{"id":"adfb1dc0-6b16-4e7f-9f0e-85b480e42022","arxiv_id":"2509.00727","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A multi-subcarrier positioning error bound and beamforming optimization are combined in an alternating transmit-receive (ping-pong) scheme to improve mmWave user positioning accuracy by at least 16% over non-optimized beams.","lead":"This paper proposes a ping-pong positioning method for millimeter-wave wireless systems, in which a base station and a user device take turns sending carefully shaped signals to find the user's location. It contributes a new multi-subcarrier error bound and a beam-shaping procedure, which the authors report improves positioning accuracy by at least 16% while using fewer time slots.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (63) in Appendix C defines the multi-subcarrier FIM as (1/Nc)ΣJ_n, not as the FIM of the concatenated signal; the resulting MSCPEB is Nc times the true CRLB, so the claimed lower bound and its numerical comparisons are not valid as stated.","rationale":"The reader correctly identifies eq. (63) as the load-bearing step. I focus on the exact consequence: the 1/Nc normalization means J is not the FIM of the concatenated observation; the true FIM is the sum. The resulting e(p) is Nc times the true CRLB, so it is not a guaranteed lower bound. This directly undermines the paper's theoretical contribution and all numerical values labeled MSCPEB. However, I do not fully endorse the reader's claim that the optimized beamformers fail to minimize the true bound: multiplying the objective by the constant Nc does not change the argmin of P1/P4/P5, so the algorithmic part and the simulated 16% RMSE improvement could remain valid. That is why my agreement is partial. The verdict remains conditional rather than reject: the error is local and, if corrected, the Lemma 2 inequality still holds in a stronger form, so the paper can be repaired. The concrete test above would settle whether the reported MSCPEB values are artefacts of the normalization. Other issues, such as eq. (22)(b)'s expectation being written with exponents on the probabilities, are secondary to this main concern.","tokens_in":25914,"tokens_out":11769,"duration_ms":144531,"concrete_test":"Using the Fig. 12 parameters (Nc≈2400, SNR=15 dB), compute the FIM of Y'_k[Nc] directly from the joint Gaussian log-likelihood (17)–(19), without imposing eq. (63): J_true = Σ_n J_n, and compare e_true = tr(J_true^{-1}) with the plotted MSCPEB. If e_true is a factor of Nc smaller and lies below the near-field PELB, then eq. (63)'s normalization is the source of the reported bound. As a secondary check, re-solve P4/P5 with e_true in place of e(p); since the scaling is constant, the optimal beamformers should be unchanged, confirming that the practical RMSE claims can be retained but the lower-bound claim must be amended.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Appendix C, eq. (63), states that the FIM of Y'_k[Nc] is J = (1/Nc)Σ_n J_n. For independent subcarrier observations the FIM is additive: J_true = Σ_n J_n. The factor 1/Nc makes the 'MSCPEB' e(p)=tr(J^{-1}) equal Nc·tr(J_true^{-1}), i.e., Nc times the actual CRLB. Such a quantity is not guaranteed to be a lower bound on the MSE of any unbiased estimator, and the proof of Lemma 2 in (65) is really an inequality for this inflated object, not for the CRLB of the concatenated signal. The text even says 'sum' before writing the average, so the formula is internally inconsistent. A constant rescaling of J does not change the argmin of P1, so the beamformer optimization may survive; but the bound values reported as 'MSCPEB' and the comparison in Fig. 12 are not CRLBs as claimed. If eq. (63) were corrected to J_true, the stated inequality would still hold — Jensen gives tr(J_true^{-1}) ≤ (1/Nc^2)Σ tr(J_n^{-1}), which is stronger than the claimed arithmetic-mean inequality — so the fix is local but must be made before the theoretical claims are accepted.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a PELB-driven ping-pong positioning framework for multi-user wideband mmWave MIMO-OFDM systems. The BS and UE alternately transmit/receive adaptive beamformed pilots, using locally evaluated position-error bounds to schedule beams. The theoretical centerpiece is a multi-subcarrier collaborative positioning error bound (MSCPEB), together with Lemma 2 claiming that the MSCPEB does not exceed the arithmetic mean of the per-subcarrier PELBs. An alternating-optimization algorithm with closed-form hybrid precoder/combiner updates is then developed, followed by an uninformed-to-informed channel and position estimator and a multipath collaborative positioning method. Simulations report at least 16% RMSE improvement over non-optimized baselines and about one-quarter slot-resource usage.","tokens_in":26297,"tokens_out":8878,"duration_ms":109960,"significance":"The general direction is timely and potentially useful: adaptively configuring beams according to a positioning-centric lower bound, exploiting frequency diversity, and avoiding the need for initial CSI are all worthwhile goals for mmWave positioning. The paper contains substantial algorithmic material, including a full signal model, a detailed optimization framework, complexity/convergence discussion, and extensive benchmarks. However, the theoretical foundation currently has several load-bearing errors that affect the definition and interpretation of the MSCPEB, the Gaussian likelihood, and the optimization relaxation. If these are repaired, the proposed framework could be a solid contribution; in its present form the central claims are not established.","major_comments":[{"comment":"The text before Eq. (63) says the multi-subcarrier FIM is the sum of the per-subcarrier FIMs, but the displayed formula is J = (1/Nc) Σ_n J_n. For independent subcarrier observations the FIM is additive: J_true = Σ_n J_n. With the displayed averaging, e(p) = tr(J^{-1}) equals Nc · tr(J_true^{-1}), i.e., the reported MSCPEB is Nc times the actual CRLB of the concatenated signal. This invalidates the numerical MSCPEB values and the comparison in Fig. 12. The constant scaling does not change the argmin in P1–P5, so the beamformer optimization may survive, but the bound interpretation must be corrected. If Eq. (63) is replaced by J_true, Jensen's inequality still gives tr(J_true^{-1}) ≤ (1/Nc^2)Σ tr(J_n^{-1}) ≤ (1/Nc)Σ tr(J_n^{-1}), so Lemma 2 remains true; the fix is local but essential.","section":"Appendix C, Eq. (63)"},{"comment":"The mean and covariance of the concatenated signal Y'_k[Nc] are not correctly specified. With C_k[n] ∈ C^{Ns×Ns} and ρ ∈ C^{1×Nc}, the expression C'_k[Nc] = diag(C_k[n] ⊗ ρ) is not a well-formed covariance for a stacked vector; independent subcarrier observations would give a block-diagonal covariance with blocks C_k[1], ..., C_k[Nc]. Similarly, µ'_k[Nc] = µ_k[n] ⊗ ρ^T assumes the per-subcarrier mean is independent of n, which is not true since H_k[n], F_BB[n], and s[n] vary with the subcarrier. These equations underpin the Gaussian PDF (17) and the FIM formula (25), so they must be re-derived before Lemma 1 and the subsequent FIM computation are valid.","section":"Section III, Eqs. (18)–(19)"},{"comment":"The expression E_{pr,k}{E_{H_k}{tr(J^{-1}(pr,k|H_k))}} is not a lower bound on the marginal MSE E[∥ˆp - p∥²] when pr,k and H_k are random. The CRLB is conditional on the true parameters; averaging the trace of the inverse FIM over a prior does not give the Bayesian CRLB (which involves E[J] plus prior information) and is not guaranteed to bound the averaged MSE. The MSCPEB should be defined as a conditional CRLB, or derived properly as a Bayesian bound, before it is claimed to be a lower bound on positioning error.","section":"Section III, Eq. (20)"},{"comment":"The auxiliary variable is introduced as Ω ∈ R^{3Nc×3Nc} with E a 3Nc×3Nc identity matrix, but the FIM for the user position pr,k ∈ R^3 is 3×3 after the transformation in Eq. (23). The Schur complement constraint [Ω, E; E, J(V[n])] ⪰ 0 is therefore dimensionally inconsistent as written. If E is meant to be a selection matrix embedding the 3×3 position FIM into a 3Nc×3Nc space, this must be stated explicitly; otherwise trace{Ω} rescales the objective by Nc and the relaxation is not equivalent to P1.","section":"Section IV, P3/P4, Eqs. (29)–(31)"},{"comment":"The step labeled (b) does not correctly marginalize the Bernoulli LoS indicator δ_k. The expression retains δ_k in the exponents pLoS(τc)^{δ_k} and (1−pLoS)^{1−δ_k}, so the right-hand side is still a random quantity, not the expectation E_{δ_k}. Marginalizing gives pLoS · tr(J^{-1}(·|tilde H_k)) + (1−pLoS) · tr(J^{-1}(·|H_0k)); the notation should be corrected. The mixture of '≈' and '=' in (a)–(b) also obscures whether this is an approximation or an identity.","section":"Section III, Eq. (22)"}],"minor_comments":[{"comment":"The phrase 'the sum of the FIM across all subcarriers' contradicts the displayed average; also 1_{Nc×NcNs} is called a 'vector' although it has two dimensions.","section":"Appendix C, Eq. (63) and notation"},{"comment":"In Eq. (10b), the product e^{-j2π fn/fc} · (e^{-j2π fn/fc})^H equals 1, so the 'array phase difference' cancels and ρ_n reduces to e^{-j2π fn τ}. Please clarify whether the intended ρ_n includes additional coupling or whether the simplification is intentional.","section":"Section II, Eq. (10)"},{"comment":"Typo: 'scretizing' should be 'discretizing'. Also in Eq. (42), the bracket notation [vec(ˆY'_1[n]), ..., vec(ˆY'_{ℓ_k}[n])] is confusing; the index should be over paths, not over ℓ_k itself.","section":"Section V-A"},{"comment":"The convergence argument is heuristic: it states that the SDP subproblems ensure monotonicity, but no formal proof is given that each subproblem is solved globally or that the objective is bounded away from −∞. The statement 'constrained by system parameters and SNR' is not a proof. This should be tightened, or the claim softened.","section":"Section VI-C"},{"comment":"Several caption/reference inconsistencies: Fig. 2 lists 'Rank-1 EFIM [42]' and later 'Rank-1 EFIM [39]' in different panels; Fig. 11(a) labels both vehicle traces as 'Vehicle 1'; reference numbering for [42]–[44] is inconsistent in the text. Please proofread.","section":"Figs. 2, 11 and references"}],"recommendation":"major_revision","confidential_remarks":"The paper's central theoretical contribution—the MSCPEB and Lemma 2—is currently built on an incorrect FIM scaling in Eq. (63) and on dimensionally inconsistent mean/covariance and Schur-complement formulas. The fixes appear local in spirit (the correct additive FIM still satisfies Lemma 2), but the authors must re-derive the likelihood, the FIM, and the SDP relaxation coherently, and rerun any plots that report absolute MSCPEB values. I do not see this as a reject because the overall framework and optimization machinery are potentially sound and the errors are identifiable and fixable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the ping-pong uninformed-to-informed framework is genuinely new, and the multipath collaborative position estimator is clever. The paper deserves a serious referee, but the MSCPEB derivation has a real error that must be fixed before the theoretical claims can stand.\n\nWhat is actually new: bidirectional beam training where BS and UE alternate PELB-driven beams; the multi-subcarrier collaborative bound as a design criterion; and the line/polyline-based multipath least-squares positioning that avoids explicit path resolution. The AO/SDR approach is standard but competently executed. Simulations are self-consistent and show the expected gains (16-36%, quarter slot usage) for large arrays.\n\nThe soft spots are in the theory. Appendix C, eq. (63), says the multi-subcarrier FIM is \"the sum\" and then writes J = (1/Nc)ΣJn. For independent subcarriers the FIM is additive; the 1/Nc makes the \"MSCPEB\" Nc times the true CRLB. The proof of Lemma 2 then proves an inequality for that inflated object. The good news: since the scaling is constant, the argmin of the beamformer optimization is unchanged, and if the formula is corrected to J = ΣJn, Jensen still gives the claimed inequality (in fact stronger). So the fix is local, but the bound values reported in Fig. 12 and the absolute comparisons are not valid CRLBs as written.\n\nAlso, eq. (22)(b) leaves the Bernoulli indicator δk inside the expectation, which is not the expectation; it should be pLoS times the LoS bound plus (1-pLoS) times the NLoS bound. And eq. (23) has dimension problems with the all-ones matrix in the Kronecker product. These should be cleaned up. The subcarrier correlation factor in eq. (10) simplifies to e^{-j2πfnτ}; as written it adds no new information, though that doesn't break the framework.\n\nOne more thing: no code or data are provided, and the simulation section omits some setup details (number of runs, exact channel generation, Lk values). That limits reproducibility but is not fatal.\n\nBottom line: this is a plausible and useful method paper, not a breakthrough. The core algorithm may survive the fixes. Send it to review, but require the FIM scaling and expectation errors to be corrected and the absolute bound comparisons to be redone. I would not cite it in its current form.","headline":"A useful ping-pong beamforming idea with a definite but local FIM-scaling error in the MSCPEB derivation; worth serious review after a major revision.","tokens_in":26788,"tokens_out":6205,"would_cite":false,"duration_ms":71347,"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":"The paper presents a ping-pong positioning framework for wideband mmWave MIMO-OFDM systems, claiming that a multi-subcarrier error lower bound can be minimized through alternating hybrid beamforming to improve positioning accuracy by at lea","keywords":["mmWave positioning","Cramér-Rao lower bound","hybrid beamforming","ping-pong positioning","multi-subcarrier","wideband MIMO-OFDM","multipath positioning","closed-form beamforming"],"falsifier":"Compute the exact Fisher information matrix for a simple two-subcarrier, single-path system by differentiating the joint log-likelihood of the concatenated received signal with respect to position, and compare it with the paper's J = (1/Nc) Σ J_n. If the matrices differ beyond a constant factor, Lemma 2 and the beamformer design would need revision. An experimental alternative: run a maximum-likelihood position estimator at high SNR in a wideband multi-subcarrier system and check whether its RMSE approaches the MSCPEB, or whether a different bound—for example, the sum of per-subcarrier FIMs—is","tokens_in":25821,"feed_emoji":"📍","tokens_out":5553,"duration_ms":56871,"temperature":0.7,"pith_summary":"The paper tries to show that positioning accuracy in wideband millimeter-wave MIMO-OFDM systems can be improved by treating the signal configuration—not just the estimation algorithm—as a resource to be optimized. It introduces the multi-subcarrier collaborative positioning error lower bound (MSCPEB), a CRLB-type bound derived from all subcarriers jointly, and proves it is no larger than the average of the per-subcarrier bounds. On this foundation, it designs an alternating-optimization procedure that minimizes the MSCPEB through hybrid beamforming at both the base station and the user, plus a multipath collaborative positioning step that weights paths by reliability. The reported outcome is a positioning method that is more accurate and uses far fewer pilot symbols than conventional schemes, without needing prior channel state information or position knowledge.","feed_headline":"Ping-pong beams cut mmWave positioning error by 16 percent","feed_subtitle":"A multi-subcarrier lower bound guides BS and UE to refine positions alternately, using only a quarter of the slot resources.","key_machinery":"The key object is the multi-subcarrier collaborative positioning error lower bound (MSCPEB), a Cramér-Rao-type bound computed from the Fisher information matrix of the received signals concatenated across all OFDM subcarriers. The MSCPEB is built from a subcarrier correlation factor vector that captures frequency-dependent phase responses, allowing a unified expression for the mean and covariance of the concatenated signal and decoupling the beamformers per subcarrier. The optimization machinery is an alternating optimization algorithm that uses semidefinite relaxation, Schur complements, and matrix decomposition to convexify the non-convex MSCPEB minimization and produce closed-form hybrid","core_discovery":"The central claim is that the positioning error lower bound for a multi-subcarrier wideband system can be collaboratively minimized across subcarriers, and that this bound is provably no greater than the arithmetic mean of the per-subcarrier PELBs. The paper derives this MSCPEB from the Fisher information of the concatenated received signals, then formulates and convexifies a hybrid beamforming design problem to minimize it. It further develops a multipath position estimation method that avoids explicit path resolution and triangulation, using weighted least squares with path-reliability weights. Simulations validate that the resulting ping-pong framework improves estimation accuracy by at l","pith_inferences":["The scalability of the MSCPEB approach suggests that similar collaborative bounds could be constructed across time, frequency, and space jointly, potentially unifying sensing and communication resource allocation—an extension the paper does not explore.","The proof of Lemma 2 relies on the FIM being the arithmetic mean across subcarriers; if the standard CRLB scaling (the sum, not the average) is used, the bound and the beamformer design would change by a factor equal to the number of subcarriers—a testable check for the theory.","The reported 16% improvement is for the smallest antenna array (Nt=8); for larger arrays the gains are 29–36%, so the true benefit may grow with array size, which could guide deployment choices.","The method's reliance on far-field array responses means it cannot capture near-field phase curvature; extending the bound to near-field models could unlock additional accuracy at short range."],"forward_implications":["If the MSCPEB bound is correct, beamformers scheduled to minimize it will yield positioning accuracy at the bound, so the derived closed-form beamformers provide a practical lower-cost alternative to brute-force optimization.","The ping-pong procedure implies that positioning and beam tracking can bootstrap from uninformed to informed estimates without requiring CSI or position priors, simplifying deployment in dynamic urban environments.","The use of only about four OFDM symbols (a quarter of a 5G slot) suggests that high-accuracy positioning can be achieved with low pilot overhead, freeing resources for communication.","The multipath collaborative positioning method, by avoiding explicit path resolution and triangulation, may offer robustness in dense multipath and NLoS conditions."],"supporting_citations":[{"why":"Provides the single-subcarrier far-field PELB used as a baseline in Fig. 12 to show that MSCPEB is lower.","marker":"[26]"},{"why":"Provides the single-subcarrier near-field PELB used in Fig. 12, showing that MSCPEB approaches near-field accuracy.","marker":"[44]"},{"why":"Supplies the semidefinite relaxation and Schur complement tools used to convexify the MSCPEB minimization problem.","marker":"[29]"},{"why":"Supplies the matrix decomposition method used to recover hybrid precoders/combiners from the SDP solution.","marker":"[30]"},{"why":"Supplies the alternating minimization framework and unitary-matrix decomposition for hybrid precoding that the AO algorithm adapts.","marker":"[31]"},{"why":"Provides the Rank-1 EFIM baseline that the proposed method is compared against in the simulations.","marker":"[39]"},{"why":"Defines the 3GPP positioning accuracy requirements that the reported CDF results are checked against.","marker":"[45]"}],"fun_headline_variants":["Ping-pong beamforming cuts mmWave positioning error 16% with quarter slots","Ping-pong beamforming: 16% better mmWave positioning, 1/4 resources","Quarter-slot ping-pong beams improve mmWave positioning by 16%","Multiuser ping-pong beamforming: 16% lower mmWave positioning error"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The load-bearing premise is that the Fisher information matrix of the concatenated multi-subcarrier signal is the arithmetic mean of the per-subcarrier Fisher information matrices; for independent subcarrier observations the standard FIM is the sum, so if this scaling is wrong the MSCPEB and the beamformers optimized against it would not correspond to the true positioning error bound.","fun_headline_variants_meta":{"raw":{"variants":["Ping-pong beamforming cuts mmWave positioning error 16% with quarter slots","Ping-pong beamforming: 16% better mmWave positioning, 1/4 resources","Quarter-slot ping-pong beams improve mmWave positioning by 16%","Multiuser ping-pong beamforming: 16% lower mmWave positioning error"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00121,"raw_usage":{"total_tokens":4843,"prompt_tokens":794,"completion_tokens":4049,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":538,"completion_tokens_details":{"reasoning_tokens":3966}},"tokens_in":538,"tokens_out":4049,"duration_ms":36095,"temperature":1.0,"reasoning_tokens":3966,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T13:18:00.247538+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the exact Fisher information matrix for a simple two-subcarrier, single-path system by differentiating the joint log-likelihood of the concatenated received signal with respect to position, and compare it with the paper's J = (1/Nc) Σ J_n. If the matrices differ beyond a constant factor, Lemma 2 and the beamformer design would need revision. An experimental alternative: run a maximum-likelihood position estimator at high SNR in a wideband multi-subcarrier system and check whether its RMSE approaches the MSCPEB, or whether a different bound—for example, the sum of per-subcarrier FIMs—is","supporting_citations":[{"cited_title":"Cram´ er-rao lower bound anal ysis of positioning with planar large intelligent surfaces under r ician channel,","cited_arxiv_id":null,"evidence_quote":"Provides the single-subcarrier far-field PELB used as a baseline in Fig. 12 to show that MSCPEB is lower."},{"cited_title":"Performance analysis of near -field sensing in wideband MIMO systems,","cited_arxiv_id":null,"evidence_quote":"Provides the single-subcarrier near-field PELB used in Fig. 12, showing that MSCPEB approaches near-field accuracy."},{"cited_title":"Boyd and L","cited_arxiv_id":null,"evidence_quote":"Supplies the semidefinite relaxation and Schur complement tools used to convexify the MSCPEB minimization problem."},{"cited_title":"Performance limits of single-anchor millime ter-wave positioning,","cited_arxiv_id":null,"evidence_quote":"Supplies the matrix decomposition method used to recover hybrid precoders/combiners from the SDP solution."},{"cited_title":"Alternat ing minimization algorithms for hybrid precoding in millimeter wave MIMO sys tems,","cited_arxiv_id":null,"evidence_quote":"Supplies the alternating minimization framework and unitary-matrix decomposition for hybrid precoding that the AO algorithm adapts."},{"cited_title":"Harness- ing NLOS components for position and orientation estimatio n in 5G millimeter wave MIMO,","cited_arxiv_id":null,"evidence_quote":"Provides the Rank-1 EFIM baseline that the proposed method is compared against in the simulations."},{"cited_title":"Study on NR positioning support (release 16),","cited_arxiv_id":null,"evidence_quote":"Defines the 3GPP positioning accuracy requirements that the reported CDF results are checked against."}],"review_version":1}