{"id":"5d85c746-6bbc-47b7-a812-5f59d45f5cdf","arxiv_id":"2505.01223","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A pilot-free multi-user OFDM uplink framework jointly estimates target delay, Doppler, and angle and decodes messages, with multi-user fusion of dual polynomials improving accuracy in simulations.","lead":"This paper proposes a pilot-free uplink system where several users' OFDM signals are used both to send data and to locate moving targets, using a base station that estimates delays, Doppler shifts, and angles via atomic norm minimization. A smart generalist might read it to see whether multi-user views of the same target can be fused to improve both sensing and decoding, a key question for future ISAC networks.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"3D multi-user fusion assumes common delay-Doppler peak; paper's own Eq. (32) and Section V-C say delays differ per user, leaving the central fusion claim untested.","rationale":"The reader's weakest assumption identifies exactly the load-bearing issue: fusing dual polynomials pointwise over a shared 3D domain requires a common peak, but common targets induce user-specific delays and Dopplers in the paper's own model. This is not merely a missing baseline or an untested scenario; it is an internal inconsistency between Section IV, which states that all users measure the same key parameters, and Section V-C, which concedes that delays must differ across users. The numerical results avoid the problem by testing only AoA fusion (where the common-peak assumption holds) and delay-based localization via per-user estimates plus nonlinear least squares, not the claimed pointwise 3D dual-polynomial fusion. I therefore agree with the reader's CONDITIONAL verdict rather than moving to REJECT, because a revision could repair the paper by restricting fusion to genuinely common parameters, aligning delay/Doppler coordinates before fusion, or clearly limiting the collaborative claim to common AoA while treating delay and Doppler with user-specific estimation followed by decision-level fusion. The proposed concrete test would settle whether the 3D fusion assumption is merely unvalidated or actually fails numerically.","tokens_in":12543,"tokens_out":4875,"duration_ms":52873,"concrete_test":"Simulate the full 3D experiment of Section IV with R=2 users at different locations and one common target. Use Eq. (32) for the true delays and assign distinct Doppler shifts to the two users; compute each f_i(zeta) by solving (28) or by constructing ideal noiseless dual polynomials. Then form f_avg = (f_1 + f_2)/2 on a common (tau, nu, theta) grid. Check whether f_avg has a single dominant peak and whether argmax corresponds to any true common-target parameter. Compare target parameter MAE and SER for message recovery using fused 3D parameters versus using each user's own parameters. If f_avg has multiple comparable peaks or fused parameters are worse, the common-peak assumption in Section IV fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that multi-user fusion of dual polynomials jointly enhances 3D target estimation and message recovery rests on the premise that all users' dual polynomials share a single 3D peak for a common target. That premise is false for the paper's own model. In Eq. (8), user i's path has delay tau_{ell,i} and Doppler nu_{ell,i}; for a common target, Eq. (32) gives tau_{i,1} = (||x_i - x_T|| + ||x_T - x_BS||)/c, which depends on the user's location, and the bistatic Doppler is likewise user-dependent. Hence f_i(zeta) has peaks at different (tau, nu) for different i. Pointwise averaging, max, weighted averaging, and codebook alignment all combine f_i on a common grid without any geometric alignment or warping of the delay/Doppler coordinates; codebook alignment removes only the phase 1/c_user(i), not the physical parameter offsets. The paper even concedes in Section V-C that delay parameters must be different for different users since they are located at different places, and its numerical collaboration experiments are restricted to AoA-only fusion (P=Q=1) or to per-user delay estimates fed into the least-squares localizer (Eq. 35). The claimed 3D collaborative dual-polynomial fusion is therefore never demonstrated and, as stated, is internally inconsistent with the signal model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a pilot-free multi-user uplink ISAC framework in which single-antenna users transmit OFDM data symbols, and the base station jointly decodes the messages and estimates delay, Doppler, and angle-of-arrival parameters of sparse multipath components. The received signal is modeled as a superposition of user-specific atoms (Eq. 8), and the problem is formulated as a 3D atomic norm minimization solved by SDP, with a primal Vandermonde-decomposition route and a dual-polynomial route. The authors then propose collaborative fusion methods—pointwise averaging, pointwise maximum, weighted averaging, and codebook-aligned aggregation of the per-user dual polynomials—and claim that multi-user fusion enhances both target estimation and communication performance. Numerical experiments address continuous parameter recovery, target localization from per-user delay estimates, AoA-only collaborative estimation, and symbol error rate. The central advertised claim is that additional uplink users improve rather than degrade sensing and decoding in a unified 3D framework.","tokens_in":12811,"tokens_out":11265,"duration_ms":120724,"significance":"If established, the proposed framework would be a useful contribution: it turns multi-user uplink transmissions into sensing diversity and removes the need for dedicated pilots, which is attractive for mm-wave ISAC. The paper has some genuine strengths: a concrete 3D atomic norm/SDP formulation built on a structured codebook, two algorithmic routes (primal and dual), and numerical evidence that AoA-only collaboration and delay-based least-squares localization can benefit from multiple users. However, the load-bearing claim of 3D collaborative dual-polynomial fusion is not supported by the evidence and is, as stated, inconsistent with the signal model. The experimental validation also contains an oracle-dependent normalization step. The paper does not provide theoretical recovery guarantees, complexity analysis, or code, so the case for the central claim rests entirely on the simulations, which conspicuously avoid the problematic 3D fusion scenario. The work is therefore of moderate significance and requires substantial revision before its main contribution can be credited.","major_comments":[{"comment":"The central premise of the 3D fusion methods is inconsistent with the paper's own signal model. In Eq. (8), each path has a user-dependent triple ζ_{ℓ,i}=(τ_{ℓ,i},ν_{ℓ,i},θ_{ℓ,i}), and for a common target Eq. (32) gives τ_{i,1}=(‖x_i-x_T‖+‖x_T-x_BS‖)/c, which depends on the user's location; the bistatic Doppler shift likewise depends on the user-target geometry. Therefore the dual polynomials f_i(ζ) have peaks at different (τ,ν) values for different users, and pointwise averaging, pointwise maximum, weighted averaging, and codebook-aligned aggregation on a common grid do not produce a common peak. The alignment step removes only the constant c_user(i) from the codebook, and since f_i is defined as a norm the phase of c_user(i) is lost anyway. The numerical experiments confirm that the 3D fusion is never actually demonstrated: Figure 4 restricts to AoA-only estimation with P=Q=1, and the localization experiment in Eq. (35) uses per-user delay estimates rather than fused dual polynomials. The authors should either restrict the fusion claim to genuinely common parameters (e.g., AoA or target location) and use per-user delay/Doppler estimates as inputs to a geometric fusion step, or explicitly warp/align the per-user parameter spaces before aggregation. Without such a change, the claimed 3D collaborative fusion is not validated.","section":"Section IV (collaborative fusion); Eqs. (8), (32); Section V-C"},{"comment":"The localization experiment normalizes the true physical delays using the ground-truth minimum and maximum over users, τ_{i,1}=(τ_{i,1}-min_i τ_{i,1})/(max_i τ_{i,1}-min_i τ_{i,1}). This is an oracle step: in a real pilot-free ISAC system these constants are not known in advance, and they depend on the unknown user and target geometry. The reported MAE reduction with increasing R in Fig. 3b therefore reflects, at least in part, the use of information that the method would not have access to. The authors should either estimate the normalization constants from the data, or study the sensitivity of the result to the choice of the affine mapping, or re-run the experiment without oracle normalization.","section":"Section V-B, Eq. (33)"},{"comment":"The message-recovery step solves for the products c_{ℓ,i} f_i as independent unknowns, one per path. However, in the model (8) the same symbol vector f_i is shared by all paths of user i. As written, the least-squares problem in Eq. (30) has s_i k_i unknowns per user, whereas the model has only k_i + s_i degrees of freedom for that user. The text refers to [20, Eq. (29)] for f_i extraction, but the paper should specify how the common f_i is recovered from the s_i estimated vectors and why the least-squares solution is not adversely affected by this over-parameterization. Since the reported SER results depend directly on this step, the procedure needs to be stated precisely and validated, otherwise the communication-performance claims are not reproducible from the text alone.","section":"Section IV-B, Eq. (30)"}],"minor_comments":[{"comment":"The delay phase in Eq. (5) appears as e^{-j2πτ_{ℓ,i}q/T}, while the atom in Eq. (8) is defined as e^{+j2π(qτ+pν+rθ)} with normalized τ=τ/T. This sign inconsistency should be fixed; as written, the delay component in the atomic model is mirrored relative to the received-signal model.","section":"Eq. (5) vs. Eq. (8)"},{"comment":"The constraint in Eq. (27) should hold for all ζ∈[0,1)^3, but the notation ζ_i∈[0,1)^3 suggests that ζ_i is a single optimization variable per user. Please correct the quantifier and the notation to avoid confusion.","section":"Eqs. (26)-(27)"},{"comment":"The role of W_i in the SDP (19)-(20) is under-specified: it should be explicitly defined as a Hermitian matrix variable of appropriate dimension, and the text should clarify why the objective contains tr(W_i) while the constraint couples it with T3L(V_i) and Z_i.","section":"Section III-B4 and Eq. (19)-(20)"},{"comment":"The statement that the number of unknowns in (8) is O(LR+Σ_i s_i) is imprecise: the user messages contribute k_i symbols per user, and the continuous delay/Doppler/AoA parameters are not naturally counted by this expression. Please clarify the counting and the role of L and R.","section":"Section III-A"},{"comment":"There are several typographical and formatting issues, including 'wherer' in Section II, 'paramters' in Section III-B4, the unusual notation 'Rexq,yy' in Eq. (26), and the formatting of '1l=0' in Eq. (28). These should be cleaned up.","section":"General presentation"}],"recommendation":"major_revision","confidential_remarks":"The paper's advertised 3D multi-user fusion claim is internally inconsistent with its own bistatic model; the experiments only validate AoA-only fusion or per-user delay estimates fed into a least-squares localizer. I believe this is fixable by re-scoping the central claim, but the revision must be substantive: either fuse only common parameters (AoA, target location) or introduce a principled alignment of the per-user delay/Doppler coordinates before aggregation. If the revision does not address this, the manuscript's main contribution would not be supported. Note also the heavy reliance on the authors' prior SDP and demixing results (Refs. [18]-[21]); the novelty of the 3D extension should be stated more carefully relative to those works."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper has a real idea and one clean result, but its central claim is oversold. The clean result is collaborative AoA estimation for a common target: at 0 dB, averaging/max/weighted dual polynomials over users does better than single-user AoA and improves SER. That is a valid, if incremental, contribution.\n\nWhat is genuinely new is the formulation: blind multi-user uplink ISAC where each user's known codebook is exploited to demix users and recover continuous delay-Doppler-AoA parameters without pilots. The atomic-norm SDP, the MaPP3D Vandermonde decomposition, and the dual-polynomial construction are adapted from prior work, including three of the authors' own papers, but the multi-user codebook alignment and fusion framing is a new combination. I'd credit that.\n\nThe soft spots are real and one is load-bearing. The fusion methods in Section IV are defined on the full 3D parameter vector ζ. But for a common target, the delay in Eq. (32) is user-dependent, and the Doppler is too in bistatic geometry. So the dual polynomials f_i(ζ) have peaks at different delay/Doppler coordinates. Pointwise averaging or max over users on a common grid will average unrelated peaks; multiplying by 1/c_user removes only the code phase, not the physical offsets. The paper concedes this in Section V-C, where it says delay parameters must differ across users, and then only demonstrates fusion for AoA (P=Q=1) or uses per-user delay estimates in the least-squares localizer of Eq. (35). As written, the claimed 3D collaborative fusion is neither demonstrated nor consistent with the signal model. That is a serious overclaim, not a minor missing plot.\n\nNext, Eq. (33) normalizes delays using the true min and max of the simulated delays. That is a post-hoc, data-dependent step; in a real blind setting you wouldn't know those constants. The localization experiment also uses only delay, and the reduction in MAE with more users is expected from the nonlinear least-squares, not from dual-polynomial fusion. There are no recovery guarantees, no pilot-based baseline, and no code, so reproducibility is limited.\n\nWho is this for? ISAC signal processing folks working on pilot-free/off-the-grid multi-user estimation will find the problem setup and AoA fusion experiment useful. But the paper needs major revision: either restrict the collaborative claims to AoA (or to parameters that are truly common), or show how to align delay/Doppler across users before fusion, and replace the oracle normalization with a principled blind calibration.\n\nI'd send it to peer review, but with the clear expectation that the 3D fusion claim be reworked and the localization experiment fixed. It is not a desk reject; it is a conditional-accept-level paper hiding under a claim it cannot support.","headline":"Worth engaging: the pilot-free multi-user uplink ISAC setup and AoA fusion are useful, but the headline 3D collaborative fusion claim is not supported by the simulations and cuts against the paper's own bistatic model.","tokens_in":13372,"tokens_out":2900,"would_cite":false,"duration_ms":28190,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that pilot-free multi-user uplink signals can be jointly decoded and used for 3D target sensing, and that fusing many users' views improves both.","keywords":["integrated sensing and communication","multi-user uplink","pilot-free OFDM","atomic norm minimization","3D super-resolution","dual polynomial","delay-Doppler-AoA estimation","collaborative fusion"],"falsifier":"Place two users at well-separated distances from the same target so their bistatic delays differ by more than a super-resolution grid cell, run the aligned dual-polynomial fusion, and check whether the fused 3D polynomial has a single peak at the true common AoA while also recovering each user's distinct delay and Doppler. If the fused peak falls at the average of the users' delays or at no physically realizable path, the common-3D-peak premise fails.","tokens_in":12285,"feed_emoji":"📡","tokens_out":7702,"duration_ms":71770,"temperature":0.7,"pith_summary":"This paper tries to show that in a millimeter-wave uplink, the data signals users already send can double as radar-like probes, removing the need for dedicated pilot transmissions. The base station treats the channels as sparse sums of delay, Doppler, and angle-of-arrival paths, and solves a 3D super-resolution problem to recover those paths while decoding messages. The central wager is that extra users are not interference but an asset: because each user sees the same target from a different position and with a different velocity, fusing their estimates sharpens target localization and, in turn, message recovery. Numerical experiments with up to five users support this, reporting lower angle-of-arrival error and lower symbol error rate for collaborative fusion at 0 dB signal-to-noise ratio.","feed_headline":"Extra users sharpen both sensing and data recovery","feed_subtitle":"A 3D super-resolution scheme fuses multi-user delay-Doppler-AoA views, turning interference into sensing gains.","key_machinery":"The load-bearing object is the 3D atomic norm and its SDP relaxation: the atomic norm $\\|X_i\\|_{A_i}$ is the convex proxy for the sparsest sum of atoms $f_i a_{3D}(\\zeta)^T$, where $a_{3D}(\\zeta)$ is the steering vector spanning subcarrier, OFDM-block, and antenna dimensions. The semidefinite program enforces a three-level Toeplitz structure on the dual variable, which is what allows continuous-valued delays, Dopplers, and AoAs to be recovered without a grid. The companion machinery is the dual polynomial $f_i(\\zeta)$, whose peaks mark the estimated paths; the collaborative fusion step aggregates these polynomials across users, and the aligned variant removes user-specific codebook phase offsets before averaging.","core_discovery":"The paper's central claim is that a pilot-free multi-user OFDM uplink can perform integrated sensing and communication by solving a single 3D super-resolution problem over the unified delay–Doppler–AoA parameter space. Each user's known codebook structure lets the base station recover the matrix $X_i = \\sum_\\ell c_{\\ell,i} f_i a_{3D}(\\zeta_{\\ell,i})^T$ through atomic norm minimization, implemented as a semidefinite program with a three-level Toeplitz constraint. The delay, Doppler, and AoA values are then extracted either by a Vandermonde decomposition of the Toeplitz matrix (the MaPP3D matrix-pencil and pairing procedure) or by locating peaks of the dual polynomial $f_i(\\zeta)$. With multiple users observing the same target, the paper proposes fusing these dual polynomials pointwise, by maximum, by weighting, or by phase-aligning user codebooks, and reports that these collaborative estimates reduce target parameter error and symbol error rate relative to single-user or non-collaborative estimation.","pith_inferences":["A natural extension the paper leaves implicit is geometry-aware fusion: since delays and Dopplers are user-dependent in bistatic geometries, fusing in target position-velocity coordinates rather than raw parameter space could retain the collaboration benefit across users at very different locations.","In multi-target scenes, peak association across users becomes necessary; a naive pointwise average of dual polynomials could merge peaks from different targets. One testable extension is to cluster each user's peaks and fuse only matched targets.","Because the dual-polynomial SDP is solved per user or jointly, the complexity grows with user count; an online or streaming variant could make the approach practical for fast-moving users, but the paper does not address real-time implementation."],"forward_implications":["If the central claim holds, uplink ISAC needs no dedicated pilots: the base station can sense targets and decode data from the same OFDM transmissions, freeing spectrum and time resources.","Spatially separated users provide multiple independent delay and Doppler measurements of a shared target, so target localization ambiguity shrinks as the number of users grows.","Communication scatterers, which cluster at near-zero Doppler, can be separated from moving targets in the 3D parameter space, enabling simultaneous communication-channel estimation and radar detection.","Collaborative fusion should make the system more robust to noise: the paper reports that at SNR = 0 dB, weighted, maximum, and aligned averaging all outperform single-user and non-collaborative estimation in both AoA error and aggregate symbol error rate."],"supporting_citations":[{"why":"Supplies the super-resolution theory that identifies target parameters from dual-polynomial peaks.","marker":"[13]"},{"why":"Provides the off-the-grid atomic-norm SDP formulation that the primal approach adapts.","marker":"[14]"},{"why":"Contributes the atomic-norm SDP relaxation adapted here to 3D delay-Doppler-AoA recovery.","marker":"[18]"},{"why":"Provides the dictionary-based least-squares message recovery and the user-demixing setting the communication side builds on.","marker":"[20]"},{"why":"Supplies the OFDM passive-radar delay-Doppler model and frequency-domain sampling used in the signal model.","marker":"[22]"},{"why":"Defines the atomic norm as the convex geometry tool for sparsity in continuous parameter spaces.","marker":"[23]"},{"why":"Provides Vandermonde decomposition of multilevel Toeplitz matrices, which the MaPP3D parameter extraction relies on.","marker":"[25]"},{"why":"Supplies the ESPRIT matrix-pencil machinery behind MaPP3D's eigen-decomposition and generalized eigenvalue steps.","marker":"[27]"}],"fun_headline_variants":["Pilot-free uplink fuses user views to boost ISAC","Multi-user fusion sharpens sensing and decoding","3D super-resolution turns users into sensors","Collaborative uplink: one target, many viewpoints","Atomic norm scheme merges users for better ISAC"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The fusion step assumes every user's measurement of a common target shares one identical 3D peak in delay-Doppler-AoA space, but physically only the angle of arrival is common; delay and Doppler depend on each user's position and velocity.","fun_headline_variants_meta":{"raw":{"variants":["Pilot-free uplink fuses user views to boost ISAC","Multi-user fusion sharpens sensing and decoding","3D super-resolution turns users into sensors","Collaborative uplink: one target, many viewpoints","Atomic norm scheme merges users for better ISAC"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000505,"raw_usage":{"total_tokens":2481,"prompt_tokens":975,"completion_tokens":1506,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":591,"completion_tokens_details":{"reasoning_tokens":1431}},"tokens_in":591,"tokens_out":1506,"duration_ms":10718,"temperature":1.0,"reasoning_tokens":1431,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:24:06.208046+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Place two users at well-separated distances from the same target so their bistatic delays differ by more than a super-resolution grid cell, run the aligned dual-polynomial fusion, and check whether the fused 3D polynomial has a single peak at the true common AoA while also recovering each user's distinct delay and Doppler. If the fused peak falls at the average of the users' delays or at no physically realizable path, the common-3D-peak premise fails.","supporting_citations":[{"cited_title":"Towards a mathematical theory of super-resolution,","cited_arxiv_id":null,"evidence_quote":"Supplies the super-resolution theory that identifies target parameters from dual-polynomial peaks."},{"cited_title":"Compressed sensing off the grid,","cited_arxiv_id":null,"evidence_quote":"Provides the off-the-grid atomic-norm SDP formulation that the primal approach adapts."},{"cited_title":"Separating radar signals from impulsive noise using atomic norm minimization,","cited_arxiv_id":null,"evidence_quote":"Contributes the atomic-norm SDP relaxation adapted here to 3D delay-Doppler-AoA recovery."},{"cited_title":"Vandermonde decomposition of mul- tilevel toeplitz matrices with application to multidimensional super- resolution,","cited_arxiv_id":null,"evidence_quote":"Provides Vandermonde decomposition of multilevel Toeplitz matrices, which the MaPP3D parameter extraction relies on."}],"review_version":1}