{"id":"607d6f8d-f4fe-4d64-a92f-5735851a7c09","arxiv_id":"2505.01125","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Closed-form expressions quantify how insufficient cyclic prefix raises sidelobes and degrades range-Doppler maps in OFDM-ISAC, revealing a noise-amplification versus inter-target-interference trade-off between reciprocal and matched filtering.","lead":"This paper analyzes how a cyclic prefix shorter than the maximum target round-trip delay degrades radar sensing in OFDM-ISAC systems, deriving closed-form expressions for the range-Doppler map's second-order statistics under matched and reciprocal filtering. It shows a trade-off: reciprocal filtering suppresses inter-target interference but amplifies noise, while matched filtering does the opposite.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (20) omits the summed ITI contributions of other targets, so it is not the second-order moment of the full MF RDM in multi-target scenes.","rationale":"The reader's verdict of CONDITIONAL is appropriate, but the most load-bearing issue is not exactly the one stated. The reader focused on the unproven exponential distribution of off-peak MF samples used in the PSLR formulas. In this setup, that assumption is actually well supported: off-peak χ_MF is a sum of MN independent, zero-mean, bounded symbol-energy terms with complex phases, so for N=256 and M=128 the CLT yields an approximately proper complex-Gaussian distribution, and hence approximately exponential power. The larger problem is an internal inconsistency in the central second-order moment claim. Equation (20) is labeled as the second-order moment of the MF RDM, but it contains only the contribution of one target. Since the RDM is a sum over Q targets, the off-peak mean must include (µ4−1) times the sum of all target powers, and the target-bin mean must include the ITI from all other targets. The later PSLR/ISLR derivations in Eqs. (25)-(26) do use the summed version, which is why the numerical validation appears to support the final formulas. Nevertheless, the standalone Eq. (20) is incorrect as a description of the full RDM, and a reader relying on it would obtain wrong PSLR predictions in multi-target scenarios. This is a correctness issue in the stated central result, though it is readily fixable and does not invalidate the PSLR/ISLR conclusions if the summed expressions are adopted. The minor typo in Eq. (16a) noted by the reader is real but secondary. Overall, the paper needs a corrected Eq. (20) and a brief justification of the CLT-based exponential approximation for MF samples; with those changes the central claims are likely sound.","tokens_in":10308,"tokens_out":12135,"duration_ms":130499,"concrete_test":"Run a two-target simulation with equal |α|, 1024-QAM, N=256, M=128, and a normal CP, with 5000 realizations. Compute the sample mean of |χ_MF|² at an off-peak range-Doppler bin and at one target bin. Compare these values with Eq. (20) and with the summed expressions above. If the summed expressions match the simulation while Eq. (20) is off by roughly a factor of two at the off-peak bin for two equal-strength targets, then Eq. (20) requires correction even if Eqs. (25)-(26) remain valid.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Eq. (20) is presented as the second-order moment of the MF RDM, but it is written as if only one target contributes: the off-peak mean is (µ4−1)|α_q|² and the target-bin mean is (MN+µ4−1)|α_q|²+σ²_IN. From Eq. (12b), χ_MF is a sum over Q targets plus noise, and Eq. (18d) shows that each T_MF_q contributes (µ4−1)|α_q'|² away from its own bin. Hence the correct total moments are (MN+µ4−1)|α_q|² + (µ4−1)Σ_{q'≠q}|α_q'|² + σ²_IN at (lq,νq), and (µ4−1)Σ_{q'}|α_q'|² + σ²_IN off-peak. The paper's PSLR/ISLR formulas in Eqs. (25)-(26) silently use this summed version, so they are internally consistent with the simulations, but Eq. (20) as printed is not the moment of the RDM in a multi-target scene. The exponential-PSLR step flagged by the reader is less problematic: for the large M,N used here, off-peak χ_MF is a sum of many independent symbol-energy terms with zero-mean phases, so the CLT gives an approximately complex-Gaussian (hence exponential-power) sample. The concrete defect is the missing ITI sum in Eq. (20).","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript analyzes OFDM-ISAC sensing when target round-trip delays exceed the cyclic prefix (CP) duration, so that inter-symbol interference (ISI) and inter-carrier interference (ICI) contaminate the received echo. Assuming the interference-plus-noise (IN) term is circularly symmetric complex Gaussian (CSCG) with variances taken from prior work, the authors derive closed-form expressions for the second-order moments of the range-Doppler map (RDM) under both matched filtering (MF) and reciprocal filtering (RF). They then convert these moments into peak sidelobe level ratio (PSLR) and integrated sidelobe level ratio (ISLR) formulas, leading to the conclusion that RF suppresses inter-target interference but amplifies noise (via a constellation-dependent factor xi_s) while MF has a lower noise floor but suffers from symbol-induced leakage. The theoretical predictions are validated by Monte Carlo simulations with 5000 realizations for 1024-QAM.","tokens_in":10628,"tokens_out":7750,"duration_ms":75681,"significance":"If the technical issues raised below are resolved, this is a useful contribution to OFDM-ISAC sensing. It extends the ISI/ICI modeling of prior work on reciprocal filtering to a unified treatment of both RF and MF, and it offers closed-form PSLR/ISLR expressions that quantify the CP-length/constellation trade-off. The paper provides reproducible simulation validation for the main formulas and explicitly identifies a design trade-off (noise amplification in RF versus inter-target interference in MF). However, the central moment derivation contains an inconsistency in Eq. (20) and the PSLR step relies on an unproven distributional assumption for MF; these need to be fixed before the claims of exact closed-form characterization are fully supported.","major_comments":[{"comment":"","section":"Sec. III-A, Eq. (20)"},{"comment":"","section":"Sec. III-B, Eqs. (22)-(25)"},{"comment":"","section":"Sec. III-A, Eq. (16a)"}],"minor_comments":[{"comment":"","section":"Sec. III-A, Eq. (14)"},{"comment":"","section":"Sec. III-B, Eq. (22)"},{"comment":"","section":"Sec. II and Sec. III"},{"comment":"","section":"Abstract and Conclusion"},{"comment":"","section":"Sec. II-B, Eq. (10)"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable extension of the prior ISI/ICI analysis to RDM moments and PSLR/ISLR for both RF and MF. The main technical issue is the inconsistency in Eq. (20), which as printed does not describe the full-RDM moment in multi-target scenarios; although the final PSLR/ISLR formulas appear to use the correct summed expressions, the central derivation needs to be corrected. In addition, the exponential-sample assumption for the MF PSLR should be justified or explicitly flagged as approximate. These points are fixable within the manuscript's scope, so major revision is appropriate rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: a competent incremental theory paper that puts the insufficient-CP ISI/ICI floor into closed-form PSLR/ISLR formulas for both matched and reciprocal filtering. It is not a breakthrough, and Eq. (20) has a genuine multi-target omission that should have been caught.\n\nWhat is new: the paper takes the existing Gaussian approximation for CP-induced interference from [8], [9], extends the second-order moment calculation for random OFDM symbols from RF to MF, and turns those moments into PSLR/ISLR formulas. That combination is new and practically useful for 6G sensing design. The simulation support is honest: 5000 realizations, realistic NR parameters, and the curves match the formulas. The qualitative conclusion—RF suppresses inter-target interference but amplifies noise, MF keeps the noise floor but leaks symbol energy—is correct and worth having stated cleanly.\n\nSoft spots. First, Eq. (20) as printed is not the second-order moment of the MF range-Doppler map in a multi-target scene. From (12b) there is a sum over Q targets, and each target contributes (μ4−1)|α~_q'|² away from its own bin. The correct off-peak mean is (μ4−1)Σ_{q'}|α~_q'|² + σ_IN², and the target-bin mean includes the same sum, not just the q-th target term. The later PSLR/ISLR formulas in (25)–(26) use the summed version, so they are internally consistent with the simulations; the issue is that Eq. (20) is written as if only one target exists. Fixable, but wrong as published. Second, the conversion of second-order moments into PSLR assumes the off-peak MF samples are exponentially distributed. That is not proven in the text. For the large M and N used here the CLT argument is plausible, and the simulations bear it out, so I would call it a minor caveat rather than a flaw. There is also a typo in Eq. (16a) where reciprocal symbol expectations are misprinted; the final RF result is correct.\n\nThe citation pattern is fine. The ISI/ICI variance is taken from independent work, no parameter fitting, no circularity. The novelty claim is appropriately limited.\n\nThis paper is for readers working on CP-aware OFDM-ISAC analysis or 6G sensing waveform design. It deserves a serious referee: the central moment derivation is useful and likely correct, but the manuscript needs the Eq. (20) correction and a clearer flag on the exponential assumption. I would accept with revisions, not desk-reject.","headline":"Useful incremental theory paper that quantifies insufficient-CP ISI/ICI in OFDM-ISAC, but Eq. (20) is wrong as printed for multi-target scenes and needs a fix before publication.","tokens_in":11120,"tokens_out":3901,"would_cite":true,"duration_ms":37639,"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":"This paper derives closed-form formulas for how a cyclic prefix shorter than target delays raises the sidelobe floor of OFDM range-Doppler maps under both matched and reciprocal filtering.","keywords":["OFDM-ISAC","cyclic prefix","sensing performance","peak sidelobe level ratio","integrated sidelobe level ratio","matched filtering","reciprocal filtering","inter-carrier interference"],"falsifier":"Run a noiseless matched-filter simulation with two QAM targets beyond the CP and many random symbol draws, then compare the empirical mean of the largest off-peak bin to $H_{MN-Q}\\big((\\mu_4-1)\\sum|\\tilde\\alpha_q|^2\\big)$; if the ratio deviates from $H_{MN-Q}$ as $MN$ or $\\mu_4$ changes, the exponential assumption behind Eq. (26) is false.","tokens_in":10104,"feed_emoji":"📡","tokens_out":6247,"duration_ms":60620,"temperature":0.7,"pith_summary":"This paper asks what happens to an OFDM integrated sensing and communication system when the cyclic prefix is too short to cover target delays, and it answers with explicit statistical formulas. The authors derive closed-form expressions for the average power of every cell in the range-Doppler map under two standard filters: matched filtering and reciprocal filtering. From these, they obtain peak-sidelobe and integrated-sidelobe ratios that depend on CP length, constellation shape, and the number and strength of targets. If the formulas are right, engineers can predict when a too-short CP will hide weak targets and can choose between reciprocal filtering's noise amplification and matched filtering's inter-target leakage. The paper also shows that with constant-modulus modulation the two filters are equivalent, while with QAM their sensing performance diverges in a quantified way.","feed_headline":"Short cyclic prefix hurts OFDM sensing—here's the exact math","feed_subtitle":"Closed-form sidelobe formulas let engineers compare matched vs reciprocal filtering when targets arrive beyond the CP.","key_machinery":"The load-bearing object is the second-order moment of the range-Doppler map, $E\\{|\\chi(l,\\nu)|^2\\}$, computed separately for reciprocal filtering (dividing by the transmitted symbol before correlating) and matched filtering (multiplying by its conjugate). The argument is carried by decomposing each echo into a useful term, ISI, ICI, and noise, treating the interference as circularly symmetric complex Gaussian with variances $P_{\\mathrm{ISI}}=\\sum \\rho_q|\\alpha_q|^2$ and $P_{\\mathrm{ICI}}=\\sum \\rho_q(1-\\rho_q)|\\alpha_q|^2$, and then tracking how the random data symbols $s_{n,m}$ survive the filter: RF leaves a constellation-dependent factor $\\xi_s=E\\{1/|s_{n,m}|^2\\}$, while MF leaves a leakage floor proportional to $\\mu_4-1$. The PSLR step then invokes order statistics: for $MN-Q$ independent exponential off-peak bins, the expected maximum is the harmonic number $H_{MN-Q}$ times the per-bin mean.","core_discovery":"The central result is Eq. (20): after CP removal and FFT, the mean power of a matched-filter range-Doppler bin is $(\\mu_4-1)|\\tilde\\alpha_q|^2+\\sigma_{\\mathrm{IN}}^2$ away from a target and $(MN+\\mu_4-1)|\\tilde\\alpha_q|^2+\\sigma_{\\mathrm{IN}}^2$ at the target bin, where $\\mu_4=E\\{|s_{n,m}|^4\\}$ is the constellation fourth moment, $\\tilde\\alpha_q$ is the target amplitude attenuated by $(1-\\rho_q)$ when its delay exceeds the CP, and $\\sigma_{\\mathrm{IN}}^2$ is the summed ISI, ICI, and noise power. For reciprocal filtering, the corresponding values are $\\xi_s\\sigma_{\\mathrm{IN}}^2$ off-peak and $MN|\\tilde\\alpha_q|^2+\\xi_s\\sigma_{\\mathrm{IN}}^2$ at the peak, with $\\xi_s=E\\{1/|s_{n,m}|^2\\}$ amplifying the interference-plus-noise. Using an exponential approximation for off-peak bins, these lead to the PSLR formulas in Eqs. (24) and (26). The paper's claim is that these expressions capture, for the first time, how an insufficient CP raises sidelobes and how RF and MF trade noise amplification against inter-target interference.","pith_inferences":["If the exponential off-peak assumption fails for matched filtering, the PSLR formula in Eq. (26) will misstate the true peak sidelobe; a high-SNR simulation measuring the distribution of off-peak bins would show whether the discrepancy grows with $\\mu_4$.","The same moment-based accounting could be rerun for windowed range-Doppler processing or for other multicarrier waveforms, since the paper's decomposition into useful signal, ISI, ICI, and leakage terms is generic.","The matched-filter sidelobe floor $(\\mu_4-1)\\sum|\\tilde\\alpha_q|^2$ suggests a testable design rule: constellations with lower fourth moment should produce cleaner matched-filter range-Doppler maps even when the cyclic prefix is short.","Because reciprocal filtering amplifies noise by $\\xi_s$, the formulas imply that high-order QAM pays a sensing penalty under RF that grows with the reciprocal-power moment; ISAC systems may need to budget for this penalty when choosing constellations for communication."],"forward_implications":["When the modulation is constant-envelope, such as PSK, both $\\xi_s$ and $\\mu_4$ equal one, so RF and MF produce identical PSLR and ISLR and the filter choice makes no sensing difference.","With QAM, RF is the better filter at short range or high echo SNR because it removes inter-target leakage, while MF is better at long range or low SNR because it does not amplify the noise floor; the crossover is computable from the derived formulas.","An insufficient CP does two quantifiable things: it shrinks the effective target amplitude by $1-\\rho_q$ and injects ISI/ICI power $\\rho_q|\\alpha_q|^2+\\rho_q(1-\\rho_q)|\\alpha_q|^2$, so PSLR and ISLR rise sharply once the target range exceeds the CP-limited unambiguous range.","The framework extends earlier interference-power analyses, which were limited to reciprocal filtering, to matched filtering in multi-target scenarios.","For a fixed CP length and modulation order, the formulas give a closed-form prediction of the range beyond which sensing performance crosses a required PSLR, which is useful for system dimensioning."],"supporting_citations":[{"why":"Supplies the PSLR/ISLR assessment framework and the filter comparison that this paper extends to the insufficient-CP regime.","marker":"[3]"},{"why":"Gives the circularly symmetric complex Gaussian approximation and the closed-form ISI/ICI power expressions used as the interference model.","marker":"[8]"},{"why":"Analyzes how CP length limits sensing range and provides the ISI/ICI variance results that the multi-target model builds on.","marker":"[9]"},{"why":"Provides the order-statistics background used to convert per-bin means into the expected peak sidelobe level.","marker":"[12]"},{"why":"Supplies the harmonic-number expectation of the maximum of exponential variables used in Eqs. (22) and (25).","marker":"[13]"}],"fun_headline_variants":["Short CP degrades OFDM sensing range—exact formula now available","First closed-form sidelobe expressions for CP-limited OFDM-ISAC","CP too short? These equations reveal the sensing cost","Matched vs reciprocal filtering: new trade-off formula for CP","Insufficient CP: exact sidelobe levels in OFDM-ISAC sensing"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The PSLR formulas treat all off-peak range-Doppler bins as independent, exponentially distributed samples with the computed mean; if real sidelobes are correlated or heavier-tailed, the harmonic-number peak formula is only an approximation.","fun_headline_variants_meta":{"raw":{"variants":["Short CP degrades OFDM sensing range—exact formula now available","First closed-form sidelobe expressions for CP-limited OFDM-ISAC","CP too short? These equations reveal the sensing cost","Matched vs reciprocal filtering: new trade-off formula for CP","Insufficient CP: exact sidelobe levels in OFDM-ISAC sensing"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000275,"raw_usage":{"total_tokens":1713,"prompt_tokens":1083,"completion_tokens":630,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":699,"completion_tokens_details":{"reasoning_tokens":538}},"tokens_in":699,"tokens_out":630,"duration_ms":6660,"temperature":1.0,"reasoning_tokens":538,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:27:18.373821+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a noiseless matched-filter simulation with two QAM targets beyond the CP and many random symbol draws, then compare the empirical mean of the largest off-peak bin to $H_{MN-Q}\\big((\\mu_4-1)\\sum|\\tilde\\alpha_q|^2\\big)$; if the ratio deviates from $H_{MN-Q}$ as $MN$ or $\\mu_4$ changes, the exponential assumption behind Eq. (26) is false.","supporting_citations":[{"cited_title":"Comparison of ZF and MF filters through PSLR and ISLR assessment in automo tive OFDM radar,","cited_arxiv_id":null,"evidence_quote":"Supplies the PSLR/ISLR assessment framework and the filter comparison that this paper extends to the insufficient-CP regime."},{"cited_title":"Coherent compensat ion-based sensing for long-range targets in integrated sensing and co mmunication system,","cited_arxiv_id":null,"evidence_quote":"Gives the circularly symmetric complex Gaussian approximation and the closed-form ISI/ICI power expressions used as the interference model."}],"review_version":1}