{"id":"6af8cacb-14b6-4569-8205-36a87ba6f6cb","arxiv_id":"2501.10136","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A two-stage split of beamforming in cell-free ISAC reduces fronthaul exchange to 6NiterMK scalars, independent of antenna count, with simulated performance close to a centralized solution.","lead":"This paper describes a beamforming method for cell-free wireless networks that carry both communication and radar sensing, splitting the computation between access points and a central unit. If the simulations hold, the method keeps performance close to centralized designs while cutting the amount of data sent over the fronthaul, which grows with the antenna count.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim of comparable performance rests on an unreported centralized baseline; the load-bearing gap is not the algorithm but the absent specification of the baseline (footnote 1, Section IV-F), so Fig. 6 cannot be independently verified.","rationale":"The reader's weakest_assumption is sensing-constraint feasibility after null-space projection. That is a real omission, but it is not the most load-bearing issue for the abstract's central claim. For K=2 and generic channels, the projection P_{m,k} preserves at least one sensing direction for any target angle, so the feasibility risk is limited to special geometries; the paper should still analyze it, but it does not immediately invalidate Fig. 6. The more decisive issue is that the centralized baseline itself is not described. The paper's strongest quantitative evidence is the small gap in Fig. 6, and that gap is only meaningful if the centralized solution is a fair, well-converged solution of the same nonconvex problem. Without the baseline algorithm, initialization, and convergence criteria, the comparison is not reproducible and the central claim cannot be verified. An independent full-variable MM implementation of (18) would settle whether the reported gap is genuine. Since the reader already issued a CONDITIONAL verdict and flagged the underspecified baseline in the rationale, my stress-test does not move the verdict; it sharpens the condition: the revision must specify and preferably share the centralized baseline before the comparable-performance claim is accepted. The fronthaul-reduction claim, by contrast, is supported by a direct counting argument that is independent of the simulation and is not in question.","tokens_in":16376,"tokens_out":12760,"duration_ms":141004,"concrete_test":"Independently reimplement the centralized baseline of (18): solve it with a full-dimensional MM over all F_m (no null-space projection), using the same channel realizations as Fig. 6, 50 random initializations, and a tight convergence tolerance; report the mean sum SINR at each Delta in 30 to 44 dB together with the communication noise variance sigma_k^2. If the centralized curve exceeds the TsDBA curve by more than about 10 SINR units at any Delta, the claimed 'comparable performance' is not established and the comparison must be rerun with a fully specified baseline.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline result—'comparable to centralized methods' (Abstract, Fig. 6)—is asserted against a centralized solution of (18) that is never specified. Footnote 1 in Section IV-F states that the nonconvex centralized problem is handled with the MM technique, but 'detailed insights into the centralized optimization problem's solution are not provided.' Because (18) is nonconvex, the quality of this baseline depends heavily on initialization, surrogate choice, and convergence criteria. If the baseline stops at a poor local minimum or uses fewer iterations than the TsDBA, the small gap in Fig. 6 could be an artifact of a weak comparator rather than evidence of near-optimality. The reader's sensing-feasibility concern is secondary here: with generic channels and K=2, the null-space projections retain at least some sensing gain for typical target angles, but the paper does not report whether the angles used in the mean curves avoid adversarial alignments. The absent baseline is the direct load-bearing support for the strongest claim; the fronthaul-reduction advantage is structurally valid, but the 'comparable performance' component needs a specified comparator to be meaningful.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a two-stage distributed beamforming design for cell-free massive MIMO integrated sensing and communication (ISAC) systems. The precoder at each access point is decomposed into a local precoder computed at the AP and a complex weight computed at the central unit, enabling a division of processing that reduces fronthaul exchange. Inter-user interference is explicitly zero-forced through null-space projection at each AP, and the resulting nonconvex optimization problems are solved via majorization-minimization, with convex surrogates solved by standard tools. Numerical results show convergence within a few iterations, a sensing-communication trade-off, and a fronthaul load independent of the number of transmit antennas, while claiming communication performance close to a centralized MM-based solution.","tokens_in":16658,"tokens_out":7241,"duration_ms":67836,"significance":"If the claims are correct, the paper offers a sensible scalability-oriented design for cell-free ISAC, with two concrete structurally valid advantages: the per-iteration fronthaul exchange scales as O(M K) rather than O(N_tx M K), and the CU complexity scales independently of N_tx. The MM surrogates are theoretically grounded by a proved subset relaxation (Proposition 1), and the algorithmic description is sufficiently detailed to be implemented. The main open questions concern the reproducibility and fairness of the performance comparison against an unspecified centralized baseline, and the feasibility of the sensing constraint after null-space projection in adversarial channel-target alignments.","major_comments":[{"comment":"The central claim of 'comparable performance to centralized methods' is supported only by an unspecified baseline. Footnote 1 states that the centralized problem (18) is handled with the MM technique, but does not specify the surrogate function, the initialization, the number of iterations, or the convergence criteria. Since (18) is nonconvex, the quality of that baseline depends crucially on these choices, and the small gap reported in Fig. 6 could be an artifact of a poor local optimum. The paper needs to either rigorously specify the centralized algorithm (e.g., in an appendix) or soften the claim to 'close to the centralized MM benchmark' and provide the associated parameters.","section":"Section IV-F, Fig. 6"},{"comment":"The communication noise variance σ_k^2 is never specified in the numerical setup, although it appears directly in the SINR expression (9) and therefore determines the absolute values of the sum SINR in Figs. 4 and 6. Without this parameter, the reported SINR values cannot be reproduced by an independent implementation. Please state the value used (e.g., σ_k^2 = 1, 0 dB, or per-user noise power) and specify whether the same value is used for the centralized and distributed solutions.","section":"Section V"},{"comment":"The feasibility of the sensing constraint after null-space projection is not analyzed. When the target angle θ_m is aligned with the subspace spanned by the interference channels used to build P_{m,k}, the projected steering vector a_{m,k} = P_{m,k}^H a_{Ntx}(θ_m) can have a very small norm, making the sensing SNR constraint (19c) or (23c) infeasible for the reported Δ values. The paper does not discuss how infeasible random channel realizations are handled in the Monte Carlo averages, nor does it report the distribution of the projected steering-vector gains for the chosen θ_m. Please address this by either providing a feasibility analysis, reporting the number of discarded realizations, or selecting experimental angles that avoid adversarial alignments.","section":"Section IV-B, Figs. 5-6"}],"minor_comments":[{"comment":"The steering vector is written as a_k^H(θ_m), but the projected steering vector was defined as a_{m,k} in (21). Use a_{m,k} consistently to avoid confusion with the array response a_{Ntx}(θ_m).","section":"Equations (23c), (24c)"},{"comment":"Typographical errors: 'distibuted' in the Algorithm 1 title and 'Distributted' in its caption should be corrected to 'distributed'.","section":"Algorithm 1"},{"comment":"The initialization g_{m,k} = (1/M) sqrt(Δ̃/K) seems inconsistent with its definition g_{m,k} = a_{m,k}^H w_{m,k} in Section IV-D, which is a channel-dependent quantity. Please clarify the rationale or the intended meaning of this initialization.","section":"Algorithm 1, step 4"},{"comment":"The paper does not specify the number of Monte Carlo realizations used for the mean curves in Figs. 4 and 6 beyond '100 random realizations' for Fig. 4; please state the number used for Fig. 6 as well.","section":"Section V"}],"recommendation":"major_revision","confidential_remarks":"The paper's contribution is incremental but potentially useful for scalability-focused CF-ISAC work. The main concern is that the headline performance result rests on an unreported centralized baseline; without a precise specification, the comparison is not verifiable. I would recommend asking the authors to either provide the centralized algorithm in detail (perhaps in an appendix or as supplementary code) or to reframe the claim as a comparison against a particular MM-based centralized benchmark. The missing noise variance is a simpler fix. The feasibility issue, while secondary, should be addressed because it affects the validity of the numerical experiments for adversarial geometries."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Kale, quick take on arXiv:2501.10136. The genuinely new thing is the two-stage split: each precoder is factored into a local AP vector and a central complex weight, and the APs exchange only equivalent channels (3MK scalars per direction) rather than full CSI. That makes fronthaul independent of array size, which is a real structural advantage over the centralized CF-ISAC designs in [21]–[25]. The MM-based alternating solution is competent, the null-space MUI cancellation is a sensible decoupling trick, and the local/central subproblems are convex after the surrogates. Proposition 1 gives a valid (if terse) containment argument for the sensing constraint relaxation. The convergence plots show the algorithm settling in about three iterations.\n\nThe soft spot is exactly where the stress-test lands: the 'comparable performance' claim in Fig. 6 rests on a centralized baseline that is never specified. Footnote 1 says the nonconvex centralized problem is handled with MM but 'detailed insights into the centralized optimization problem's solution are not provided.' Since (18) is nonconvex, the gap in Fig. 6 is a comparison to some undisclosed local solution, not to the optimum. That is load-bearing for the abstract's central claim. The missing communication noise variance sigma_k^2 is a smaller but real reproducibility gap — absolute SINR values cannot be re-derived. And there are no error bars on the mean curves, so the 10–15% gap shown could be within noise.\n\nThe sensing-feasibility concern is secondary but worth a sentence in revision. With K=2 and Ntx=32, the null-space projection usually leaves enough gain, but the paper should either prove a bound on the projected steering gain or report the distribution of target angles used in the averaged curves. The beampattern plots use a single channel realization and do not address adversarial alignments.\n\nWho is this for? A group working on scalable CF-ISAC beamforming. The architecture idea deserves a serious referee. Send it to peer review, but the revisions must include a spelled-out centralized baseline (initialization, surrogate, iterations) or an appendix with the MM details, plus the missing noise variance and error bars. Without that, Fig. 6 is unverifiable.","headline":"A genuinely useful distributed beamforming architecture for CF-ISAC, but the central 'comparable performance' claim leans on an unspecified centralized baseline that needs to be pinned down before the paper is fully verifiable.","tokens_in":642,"tokens_out":1642,"would_cite":true,"duration_ms":33828,"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 two-stage split of beamforming computation cuts cell-free ISAC fronthaul load while keeping performance close to centralized design.","keywords":["cell-free massive MIMO","integrated sensing and communication","distributed beamforming","fronthaul load","majorization-minimization","null-space projection","sum SINR optimization","ISAC"],"falsifier":"Pick a target angle that coincides with or lies very close to one of the user channel angles, compute the projected steering-vector gains $\\|\\mathbf{P}_{m,k}^H\\mathbf{a}_{N_{\\mathrm{tx}}}(\\theta_m)\\|^2$, and check whether any feasible precoder can meet the sensing threshold; if these gains are near zero, the optimization problem becomes infeasible and the claimed sensing performance cannot be delivered.","tokens_in":16165,"feed_emoji":"📡","tokens_out":9169,"duration_ms":77854,"temperature":0.7,"pith_summary":"This paper proposes a two-stage distributed beamforming design for cell-free massive MIMO systems that serve communication users and sense a target at the same time. The claim is that splitting each beamforming vector into a local access-point component and a central-unit scalar weight, then exchanging only compact equivalent channels between the two stages, yields performance close to a fully centralized solution while dramatically reducing the fronthaul load. Concretely, the beamforming-design data exchange becomes independent of the number of antennas per access point, removing a key scalability bottleneck for cell-free integrated sensing and communication (ISAC). A careful reader should take away that most of the benefit of joint optimization survives distribution, and that the practical cost is small: roughly three exchange iterations are enough to approach the converged result.","feed_headline":"Split beamforming cuts ISAC fronthaul load, keeps performance","feed_subtitle":"Compact equivalent-channel exchange means fronthaul no longer grows with antennas per access point.","key_machinery":"The engine is the two-stage precoder decomposition combined with null-space interference cancellation and majorization-minimization. Null-space projection turns the multi-user SINR objective into a sum of projected desired-signal powers that each access point can compute from its local channel, eliminating multi-user interference without exchanging full channel matrices. The remaining non-convex problems, one at each access point and one at the central unit, are replaced by convex surrogates built from a first-order Taylor lower bound and a linearized sensing constraint, and the two stages are iterated alternately. The compact scalars exchanged per iteration, namely the equivalent channels $z_{m,k}$ and $g_{m,k}$, the precoder powers $w_{m,k}$, and the central weights $\\delta_{m,k}$ (with derived coefficients $\\alpha_{m,k}$ and $\\beta_{m,k}$), are what make the fronthaul count independent of $N_{\\mathrm{tx}}$.","core_discovery":"The central discovery is that the joint beamforming problem decomposes with little loss: every precoding vector is written as $\\mathbf{f}_{m,k}=\\delta_{m,k}\\mathbf{w}_{m,k}$, where $\\mathbf{w}_{m,k}$ is computed locally at the $m$-th access point and $\\delta_{m,k}$ is a scalar weight computed at the central unit. Inter-user interference is cancelled locally by projecting each local precoder into the null space of the other users' channels, so the access points optimize in parallel with no inter-access-point channel sharing. The two sides exchange only equivalent communication channels, equivalent sensing channels, and precoder powers, giving a total of $6N_{\\mathrm{iter}}MK$ complex scalars over $N_{\\mathrm{iter}}$ iterations, independent of the antenna count $N_{\\mathrm{tx}}$; the centralized baseline exchanges $2N_{\\mathrm{tx}}MK$ scalars. In the reported scenario the sum SINR stays close to the centralized solution across the tested sensing thresholds, and three iterations already reach roughly 98--99% of the final value.","pith_inferences":["Because the exchanged quantities depend only on $M$, $K$, and the iteration count, the same compact-exchange pattern should transfer to other distributed beamforming problems that summarize each access point through aggregate equivalent channels, not only cell-free ISAC.","The method's practical limit is likely the null-space projection: if a target direction nearly coincides with a user channel direction, the projected sensing gain may be too small to meet the sensing constraint, so a safeguard that detects low projected gain and reconfigures user-to-AP assignments would be a natural extension.","Extending to multiple targets would presumably require one sensing constraint per target and extra scalar sensing gains per iteration, trading some of the fronthaul saving for broader sensing coverage."],"forward_implications":["Beamforming-design fronthaul becomes independent of the antenna count: the total exchange is $6N_{\\mathrm{iter}}MK$ complex scalars versus $2N_{\\mathrm{tx}}MK$ for the centralized approach.","Central-unit computational complexity drops from $O(N_{\\mathrm{tx}}^3M^3K^3\\sqrt{N_{\\mathrm{tx}}MK})$ to $O(M^3K^3\\sqrt{MK})$, because the central unit optimizes only $MK$ scalar weights.","A small number of exchange iterations is sufficient: about three iterations reach 99% of the converged sum SINR at $\\Delta=30$ dB and about 98% at $\\Delta=40$ dB.","Increasing the sensing requirement $\\Delta$ shifts power toward the target and lowers the communication sum SINR, and the distributed design tracks the centralized trade-off curve closely."],"supporting_citations":[{"why":"supplies the null-space projection and the linearized sensing constraint used to convexify both the AP and CU subproblems.","marker":"[13]"},{"why":"defines the centralized cell-free ISAC sensing-centric beamforming problem that serves as a baseline for comparison.","marker":"[21]"},{"why":"provides another centralized beamforming design in cell-free massive MIMO ISAC that the proposed method is set against.","marker":"[22]"},{"why":"establishes the communication-sensing region for centralized cell-free ISAC, framing the trade-off the distributed method preserves.","marker":"[23]"},{"why":"gives a centralized joint beamforming and AP-mode-selection design for cooperative cell-free ISAC.","marker":"[24]"},{"why":"provides a communication-centric centralized benchmark with a radar estimation rate constraint.","marker":"[25]"},{"why":"models the narrowband block-fading channel used in the numerical evaluation.","marker":"[26]"},{"why":"supplies the Swerling I target model that makes the sensing power a sum of per-AP terms.","marker":"[27]"},{"why":"is the convex optimization solver used to implement the AP and CU subproblems.","marker":"[28]"}],"fun_headline_variants":["Two-stage distributed beamforming slashes fronthaul in CF ISAC","Local beamforming achieves comparable ISAC with less fronthaul","Fronthaul load reduced by distributing beamforming in ISAC","Two-stage design keeps sum SINR high, cuts fronthaul cost","Distributed precoding for CF ISAC: less fronthaul, same performance"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The design stands on the assumption that after each access point projects its sensing direction into the null space of its users' interference channels, the remaining energy pointed at the sensing target is still enough to satisfy the sensing SNR requirement.","fun_headline_variants_meta":{"raw":{"variants":["Two-stage distributed beamforming slashes fronthaul in CF ISAC","Local beamforming achieves comparable ISAC with less fronthaul","Fronthaul load reduced by distributing beamforming in ISAC","Two-stage design keeps sum SINR high, cuts fronthaul cost","Distributed precoding for CF ISAC: less fronthaul, same performance"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000509,"raw_usage":{"total_tokens":2508,"prompt_tokens":1007,"completion_tokens":1501,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":623,"completion_tokens_details":{"reasoning_tokens":1406}},"tokens_in":623,"tokens_out":1501,"duration_ms":10375,"temperature":1.0,"reasoning_tokens":1406,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T19:24:12.520331+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Pick a target angle that coincides with or lies very close to one of the user channel angles, compute the projected steering-vector gains $\\|\\mathbf{P}_{m,k}^H\\mathbf{a}_{N_{\\mathrm{tx}}}(\\theta_m)\\|^2$, and check whether any feasible precoder can meet the sensing threshold; if these gains are near zero, the optimization problem becomes infeasible and the claimed sensing performance cannot be delivered.","supporting_citations":[{"cited_title":"Leyva, D","cited_arxiv_id":null,"evidence_quote":"supplies the null-space projection and the linearized sensing constraint used to convexify both the AP and CU subproblems."},{"cited_title":"Demirhan and A","cited_arxiv_id":null,"evidence_quote":"defines the centralized cell-free ISAC sensing-centric beamforming problem that serves as a baseline for comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides another centralized beamforming design in cell-free massive MIMO ISAC that the proposed method is set against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"establishes the communication-sensing region for centralized cell-free ISAC, framing the trade-off the distributed method preserves."},{"cited_title":"Cooperative Cell-Free ISAC Networks: Joint BS Mode Selection and Beamforming Design","cited_arxiv_id":"2305.10800","evidence_quote":"gives a centralized joint beamforming and AP-mode-selection design for cooperative cell-free ISAC."},{"cited_title":"Cao and Q","cited_arxiv_id":null,"evidence_quote":"provides a communication-centric centralized benchmark with a radar estimation rate constraint."},{"cited_title":"Ayach, S","cited_arxiv_id":null,"evidence_quote":"models the narrowband block-fading channel used in the numerical evaluation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the Swerling I target model that makes the sensing power a sum of per-AP terms."}],"review_version":1}