{"id":"14c7668c-3af7-4252-90d9-bf89af0c22fe","arxiv_id":"2501.18264","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A CRB-minimizing signal design framework for noncoherent distributed ISAC that jointly optimizes per-subcarrier sensing waveforms and CoMP communication precoders.","lead":"This paper designs transmit signals for a network of base stations that jointly sense targets and serve cellphone users, without requiring the base stations to be phase-synchronized. Three designs are offered, trading sensing accuracy against communication quality and computational cost.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'optimal design' (P.1) is an SDR lower bound, not an achievable design; the paper admits the relaxation is not tight, so the claimed optimal CRB-SINR trade-off is not established.","rationale":"The reader identified genie-aided target knowledge as the weakest assumption and mentioned the non-tight SDR only in passing. I agree with the CONDITIONAL verdict but for a more central reason: the paper's own Section IV-B admits the SDR relaxation for P.1 is not tight, and the extracted solutions 'are not necessarily the optimal solution of the original problem (32)'. The plotted curves labeled 'Optimal design (P.1)' in Figs. 5-7 are therefore the SDR lower bounds, not achievable performance, unless the extracted markers coincidentally attain them. The paper does not quantify the gap except to note degradation at low SINR. This directly affects the strongest claim that the three designs achieve the claimed CRB-SINR trade-offs: for P.1, only the extracted markers are demonstrated feasible, and even there the extraction involves a PSD projection that may change sensing performance. The genie-aided target knowledge is a real practical limitation, but it is common in CRB-based waveform design and can be framed as a design assumption; the unquantified SDR gap is an internal correctness issue that must be resolved or explicitly relabeled. The proposed test would settle whether the P.1 curve is achievable, and the paper should then either provide achievable curves or clearly distinguish the SDR bound from the feasible design.","tokens_in":26249,"tokens_out":36051,"duration_ms":361062,"concrete_test":"Take the setup of Fig. 5 at Γ_c = 10 dB and 20 dB. Solve (P.1), extract ŵ_c and Ŵ_s using (34)-(36), reconstruct the full augmented transmit covariance, and evaluate both the actual SINR via (11) and the actual localization CRB using the reconstructed covariance in the FIM. Compare the resulting (SINR, RCRB) point to the plotted 'Optimal design (P.1)' curve. If the point lies strictly above the curve, the curve is not achievable. Repeat across the SINR range to quantify the gap; this directly tests whether P.1's claimed trade-off is realized.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section IV-B solves (P.1) by dropping the rank-one constraints and states: 'Although the relaxation to problem (P.1) is not tight, we can extract approximate solutions... The obtained solutions are not necessarily the optimal solution of the original problem (32).' Despite this, Figs. 5-7 plot the SDP objective value as 'Optimal design (P.1)' and present it as achieving the best CRB-SINR trade-off. The extraction in (34)-(36) projects \\tilde R_s onto the PSD cone and does not realize the off-diagonal blocks of \\tilde R_l; hence the SDP curve is a lower bound on the localization CRB, not an achievable design. The markers represent extracted designs at only a few selected SINR values, and the paper itself notes degradation at low SINR, but no bound on the gap is given. Since the central claim is that P.1 achieves the optimal sensing-communication trade-off, an unquantified relaxation gap leaves the headline performance unsupported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a transmit signal design framework for noncoherent distributed integrated sensing and communication (D-ISAC), in which multiple ISAC nodes without phase-level synchronization cooperate for downlink CoMP communication and distributed MIMO radar target localization. A received signal model is developed for both communication and sensing, the communication metric is the per-subcarrier SINR, and the sensing metric is the Cramér-Rao bound on target localization based on hybrid AOA/TOF estimation. The central optimization (23) minimizes the localization CRB subject to per-antenna power and per-user SINR constraints. The authors prove that the FIM is linear in the augmented per-subcarrier transmit covariance matrices, enabling an SDR formulation. Three designs are presented: an optimal design (P.1), an orthogonal design (P.2), and a beamforming design (P.3), together with complexity analysis and simulations showing CRB-SINR trade-offs, RMSE versus CRB, and execution times.","tokens_in":26394,"tokens_out":6325,"duration_ms":60414,"significance":"If the results are taken with the stated caveats, the paper makes a useful contribution to networked ISAC: it addresses a regime (noncoherent, distributed, OFDM-based) that is less explored than single-node ISAC, and it shows that subcarrier-level design matters for TOF estimation in D-ISAC. The FIM linearity result (Theorem 1) and the three-design taxonomy provide a reasonable framework for comparing complexity and performance. The paper also gives Monte Carlo evidence that the CRB trends are reflected in an MLE for high target SNR. However, the headline 'optimal design' claim is not established because the SDR relaxation is acknowledged to be non-tight and the waveform extraction is approximate; the plotted P.1 curves are lower bounds rather than achievable performances. The objective also depends on target position knowledge that the paper does not explain how to obtain. These issues are load-bearing for the central claims and require revision.","major_comments":[{"comment":"The relaxation to (P.1) is explicitly stated to be non-tight, and the extraction of w-hat and W-hat via (34)-(36) only approximates \tilde R_s l after projection onto the PSD cone. Nevertheless, Figs. 5-7 plot the SDP objective as 'Optimal design (P.1)' and the text describes this design as achieving the best sensing performance. This conflates a lower bound with an achievable design. To support the claimed optimal CRB-SINR trade-off, the authors should either quantify the relaxation gap and show that the extracted solutions achieve it, or relabel the P.1 curves as an SDP lower bound and discuss the gap.","section":"§IV-B, Eqs. (33)-(36), Figs. 5-7"},{"comment":"The CRB objective (23a) depends on the true target positions q_k through the steering vectors, TOFs, and the Jacobian J in (19)-(22), but the paper does not state how the transmitter obtains these positions. In a sensing scenario these are exactly the quantities to be estimated. If the design is applied with erroneous target knowledge, the CRB-minimizing waveform is not guaranteed to improve, and may degrade, actual localization performance. The authors should state the underlying assumption (e.g., tracking with prior estimates) and include a sensitivity analysis with mismatched target positions, since this is not a merely cosmetic caveat but affects whether the optimized signaling is implementable.","section":"§III-B and §IV-A, Eqs. (7), (19)-(22), (23)"},{"comment":"The parameter vector Theta in (14) includes b_R and b_I, so F(Theta) is of dimension (2KN^2 + 2K). If the trace in (20) is taken over the full inverse FIM, then CRB=tr([F(Theta)]^{-1}) is not the target-localization CRB but includes variances of the nuisance amplitude parameters. If the intended metric is the trace over the position block only, then Eq. (20) is misstated, and the index range in (32b), i in {1,...,2K+2KN^2}, is inconsistent with the objective (32a) that sums only 2K terms. This should be corrected either by defining the position-subblock trace and restricting (32b) to i=1,...,2K, or by explaining why the nuisance parameters are included in the trace.","section":"§III-B, Eqs. (14), (20), (32a)-(32b)"},{"comment":"The proof of Theorem 2 is not self-contained: after the subcarrier-interleaving argument, it states that the remainder follows from Appendix A of [41], which addresses a single-node or otherwise different problem. Since Theorem 2 is the basis for claiming that the orthogonal design (P.2) and, by extension, the beamforming design (P.3) achieve the optimal solution of the original problem under the orthogonal signal model, the proof of rank-one recovery and subsequent optimality should be provided in full or the claim should be weakened accordingly.","section":"§IV-C, Theorem 2"}],"minor_comments":[{"comment":"The index range in constraint (32b) should match the number of trace variables t_i; as written, t_i is only defined for i=1,...,2K, so the range 'all i in 1,...,2K+2KN^2' is either a typo or requires additional t_i variables.","section":"§IV-B, Eq. (32)"},{"comment":"Constraint (33e) uses R_{nn,l} but the variable list of (P.1) only specifies R_{c,n,u,l} and \tilde R_l; R_{nn,l} should be explicitly defined as the corresponding diagonal block of \tilde R_l, as was done earlier in (29).","section":"§IV-B, Eq. (33)"},{"comment":"The sentence describing how the TOF-based CRB is evaluated says 'setting dot A_{r,n} and dot A_{t,n} to zero'; this is correct if those symbols denote derivatives with respect to angles, but the notation should be clarified in the text so that readers do not mistake it for zeroing the steering matrices themselves.","section":"§V-A, Fig. 4"},{"comment":"The manuscript's notation paragraph contains several rendering artifacts (for example, the list of operators and the definition of the Hadamard, Khatri-Rao, and face-splitting products), which should be cleaned up in the final version.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper has a solid system model and a plausible FIM derivation, but the central 'optimal design' claim currently rests on a non-tight SDR whose gap is unquantified, and the sensing objective depends on target knowledge that is not addressed. I believe these issues are fixable within the manuscript's scope by reframing P.1 as a lower-bound benchmark, quantifying or discussing the extraction gap, and adding a mismatched-target analysis. I would not recommend rejection if the authors address these points."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a real step for noncoherent distributed ISAC — per-subcarrier sensing waveform design that explicitly targets TOF estimation, plus a menu of three designs with clear complexity/performance trade-offs. The FIM derivation is heavy but coherent, the three problems are carefully stated, and the simulations are internally consistent, including an MLE check against the CRB.\n\nWhat I’d push back on is the label “optimal” for P.1. The SDR relaxation is admitted to be non-tight, and the extraction in (34)-(36) projects the sensing covariance onto the PSD cone and discards the off-diagonal blocks. That means the P.1 curves in Figs. 5-7 are a lower bound on the localization CRB, not an achievable design. The paper states this in words but then plots the bound as “Optimal design (P.1)” and uses it to headline the CRB-SINR trade-off. The markers show extracted solutions at a handful of SINR points, and the text notes degradation at low SINR, but there is no bound on the gap. So the central claim that P.1 achieves the optimal trade-off is not established. This is fixable: P.2 and P.3 are achievable, and P.1 can be repositioned as a benchmark or as insight into what cross-node correlation buys you.\n\nThe other soft spot is the genie-aided target knowledge. The CRB objective depends on the true target angles and TOFs through the steering vectors and Jacobian. The paper doesn’t state where these come from. In practice you would use estimates from a prior stage; that is standard in CRB-based design, but it should be said.\n\nMinor: perfect inter-node interference cancellation assumes shared waveforms and CSI. Standard in this literature but worth flagging.\n\nWho it’s for: people working on network-level ISAC, CRB-based waveform design, or CoMP. The framework is useful, and the main issue is a presentation/claim problem rather than a broken method. Send it to review; a good referee can get the authors to clarify the status of P.1 and add a note on the gap.","headline":"Per-subcarrier TOF-aware signaling for noncoherent D-ISAC is genuinely new, but the 'optimal' design is an SDR lower bound with an unquantified gap, so the headline trade-off is overstated.","tokens_in":26956,"tokens_out":2818,"would_cite":true,"duration_ms":26933,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["94A12","94A13","90C22"],"pacs":[],"model":"deepseek-v4-flash","headline":"Noncoherent distributed ISAC can be designed to minimize target-localization CRB while meeting per-user SINR constraints, using three SDR-based signaling schemes.","keywords":["distributed integrated sensing and communication","noncoherent coordinated multipoint","Cramér-Rao bound","MIMO radar","OFDM signaling","semidefinite relaxation","target localization","TOF/AOA hybrid localization"],"falsifier":"Run the P.1 design for a known two-node geometry and target, then evaluate maximum-likelihood localization RMSE when the assumed target position used to build the FIM is offset by half a beamwidth; if the mismatched-design RMSE is not worse than a simple equal-power waveform at the same SINR, the claim that CRB minimization transfers to actual localization error fails. A hardware testbed with GPS-disciplined clocks and unsynchronized phases could similarly check whether the predicted CRB-versus-SINR curves are reproduced.","tokens_in":26015,"feed_emoji":"📡","tokens_out":8396,"duration_ms":73844,"temperature":0.7,"pith_summary":"This paper tries to establish that a network of radio nodes can perform radar-style target localization and multi-user downlink communication at the same time without phase-level synchronization between nodes. The proposed framework uses OFDM transmit signals whose per-subcarrier covariance matrices are optimized, by semidefinite relaxation, to minimize the Cramér-Rao bound on target location error while guaranteeing a minimum SINR for every user on every subcarrier. The key enabling fact is that the Fisher information matrix for localization is linear in those covariance matrices, which turns a nonconvex waveform problem into a convex one. Three design variants are offered—optimal, orthogonal (subcarrier-interleaved across nodes), and beamforming-only—and the paper argues they trace different CRB-versus-SINR trade-offs with different computational costs. If these claims hold, coordinated sensing in cellular networks becomes practical without the strict phase alignment that coherent distributed MIMO would require.","feed_headline":"Noncoherent cell coordination can localize targets without phase sync","feed_subtitle":"SDR minimizes the localization error bound while holding per-user SINR; three designs span a complexity spectrum.","key_machinery":"Central object: the augmented per-subcarrier transmit covariance $\\tilde{R}_l = \\mathbb{E}[\\tilde{x}_l \\tilde{x}_l^H] \\in \\mathbb{C}^{M_t N \\times M_t N}$, which stacks all ISAC nodes' signals for subcarrier $l$. Theorem 1 shows the target-localization FIM is linear in $\\tilde{R}_l^T$, via Lemma 1's face-splitting product identity that rewrites products of steering and waveform matrices as functions of per-subcarrier covariances; this converts the nonconvex QCQP (23) into an SDR. The orthogonal design uses subcarrier interleaving, $x_{n,l} = 0$ unless $n = l \\pmod{N}$, which zeroes all off-diagonal blocks of $\\tilde{R}_l$ and cuts the variable count from $O(M_t^2 N^2 L + M_t^2 N U L)$ to $O(M_t^2 (L + U L))$. The beamforming design replaces per-subcarrier sensing covariances with one averaged covariance $\\bar{R}_{\\bar{n}\\bar{n}}$, which makes the sensing FIM depend only on AOA and reduces complexity by a further factor of $L/N$.","core_discovery":"The paper's central claim is that noncoherent D-ISAC transmit signal design can be formulated as a convex problem: minimize $\\mathrm{tr}([F(\\boldsymbol{\\Theta})]^{-1})$ subject to per-antenna power constraints and per-user SINR constraints (problem (23)). The enabling identity, stated as Theorem 1, is that the Fisher information matrix for target localization is a linear function of the augmented per-subcarrier transmit covariance matrices $\\tilde{R}_l = \\mathbb{E}[\\tilde{x}_l \\tilde{x}_l^H]$, where $\\tilde{x}_l$ stacks all nodes' signals on subcarrier $l$. Because the FIM enters the objective through a Schur complement, this linearity makes the CRB minimization a semidefinite program (P.1). Theorem 2 adds that under the orthogonal subcarrier-interleaving model of (37), the relaxed problem's solution is already optimal for the original orthogonal design, so rank-one extraction is exact. The paper presents numerical evidence that the three designs form a performance-complexity spectrum: P.1 has the lowest localization CRB, P.2 approaches it at wide bandwidth, and P.3—which optimizes only angle-of-arrival estimation—is the cheapest but cannot exploit time-of-flight information.","pith_inferences":["Editorial inference: because the CRB is built from true target angles and delays, the design as stated is genie-aided; a practical deployment would need a two-stage approach that first acquires coarse target positions and then applies the proposed optimization, or a robust variant minimizing worst-case CRB over an uncertainty set.","Editorial inference: the same linear-FIM structure should extend to estimation of velocity or Doppler states if the OFDM signal model is augmented with a Doppler steering vector, and the subcarrier-interleaving trade-off would then also affect Doppler resolution.","Editorial inference: since the orthogonal design's gap to optimal shrinks with bandwidth, the paper implicitly predicts an adaptive mode-switching strategy—use P.1 in narrowband or AOA-dominated regimes and P.2 in wideband regimes.","Editorial inference: the complexity comparison suggests a resource-aware scheduler: P.3 for large numbers of subcarriers, P.2 for moderate sizes, and P.1 for small networks, with the crossover points measurable from the reported execution-time scaling."],"forward_implications":["A D-ISAC system can be designed with only time-frequency synchronization, avoiding per-node phase alignment, which is the main practical obstacle to coherent distributed ISAC.","The CRB-versus-SINR frontier for a given node geometry is computable as a semidefinite program, so an operator can choose an operating point on the trade-off curve.","Orthogonal subcarrier allocation across nodes is near-optimal in wideband regimes where TOF information dominates localization accuracy, and its SDR relaxation is provably tight.","Per-subcarrier sensing waveform optimization is necessary for full localization gain; a beamforming-only design captures only AOA gains and loses TOF-based accuracy.","Under the orthogonal design, optimal solutions of the relaxed SDP transfer to feasible transmit signals without rank-one approximation loss (Theorem 2)."],"supporting_citations":[{"why":"Supplies the distributed MIMO radar FIM/CRB framework and the TOF localization gain on which the sensing metric in Section III-B is built.","marker":"[31]"},{"why":"Gives the tractable noncoherent joint-transmission SINR model used to write the communication constraint (32f).","marker":"[44]"},{"why":"Provides the single-node ISAC SDR and rank-one extraction whose proof Theorem 2 extends to the orthogonal D-ISAC design.","marker":"[41]"},{"why":"Shows CRB-based SDR beamforming for joint radar-communication, the method P.1 generalizes to per-subcarrier D-ISAC.","marker":"[40]"},{"why":"Supplies the face-splitting product identity used in Lemma 1 to linearize products of steering and waveform matrices.","marker":"[45]"},{"why":"Provides the interior-point SDP complexity formula (48) used for the complexity comparison of P.1, P.2, and P.3.","marker":"[49]"},{"why":"Gives the target localization geometry gain that explains the node-geometry dependence and the cooperative gain observed in Section V.","marker":"[42]"},{"why":"Provides the nearest-positive-semidefinite projection used to extract a feasible radar covariance from the relaxed P.1 solution.","marker":"[47]"}],"fun_headline_variants":["Noncoherent ISAC: convex design shrinks localization error","Joint comms and sensing without sync: a convex solution","Optimal D-ISAC signals via convex CRB minimization","Distributed sensing, no sync: convex signal design","Noncoherent D-ISAC: trade-offs in a convex frame"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The design must know the targets' positions (or at least their angles and delays) to compute the CRB it minimizes, and the paper does not explain where that knowledge comes from; with wrong target knowledge the optimized waveform may not improve, and could degrade, actual localization.","fun_headline_variants_meta":{"raw":{"variants":["Noncoherent ISAC: convex design shrinks localization error","Joint comms and sensing without sync: a convex solution","Optimal D-ISAC signals via convex CRB minimization","Distributed sensing, no sync: convex signal design","Noncoherent D-ISAC: trade-offs in a convex frame"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0006,"raw_usage":{"total_tokens":2887,"prompt_tokens":1112,"completion_tokens":1775,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":728,"completion_tokens_details":{"reasoning_tokens":1690}},"tokens_in":728,"tokens_out":1775,"duration_ms":13638,"temperature":1.0,"reasoning_tokens":1690,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T00:07:06.537327+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the P.1 design for a known two-node geometry and target, then evaluate maximum-likelihood localization RMSE when the assumed target position used to build the FIM is offset by half a beamwidth; if the mismatched-design RMSE is not worse than a simple equal-power waveform at the same SINR, the claim that CRB minimization transfers to actual localization error fails. A hardware testbed with GPS-disciplined clocks and unsynchronized phases could similarly check whether the predicted CRB-versus-SINR curves are reproduced.","supporting_citations":[{"cited_title":"Target localization accuracy gain in MIMO radar-based systems,","cited_arxiv_id":null,"evidence_quote":"Supplies the distributed MIMO radar FIM/CRB framework and the TOF localization gain on which the sensing metric in Section III-B is built."},{"cited_title":"A tractable model for noncoherent joint-transmission base station cooperation,","cited_arxiv_id":null,"evidence_quote":"Gives the tractable noncoherent joint-transmission SINR model used to write the communication constraint (32f)."},{"cited_title":"Cramér-Rao bound optimization for joint radar-communication beamforming,","cited_arxiv_id":null,"evidence_quote":"Shows CRB-based SDR beamforming for joint radar-communication, the method P.1 generalizes to per-subcarrier D-ISAC."},{"cited_title":"A family of face products of matrices and its properties,","cited_arxiv_id":null,"evidence_quote":"Supplies the face-splitting product identity used in Lemma 1 to linearize products of steering and waveform matrices."},{"cited_title":"A faster interior point method for semidefinite programming,","cited_arxiv_id":null,"evidence_quote":"Provides the interior-point SDP complexity formula (48) used for the complexity comparison of P.1, P.2, and P.3."},{"cited_title":"Target localization geometry gain in distributed mimo radar,","cited_arxiv_id":null,"evidence_quote":"Gives the target localization geometry gain that explains the node-geometry dependence and the cooperative gain observed in Section V."},{"cited_title":"Computing a nearest symmetric positive semidefinite matrix,","cited_arxiv_id":null,"evidence_quote":"Provides the nearest-positive-semidefinite projection used to extract a feasible radar covariance from the relaxed P.1 solution."}],"review_version":1}