{"id":"ea6f45c8-43a4-49ab-8fb8-0d29f8be7700","arxiv_id":"2506.07019","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Passive target detection with unknown communication signals in multi-static ISAC is feasible, and transmit beamforming that accounts for both target and direct paths substantially improves detection probability.","lead":"This paper studies how a cellular base station can detect a target using its own communication signals that the sensing receivers have never seen before. It derives a detection rule, analyzes how well it works in the large-sample limit, and designs transmit beamforming that balances detection and communication quality.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Proposition 2's DOF ν=2MC is not valid for C>M: the unitary gauge makes the FIM singular and the null lies on a rank boundary; the paper only simulates C≤M, so the error is concealed.","rationale":"The reader's weakest_assumption was perfect decoupling of surveillance and reference channels after receive beamforming. That is a legitimate modeling idealization explicitly acknowledged as an upper bound in Section II-B, so it does not by itself invalidate the mathematical claim within the stated model. The DOF issue, by contrast, is an internal inconsistency: under the paper's own Gaussian model, the parametrization is non-identifiable (unitary gauge), and for C>M the null Ht=0 sits on a rank boundary. The central claim that the asymptotic detection probability is controlled by the non-centrality parameter through a single χ² distribution with DOF 2MC therefore fails for a range of system parameters the paper does not exclude. This is more load-bearing than the coupling idealization because it affects the analytical core even in the idealized model. The fix is straightforward: state the condition C≤M for Proposition 2, or derive the correct rank-based DOF and boundary mixture. With that revision, the paper's simulation-verified results for C≤M remain intact, so a conditional accept is appropriate rather than a rejection.","tokens_in":18759,"tokens_out":27431,"duration_ms":312561,"concrete_test":"Run the GLRT statistic (15) under H0 for M=1, C=2, L=1000, with Gaussian S, Hd=[1,0], σ²=1, and 10^4 Monte Carlo trials. Compare the empirical 0.95 quantile of 2Λ with the χ²_{2MC}=χ²_4 quantile claimed by the paper and with the χ²_2 quantile suggested by rank(Hd)=1. If the empirical quantile does not match χ²_4, Proposition 2's DOF is refuted. Additionally, compute the numerical rank of J_{ξdξd} at H0 from Appendix B to confirm that the inverse used in Eq. (22) is undefined.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Proposition 2 (Eqs. 21-23) asserts ν=2MC for all C,M, but the model is invariant under H→HU, S→U^H S for any unitary U, so the Fisher information J(ξ) is singular along gauge directions. The proof in Appendix B uses J_{ξdξd}^{-1} in Eq. (22) without gauge fixing or a generalized inverse. More seriously, when C>M, Hd is M×C of rank M, so the null Ht=0 lies on the boundary of the rank-C covariance model: the first-order effect of Ht on the covariance enters only through Ht Hd^H (rank M), giving a smaller tangent dimension, and the Wilks limit is not a single χ²_{2MC}. The correct DOF in that regime is at most 2M·rank(Hd)=2M², or a boundary mixture. The paper's simulations only use C≤M (e.g., C=2,M=4), so the overcount is never exposed. Because the threshold setting (24) and the detection-probability formula (25) depend on ν, the analytical claims are not valid as stated for C>M configurations.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies passive target detection in a multi-static ISAC downlink, where a base station transmits Gaussian (and later OFDM) data symbols to C single-antenna users and M two-channel sensing receivers jointly detect a target using random, unknown communication signals. The paper derives a GLRT detector in Proposition 1, then uses Wilks-type asymptotics in Proposition 2 to claim that the test statistic is asymptotically half a central chi-square with 2MC degrees of freedom under H0 and half a noncentral chi-square with noncentrality parameter kappa in Eq. (23) under H1. Closed-form insight is given for the single-CU case (Eq. (26)) and for the high-direct-path-SNR case (Proposition 3). Based on this analysis, two joint transmit beamforming designs are proposed: a max-Pd design using quadratic transform, SDR, and alternating optimization, and a lower-complexity heuristic that maximizes target energy subject to a direct-path SNR threshold. Numerical simulations with Gaussian and OFDM signals validate the asymptotic approximations in the tested regimes and show performance gains over the benchmarks.","tokens_in":18973,"tokens_out":31216,"duration_ms":319314,"significance":"If the asymptotic model is valid, the paper offers a genuinely useful, analytically tractable treatment of passive detection with unknown multi-user communication signals, together with a concrete performance metric kappa that can be optimized. The single-CU formula (26), the eigen-decomposition in Proposition 3, the two beamforming algorithms, and the OFDM validation are positive strengths. The central qualitative conclusion that target-path SNR dominates while direct-path SNR acts as a constraint is well supported in the C <= M regime. However, as detailed below, a load-bearing generality claim about the degrees of freedom is not correct for C > M, so the contribution as stated is overstated until that scope is fixed.","major_comments":[{"comment":"The asserted DOF nu = 2MC is not valid for C > M. The likelihood in Eq. (13) depends on Ht and Hd only through the covariance Ry, which is a function of HH^H with H = [Ht; Hd]; the model is invariant under (Ht, Hd) -> (Ht U, Hd U) for any unitary U. Consequently, the Fisher information J(xi) in Eqs. (19)-(20) is singular along gauge directions when C exceeds the rank of Hd. At Ht = 0, the first-order effect of Ht enters only through Ht Hd^H, so the tangent dimension of the alternative relative to the null is 2M * rank(Hd) real; for full-rank Hd this is 2M^2, not 2MC, when C > M. The proof in Appendix B uses J_{xid xid}^{-1} in Eq. (22) without verifying invertibility, and the Wilks limit is therefore not a single chi-square with 2MC degrees of freedom in this regime. The threshold (24) and detection probability (25) inherit the error. All simulations in Section V use C < M (C = 2, M = 4; Figs. 5 and 8 use C <= 3, M = 4; the OFDM setup has C = 1, M = 2), so the overcount is never exposed. The paper should either restrict all statements to C <= M with rank(Hd) = C, or re-derive the correct boundary distribution for C > M.","section":"Section III-A, Proposition 2 and Appendix B (Eqs. (21)-(23), (24)-(25))"},{"comment":"Proposition 3 states that when the minimum eigenvalue sigma_bar_C of Hd^H Hd / sigma_r^2 is large, the noncentrality parameter satisfies kappa approx 2L M SNR_t. For C > M, however, the C x C matrix Hd^H Hd has rank at most M, so its minimum eigenvalue is exactly zero; the condition sigma_bar_C >> 1 is never satisfied in that regime. Thus the claimed approach to the active-detection upper bound via increasing direct-path SNR holds only when C <= M (and Hd has full column rank). This is the same overcounting as in Proposition 2 and should be corrected in the same revision, ideally by explicitly stating the rank condition or by deriving the C > M counterpart of Eq. (29).","section":"Section III-B, Proposition 3 (Eqs. (29), (66))"}],"minor_comments":[{"comment":"The denominator in the second inequality appears to be 1 + M SNR_t; it should be 1 + M SNR_d to be consistent with the preceding inequality sigma_bar_1/(1+sigma_bar_1) <= M SNR_d/(1+M SNR_d) and with the single-CU formula (26).","section":"Eq. (68)"},{"comment":"The statistic Lambda_a defined in Eq. (62) is gamma(MC, 1) under H0; it is 2*Lambda_a that follows a central chi-square distribution with 2MC degrees of freedom. The stated noncentrality parameter kappa_act likewise applies to 2*Lambda_a. Since the thresholds in Fig. 4 are Monte-Carlo calibrated, the numerical conclusions are unaffected, but the distributional statement should be corrected.","section":"Appendix C (Eq. (62))"},{"comment":"The assumption that receive beamforming perfectly separates the target echo from the direct path is not explicitly acknowledged as an idealization. Residual direct-path leakage or correlated noise between the surveillance and reference arrays would introduce cross terms in the covariance (12) and would invalidate the exact GLRT formula (15). The paper flags the clutter-free assumption as an upper bound; a similar caveat for the direct-path separation would be helpful.","section":"Section II-B, Eq. (8)"},{"comment":"The monotonicity proof (38) is written as if a beamforming matrix W exists at every iteration, but the SDR subproblem (P1.2) returns covariance matrices R_n that are not guaranteed to be rank-one, and the Gaussian randomization step is only applied after the loop. Please state explicitly that the convergence guarantee applies to the SDR-relaxed problem, and that the final rank-1 extraction is a heuristic post-processing step. Also specify the number of Gaussian randomizations used in the simulations.","section":"Algorithm 1 and Eq. (38)"}],"recommendation":"major_revision","confidential_remarks":"The DOF issue is central: Proposition 2 and Proposition 3 are stated for all C and M, but they are only valid (as written) for C <= M with full-rank Hd. The simulations never exercise C > M, so the error is concealed. If the authors restrict the scope to C <= M, correct the distributional statements, and add the appropriate caveats, the paper's analytical and numerical results in that regime appear sound and would be a useful contribution. I do not see a need for rejection if the scope is fixed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a genuinely useful paper for the C≤M regime, and that's where all its experiments live. The problem is Proposition 2 states ν=2MC for all C and M, and that is not true when C>M. The paper only runs C≤M simulations (C=2, M=4; C=1,2,3 with M=4), so the overcount is never exposed.\n\nWhat's actually new and good: it's the first treatment of passive detection in multi-static MIMO ISAC with unknown Gaussian data signals and arbitrary multi-user streams. The GLRT in (15) is a careful extension of passive radar machinery from [13] and [22], and the closed-form noncentrality parameter κ in (23) is a useful result—it correctly shows that target-path SNR dominates and direct-path SNR constrains. The single-CU reduction (26) is correct, and the beamforming designs are reasonable; the max-Pd algorithm is monotone and the simulations back it up. The paper is mostly careful about geometry and finite-sample checks.\n\nThe load-bearing soft spot is the DOF. For C≤M, the model H→HU, S→U^H S has a unitary gauge, but a gauge-fixed reparameterization gives codimension 2MC, so the chi-square holds. For C>M, H_d is M×C of rank at most M, the null H_t=0 sits on the boundary of the rank-C covariance model, and the effective number of parameters is smaller. For M<C≤2M the codimension is 4MC−C²−M², and for C≥2M it saturates at 3M², not 2MC. So the threshold-setting formula (24) and detection probability (25) are not valid as stated. This is fixable by restricting the claims to C≤M or by doing the proper boundary analysis.\n\nThe other soft spots are milder. The perfect decoupling of surveillance and reference channels is an idealization—residual direct-path leakage would break the exact GLRT; the paper calls the model clutter-free and an upper bound, but doesn't discuss leakage. The Wilks regularity conditions are cited rather than verified, and no code is released. Those are minor-to-moderate.\n\nWho it's for: ISAC and passive radar researchers. The core result is useful and likely correct for C≤M, which is the common case. It deserves a serious referee; I'd send it to review and ask the authors to address the C>M DOF and make the regime restriction explicit.","headline":"Useful passive-detection analysis for multi-static ISAC, but the claimed asymptotic DOF ν=2MC is invalid for C>M, and the paper never simulates that regime.","tokens_in":19500,"tokens_out":11722,"would_cite":true,"duration_ms":126271,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In multi-static ISAC systems, passive detection with random unknown communication signals is feasible and analytically tractable: the paper derives a GLRT detector whose asymptotic detection probability is controlled by a closed-form…","keywords":["integrated sensing and communication","passive radar detection","generalized likelihood ratio test","multi-static ISAC","joint beamforming design","random unknown communication signals","asymptotic detection probability","non-centrality parameter"],"falsifier":"In a testbed with a two-channel sensing receiver, deliberately inject a controlled amount of direct-path leakage into the surveillance array (or a controlled mutual coupling between the two arrays), then compare the empirical distribution of the GLRT statistic under the target-present hypothesis with the predicted $\\frac{1}{2}\\chi'^2(2MC,\\kappa)$ using $\\kappa$ from Eq. (23); a systematic deviation that grows with the leakage level would falsify the perfect-decoupling premise on which the analysis rests.","tokens_in":18550,"feed_emoji":"📡","tokens_out":16878,"duration_ms":135457,"temperature":0.7,"pith_summary":"This paper asks whether a set of sensing receivers can detect a target using ordinary downlink communication data that the receivers never see in advance, and it answers with a quantitative yes. The authors derive a generalized likelihood ratio test for the two-channel passive radar setup and prove that, for long data blocks, its detection probability is a monotone function of a single non-centrality parameter built from the target-path and direct-path signal-to-noise ratios. The formula shows a clear hierarchy: target-path SNR dominates the achievable detection performance, while direct-path SNR acts as a gate that must be strong enough for the unknown-signal reference to be usable. On this basis the paper formulates and solves two transmit beamforming problems that jointly serve communication users and improve detection probability, and validates the analysis with simulations including OFDM signals. The payoff would be ISAC networks that sense passively without dedicating pilot or sensing waveforms.","feed_headline":"The odds of passive ISAC target detection now fit a formula","feed_subtitle":"Target-path SNR dominates, a fact the authors exploit in two beamforming designs that meet per-user SINR targets.","key_machinery":"The central object carrying the argument is the non-centrality parameter $\\kappa$ of the asymptotic GLRT statistic. It condenses the whole passive-detection geometry into one scalar that is monotonically equivalent to the detection probability: $\\kappa = \\frac{2L}{\\sigma_r^2} \\mathrm{tr}\\left[ \\tilde{H}_t^\\mathrm{H} \\tilde{H}_d^\\mathrm{H} (\\sigma_r^2 I_M + \\tilde{H}_d \\tilde{H}_d^\\mathrm{H})^{-1} \\tilde{H}_d \\tilde{H}_t^\\mathrm{H} \\right]$. The argument chain uses a two-channel reception model with isolated surveillance and reference arrays, the spectral-decomposition-based MLE of the covariance to form the GLRT, Wilk's theorem for the asymptotic chi-square and non-central chi-square distributions, a Woodbury expansion that separates the target-path energies $\\{\\delta_n\\}$ from the direct-path spectral factors $\\{\\bar{\\sigma}_n/(1+\\bar{\\sigma}_n)\\}$, and a quadratic-transform/SDR reformulation that turns $\\kappa$-maximization into an alternating convex optimization. The same $\\kappa$ serves as the objective for the beamforming problems, which is why the two designs target either $\\kappa$ directly or its two ingredients.","core_discovery":"The paper's central claim is that in a multi-static ISAC system with one multi-antenna base station, $M$ two-channel sensing receivers, and $C$ single-antenna users, passive detection using random unknown Gaussian communication signals is feasible and its asymptotic performance admits a closed form. The GLRT statistic $\\Lambda(Y)$ from Proposition 1, built from the sample covariances of the aggregated surveillance and reference channels, converges in distribution to $\\frac{1}{2}\\chi^2(2MC)$ under the null hypothesis and to $\\frac{1}{2}\\chi'^2(2MC, \\kappa)$ under the alternative, where the non-centrality parameter is $\\kappa = \\frac{2L}{\\sigma_r^2} \\mathrm{tr}\\left[ \\tilde{H}_t^\\mathrm{H} \\tilde{H}_d^\\mathrm{H} (\\sigma_r^2 I_M + \\tilde{H}_d \\tilde{H}_d^\\mathrm{H})^{-1} \\tilde{H}_d \\tilde{H}_t^\\mathrm{H} \\right]$. For a single user this reduces to $\\kappa = 2LM^2 \\mathrm{SNR}_t \\mathrm{SNR}_d / (1 + M \\mathrm{SNR}_d)$, showing that detection probability rises monotonically with both SNRs but is dominated by the target-path SNR; the direct-path SNR enters as a saturating factor, so that when it is large the passive detector approaches the active-detection upper bound $\\kappa_{\\mathrm{act}} = 2LM \\mathrm{SNR}_t$. In the multi-user case $\\kappa$ decomposes as $\\frac{2L}{\\sigma_r^2} \\sum_{n=1}^{C} \\frac{\\bar{\\sigma}_n}{1+\\bar{\\sigma}_n} \\delta_n$, with $\\bar{\\sigma}_n$ the eigenvalues of the direct-path Gram matrix and $\\delta_n$ the target energy along the corresponding eigenvectors, and approaches the upper bound when the smallest $\\bar{\\sigma}_n$ is large. These formulas motivate two beamforming designs: one maximizes the asymptotic detection probability under per-user SINR and total power constraints via an alternating quadratic transform and semidefinite relaxation, and the other maximizes target energy subject to a direct-path SNR threshold, with lower complexity.","pith_inferences":["Since $\\kappa$ saturates in the direct-path SNR, a practical operating rule suggested by the analysis is to set the direct-path SNR threshold in design P2 just above the knee of the saturation region; beyond that, extra direct-path energy is wasted, and the remaining gains must come from target-path SNR.","The OFDM 16-QAM simulation suggests the asymptotic distribution may be robust beyond Gaussian symbols; one testable extension is to derive the characteristic function of the GLRT statistic for finite-alphabet signals and check whether $\\kappa$ remains the correct non-centrality parameter.","The dependence of $\\kappa$ on the direct-path eigenvectors implies that the identity of the served users matters: choosing which $C$ user streams are used for sensing could be a future scheduling lever that the paper does not optimize.","If the perfect-decoupling assumption fails in practice, the covariance in Eq. (12) would acquire off-diagonal blocks; a natural extension is to add a residual-leakage matrix and study how much direct-path suppression is needed for the derived formulas to remain within an acceptable error margin."],"forward_implications":["In the single-user case, detection probability depends only on the number of SRs $M$, the block length $L$, and the two SNRs, so a network operator can predict and guarantee passive detection performance without knowing the transmitted symbols.","When the smallest eigenvalue of the direct-path Gram matrix is much larger than 1, passive detection approaches the active-detection upper bound $\\kappa \\approx 2LM\\,\\mathrm{SNR}_t$, meaning the random communication signal becomes an essentially perfect reference.","Increasing the number of SRs $M$ improves detection probability and narrows the gap to active detection, while increasing the number of users $C$ widens that gap for both proposed designs.","The 'max $\\tilde{P}_d$' beamforming design outperforms the heuristic SNR-threshold design and all benchmarks in the simulated regimes, and the asymptotic approximation becomes accurate as $L$ grows and the direct-path SNR is high."],"supporting_citations":[{"why":"It supplies the passive detection formulation for correlated subspace signals in two MIMO channels that the paper extends to a multi-static ISAC system with collaborative beamforming.","marker":"[13]"},{"why":"It provides the two-channel passive radar receiver architecture (surveillance and reference arrays) that each sensing receiver in this paper adopts.","marker":"[15]"},{"why":"It introduces the delay-Doppler operator and the passive MIMO radar detection model on which the signal aggregation in Eqs. (6)-(9) is based.","marker":"[22]"},{"why":"It provides the general theory of the GLRT asymptotic distributions used in Proposition 2 to derive the chi-square and non-central chi-square limits.","marker":"[28]"},{"why":"It supplies the spectral-decomposition theorem used to compute the maximum likelihood estimates of the covariance matrices under both hypotheses in Proposition 1.","marker":"[30]"},{"why":"It provides the MIMO radar detector design and its non-central chi-square performance that the paper uses as the active-detection upper bound.","marker":"[31]"}],"fun_headline_variants":["Passive ISAC detection odds, now a closed-form formula","Target SNR drives passive ISAC detection performance","GLRT analysis sets passive ISAC detection odds","Closed-form odds for passive ISAC detection","Beamforming optimizes passive ISAC detection"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire detection model depends on the assumption that, after receive beamforming, the two arrays at each sensing receiver are perfectly decoupled: the target echo appears only in the surveillance array, the direct-path signal only in the reference array, and the noises in the two arrays are statistically independent.","fun_headline_variants_meta":{"raw":{"variants":["Passive ISAC detection odds, now a closed-form formula","Target SNR drives passive ISAC detection performance","GLRT analysis sets passive ISAC detection odds","Closed-form odds for passive ISAC detection","Beamforming optimizes passive ISAC detection"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001856,"raw_usage":{"total_tokens":7451,"prompt_tokens":1270,"completion_tokens":6181,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":886,"completion_tokens_details":{"reasoning_tokens":6109}},"tokens_in":886,"tokens_out":6181,"duration_ms":37623,"temperature":1.0,"reasoning_tokens":6109,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:44:26.652639+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"In a testbed with a two-channel sensing receiver, deliberately inject a controlled amount of direct-path leakage into the surveillance array (or a controlled mutual coupling between the two arrays), then compare the empirical distribution of the GLRT statistic under the target-present hypothesis with the predicted $\\frac{1}{2}\\chi'^2(2MC,\\kappa)$ using $\\kappa$ from Eq. (23); a systematic deviation that grows with the leakage level would falsify the perfect-decoupling premise on which the analysis rests.","supporting_citations":[{"cited_title":"Passive detection of correlated subspace signals in two MIMO channels,","cited_arxiv_id":null,"evidence_quote":"It supplies the passive detection formulation for correlated subspace signals in two MIMO channels that the paper extends to a multi-static ISAC system with collaborative beamforming."},{"cited_title":"Detection in passive MIMO radar networks,","cited_arxiv_id":null,"evidence_quote":"It introduces the delay-Doppler operator and the passive MIMO radar detection model on which the signal aggregation in Eqs. (6)-(9) is based."},{"cited_title":"Englewood Cliffs, NJ, USA: Prentice-Hall, 1993, vol","cited_arxiv_id":null,"evidence_quote":"It provides the general theory of the GLRT asymptotic distributions used in Proposition 2 to derive the chi-square and non-central chi-square limits."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the spectral-decomposition theorem used to compute the maximum likelihood estimates of the covariance matrices under both hypotheses in Proposition 1."},{"cited_title":"Design principles of MIMO radar detectors,","cited_arxiv_id":null,"evidence_quote":"It provides the MIMO radar detector design and its non-central chi-square performance that the paper uses as the active-detection upper bound."}],"review_version":1}