{"id":"86a06bc4-4aa7-4808-8e53-00a573b5a13a","arxiv_id":"2509.07482","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A BiGaBP-based receiver jointly tracks channel, detects data, and computes an over-the-air sum in time-varying mmWave channels, with simulations showing small gaps to genie-aided bounds.","lead":"The paper combines a joint channel-and-data estimation algorithm with over-the-air computing, letting a base station compute a sum of device signals in fast-changing millimeter-wave channels without perfect channel knowledge. This targets 6G and vehicle-to-everything scenarios where channel tracking and computation must happen simultaneously.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (34a) appears to use the true channel h_m[k] inside the channel-estimation update; if literal, the JCCCT receiver is genie-aided and the no-perfect-CSI claim is unsupported.","rationale":"The paper's central claim is that the proposed JCCCT framework performs communication and AirComp in time-varying mmWave channels without perfect CSI, relying on BiGaBP-based joint channel/data estimation aided by channel prediction. For this claim to hold, the channel-estimation recursion must be implementable from received signals and previous estimates only. Equation (34a) as printed feeds the true channel h_m[k] into the update, which would make the algorithm genie-aided; this is a correctness risk that directly undercuts the central claim. The reader's identified weakest assumption—that the correlation coefficient r is known and the promised estimation procedure is absent—is real and should be fixed, but it is secondary: r can in principle be supplied or estimated, whereas a non-causal channel update cannot be repaired without changing the algorithm. I am not alleging intentional concealment; a simple typo is plausible, and the paper cites a prior BiGaBP design that may contain the correct form. However, without code or an explicit correction, the manuscript as written is not verifiable. The simulation results compared against genie bounds are suggestive, but they cannot resolve this issue. Therefore the appropriate verdict is UNVERDICTED pending clarification and reproducibility; if the typo is confirmed and the r estimator is supplied, the verdict could move back to CONDITIONAL or ACCEPT depending on the corrected results.","tokens_in":11210,"tokens_out":10601,"duration_ms":129040,"concrete_test":"Re-derive Eq. (34a) from the Gaussian posterior of h_m[k] given the extrinsic messages and the AR(1) prior; then trace the data dependencies in Algorithm 1. If the RHS h_m[k] is the true channel at time k, replace it with the latest causal estimate \\hat{h}_m[k] (or with \\hat{h}_m[k-1] if that is the intended conditioning channel) and rerun the Section IV simulation. A material change in BER, channel NMSE, or AirComp NMSE would confirm that the published curves depend on genie knowledge. The authors should also state explicitly whether the conditioning channel in the prior term is a past estimate or the true channel, and provide the promised procedure for estimating r.","verdict_should_be":"UNVERDICTED","load_bearing_attack":"In Section III-C, the channel soft-replica update is written as \\hat{h}'_{m,k} = \\Omega_{m,k}\\Lambda^{-1}_{m,k}\\bar{h}_{m,k} + r^k \\bar{\\Psi}^h_{k,m}\\Lambda^{-1}_{m,k} h_m[k] (Eq. 34a). The notation fixed at the start of Section III makes h_m[k] the true channel, distinct from the soft replica \\hat{h}_m[k], and Algorithm 1 lists only y[k], H[0], r, \\tilde{N}_0, and design parameters as inputs. If Eq. (34a) is taken literally, the channel estimator needs the true channel at the same time index it is estimating; the algorithm is then not a decision-directed tracker, and the Figure 2 JCCCT curves are obtained with hidden genie information. This is more fundamental than the acknowledged missing r-estimation procedure: even with r and H[0] perfectly known, the recursive update (34a) is non-causal. A typo (e.g., h_m[k] intended as \\hat{h}_m[k] or a past estimate) would rescue the scheme, but the text as written does not say so, and no code or reproducibility material is provided to disambiguate. The AirComp combiner also ignores channel estimation error (Eq. 38), but the (34a) issue affects whether the reported tracking is achievable at all.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes an integrated communication and computing (ICC) receiver for a time-varying millimeter-wave SIMO uplink. The receiver combines a bilinear Gaussian belief propagation (BiGaBP) algorithm for joint channel estimation/tracking and data detection with a channel prediction (CP) step, and then computes an over-the-air arithmetic-sum function from the residual signal via an MMSE combiner. The channel is modeled as a clustered mmWave channel with an AR(1) time dependence controlled by a correlation coefficient r; the BS is assumed to know the initial channel H[0] and r. Simulations at 60 GHz for 2 users over 128 time slots report BER, channel NMSE, and AirComp NMSE for velocities 10–40 km/h, claiming near-genie performance.","tokens_in":11604,"tokens_out":7501,"duration_ms":93310,"significance":"If the receiver is implementable as described, the paper would be a useful demonstration that over-the-air computing can coexist with channel tracking in time-varying mmWave channels without perfect CSI at every time instant. The main strength is the end-to-end simulation of a nontrivial setup: clustered mmWave channels, channel prediction, joint data/channel inference, and residual-based AirComp. However, the algorithmic core is largely carried over from the authors' prior work ([19], [20], [21]); the present contribution is primarily an integration and a simulation study. No code or reproducibility material is provided, and the text contains a load-bearing ambiguity in the channel update that must be resolved before the simulation claims can be accepted.","major_comments":[{"comment":"As written, the channel soft-replica update uses the true channel h_m[k] at the same time index being estimated: h'_m,k = Omega_m,k Lambda^{-1}_m,k hbar_m,k + r^k Psi^h_k,m Lambda^{-1}_m,k h_m[k]. Throughout Section III, h_m[k] denotes the true channel, whereas the soft replica is hhat_m,k, and Algorithm 1 does not list h_m[k] as an input. Taken literally, this makes the channel estimator non-causal and genie-aided, which would invalidate the central 'no perfect CSI' claim and the Figure 2 JCCCT curves. If this is a typo (e.g., h_m[0] or a past estimate was intended), it must be corrected and the notation reconciled with Algorithm 1; otherwise, the feasibility of the tracking loop is not established.","section":"Section III-C, Eq. (34a)"},{"comment":"The text states 'The procedure for the estimation of r follows consecutively,' but no such procedure appears anywhere in the manuscript. The correlation r is an input to Algorithm 1 and enters the second-order statistics (15), the channel prediction (17)–(19), the message variances (30), and the channel denoiser (34). Since all tracking and detection performance depends on r, the absence of an estimator is a significant gap. The authors should either provide a concrete estimation procedure or clearly state that r is assumed known and discuss the sensitivity of the results to r mismatch.","section":"Section II-A, after Eq. (4)"},{"comment":"The combiner is called 'MMSE' and 'optimal' in the abstract and in Eq. (37), but the closed form in Eq. (38) is derived under the assumption that the estimated channel Hhat[k] is exact, as the preceding sentence acknowledges ('computed without considering channel estimation error'). In a no-perfect-CSI setting, the true MMSE combiner should account for the channel estimation error covariance. The authors should either soften the optimality claim or quantify the impact of channel estimation error on the AirComp NMSE, especially because Figure 2(c) compares against genie-aided bounds.","section":"Section III-D, Eq. (38)"},{"comment":"The computing signal term H[k]s[k] is folded into an effective white noise term with variance N0 + E_c. Since s[k] has covariance E_c I_M, the actual covariance of H[k]s[k] is E_c H[k]H[k]^H, which is not generally proportional to the identity after the quasi-SVD beamformer. The scalar approximation may be acceptable, but it should be justified, and its effect on the reported BER/NMSE should be discussed.","section":"Section III-B, Eqs. (20)–(22)"}],"minor_comments":[{"comment":"The simulation paragraph states 'N_RX = 16 receive antennas, P = 2 receive antennas.' This is confusing: P is presumably the number of UPA elements in one dimension, not a second count of receive antennas. Please clarify the relationship between N_RX, P, and N in Eq. (2) and the simulation setup.","section":"Section IV"},{"comment":"The sentence 'The transmit power was set to E_d = 0.99 for communications and E_c = 0.01 for communications' contains a typo: E_c should be 'for computing.'","section":"Section IV"},{"comment":"The data-symbol term is written as dhat*_{nm,s}; the symbol estimate should not depend on the receive-antenna index n. This is likely a typesetting issue, but it should be fixed to dhat*_{m,s} or similar.","section":"Algorithm 1, line 26"},{"comment":"The AR model parameter r is defined as the correlation between adjacent OFDM symbols, but Eq. (7) derives it from coherence time via exp(ln(0.5)/K_max). The connection between the two definitions and the specific OFDM parameters should be made explicit, since K_max depends on Ts and fc.","section":"Section II-A, Eq. (4)"},{"comment":"The simulation results have no error bars, number of Monte Carlo runs, or complexity measurements. Adding these would strengthen the reproducibility of the claims.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is incremental over the authors' own prior work, and the reference list is heavily self-referential ([10], [19], [20], [21]). This is not by itself disqualifying, but the editor may wish to weigh whether the integration alone provides sufficient novelty for the target venue. The Eq. (34a) issue and the missing r-estimation procedure are the key technical blockers; if the authors can clarify or fix them, the paper could become acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is an honest integration of known pieces—BiGaBP-based JCDE from [20] and the AirComp combiner from [10]/[21]—into a time-varying mmWave setting. The authors clearly state what they borrow, which I appreciate. The system model and algorithm presentation are clean, and the simulation study compares against genie-aided bounds, which is the right baseline. For a subfield that often hand-waves perfect CSI, the goal is worthwhile.\n\nThe load-bearing soft spot is Eq. (34a). As written, the channel soft-replica update depends on h_m[k]—the true channel at the same time index being estimated. The notation at the start of Section III explicitly distinguishes the true channel from the soft replica \\hat{h}_m[k], and Algorithm 1 lists only y[k], H[0], r, \\tilde{N}_0, and design parameters as inputs. If that equation is literal, the estimator is non-causal and the central claim of operating without perfect CSI is unsupported. It could be a typo—perhaps h_m[k] should be the predicted channel from the CP step, which in the first window is r^k H[0]—but the text does not say that, and there is no code or reproducibility material to disambiguate. This is more fundamental than the acknowledged missing r-estimation procedure, and it should be fixed and clarified before the paper can be trusted.\n\nOther issues are secondary but real. The paper promises an estimator for the correlation coefficient r (“the procedure follows consecutively”) and never delivers it. The MMSE AirComp combiner in (38) is derived without modeling channel estimation error, so calling it optimal is an overstatement. There is also a small typo in the simulation section where E_c is twice described as the power for “communications.” These are fixable.\n\nIf (34a) is a typo, this is a competent engineering extension. If it is not, the simulation results in Figure 2 carry no weight. Either way, the paper deserves a serious referee: the issue is exactly what peer review is for, and the integration of AirComp into a high-mobility mmWave JCDE receiver is relevant to the ICC and V2X communities. I would not cite it in its current form, but I would engage with a revised version.","headline":"The integration of known JCDE and AirComp components is legitimate, but Eq. (34a) appears to use the true channel inside the channel estimator, which if literal makes the whole no-perfect-CSI claim genie-aided.","tokens_in":12036,"tokens_out":3435,"would_cite":false,"duration_ms":38773,"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":"A single receiver can track time-varying mmWave channels while simultaneously decoding data and performing over-the-air computing, approaching perfect-CSI bounds without perfect CSI.","keywords":["integrated communication and computing","over-the-air computing","bilinear Gaussian belief propagation","channel tracking","channel prediction","mmWave channels","joint channel and data detection","time-varying channels"],"falsifier":"Run the receiver with a deliberately mismatched correlation coefficient—say, the r corresponding to 40 km/h while the true channel evolves at 10 km/h—and record BER, channel NMSE, and computing NMSE. If the gap to the genie-aided bounds becomes large, the near-genie results depend on privileged knowledge of mobility rather than on the tracking itself.","tokens_in":11182,"feed_emoji":"📡","tokens_out":6774,"duration_ms":69491,"temperature":0.7,"pith_summary":"Integrated communication and computing usually assumes the base station knows the channel perfectly at every instant. This paper tries to remove that assumption for millimeter-wave links by tracking the time-varying channel and decoding data in parallel while computing a target function over the air. The proposed receiver builds on bilinear Gaussian belief propagation for joint channel and data estimation, adds a channel-prediction step before each estimation window, and then applies an MMSE combiner to the residual signal to recover the desired over-the-air computation. Simulation results at 60 GHz with relative velocities of 10–40 km/h show bit error rate, channel-estimation NMSE, and computing NMSE close to genie-aided perfect-CSI bounds, which would make AirComp feasible in high-mobility mmWave scenarios such as vehicle-to-everything links.","feed_headline":"One receiver tracks mmWave channels, decodes data, and computes","feed_subtitle":"Time-varying channels are tracked alongside communication and over-the-air computing, approaching perfect-CSI bounds.","key_machinery":"The load-bearing mechanism is bilinear Gaussian belief propagation (BiGaBP): message passing on a tripartite graph in which channel coefficients and data symbols are treated as Gaussian unknowns, enabling joint channel and data detection (JCDE). A channel-prediction (CP) step computes the conditional expectation of the channel given the lowest-MSE prior estimate in the current window, seeding the message passing with better starting points. The AirComp operation is carried by an MMSE combiner applied to the residual signal after the detected communication symbols are subtracted, with the combiner built from the estimated channel, the data-estimation error covariance, and the noise power.","core_discovery":"The paper claims that a BiGaBP-based joint channel and data estimation algorithm, seeded by a Kalman-like channel predictor, can keep up with a time-varying mmWave channel while simultaneously detecting QPSK communication symbols and supporting an over-the-air computation. The detection treats the superimposed computing signal as effective noise; the channel estimator propagates beliefs over time windows and combines them across antennas; the AirComp stage then applies an MMSE combiner to the residual after subtracting the detected communication contribution. With only the initial channel and the channel correlation coefficient r given, the scheme is shown to reach BER, channel NMSE, and com","pith_inferences":["A natural test is to replace the assumed correlation coefficient r with an online estimate; the paper promises such a procedure but never gives it, so the sensitivity of the near-genie results to r is the main open question.","Because r is a hyperparameter of the AR(1) channel model, the same belief-propagation machinery could be extended to infer r jointly with the channel, which would remove the strongest remaining assumption.","The AirComp stage currently runs after the JCDE loop; feeding the computing estimate back into detection could improve both tasks, since the detection already treats computing signals as noise.","The beamformer is fixed from the initial SVD; updating it from tracked channel estimates would likely push the operating range beyond 40 km/h."],"forward_implications":["A 60 GHz uplink with two single-antenna users moving at up to 40 km/h can sustain BER within a small margin of the perfect-CSI bound while devoting only 1% of transmit power to computing symbols.","The computing NMSE of the estimated sum function also tracks the genie-aided bound, meaning AirComp does not require known data symbols or known channel at run time.","Channel tracking and pilot-free operation become possible after an initial channel estimate, because each window is seeded by prediction rather than new pilots.","The same framework supports integrated communication and computing in high-mobility settings such as vehicle-to-everything links, and can be extended to multi-stream or general nomographic computations."],"supporting_citations":[{"why":"Supplies the BiGaBP joint channel tracking and data detection algorithm and the channel-prediction procedure that the proposed framework reuses.","marker":"[20]"},{"why":"Provides the adaptively scaled belief BiGaBP design that underlies the JCDE message passing.","marker":"[19]"},{"why":"Introduces the ICC receiver design that combines a Gaussian BP detector with an MMSE residual combiner for AirComp.","marker":"[10]"},{"why":"Extends the ICC receiver design framework and details the residual MMSE combiner adopted for the computing stage.","marker":"[21]"},{"why":"Establishes the theory of computation over multiple-access channels that motivates AirComp.","marker":"[5]"},{"why":"Supplies the 60 GHz OFDM numerology and guard-interval settings used in the performance evaluation.","marker":"[26]"}],"fun_headline_variants":["Track mmWave channel while decoding and computing, all at once","Joint channel-data estimation keeps ICC alive in dynamic mmWave","Parallel channel tracking and AirComp for time-varying mmWave","BiGaBP handles CSI and symbols together without perfect knowledge","No perfect CSI? This receiver still tracks, decodes, and computes"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The tracking loop assumes the receiver knows the channel correlation coefficient r between adjacent OFDM symbols (and the exact channel at time zero), and the promised estimation procedure for r is never provided.","fun_headline_variants_meta":{"raw":{"variants":["Track mmWave channel while decoding and computing, all at once","Joint channel-data estimation keeps ICC alive in dynamic mmWave","Parallel channel tracking and AirComp for time-varying mmWave","BiGaBP handles CSI and symbols together without perfect knowledge","No perfect CSI? This receiver still tracks, decodes, and computes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00069,"raw_usage":{"total_tokens":2972,"prompt_tokens":766,"completion_tokens":2206,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":510,"completion_tokens_details":{"reasoning_tokens":2121}},"tokens_in":510,"tokens_out":2206,"duration_ms":17131,"temperature":1.0,"reasoning_tokens":2121,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T22:06:58.111353+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the receiver with a deliberately mismatched correlation coefficient—say, the r corresponding to 40 km/h while the true channel evolves at 10 km/h—and record BER, channel NMSE, and computing NMSE. If the gap to the genie-aided bounds becomes large, the near-genie results depend on privileged knowledge of mobility rather than on the tracking itself.","supporting_citations":[{"cited_title":"Bayesian bilinear inference for joint channel tracking and data detection in millimeter-wave mimo systems,","cited_arxiv_id":null,"evidence_quote":"Supplies the BiGaBP joint channel tracking and data detection algorithm and the channel-prediction procedure that the proposed framework reuses."},{"cited_title":"Design of adaptively scaled belief in multi-dimensional signal detection for higher-order modulation,","cited_arxiv_id":null,"evidence_quote":"Provides the adaptively scaled belief BiGaBP design that underlies the JCDE message passing."},{"cited_title":"From theory to reality: A design framework for integrated communication and computing receivers,","cited_arxiv_id":null,"evidence_quote":"Introduces the ICC receiver design that combines a Gaussian BP detector with an MMSE residual combiner for AirComp."},{"cited_title":"A Flexible Design Framework for Integrated Communication and Computing Receivers","cited_arxiv_id":"2506.05944","evidence_quote":"Extends the ICC receiver design framework and details the residual MMSE combiner adopted for the computing stage."},{"cited_title":"Computation over multiple-access channels,","cited_arxiv_id":null,"evidence_quote":"Establishes the theory of computation over multiple-access channels that motivates AirComp."},{"cited_title":"Ieee 802.11ad: introduction and performance evaluation of the first multi-gbps wifi technology,","cited_arxiv_id":null,"evidence_quote":"Supplies the 60 GHz OFDM numerology and guard-interval settings used in the performance evaluation."}],"review_version":1}