{"id":"ed02b560-2273-40db-8e91-b97612d41e2c","arxiv_id":"2509.00478","paper_version":3,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A manifold-optimization pilot design and a Gaussian belief propagation receiver are proposed for CF-mMIMO ISAC, but the frequency-domain unimodularity constraint that drives the sensing benefit is not enforced by the algorithm as written.","lead":"This paper designs pilot signals for cell-free massive MIMO systems that are meant to work for both communication and radar-like sensing, optimizing them on a curved mathematical space called a manifold. It also proposes a low-complexity message-passing receiver; however, the algorithm as written enforces a different constraint from the one the sensing claim requires.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Time-domain unit-modulus manifold does not enforce the frequency-domain unimodularity required for the sensing claim; Eq. (15) vs Eq. (21) are inequivalent.","rationale":"The manuscript's principal novelty is the ISAC pilot-design contribution; the GaBP receiver is a plausible but unverified variant. For the pilot claim to hold, the optimized Fbar must have flat Fourier magnitude per column. The paper asserts this via Eq. (15) but immediately replaces it with Eq. (16) and the manifold C(τ,K) of time-domain unit-modulus matrices. The reader's weakest_assumption correctly identifies this inequivalence. I agree: the proof in Sec. II-C is valid only for a flat power spectrum, and that condition is not enforced by Algorithm 1. Since the sum-rate objective depends only on cross-correlations, there is no mechanism driving the iterates toward CAZAC-type sequences. Moreover, the evaluation metric is the aperiodic ACF, for which perfect zero sidelobes are impossible; this reinforces the inconsistency rather than rescuing it. The communication-rate results might survive independently, but the claimed ISAC sensing advantage is unsupported. A single computational check can settle this: run the described algorithm and inspect the DFT magnitude and ACF of its output. Therefore, the current REJECT verdict is appropriate, with revision possible by enforcing the correct frequency-domain constraint and providing reproducible code.","tokens_in":18119,"tokens_out":5736,"duration_ms":73474,"concrete_test":"Implement Algorithm 1 exactly as specified (time-domain complex-circle manifold C(τ,K), retraction Eq. (20), gradients Eqs. (24)-(35)) for τ=10, K=20. Compute per-column DFT magnitudes |FFT(f_k)| and both periodic and aperiodic autocorrelations of the output. If the DFT magnitudes are not constant (or if the aperiodic sidelobes are not exactly zero), the reported perfect sensing property does not follow. As a control, run the same objective on a manifold that enforces |FFT(F)| = J (or use Zadoff-Chu sequences) and check whether Fig. 5's 'ManoptPilots' curve is reproduced only in the frequency-constrained control.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim requires the optimized pilots to have flat Fourier magnitude per column, |F{f_k}| = 1, so that the power spectrum is flat and the autocorrelation is a delta. The optimization, however, is run on C(τ,K) = {X : |X| = J} (Eq. 21), and Algorithm 1 retracts onto this time-domain unit-modulus manifold. These constraints are not equivalent: a time-domain unit-modulus sequence does not generally have a flat DFT magnitude (e.g., [1,1] has magnitude |1+e^{-jω}|). Nothing in the objective or the gradients (Eqs. 24-35) penalizes spectral flatness; the gradient only involves cross-correlations f_k^H f_k' for the sum-rate objective. Hence the 'ManoptPilots' perfect autocorrelation in Fig. 5 is not explained by the algorithm as described. Additionally, the proof in Sec. II-C establishes perfect periodic autocorrelation from a flat power spectrum, while the evaluation uses aperiodic A-ACF (Eq. 39); exactly zero aperiodic sidelobes cannot be achieved by nonzero sequences, so the sensing claim is internally inconsistent as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a pilot-allocation scheme for cell-free massive MIMO ISAC systems in which pilot sequences are directly optimized on a complex-circle manifold to maximize the achievable uplink sum rate, together with a Gaussian belief propagation (GaBP) receiver. The authors claim that enforcing unit-modulus pilots in the frequency domain yields perfect autocorrelation properties for sensing, while the communication performance is close to tabu-search pilot assignment. Simulations compare the proposed pilots against random, greedy, and tabu-search allocation and evaluate the GaBP receiver against MRC, LMMSE, and EP receivers.","tokens_in":18382,"tokens_out":10694,"duration_ms":120543,"significance":"If the manifold algorithm actually produced pilots with flat frequency-domain magnitude, the joint communication-sensing pilot design would be an interesting contribution, and the GaBP receiver's O(LK) per-iteration complexity is practically appealing. However, the central sensing claim rests on a false equivalence between time-domain and frequency-domain unimodularity, and the aperiodic-autocorrelation claim is internally inconsistent. As presented, the paper's distinctive ISAC contribution is not established. The sum-rate optimization and the GaBP receiver may still be valuable, but they are secondary to the manuscript's stated main contribution.","major_comments":[{"comment":"The constraint in Eq. (15) is frequency-domain unimodularity, |F{\\bar F}|=1, while Eq. (16) and the manifold C(τ,K) in Eq. (21) enforce time-domain unit modulus, |\\bar F|=J. These constraints are not equivalent; for example, [1,1] is time-domain unimodular but has DFT magnitude |1+e^{-jω}|. Algorithm 1 retracts onto C(τ,K), and the gradients in Eqs. (24)-(35) depend only on cross-correlations f_k^H f_{k'} with no spectral-flatness term. Therefore the 'perfect autocorrelation' of ManoptPilots in Fig. 5 does not follow from the described optimization. This invalidates the sensing-superiority claim as stated.","section":"Sec. III-A, Eqs. (15)-(16), Eq. (21), Algorithm 1"},{"comment":"The proof in Sec. II-C (Eqs. 11-14) shows that a flat frequency-domain magnitude gives zero periodic autocorrelation at nonzero lags. The evaluation, however, uses the aperiodic A-ACF in Eq. (39) and calls this 'without loss of generality.' For a nonzero length-τ sequence with |x[n]|=1 for all n, the aperiodic lag-1 term r_1=Σ_n x[n+1]x^*[n] has magnitude τ−1 and cannot vanish. Hence the claim in Sec. III-D2 that the proposed pilots attain 'a single peak at the origin and zero elsewhere' is internally inconsistent with the stated metric. Figures 5 and 6 need to be re-examined under a correctly defined autocorrelation metric.","section":"Sec. II-C vs Sec. III-D2, Eq. (39)"},{"comment":"The closed-form gradients are load-bearing for Algorithm 1. Differentiating γℓk in Eq. (6) with respect to f_k appears to produce a factor involving 1/τ² that is not present in Eq. (28); as written, Eq. (28) seems off by a factor of τ² or its inverse depending on the gradient convention. Additionally, Eq. (33) uses k' both as the outer summation index and as the inner summation index, making the formula ill-defined. Since the algorithm's convergence and the reported sum-rate results rest on these gradients, they must be corrected and the simulations re-run.","section":"Sec. III-C, Eqs. (28) and (33)"}],"minor_comments":[{"comment":"The notation F{\\bar F_{i,k}} is unclear: the Fourier transform is presumably applied column-wise to each pilot sequence, but this is not stated. Please define the DFT normalization and the dimension along which F acts.","section":"Sec. III-A, Eq. (15)"},{"comment":"The simulation description says 'A total of M APs' but the system model uses L throughout; please unify the notation.","section":"Sec. III-D"},{"comment":"Equation (10) uses ρ_p in the SINR expression while Eq. (8) contains √ρ_u. Please clarify the relation between ρ_u, ρ_p, and the power-control coefficients η_k, and state any normalization assumptions.","section":"Sec. II-B, Eq. (10)"},{"comment":"The caption of Fig. 5 states that the sidelobe level is the average of 200 autocorrelation functions; please specify the number of Monte Carlo drops and whether the displayed curves correspond to periodic or aperiodic autocorrelation.","section":"Sec. III-D2, Fig. 5"},{"comment":"There are several typos ('primarly', 'cyrcularly', 'choosen', 'succesful') and inconsistent uses of M vs L. A careful proofread is needed.","section":"Throughout"}],"recommendation":"reject","confidential_remarks":"The central ISAC claim is not supported by the algorithm as described, and the aperiodic-autocorrelation claim is internally inconsistent. The communication-only pilot optimization and the GaBP receiver may be salvageable, but the manuscript's main contribution requires a substantially reworked constraint formulation, corrected gradients, and rerun simulations. This is beyond a minor revision; I recommend rejection, though a resubmission focused on the communication-only formulation or with a properly implemented frequency-domain unimodularity constraint could be reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Hi,\n\nQuick take: the sum-rate pilot optimization is a legitimate extension, but the ISAC sensing claim doesn't hold up. The paper formulates the problem with a frequency-domain unimodularity constraint (Eq. 15) to get perfect autocorrelation, then 'alternatively' drops the Fourier transform and solves a time-domain unit-modulus problem (Eqs. 16, 21, Algorithm 1). Those constraints are not equivalent. A time-domain constant-modulus sequence does not generally have a flat spectrum, and nothing in the gradients (Eqs. 24-35) penalizes spectral flatness. So the claimed perfect autocorrelation in Fig. 5 isn't explained by the algorithm as described.\n\nThere's a second, independent issue: the proof in Sec. II-C shows flat power spectrum gives perfect periodic autocorrelation, but the evaluation (Eq. 39, Fig. 5) uses aperiodic autocorrelation. For nonzero sequences of length > 1, aperiodic sidelobes cannot be identically zero. So even if the frequency-domain constraint were enforced, the 'zero elsewhere' claim would be impossible for the metric used.\n\nWhat's good: directly designing the pilot matrix rather than assigning predefined orthogonal pilots is a real departure from assignment-based prior work, and the manifold machinery is standard but competently applied. The communication results are believable—near tabu search, better than greedy/random. The GaBP receiver is a plausible low-complexity detection scheme, though damping and other hyperparameters aren't specified and no code is provided. The citation pattern looks fine.\n\nThe fix isn't hard in principle: enforce the frequency-domain unimodularity on the appropriate manifold or add a spectral-flatness penalty, and measure sidelobes honestly. But as it stands, the central ISAC contribution is not supported.\n\nI'd send this out for review—there's enough substance to warrant careful refereeing—but it needs major revision, and a reviewer who will check the constraint equivalence.\n\nBest,","headline":"The communication pilot design is a reasonable extension, but the ISAC sensing claim rests on a false equivalence between time-domain and frequency-domain unit modulus; the paper needs major revision.","tokens_in":18880,"tokens_out":4608,"would_cite":false,"duration_ms":52645,"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":"Pilot design on a manifold of unit-modulus matrices is claimed to give near-tabu communication rates and ideal radar autocorrelation in one shot.","keywords":["cell-free massive MIMO","pilot allocation","manifold optimization","integrated sensing and communications","unimodular sequences","Gaussian belief propagation","pilot contamination","sum-rate maximization"],"falsifier":"Run Algorithm 1 for τ=10, take the discrete Fourier transform of each designed pilot column, and check whether every frequency-domain magnitude equals 1; a single deviation falsifies the perfect-autocorrelation claim. Equivalently, compute the aperiodic autocorrelation of the designed pilots and look for any nonzero sidelobe at a nonzero lag.","tokens_in":17980,"feed_emoji":"📡","tokens_out":7741,"duration_ms":83334,"temperature":0.7,"pith_summary":"This paper tries to show that pilot sequences in a cell-free massive MIMO system can be designed directly, rather than assigned from a fixed codebook, by optimizing on a smooth search space where every pilot entry lies on the complex unit circle. The optimization maximizes the achievable uplink sum rate while keeping the pilot entries unimodular, which the authors argue makes the same pilots suitable for radar sensing because it yields perfect autocorrelation. Simulation results are presented to support that the designed pilots reach communication rates close to the best combinatorial benchmark, tabu search, while producing autocorrelation sidelobes near zero and resolving two targets at 8 and 19 meters. A Gaussian belief propagation receiver is then proposed to decode the uplink with near-optimal detection performance at substantially lower complexity. If correct, the contribution is a single pilot-design procedure that serves both communication throughput and sensing accuracy in dense distributed antenna systems.","feed_headline":"Manifold-optimized pilots hit near-tabu rates with zero sidelobes","feed_subtitle":"The same unimodular pilot sequences maximize sum rate in cell-free massive MIMO and keep sensing autocorrelation sidelobes at zero.","key_machinery":"The central object is the complex circle manifold C(τ,K), the set of τ×K matrices whose entries all have unit modulus. The paper treats this set as the search space for the pilot matrix and uses Riemannian conjugate-gradient ascent: project the Euclidean gradient of the sum-rate objective onto the tangent space, move along a conjugate direction, and retract back to the manifold with x+z/|x+z|. The other load-bearing identity is the autocorrelation theorem used for sensing: if a frequency-domain sequence has |X[k]|=1 for all k, its power spectrum is flat and its inverse-DFT autocorrelation is a single delta at zero lag, which is what makes the pilots useful for radar range estimation.","core_discovery":"The central claim is that pilot allocation for cell-free massive MIMO ISAC can be reformulated as an unconstrained optimization on the complex circle manifold C(τ,K) = {X ∈ C^{τ×K} : |X| = J}, where the objective is the sum of per-user log2(1+SINR) rates. The paper derives a closed-form Riemannian gradient of that objective and runs conjugate-gradient ascent with retraction, so every iterate remains on the manifold. It then asserts that the resulting pilots are unimodular in the frequency domain, which by the paper's proof (flat power spectrum → delta autocorrelation) gives ideal sensing autocorrelation with a single peak at zero lag. The contribution is thus a dual-purpose pilot design: nea","pith_inferences":["The paper's proof of perfect autocorrelation applies to a frequency-domain unimodularity constraint, while Algorithm 1 enforces time-domain unit modulus; a direct check of the DFT magnitude of the produced pilots would settle whether the sensing claim actually holds for the implemented design.","If the time-domain search does not yield flat spectra, the same manifold machinery could be run on the DFT of the pilot matrix, or seeded with CAZAC sequences, to obtain the claimed sensing guarantee.","The closed-form gradient framework likely extends to other ISAC waveform-shaping objectives, such as minimizing OFDM ranging sidelobes or shaping the local ambiguity function.","The receiver and pilot contributions are independent: the GaBP receiver does not rely on the manifold-designed pilots, so either could be deployed separately."],"forward_implications":["The same optimized pilot waveforms can be reused for channel estimation and radar ranging, removing the need for separate sensing waveforms in cell-free massive MIMO ISAC.","Pilot contamination can be reduced without combinatorial search, giving a gradient-based alternative to tabu search that tracks its throughput.","Users with the worst channels gain the most from the optimized assignment, improving fairness in dense deployments.","The GaBP receiver achieves near-EP bit error rates at O(LK) per iteration, making near-optimal detection feasible when the number of APs is large.","Because the pilots are unimodular, matched-filter range profiles have sidelobes near zero, allowing two targets separated by 11 meters to be resolved at 20 MHz bandwidth."],"supporting_citations":[{"why":"Supplies the tabu-search pilot assignment that the proposed design must match or beat in communication throughput.","marker":"[15]"},{"why":"Gives the result that frequency-domain unimodularity yields perfect detection for radar parameter estimation, the sensing rationale of the pilot constraint.","marker":"[37]"},{"why":"Provides the manifold-optimization framework used to turn the constrained pilot-design problem into an unconstrained search.","marker":"[23]"},{"why":"Defines the cell-free massive MIMO pilot-training and data-transmission model with MMSE channel estimation that the SINR expressions are built on.","marker":"[5]"},{"why":"Motivates designing unimodular sequence sets with good correlation properties for sensing applications.","marker":"[21]"},{"why":"Provides the expectation-propagation detector whose near-optimal performance and complexity the proposed GaBP receiver is benchmarked against.","marker":"[30]"}],"fun_headline_variants":["Manifold pilots: near-optimal rates, zero sensing sidelobes","Unimodular pilot sequences cut sensing sidelobes to zero","Pilot allocation on a complex circle for dual-purpose ISAC","Riemannian gradient ascent designs pilots for CF-mMIMO ISAC","Near-tabu rates and ideal autocorrelation via manifold pilot design"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The load-bearing premise is that the time-domain unit-modulus search space used in the algorithm is equivalent to the frequency-domain unimodularity constraint that the autocorrelation proof requires; if that equivalence fails, the claimed perfect autocorrelation and sensing advantage do not follow.","fun_headline_variants_meta":{"raw":{"variants":["Manifold pilots: near-optimal rates, zero sensing sidelobes","Unimodular pilot sequences cut sensing sidelobes to zero","Pilot allocation on a complex circle for dual-purpose ISAC","Riemannian gradient ascent designs pilots for CF-mMIMO ISAC","Near-tabu rates and ideal autocorrelation via manifold pilot design"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000255,"raw_usage":{"total_tokens":1367,"prompt_tokens":661,"completion_tokens":706,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":405,"completion_tokens_details":{"reasoning_tokens":614}},"tokens_in":405,"tokens_out":706,"duration_ms":8715,"temperature":1.0,"reasoning_tokens":614,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T13:33:11.287930+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run Algorithm 1 for τ=10, take the discrete Fourier transform of each designed pilot column, and check whether every frequency-domain magnitude equals 1; a single deviation falsifies the perfect-autocorrelation claim. Equivalently, compute the aperiodic autocorrelation of the designed pilots and look for any nonzero sidelobe at a nonzero lag.","supporting_citations":[{"cited_title":"Tabu- Search-Based Pilot Assignment for Cell-Free Massive MIMO Systems,","cited_arxiv_id":null,"evidence_quote":"Supplies the tabu-search pilot assignment that the proposed design must match or beat in communication throughput."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the result that frequency-domain unimodularity yields perfect detection for radar parameter estimation, the sensing rationale of the pilot constraint."},{"cited_title":"Cell-Free massive MIMO Versus Small Cells,","cited_arxiv_id":null,"evidence_quote":"Defines the cell-free massive MIMO pilot-training and data-transmission model with MMSE channel estimation that the SINR expressions are built on."},{"cited_title":"Designing unimodular sequence sets with good correlations—including an application to mimo radar,","cited_arxiv_id":null,"evidence_quote":"Motivates designing unimodular sequence sets with good correlation properties for sensing applications."},{"cited_title":"Improving Cell-Free Massive MIMO Detection Perfor- mance via Expectation Propagation,","cited_arxiv_id":null,"evidence_quote":"Provides the expectation-propagation detector whose near-optimal performance and complexity the proposed GaBP receiver is benchmarked against."}],"review_version":1}