayleigh and Nakagami for TARF amplitudes","Surface waves drive TARF nonlinearity and time variance","TARF residual errors grow with depth and settling time"],"cache_read_input_tokens":128,"weakest_assumption_plain":"That the observed residual bias, variance, and growth of pilot error with time are caused by intrinsic channel non-linearity and surface dynamics rather than by radar noise, imperfect unwrapping, pool multipath, or insufficient settling between symbols.","fun_headline_variants_meta":{"raw":{"variants":["TARF amplitudes fit none of the classical fading models","Cross-medium TARF channel fails linearity and stationarity","Pool data reject Rayleigh and Nakagami for TARF amplitudes","Surface waves drive TARF nonlinearity and time variance","TARF residual errors grow with depth and settling time"]},"model":"grok-4.5","effort":"low","cost_usd":0.008622,"raw_usage":{"total_tokens":1965,"prompt_tokens":696,"num_sources_used":0,"completion_tokens":61,"cost_in_usd_ticks":86220000,"prompt_tokens_details":{"text_tokens":696,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1208,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":696,"tokens_out":61,"duration_ms":9169,"temperature":1.0,"reasoning_tokens":1208,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-12T12:12:55.795918+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Repeat the identical OFDM pilot sequence in a larger, quieter basin with longer inter-symbol gaps and independent hydrophone surface measurements; if residual bias vanishes and pilot error no longer grows with symbol index, the non-linearity and time-variance claims fail.","supporting_citations":[],"review_version":2}