{"id":"a1c7f8ac-4f8d-49d6-94aa-9969f65314fc","arxiv_id":"2412.17062","paper_version":2,"verdict":"REJECT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"Dedicated sensing beams are claimed to be unnecessary for near-field multi-target ISAC detection under RSMA with hybrid beamforming, and an iterative algorithm is proposed that achieves near-fully-digital communication rates.","lead":"This paper designs a hybrid analog-digital beamforming scheme for a near-field base station that simultaneously serves communication users and detects targets using rate-splitting multiple access. It claims dedicated sensing beams are unnecessary and provides an iterative optimization algorithm, with simulations showing performance close to fully digital beamforming.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Proposition 2's rank-reduction proof omits the transmit power term and uses dimensionally incompatible matrices, leaving the central V=0 claim unsupported.","rationale":"The reader's weakest-assumption identifies exactly the load-bearing gap: Proposition 2's trace-preservation argument omits the transmit power term and also contains a dimension mismatch. I agree with this assessment, and the failure is even sharper than stated. The preserved set \\hat B_i in (44) excludes F^H F, the defining matrix of constraint (12b). Moreover, a positive-definiteness argument shows that no nonzero PSD X_k can preserve the power term when F has full column rank, so the rank-reduction mechanism cannot respect (12b). The dimension mismatch (N_t \\times N_t matrices multiplied against N_f \\times A_k factors with N_f < N_t) independently invalidates equations (45)-(47). These are internal inconsistencies, not disagreements with external consensus. The subsequent PDD/WMMSE algorithm and simulations may be reasonable engineering heuristics, but they do not test the V=0 conclusion: the simulations fix N_s = 0 and never compare against the same design with dedicated sensing beams. Therefore the paper's advertised theoretical contribution—the proof that dedicated sensing beams are unnecessary for NF multi-target detection—is unsupported, and the reader's rejection is appropriate. The proposed concrete test would definitively settle the matter by showing the reconstructed solution cannot satisfy the power budget.","tokens_in":23619,"tokens_out":8660,"duration_ms":71854,"concrete_test":"Analytical check: fix any full-column-rank analog beamformer F (e.g., N_t = 64, N_f = 8), take a rank-2 \\hat W_k from a feasible point of (12), and attempt to construct the PSD matrix X_k required by Appendix B. For constraint (12b) to be preserved, X_k must satisfy Tr(\\hat P_k^H F^H F \\hat P_k X_k) = 0. Since \\hat P_k^H F^H F \\hat P_k \\succ 0, this forces X_k = 0, contradicting any rank reduction. Equivalently, recompute the left-hand side of (12b) for the reconstructed \\bar W_k: it will be strictly smaller than the original power, so Q3 violates the power constraint whenever the original solution used the full power budget. This single computation settles that Proposition 2 cannot produce a feasible Q3.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim (Section III, Eq. (15)) is that Q3 = {F*, \\bar W_k, \\hat V=0, U*, c*} is an optimal solution of (12), so dedicated sensing beams are unnecessary. This rests on Proposition 2, whose proof (Appendix B) constructs a rank-one \\bar W_k by showing Tr(\\hat B_i \\bar W_k) = Tr(\\hat B_i \\hat W_k) for the set \\hat B_i in (44). That set contains only sensing matrices G_a^H u_b u_b^H G_a and communication Gramians H_i; it does not contain the transmit power matrix F^H F. Constraint (12b) is \\sum_k Tr(F^H F \\tilde W_k) + Tr(F^H F \\tilde V) \\le P_th, so preserving Tr(\\hat B_i \\bar W_k) for the listed \\hat B_i says nothing about whether (12b) holds. In fact, \\bar W_k = \\hat P_k(I - X_k/\\delta_k)\\hat P_k^H with X_k \\succeq 0 and X_k \\neq 0 implies Tr(F^H F \\bar W_k) = Tr(F^H F \\hat W_k) - (1/\\delta_k)Tr(\\hat P_k^H F^H F \\hat P_k X_k), which is strictly less than Tr(F^H F \\hat W_k) whenever F has full column rank. Thus the power budget shrinks unless X_k = 0, contradicting any nontrivial rank reduction. Additionally, the matrices \\hat B_i in (44) are N_t \\times N_t, while \\hat P_k \\in C^{N_f \\times A_k}; the product \\hat P_k^H \\hat B_i \\hat P_k is only defined when N_t = N_f, which is excluded by the hybrid architecture (N_f < N_t). The correct sensing term should be F^H G_a^H u_b u_b^H G_a F. Either defect alone invalidates the reconstructed Q3 as feasible, so E(Q3) = E(Q2) is not established and the conclusion N_s^* = 0 does not follow. Simulations do not repair this: the algorithm fixes N_s = 0 and never compares against the same scheme with dedicated sensing beams, so the paper's central theoretical contribution remains unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an RSMA-based hybrid beamforming design for near-field ISAC with multiple communication users and multiple sensing targets. It formulates a max-min communication rate problem subject to transmit power, sensing-rate, common-rate, unit-modulus, and receive-filter constraints, with a variable number of dedicated sensing beams. The main theoretical claim is that dedicated sensing beams are unnecessary for NF multi-target detection, established through a solution-reconstruction argument (Propositions 1 and 2) that removes the sensing covariance. The rest of the paper develops a PDD-based double-loop algorithm using WMMSE and quadratic-transform reformulations, with closed-form updates for receive filters, digital beamformers, and analog beamformers, and evaluates the scheme in simulations against five baselines.","tokens_in":24085,"tokens_out":7588,"duration_ms":71239,"significance":"If the non-necessity theorem were valid, the paper would make a useful conceptual contribution to NF-ISAC beamforming, supporting the architectural simplification of omitting dedicated sensing beams. The system model is laid out clearly, and the simulation study is substantial: 100 channel realizations, five baselines, and comparisons over transmit power, RF-chain count, number of users and targets, and sensing-rate thresholds. The algorithmic machinery (PDD, WMMSE, quadratic transform) is standard but competently assembled, and the closed-form updates for the receive filters, digital beamformer, and analog beamformer are a practical strength. However, the central theorem's proof has load-bearing gaps concerning matrix dimensions and constraint preservation; the simulations do not repair those gaps because they already operate under the assumption that dedicated sensing beams are absent.","major_comments":[{"comment":"The proof of Proposition 2 is dimensionally inconsistent. The matrices \\hat W_k are digital beamformers in C^{N_f \\times N_f}, so their factorization \\hat W_k = \\hat P_k \\hat P_k^H has \\hat P_k \\in C^{N_f \\times A_k}. However, the sensing matrices in (44) are G_a^H u_b u_b^H G_a \\in C^{N_t \\times N_t}; the product \\hat P_k^H \\hat B_i \\hat P_k is undefined unless N_t = N_f, which the hybrid architecture explicitly excludes (N_f < N_t). The communication terms H_i are N_f \\times N_f, so (44) mixes two incompatible dimensions. This invalidates the construction of B_k and the trace-preservation identity in (47).","section":"Appendix B, Eq. (44)"},{"comment":"Even if the dimension issue were set aside, the trace preservation is established only for the matrices \\hat B_i in (44), namely G_a^H u_b u_b^H G_a and H_i. The sensing SINR (10) depends on R = \\sum_k F \\tilde W_k F^H + F \\tilde V F^H, so the relevant quadratic forms are Tr(F^H G_a^H u_b u_b^H G_a F \\tilde W_k), not Tr(G_a^H u_b u_b^H G_a \\tilde W_k). Since (44) omits F^H F, the proof does not show that the rank-reduced \\bar W_k preserves the transmit power constraint (12b) or the sensing constraints (11c). The sentence in the proof that \\bar W_k 'can meet constraints (12b), (12c), and (12e)' is therefore unsupported, and the central conclusion N_s^* = 0 in Section III does not follow.","section":"Appendix B, Eqs. (45)-(47)"},{"comment":"The deduction that Q3 is an optimal solution relies on the chain E(Q3) = E(Q2) \\ge E(Q1^*). Because the equality E(Q3) = E(Q2) is not established, as explained above, the statement 'there exists an optimal solution making V = 0' is not proven. At a minimum, the authors would need to demonstrate that the constructed rank-one \\bar W_k simultaneously satisfies (12b), (12c), and all sensing constraints for N_f < N_t; the manuscript provides no such verification.","section":"Section III, Eq. (15)"},{"comment":"The convergence discussion states both that the algorithm 'always yields globally optimal solutions' and that it 'converges to a stationary point within a finite number of iterations.' The first claim is not established by the monotonicity argument in (39) and is inconsistent with the second. Since the algorithm is a core contribution, this requires either a rigorous global-optimality proof or a corrected and more modest convergence claim.","section":"Section IV-D"}],"minor_comments":[{"comment":"The organization paragraph says 'Section IV provides simulation results' and 'Section V concludes,' but the simulations are in Section V and the conclusion is in Section VI.","section":"Section I"},{"comment":"Line 13 of Algorithm 1 outputs 'the maximized minimum sensing rate,' although problem (17) maximizes the minimum communication rate; this appears to be a typo.","section":"Algorithm 1"},{"comment":"The indexing in (44) is ambiguous for the boundary value: for i = M^2, the definitions a = \\lfloor i/M \\rfloor and b = i - aM give b = 0, which is not a valid target index. The index ranges should be stated more carefully.","section":"Appendix B, Eq. (44)"},{"comment":"Notation is inconsistent in places, for example N_t versus Nt and \\hat V versus \\tilde V around equation (14); these should be harmonized.","section":"Throughout"},{"comment":"Figure 2 contains garbled non-English characters in several block labels; the figure should be regenerated with clean text.","section":"Figure 2"}],"recommendation":"reject","confidential_remarks":"The central theorem is the paper's headline contribution. My recommendation is reject rather than major revision because the proof in Appendix B is not a local typo: the construction uses matrices of incompatible dimensions and traces over the wrong quadratic forms, so the claimed feasibility of the reconstructed solution is unproven. If the authors can supply a correct proof of the non-necessity claim, or reframe the paper around a verifiable design criterion without that theorem, a resubmission could be reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Let me give you the short version: the paper's main advertised result, that dedicated sensing beams are unnecessary in RSMA-enabled near-field ISAC, is not supported by the proof. Proposition 2's reconstruction step uses a set of test matrices \\hat B_i that mixes N_t x N_t sensing matrices with N_f x N_f communication Gramians, and the product \\hat P_k^H \\hat B_i \\hat P_k is only defined if N_t = N_f. Worse, the set does not include F^H F, so the proof never checks the transmit power constraint (12b). The rank-reduced \\bar W_k changes Tr(F^H F \\bar W_k), so feasibility is lost. The conclusion that Q3 is optimal and N_s^*=0 does not follow. The simulation section also fixes N_s=0 and never compares against the same design with dedicated sensing beams, so there's no empirical rescue.\n\nThat said, the paper is not without merit. The system model is carefully set up, the hybrid beamforming formulation with RSMA and sensing rate constraints is timely, and the PDD/WMMSE/quadratic-transform algorithm is a reasonable heuristic for the problem. The complexity analysis is standard but solid, and the benchmarks (SDMA, NOMA, far-field, fully digital) are sensible. If you treat the no-sensing-beams claim as an assumption rather than a theorem, the rest of the paper stands as a useful design study.\n\nOther soft spots are minor by comparison. The convergence analysis claims global optimality for a nonconvex problem, which is wrong; they probably mean convergence to a stationary point. The notation in (44) is sloppy, and the appendix's linear-independence argument is not rigorous even setting aside the dimension mismatch.\n\nMy view: this deserves referee time because the question is real and the system-level contribution is useful, but as written the central theoretical claim is broken. A serious referee should flag Appendix B and ask for either a corrected proof with the F^H F term included and consistent dimensions, or a clear statement that the rank-zero result is conjectural. I would not cite the theorem as proven.","headline":"The paper's key theorem—that dedicated sensing beams are unnecessary in near-field ISAC—rests on a broken proof in Appendix B, though the algorithm and simulations still have heuristic value.","tokens_in":24621,"tokens_out":2894,"would_cite":false,"duration_ms":26009,"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 for near-field integrated sensing and communications with RSMA, dedicated sensing beams are never needed: a rank-zero reconstruction of the optimal beamformers always achieves the same max-min communication rate…","keywords":["near-field ISAC","rate-splitting multiple access","hybrid beamforming","dedicated sensing beams","rank-zero reconstruction","penalty dual decomposition","WMMSE","sensing rate"],"falsifier":"Take a random near-field instance, solve the rank-relaxed problem to obtain $\\tilde{W}_k^*$ and $\\tilde{V}^*$, build $\\hat{W}_k = \\tilde{W}_k^* + \\delta_k \\tilde{V}^*$, apply the Appendix B rank reduction, and compute $\\sum_{k=0}^{K} \\mathrm{Tr}(F^H F \\bar{W}_k)$; if this sum exceeds $P_{\\mathrm{th}}$ for a case where the original solution was feasible, the claim that an optimal solution with $V=0$ always exists is false.","tokens_in":23441,"feed_emoji":"📡","tokens_out":10630,"duration_ms":89602,"temperature":0.7,"pith_summary":"The paper tries to settle whether a near-field integrated sensing and communications (ISAC) base station needs separate sensing beams when it also serves users with rate-splitting multiple access (RSMA). It claims no: there is always an optimal solution in which the dedicated sensing beamformer is zero, because the communication beams can be rebuilt to carry the sensing load without hurting either task. If true, this removes the unknown beam-count variable from the design and lets all radio-frequency chains be spent on communication, which matters because near-field arrays are expensive and fully digital beamforming is impractical. The paper also contributes a penalty-dual-decomposition algorithm that optimizes the remaining hybrid beamformers, and simulations indicate near-digital performance with fewer RF chains and gains over far-field and conventional multiple-access baselines.","feed_headline":"Dedicated sensing beams are unnecessary in near-field ISAC","feed_subtitle":"A rank-zero reconstruction lets communication beams carry multi-target sensing, saving RF chains and closing in on fully digital rates.","key_machinery":"The rank-zero solution reconstruction carries the no-sensing-beam conclusion. Proposition 1 redistributes the dedicated sensing covariance $\\tilde{V}^*$ into the communication beamformers with weights $\\delta_k$ summing to one; total transmit covariance is unchanged, so sensing rates are preserved, and because sensing interference moves into the useful signal terms, each communication SINR can only rise. Proposition 2 then takes a possibly high-rank $\\hat{W}_k$ and produces a rank-one $\\bar{W}_k$ by subtracting a null-space correction, using the linear dependence structure of the blocks $\\hat{P}_k^H \\hat{B}_i \\hat{P}_k$ to guarantee $\\mathrm{Tr}(\\hat{B}_i \\bar{W}_k)=\\mathrm{Tr}(\\hat{B}_i \\hat{W}_k)$ for every sensing-channel and user-channel matrix in the problem. This converts the covariance-preserving absorption of sensing beams into a feasible rank-one communication solution, removing the discrete variable $N_s$ from the optimization. The subsequent algorithm machinery, PDD with WMMSE and quadratic transforms, optimizes the remaining hybrid beamformers.","core_discovery":"On its own terms, the central discovery is that for the formulated max-min communication-rate problem with per-target sensing-rate constraints, there exists an optimal solution with $V=0$, meaning dedicated sensing beams are unnecessary for near-field multi-target detection. Starting from an optimal solution $(F^*, \\tilde{W}_k^*, \\tilde{V}^*, U^*, c^*)$, the paper constructs $\\hat{W}_k = \\tilde{W}_k^* + \\delta_k \\tilde{V}^*$ and $\\hat{V}=0$ with $\\sum_k \\delta_k=1$, which preserves the transmit covariance, keeps the sensing rate unchanged, and weakly raises every communication SINR. It then rank-reduces each $\\hat{W}_k$ to a rank-one $\\bar{W}_k$ that preserves all sensing-channel and user-channel trace terms, so the chain $E(Q_3)=E(Q_2)\\ge E(Q_1^*)$ forces equality and $Q_3$ is optimal. With $N_s^*=0$ established, the paper optimizes the remaining variables through a penalty-dual-decomposition double-loop algorithm using WMMSE and quadratic transforms, and simulations report that hybrid beamforming with few RF chains nearly matches fully digital beamforming while the sensing constraint costs only about $0.05$ bps/Hz.","pith_inferences":["An implication not stated in the paper is that adding $F^HF$ to the set of matrices $\\hat{B}_i$ in Proposition 2 would make the power step checkable; if the trace equality still holds, the $V=0$ conclusion becomes fully established, and if not, instances with $V\\neq0$ may be optimal.","The rank-zero reconstruction idea transfers naturally to other designs with a variable number of dedicated beams or subarrays: replace the discrete count by a rank constraint, then reduce the rank while preserving the constraints that matter.","The simulation comparison at $R_{\\mathrm{th}}=10$ bps/Hz removes infeasible channel realizations for the benchmarks, so the reported gains over SDMA and NOMA at that threshold may partly reflect feasibility filtering; counting infeasible cases as failures for every scheme would be a fairer test.","A separate untested consequence is that practical near-field ISAC transmitters could drop dedicated radar waveform slots and instead shape communication beams to cover the angular-distance region of interest, but that transfer is outside the paper's RSMA-based formulation."],"forward_implications":["With $N_s=0$, every RF chain can be assigned to communication streams, removing the sensing-beam count from the optimization and simplifying the remaining beamformer design.","Hybrid arrays with few RF chains can approach fully digital performance in the simulated regime, which matters because fully digital near-field arrays require one RF chain per antenna.","The sensing-rate requirement costs only about $0.05$ bps/Hz in the simulated setting, so multi-target detection is nearly free when communication beams are reused for sensing.","RSMA-based near-field ISAC outperforms SDMA, NOMA, and far-field ISAC in max-min rate, and the near-field advantage grows with the number of targets because spherical waves separate targets by distance as well as angle.","The rank-zero reconstruction removes the variable sensing-beam count from the design, a step that generalizes to other ISAC formulations with uncertain beam counts."],"supporting_citations":[{"why":"Supplies the far-field RSMA-ISAC simulation evidence that dedicated sensing beams are not needed, which this paper extends to the near-field regime with an analytical reconstruction argument.","marker":"[14]"},{"why":"Shows a dedicated sensing beam is superfluous in a single-user dual-function radar-communication setup, cited as corroboration for the $V=0$ conclusion.","marker":"[38]"},{"why":"Shows dedicated probing signals improve multi-user ISAC only under interference mitigation or zero-forcing conditions, used to reconcile the no-sensing-beam conclusion with those results.","marker":"[37]"},{"why":"Provides the near-field hybrid-array ISAC model and channel formulation that the paper adopts for its transmit and receive arrays.","marker":"[13]"},{"why":"Supplies the near-field multi-target detection beamforming approach and sensing-rate metric that the paper uses as a comparison baseline and performance measure.","marker":"[28]"},{"why":"Establishes the rate-splitting multiple access model with common and private streams that the paper's communication formulation is built on.","marker":"[4]"},{"why":"Provides the quadratic transform used to recast the fractional sensing SINR into a convex surrogate in the inner optimization.","marker":"[40]"},{"why":"Supplies the penalty dual decomposition framework used to handle the analog-digital coupling constraint $P=FW$ in the double-loop algorithm.","marker":"[41]"}],"fun_headline_variants":["Zero sensing beams: near-field ISAC gets by on communication beams alone","Rank-zero trick eliminates dedicated sensing beams in near-field ISAC","Near-field ISAC: no extra beams needed for sensing","Communication beams can sense too, killing dedicated sensing beams"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the reconstructed rank-one beams use no more transmit power than the original solution; the proof's trace equalities cover sensing-channel and user-channel matrices but not the power term $F^HF$, so power feasibility is asserted rather than established.","fun_headline_variants_meta":{"raw":{"variants":["Zero sensing beams: near-field ISAC gets by on communication beams alone","Rank-zero trick eliminates dedicated sensing beams in near-field ISAC","Near-field ISAC: no extra beams needed for sensing","Communication beams can sense too, killing dedicated sensing beams"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000647,"raw_usage":{"total_tokens":3024,"prompt_tokens":1051,"completion_tokens":1973,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":667,"completion_tokens_details":{"reasoning_tokens":1903}},"tokens_in":667,"tokens_out":1973,"duration_ms":12226,"temperature":1.0,"reasoning_tokens":1903,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T05:50:29.139588+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a random near-field instance, solve the rank-relaxed problem to obtain $\\tilde{W}_k^*$ and $\\tilde{V}^*$, build $\\hat{W}_k = \\tilde{W}_k^* + \\delta_k \\tilde{V}^*$, apply the Appendix B rank reduction, and compute $\\sum_{k=0}^{K} \\mathrm{Tr}(F^H F \\bar{W}_k)$; if this sum exceeds $P_{\\mathrm{th}}$ for a case where the original solution was feasible, the claim that an optimal solution with $V=0$ always exists is false.","supporting_citations":[{"cited_title":"Rate-sp litting multiple access for multi-antenna joint radar and communic ations,","cited_arxiv_id":null,"evidence_quote":"Supplies the far-field RSMA-ISAC simulation evidence that dedicated sensing beams are not needed, which this paper extends to the near-field regime with an analytical reconstruction argument."},{"cited_title":"Composite Signalling for DFRC: Dedicated Probing Signal or Not?","cited_arxiv_id":"2009.03528","evidence_quote":"Shows a dedicated sensing beam is superfluous in a single-user dual-function radar-communication setup, cited as corroboration for the $V=0$ conclusion."},{"cited_title":"Joint transmit beamforming for multiuser MIMO communications an d MIMO radar,","cited_arxiv_id":null,"evidence_quote":"Shows dedicated probing signals improve multi-user ISAC only under interference mitigation or zero-forcing conditions, used to reconcile the no-sensing-beam conclusion with those results."},{"cited_title":"Near-field integrated sensin g and communications,","cited_arxiv_id":null,"evidence_quote":"Provides the near-field hybrid-array ISAC model and channel formulation that the paper adopts for its transmit and receive arrays."},{"cited_title":"Fractional programming for communic ation systems-part I: Power control and beamforming,","cited_arxiv_id":null,"evidence_quote":"Provides the quadratic transform used to recast the fractional sensing SINR into a convex surrogate in the inner optimization."}],"review_version":1}