{"id":"b5636d53-8cd4-491d-90e9-6425386cac8f","arxiv_id":"2507.19812","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A two-stage MAMP plus DFT algorithm estimates massive MIMO-ODDM channels with near-Bayesian-optimal accuracy at linear complexity.","lead":"A new two-step method estimates wireless channels in a next-generation high-speed communication scheme called ODDM, using a message-passing algorithm for path delays and Doppler shifts and a Fourier transform for arrival angles. It claims near-ideal accuracy at low computational cost, a practical bottleneck for 6G high-mobility links.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Bayes-optimality claim rests on an unproven random-matrix premise and a scalar real-valued posterior update that does not match the stated complex model, so the claim is not established even in the ideal regime.","rationale":"The Reader identifies the random-matrix premise as the weakest assumption; I agree it is central, but I find an even more basic mismatch that survives even if that premise were granted. MAMP's state-evolution-based optimality requires the denoiser to be the true posterior of the signal entries. Theorem 1 computes a posterior for real scalar Gaussian entries, while the channel vector entries carry arbitrary steering phases (Eq. (11)) and the noise is circular complex; Eqs. (52)-(53) are therefore not the MMSE denoiser for the stated problem. This is an internal-consistency issue, not simply a disagreement with the prevailing consensus. The concrete test I propose is decisive: replacing the NLE with the complex posterior either removes the gap to the random benchmark (proving the current NLE is the problem) or leaves it (proving the structured matrix is the problem). In both cases the present evidence does not support the near-Bayes-optimal headline, so I keep the Reader's conditional verdict rather than moving to acceptance.","tokens_in":21974,"tokens_out":10288,"duration_ms":117203,"concrete_test":"Run MAMP with the correct complex posterior for the observation mu_{t,i} = h_i + w_i, taking h_i = b_i g_i exp(j phi_i) with phi_i random, or equivalently run MAMP on the stacked real model [Re(y); Im(y)] = [Re(Phi), -Im(Phi); Im(Phi), Re(Phi)] h + real noise, and re-run the Nt = 128 and Nt = 256 curves of Figs. 3 and 8 with identical parameters. If the corrected NLE matches or beats the published curves and matches the random-matrix MAMP curve, the current optimality claim is invalidated by the NLE mismatch; if a gap to the random-matrix MAMP remains, it is invalidated by the structured Phi. Comparing with an oracle MMSE from numerical integration on a small subproblem would further show which link breaks.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The claim that MAMP 'can achieve the Bayes optimal MSE' has two necessary conditions, and neither is established. First, MAMP optimality is proven for i.i.d. or right-unitarily invariant sensing matrices; the load-bearing assertion in Remark 1 is that the equivalent coefficient matrix in Eq. (16) 'approach[es] completely random' as Nt grows. The only justification is that each antenna carries independent pilot symbols, but footnote 4 says those pilots are fixed, and the blocks in Eq. (12) have cyclic-shift and DFT structure. No spectral, singular-value, or asymptotic-freeness analysis is provided, and Fig. 8 compares with MAMP on a fully random matrix, which is an upper benchmark rather than the true MMSE for the actual matrix. Second, even if the matrix were random, the NLE in Theorem 1 and Appendix B is derived for a scalar real Gaussian observation y = b g + n with real g, using (y - u_g)^2 and y^2. The stated model is complex: y, the matrix, and the channel vector are complex, with steering phases in the channel vector via F_nt in Eq. (11); Remark 2 itself concedes that only the magnitudes are Bernoulli-Gaussian. No real-valued augmentation or complex posterior is given. The published NLE is therefore a mismatched denoiser, so the algorithm does not compute the posterior mean of the stated model even in the random-matrix limit.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies downlink channel estimation for massive MIMO-ODDM systems. The authors construct an effective sparse channel model whose element magnitudes are Bernoulli-Gaussian and propose a two-stage estimator: a memory approximate message passing (MAMP) stage for gains, delays, and Doppler, and a DFT-based stage for angle estimation. The paper claims that the proposed algorithm approaches Bayesian optimality as the number of antennas tends to infinity and reports roughly 30% NMSE improvement over OMP and 3D-OMP baselines, together with BER comparisons of ODDM against OTFS and OFDM.","tokens_in":22242,"tokens_out":8195,"duration_ms":101589,"significance":"If established, the main contribution would be a low-complexity channel estimator that approaches the MMSE limit for a structured massive MIMO-ODDM problem, which is a nontrivial extension of MAMP to a non-i.i.d. sensing model. The paper includes a useful complexity analysis, extensive NMSE and BER simulations across SNR, user speed, antenna count, number of paths, modulation order, and channel models, and comparisons against OMP, 3D-OMP, and a random-matrix MAMP benchmark. However, the advertised Bayesian-optimality result is currently supported only by an unproven random-matrix assertion and a scalar real-Gaussian NLE that does not match the stated complex model; these are load-bearing issues for the headline claim rather than presentation defects.","major_comments":[{"comment":"The premise that the elements of the equivalent coefficient matrix Phi_tilde 'approach completely random' as Nt grows is asserted without proof, and it is load-bearing because MAMP's Bayesian optimality is established for i.i.d. or right-unitarily invariant sensing matrices, not for the structured blocks in Eq. (12). The reasoning in Remark 1 counts independent pilot symbols per antenna, but footnote 4 states that these pilots are fixed and belong to a defined set, and the symbols enter through cyclic-shift and DFT-structured blocks; independence of the generating symbols does not by itself imply i.i.d. or asymptotically free entries of the resulting matrix. Please either prove a quantitative randomness property (e.g., convergence of the empirical singular value distribution, or asymptotic freeness of the relevant block-circulant operators) or remove/weaken the optimality claim.","section":"Section III, Remark 1"},{"comment":"The NLE in Theorem 1 is derived for a real scalar observation y = b g + n with real Gaussian g and n, as shown in Appendix B, which uses (y-u_g)^2, y^2, and real densities. The system model (9)-(10) and the effective model (16) are complex: y, Phi_tilde, and h_tilde are complex, and steering phases enter h_tilde through F_nt in Eq. (11); Remark 2 itself concedes that only the magnitudes of the elements are Bernoulli-Gaussian, not the elements. Therefore the posterior update (52)-(53) is not the posterior mean of the stated model, so the algorithm does not compute the MMSE estimate of h_tilde even in the random-matrix limit. A complex-valued derivation or an explicit real-valued model with the correct likelihood is required.","section":"Section IV-A, Theorem 1 and Remark 2; Appendix B"},{"comment":"The Bayesian-optimality comparison is partly internal: Eq. (20) defines the target MSE under the same Bernoulli-Gaussian prior used to construct the NLE, and Fig. 8 compares the proposed estimator with 'traditional MAMP' running on a fully random matrix rather than with an oracle MMSE bound for the actual structured matrix. The observed convergence in Fig. 8 shows that the structured matrix begins to behave like a random matrix in this test, but it does not establish that the algorithm achieves the MMSE of the true model, nor does it quantify the gap at finite Nt. Please add an explicit MMSE baseline (or a state-evolution prediction) for the actual matrix and report the gap.","section":"Section IV, Eq. (20); Section V-B, Fig. 8"}],"minor_comments":[{"comment":"The paragraph beginning 'Further, let Phi_tilde = ...' and Eqs. (16)-(17) are duplicated verbatim; remove one copy.","section":"Section III"},{"comment":"The Bernoulli-Gaussian prior parameters (p, u_g, v_g) and the noise variance sigma^2 are not specified in the numerical setup; state how these values are set or estimated, since the NLE is sensitive to them.","section":"Section IV, Theorem 1 and Section V"},{"comment":"The sentence 'The NMSE of all algorithms shows an increased trend with higher SNRs' appears to contradict the plotted decrease of NMSE; correct the wording and the garbled axis labels in Fig. 3.","section":"Section V, Fig. 3"},{"comment":"The complexity comparison should clarify that O(MN(2K+1)LNtTt) is per iteration, state whether Phi_tilde Phi_tilde^H is precomputed, and include the cost of the one-dimensional angle-rotation search in Algorithm 1.","section":"Section IV-C, Algorithm 1"},{"comment":"Lemma 1 is stated for an arbitrary matrix C, but the proof uses unitary diagonalization, which is only valid for normal matrices; since the lemma is applied to the Hermitian matrix theta_t B, state that assumption explicitly or prove the Neumann series directly.","section":"Section IV-A, Lemma 1"},{"comment":"References [13] and [35] appear to cite the same paper; merge them and ensure the year and venue are consistent. Also fix the typo 'prefect' in Fig. 9 and check whether the last legend entry in Fig. 12 should be 'OTFS 350 km/h ETU'.","section":"References and figures"}],"recommendation":"major_revision","confidential_remarks":"The paper fits a signal-processing venue and the empirical gains over OMP and 3D-OMP may be publishable, but I would not accept the current version with the Bayes-optimality claim as stated. The authors should either supply a rigorous random-matrix argument and a correct complex-valued posterior update, or substantially weaken the optimality language in the abstract, contributions, and conclusion."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper has one genuinely useful piece: the effective channel model in Section III, which turns massive MIMO-ODDM channel estimation into a sparse recovery problem over delay-Doppler-antenna dimensions. The two-stage design, MAMP for gains/delays/Doppler and DFT with phase rotation for angles, is new in this combination, and the complexity analysis is honest about the linear scaling. The simulated NMSE gains over OMP and 3D-OMP are plausible and roughly 30% as claimed, and the robustness across user speeds is a nice practical point.\n\nThe trouble is the headline claim: 'approaches the Bayesian optimal results when the number of antennas tends to infinity.' Two load-bearing legs are missing. First, Remark 1 asserts that the equivalent coefficient matrix becomes completely random as Nt grows, because each antenna carries independent pilots. But footnote 4 says those pilots are fixed, and the matrix has cyclic-shift and DFT structure; no spectral or asymptotic-freeness argument is given. The empirical convergence in Fig. 8 is toward MAMP with a fully random matrix, which is a comparison to an upper benchmark, not to the true MMSE for the structured matrix at hand.\n\nSecond, and more serious, the NLE in Theorem 1 is derived for a scalar real observation y = b g + n with real g and real noise variance. The stated model in (16)–(18) is complex: the channel vector includes steering phases via F_nt in (11), and the noise is complex Gaussian. Remark 2 itself admits that only the magnitudes are Bernoulli-Gaussian. The paper never provides a complex-valued posterior or a real-imaginary augmentation. So the algorithm, as published, does not compute the posterior mean for its own model, even in the random-matrix limit. That is not a minor gap; it invalidates the Bayes-optimality claim as it stands.\n\nThe relative 30% gain over OMP and 3D-OMP does not depend on that claim, so the engineering result may well survive a corrected theory. But the paper also omits code, error bars, and a discussion of how the prior and noise statistics are known. I would send it to review, but with the clear instruction that the optimality claim needs either a proof of the random-matrix condition and a correct complex NLE, or a softened statement such as 'near-optimal in the regime tested.' As written, the abstract overstates what is established.\n\nFor a reader working on ODDM message passing, the effective model is worth one look. I would not cite the optimality result in my own work until the theory is fixed.","headline":"A useful effective model and a plausible low-complexity estimator, but the Bayes-optimality claim rests on an unproven randomness premise and a mismatched real-valued NLE; the engineering gains over OMP likely survive.","tokens_in":22846,"tokens_out":3551,"would_cite":false,"duration_ms":41814,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that a two-stage MAMP-plus-DFT estimator can approach the Bayes-optimal channel estimation accuracy in massive MIMO-ODDM systems as the antenna count grows, with about 30% NMSE improvement over OMP and 3D-OMP baselines.","keywords":["massive MIMO","ODDM modulation","channel estimation","memory approximate message passing","DFT angle estimation","Bernoulli-Gaussian prior","normalized mean square error"],"falsifier":"Simulate the MAMP stage on the block-circulant matrices of Eq. (12) at $N_t = 64, 128, 256, 512$ and compare the steady-state NMSE against an exact MMSE reference at fixed SNR: if the gap does not shrink with $N_t$, or if a statistical-distance measure between the entries of $\\tilde{\\Phi}$ and a Gaussian random matrix does not decrease toward zero, the 'completely random' premise is falsified.","tokens_in":21737,"feed_emoji":"📡","tokens_out":7506,"duration_ms":79637,"temperature":0.7,"pith_summary":"The paper claims that channel estimation in massive MIMO-ODDM systems can be both accurate and low-complexity: a two-stage estimator first recovers sparse delay, Doppler, and gain information with memory approximate message passing (MAMP), then recovers angles with a discrete Fourier transform and a phase-rotation refinement. The argument rests on an effective model in which the equivalent channel vector has Bernoulli-Gaussian magnitudes and the equivalent coefficient matrix becomes effectively random as the number of antennas grows. On that basis the paper claims the MAMP stage approaches the Bayesian-optimal mean square error, and reports about 30% normalized-MSE improvement over orthogonal matching pursuit baselines. A sympathetic reader would care because high-mobility links change quickly, so an estimator that is linear-complexity and near-optimal at the same time would make ODDM practical for fast-moving terminals.","feed_headline":"Channel estimator nears Bayes-optimal limit in massive MIMO-ODDM","feed_subtitle":"Two-stage MAMP plus DFT recovers delays, Doppler, gains, and angles at linear cost with about 30% lower NMSE.","key_machinery":"The load-bearing object is the equivalent coefficient matrix $\\tilde{\\Phi}$ formed by concatenating antenna-specific circulant-block matrices $\\Phi_{n_t}$ in Eq. (12). The paper's premise is that, as the antenna count grows, the entries of $\\tilde{\\Phi}$ approach completely random, which is exactly the regime in which MAMP is known to be Bayes-optimal. The machinery then consists of MAMP's long-memory linear estimator with recursively chosen relaxation and damping parameters, a nonlinear estimator derived for the Bernoulli-Gaussian prior, and a DFT-based angle estimator with a rotation matrix $F_{N_t}^{\\Delta\\theta_p}$ that counters power leakage.","core_discovery":"The central claim is that the massive MIMO-ODDM channel estimation problem, written as $y = \\tilde{\\Phi}\\tilde{h} + n_c$, can be solved by a two-stage algorithm that separates sparse recovery from angular recovery. The first stage applies MAMP to the effective channel vector, whose nonzero entries' magnitudes follow a Bernoulli-Gaussian law, to obtain the gains, delays, and Doppler shifts; the second stage applies a normalized DFT with an optimized phase rotation to read off the angles from the angularly sparse received vector. The paper further claims that as $N_t \\to \\infty$, the symbols carried by independent antennas randomize the effective coefficient matrix enough for MAMP's long-memory orthogonalization to reach the Bayes-optimal MSE, and that numerical results show the estimator approaching that limit and improving NMSE by about 30% over OMP and 3D-OMP.","pith_inferences":["Editorial inference: the randomness premise is testable directly by measuring how fast the empirical entry distribution or spectral statistics of $\\tilde{\\Phi}$ converge to those of a random matrix as $N_t$ increases; the paper does not quantify this rate.","Editorial inference: because the pilot symbols are described as randomly generated within a fixed set, pilot design is a hidden control knob; if pilots are chosen adversarially or with structure, the Bernoulli-Gaussian and randomness assumptions could degrade.","Editorial inference: the DFT angle stage's validity is tied to the far-field ULA assumption and $d_{BS} \\le \\lambda_c/2$; applying the same split to near-field or spherical-wavefront massive MIMO would need a different angular basis.","Editorial inference: the single-user formulation omits multi-user interference, so an extension to multiple users would need to justify why the effective prior remains Bernoulli-Gaussian after interference is modeled."],"forward_implications":["If correct, massive MIMO-ODDM channel estimation can run at complexity linear in the problem dimension while meeting the MMSE limit, which is what fast CSI refresh at high mobility needs.","The paper's BER results indicate that with the estimated CSI, ODDM stays close to the perfect-CSI bound and beats OTFS, especially as speed and subcarrier count vary.","The NMSE gap between the proposed method and traditional MAMP with a fully random matrix closes as antennas grow, which the paper presents as empirical evidence for the randomness premise.","Across the tested antenna counts, path counts, speeds, and SNRs, the proposed estimator keeps an about 30% NMSE advantage over both OMP baselines."],"supporting_citations":[{"why":"Introduces ODDM modulation and the delay-Doppler plane orthogonality that the system model builds on.","marker":"[11]"},{"why":"Supplies the MAMP algorithm, whose long-memory orthogonalized linear estimator is the core of the first stage.","marker":"[37]"},{"why":"Provides the Bayes-optimality results for OAMP-type estimators that the paper invokes for the near-optimal claim.","marker":"[40]"},{"why":"Defines the 3D-OMP baseline that the proposed algorithm is compared against.","marker":"[30]"},{"why":"Defines the traditional OMP baseline used in the NMSE comparisons.","marker":"[44]"},{"why":"Supplies the asymptotic DFT power-concentration lemma that the angle estimation stage relies on.","marker":"[41]"},{"why":"Defines the EVA channel model used in the numerical validation.","marker":"[43]"},{"why":"Provides the OAMP detector used in the BER comparisons with estimated and perfect CSI.","marker":"[45]"}],"fun_headline_variants":["MAMP-DFT channel estimator nears Bayes-optimal in massive MIMO-ODDM","Low-complexity MAMP-DFT nears Bayes-optimal for massive MIMO-ODDM","MAMP-DFT channel estimation approaches Bayes-optimal in massive MIMO-ODDM","30% lower NMSE: MAMP-DFT channel estimator nears Bayes-optimal"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is Remark 1's claim that the structured coefficient matrix becomes completely random as antennas grow; if that does not happen at practical array sizes, the near-Bayes-optimality guarantee falls away, even if the gains over OMP persist.","fun_headline_variants_meta":{"raw":{"variants":["MAMP-DFT channel estimator nears Bayes-optimal in massive MIMO-ODDM","Low-complexity MAMP-DFT nears Bayes-optimal for massive MIMO-ODDM","MAMP-DFT channel estimation approaches Bayes-optimal in massive MIMO-ODDM","30% lower NMSE: MAMP-DFT channel estimator nears Bayes-optimal"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000873,"raw_usage":{"total_tokens":3795,"prompt_tokens":981,"completion_tokens":2814,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":597,"completion_tokens_details":{"reasoning_tokens":2715}},"tokens_in":597,"tokens_out":2814,"duration_ms":23954,"temperature":1.0,"reasoning_tokens":2715,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T14:00:07.038392+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the MAMP stage on the block-circulant matrices of Eq. (12) at $N_t = 64, 128, 256, 512$ and compare the steady-state NMSE against an exact MMSE reference at fixed SNR: if the gap does not shrink with $N_t$, or if a statistical-distance measure between the entries of $\\tilde{\\Phi}$ and a Gaussian random matrix does not decrease toward zero, the 'completely random' premise is falsified.","supporting_citations":[{"cited_title":"Orthogonal delay-Doppler division multiplexing modulation,","cited_arxiv_id":null,"evidence_quote":"Introduces ODDM modulation and the delay-Doppler plane orthogonality that the system model builds on."},{"cited_title":"Memory AMP,","cited_arxiv_id":null,"evidence_quote":"Supplies the MAMP algorithm, whose long-memory orthogonalized linear estimator is the core of the first stage."},{"cited_title":"On capacity optimality of OAMP: Beyond IID sensing matrices and Gaussian signaling,","cited_arxiv_id":null,"evidence_quote":"Provides the Bayes-optimality results for OAMP-type estimators that the paper invokes for the near-optimal claim."},{"cited_title":"Channel estimation for orthogonal time frequency space (OTFS) massive mimo,","cited_arxiv_id":null,"evidence_quote":"Defines the 3D-OMP baseline that the proposed algorithm is compared against."},{"cited_title":"Channel estimation for RIS-aided multiuser millimeter-wave systems,","cited_arxiv_id":null,"evidence_quote":"Supplies the asymptotic DFT power-concentration lemma that the angle estimation stage relies on."},{"cited_title":"Evolved universal terrestrial radio access (E-UTRA); user equip- ment (UE) radio transmission and reception,","cited_arxiv_id":null,"evidence_quote":"Defines the EVA channel model used in the numerical validation."},{"cited_title":"Orthogonal AMP,","cited_arxiv_id":null,"evidence_quote":"Provides the OAMP detector used in the BER comparisons with estimated and perfect CSI."}],"review_version":1}