{"id":"c7273446-ee43-460f-af61-6f0c5a8da54e","arxiv_id":"2505.02160","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"The paper derives the inter-band cross-correlation interference in multi-user OFDMA ISAC ranging and shows that spreading with periodic discrete prolate spheroidal sequences reduces sidelobe energy when the interfering user is much stronger.","lead":"This paper analyzes how signals from different users leak into each other's ranging correlations in multi-user OFDM-based ISAC, and proposes a spreading technique that reduces this leakage at the cost of spectral efficiency. It provides closed-form expressions for the interference energy and shows that the spread waveform is more robust to strong out-of-band signals, which matters for 6G joint sensing and communication.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 1 cannot justify P-DPSS: square orthogonal spreading leaves EIB invariant, and the η<1 benefit is never tied to the DPSS eigenstructure.","rationale":"The reader's weakest assumption is the idealized received-signal model y_t = x_t^(1) + α x_t^(2) with no delay, noise, or multipath. That is a legitimate external-validity concern: real channels would alter the correlation leakage structure, and the paper does not analyze it. However, the more load-bearing issue is internal: even under the paper's own model, the theoretical chain from Theorem 1 to the P-DPSS construction has a gap. The theorem is stated for square orthonormal P, for which EIB is provably independent of P, so it cannot justify the proposed spreading. The actual benefit relies on rectangular P_η, and the paper neither extends the bound to that case nor proves that the chosen DPSS subspace minimizes the relevant Hadamard-product trace. Section IV-A's admission that the η-dependence of the auto-correlation term is unknown further weakens the claimed EISL improvement. This is not an attack on the simulations—they may be correct for the selected parameters—but the theoretical support for the central claim is incomplete. A focused numerical test comparing P-DPSS with random orthonormal spreading and guard-banded OFDM at the same η would settle whether the DPSS structure is essential. If the test supports the paper, the CONDITIONAL verdict stands; if not, the central claim would need substantial revision. I therefore recommend keeping CONDITIONAL, as the issues are addressable in revision, and I partially agree with the reader's channel-model concern while identifying the spreading-optimality gap as the more fundamental risk.","tokens_in":17731,"tokens_out":6551,"duration_ms":90494,"concrete_test":"For a fixed η=0.9, compute EIB from Eq. (17) and EISL for three choices of the rectangular spreading matrix: (i) P-DPSS eigenvectors, (ii) a randomly drawn orthonormal L×ηL matrix, and (iii) no spreading with only ηL active subcarriers (guard-banded OFDM). If the EIB/EISL curves do not separate as in Figs. 5 and 7, the DPSS selection is not responsible for the claimed reduction; if they do separate, the concern is resolved and the central claim gains support.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central mechanism is not established by the presented theory. At η=1, P is square orthonormal, so W^(i)W^(i)H = A^(i)P^(i)P^(i)H A^(i)H = A^(i)A^(i)H, which makes EIB in Eq. (17) independent of the spreading matrix. Thus Theorem 1's upper bound cannot support any square spreading; the claimed benefit appears only for rectangular P_η with η<1, i.e., after discarding a fraction of signaling dimensions. But Theorem 1 was proved for square P, and the paper does not re-derive the bound for rectangular P, nor prove that the leading P-DPSS eigenvectors of Bbar minimize the Hadamard-product trace in Eq. (17). Section IV-A explicitly concedes that 'how the auto-correlation energy changes with η is not known, and thus the overall impact of η on EISL is not fully known.' The simulations pick η=0.9 from Fig. 8 and compare against guard-banded OFDM, which changes the number of active subcarriers rather than introducing a spreading transform. Consequently, the claim that P-DPSS spreading itself suppresses inter-band leakage, as opposed to the spectral sacrifice of η<1, is not supported by the analysis.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a two-user OFDMA ISAC system in which user 1 performs ranging by aperiodic correlation between its transmitted OFDM signal and a received signal that is modeled as the user's own backscatter plus a scaled version of user 2's transmission. The authors derive closed-form expressions for the expected squared aperiodic autocorrelation function (Proposition 1), the expected integrated sidelobe energy EISL (Corollary 1), and an inter-band interference energy term EIB (Eq. 17). They propose an orthogonal spreading layer based on periodic discrete prolate spheroidal sequences (P-DPSS) with a spectral utilization back-off parameter η<1, and claim that this spreading minimizes EIB and keeps EISL nearly constant as the interferer strength α grows. Simulation results compare OFDM with and without spreading for varying α, M, L, and modulation order, and show the claimed robustness at η=0.9.","tokens_in":17914,"tokens_out":9060,"duration_ms":108305,"significance":"If the central design claim holds, the paper would provide a useful analytical characterization of inter-band correlation leakage in OFDMA-based ISAC and a concrete waveform modification that trades a small amount of spectral efficiency for sidelobe robustness. The derivations of Proposition 1 and Corollary 1 appear to be validated by the simulations, which sweep α, M, L, and modulation order, and the agreement between the theoretical A-ACF curves and simulated curves in Fig. 4 is a clear strength. However, the paper's main analytical claim about the optimality of the P-DPSS spreading is not established by the presented theorem, and the received-signal model is highly idealized. The empirical comparison at η=0.9 is suggestive but does not by itself separate the effect of the spreading transform from the effect of reducing the active signaling dimensions.","major_comments":[{"comment":"Theorem 1 cannot support the claim that P-DPSS spreading minimizes EIB. For square orthonormal P, W^(i)W^(i)H = D B^(i) U_L D P^(i)P^(i)H D^H U_L^H B^(i)H D^H = D B^(i) U_L D D^H U_L^H B^(i)H D^H, so EIB in Eq. (17) and the upper bound in Eq. (18) are independent of the spreading matrix. The proposed benefit appears only for rectangular P_η with η<1, but Theorem 1 is stated and proved for square P, and no analogous bound is derived for the truncated case. Moreover, no argument is given that the leading eigenvectors of \\bar B^(1) minimize the Hadamard-product trace in Eq. (17). Section IV-A explicitly concedes that \"how the auto-correlation energy changes with η is not known, and thus the overall impact of η on EISL is not fully known.\" The simulations may support an empirical claim at η=0.9, but the analytical claim that the proposed spreading itself minimizes IB energy is not established.","section":"Section IV, Theorem 1, Eqs. (17)-(21)"},{"comment":"The received signal model y_t = x_t^(1) + α x_t^(2) omits delay, multipath, frequency selectivity, and noise on the interference path. Equations (13)-(17) and the spreading design in Eqs. (20)-(21) are therefore tied to a single-tap, frequency-flat interferer with a single scalar amplitude α. For a frequency-selective or delayed interfering path, the leakage distribution over the rows of W changes, and the P-DPSS eigenvectors of the in-band Dirichlet kernel need not be the minimizer of EIB. This is a scope restriction that should be stated prominently, and the claimed robustness of spreading should be tested at least with a one-tap delayed interferer or a simple two-tap channel.","section":"Section III-A, Eq. (11)"},{"comment":"The fairness of the η=0.9 comparison is not fully established at the modeling level. For OFDM, η is implemented by zeroing edge subcarriers as guard bands, while for P-DPSS it is implemented by truncating the spreading basis to the most concentrated eigenvectors. However, the analytical W^(1) and W^(2) in Eqs. (8)-(9) are derived for all L (respectively N-L) subcarriers being active. It is not specified whether the theoretical curves for the OFDM η=0.9 case use modified W matrices that account for the guard bands or use the full-band formulas. This matters because Fig. 8 shows that reducing η alone degrades EISL at small α, so the reader cannot tell how much of the apparent improvement of P-DPSS is due to the spreading transform itself and how much is due to the different way the active dimensions are reduced.","section":"Section V, first paragraph and Figs. 4-8"}],"minor_comments":[{"comment":"The definitions of P_η^(1) and P_η^(2) contain an undefined variable k in the diagonal exponent (z^{kL(N-1)/(2N)} and z^{k(N-L)(N-1)/(2N)}). This should be corrected to a fixed notation consistent with Eq. (8).","section":"Eqs. (20)-(21)"},{"comment":"The statement \"the supported capacity is MtηLu\" is dimensionally incorrect: with modulation order M and ⌈ηL⌉ dimensions, the number of bits per OFDM symbol is ⌈ηL⌉ log2 M, not M⌈ηL⌉. This should be corrected since the paper uses η as a spectral-efficiency back-off.","section":"Section IV-A, Eq. (22)"},{"comment":"The abstract's claim that spreading results in ISL levels \"significantly lower\" than OFDM without spreading is an overstatement without the qualifiers that the advantage appears at sufficiently large α and sufficiently large M; at low α and small M, the simulations in Figs. 4-7 show OFDM without spreading is better. The abstract should state the condition under which the benefit holds.","section":"Abstract and Section V"},{"comment":"The caption contains an incomplete sentence: \"for example α = 15 dB, sie the amplitude difference ... is 20 dB.\" This should be rewritten.","section":"Fig. 4 caption"},{"comment":"The theorem statement begins with a stray \"E\" before \"For an in-band user signal spreading matrix...\" which should be removed.","section":"Theorem 1 statement"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope for eess.SP, and the analytical derivation of the leakage terms is a genuine contribution, but the central optimality claim for P-DPSS needs to be reworked or substantially reframed. I would encourage the authors to either prove a bound for the rectangular η<1 case, or explicitly present the P-DPSS scheme as an empirical design validated only at η=0.9, and to test the sensitivity of the conclusion to a delayed or frequency-selective interference path."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper's real contribution is the closed-form analysis of two-user OFDMA ISAC ranging. Proposition 1 gives the expected squared aperiodic autocorrelation for M OFDM symbols, and Corollary 1 gives the EISL with an explicit inter-band leakage term E_IB. Those derivations are careful, the frequency-domain zero-padding trick is legitimate, and the simulations track the theory across α, M, L, and modulation order. Anyone working on multi-user ISAC ranging will want these expressions.\n\nThe soft spot is the spreading part. The stress-test note is right: Theorem 1's upper bound is proved for square orthonormal P, and in that case P P^H = I, so E_IB is invariant to the spreading matrix. The paper then switches to rectangular P_η with η<1 without re-deriving the bound, and never proves that the leading P-DPSS eigenvectors of B̄ minimize the Hadamard-product trace in (17). Section IV-A honestly admits the effect of η on the autocorrelation energy is not known. What remains is an empirical observation that, at η=0.9, P-DPSS spreading helps in the simulated high-α regime, compared with an OFDM baseline that uses guard bands. That may be a useful design, but it is not supported by Theorem 1, and the abstract overstates the claim.\n\nAlso worth noting: the received-signal model y_t = x_t^(1) + α x_t^(2) ignores delay, multipath, and noise on the interfering path. Fine as a first cut, but it should be stated as a limitation in the abstract, and it means the EIB expression is an idealized bound on what a real channel would produce. No code or error bars is a minor issue for a theory paper; the theory-experiment agreement is the real evidence.\n\nNet: the analytical core is solid and the EISL expressions will be cited; the spreading design needs either a genuine proof for rectangular P_η or a more modest claim. This deserves a serious referee, and a revision should fill that gap.","headline":"Solid closed-form analysis of OFDMA ISAC inter-band leakage, but the P-DPSS spreading claim does not follow from Theorem 1 and needs either a real proof or a more modest abstract.","tokens_in":18536,"tokens_out":3227,"would_cite":true,"duration_ms":41120,"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 claims that in a two-user OFDMA ISAC system, inter-band aperiodic cross-correlation leakage dominates ranging sidelobes at high interference and is suppressible by a P-DPSS spreading layer.","keywords":["OFDMA ISAC","integrated sensing and communications","aperiodic correlation","inter-band cross-correlation interference","integrated sidelobe level","P-DPSS spreading","OFDM ranging","multi-user interference mitigation"],"falsifier":"In a two-user OFDMA ISAC experiment or simulation, pass user-2's signal through a multipath channel with two or more taps at different delays instead of a single scaled copy, then measure EISL versus alpha with and without P-DPSS spreading. If spreading no longer keeps EISL flat as alpha grows, or if the measured leakage energy no longer tracks Eq. (17), the paper's central claim is contradicted.","tokens_in":17484,"feed_emoji":"📡","tokens_out":7953,"duration_ms":96363,"temperature":0.7,"pith_summary":"Ranging in OFDMA ISAC assumes each user's correlation is clean because users occupy disjoint subcarriers, but that is only true for circular correlation within the cyclic prefix. For target delays beyond the CP, the receiver performs aperiodic correlation, and the zero-padding that makes this operation spectrum-friendly up-samples the bands so that disjoint subcarrier allocations leak into each other. The paper derives the inter-band leakage energy E_IB, shows it dominates integrated sidelobe energy when the interfering user is much stronger than the backscatter, and proves an upper bound on it, then constructs a P-DPSS spreading layer that minimizes that bound. The central claim is that spreading keeps EISL nearly flat with interference amplitude, at a price in spectral efficiency: another concrete instance of the sensing-versus-communication trade-off.","feed_headline":"Spreading tames cross-user leakage that inflates OFDM ranging sidelobes","feed_subtitle":"A spectral-shaping spreading layer keeps ISAC sidelobe energy flat even when the neighbor's signal is 20 dB stronger.","key_machinery":"The central objects are the inter-band cross-correlation energy $E_\\mathrm{IB}$ and the upper bound on it, together with P-DPSS spreading: the eigenvectors of the discrete Dirichlet kernel that concentrate signal energy within a user's assigned band. The zero-padding used to express aperiodic correlation as a $2N$-point frequency-domain product up-samples each user's spectrum by a factor of two, so frequency-disjoint bands acquire overlapping tails; $E_\\mathrm{IB}$ captures the resulting leakage, and Theorem 1 bounds it by the cross-band Frobenius norms of $W^{(1)}$, $W^{(2)}$. The P-DPSS eigenvectors are the global leakage-minimizing signaling directions for the Dirichlet kernel, and retaining only the most concentrated fraction $\\eta$ of them forms the orthogonal spreading layer. The spectral-utilization factor $\\eta$ is the dial that trades sidelobe suppression against communication capacity.","core_discovery":"In a two-user OFDMA ISAC setting, user-1's aperiodic correlation sidelobes split into in-band auto-correlation terms plus an inter-band leakage term $E_\\mathrm{IB}=\\alpha^2(2M-1)\\operatorname{tr}(W^{(1)}W^{(1)H}\\circ W^{(2)}W^{(2)H})$, where $W^{(1)}$, $W^{(2)}$ are the zero-padded, up-sampled basis/spreading matrices of the two users and $\\alpha$ is the amplitude of user-2's signal at user-1. As $\\alpha$ grows, this term dominates the integrated sidelobe energy, so the ranging sidelobes rise roughly quadratically with the interferer's amplitude. The paper proves an upper bound on $E_\\mathrm{IB}$ and shows that the bound is controlled by the Frobenius norms of the cross-band blocks of the spreading matrices. Choosing orthonormal spreading columns from the primary eigenvectors of the discrete Dirichlet kernels, i.e. periodic DPSS sequences, minimizes the leakage for a given spectral utilization. Simulations show that with both users spread, EISL remains nearly constant as $\\alpha$ grows to 20 dB and higher, whereas plain OFDM's EISL rises sharply.","pith_inferences":["The pairwise trace form of E_IB suggests that a K-user OFDMA extension would simply sum pairwise leakage terms, one per interfering user with its own alpha; the paper does not derive this, but the P-DPSS mechanism would likely carry over if each user spreads.","P-DPSS spreading acts effectively as a soft guard band: instead of blanking edge subcarriers, it shapes each user's energy into a spectrally concentrated subspace, so the same leakage reduction can be traded with a continuous parameter eta rather than an integer number of unused subcarriers.","Because the inter-band term vanishes in the M-to-infinity limit, long coherent frames already suppress the leakage; spreading therefore matters most for short frames or fast-moving targets where M cannot be made large.","A frequency-selective interference channel would weight the terms inside the trace by per-subcarrier gains, so a fixed P-DPSS basis may not be optimal under multipath; adapting the spreading subspace to the measured interference channel is a natural testable extension."],"forward_implications":["With both users spread, EISL stays nearly constant as the interferer amplitude rises to at least 20 dB, while plain OFDM's EISL climbs; the crossover benefit appears near 12 dB for L=16, 15 dB for L=32, and 19 dB for L=64 subcarriers.","Increasing the number of OFDM symbols M lowers sidelobes in both cases, and spreading outperforms plain OFDM at high interference for M > 1; at M=10 and alpha=20 dB the gap narrows to about 1 dB.","The interference suppression is not free: lowering the spectral utilization eta below 0.9 reduces E_IB but raises autocorrelation sidelobes, so eta near 0.9 is the practical sweet spot in the simulated settings.","Higher-order modulation such as 16QAM and 64QAM worsens EISL under plain OFDM but has almost no effect under P-DPSS spreading at high interference, making the spread waveform insensitive to modulation choice in strong-interference regimes."],"supporting_citations":[{"why":"Establishes OFDM as globally optimal for periodic-correlation ranging sidelobes under random signaling, the baseline that the multi-user aperiodic-leakage problem extends, and supplies the kurtosis-based symbol statistics used in the ACF derivation.","marker":"[16]"},{"why":"Provides the single-user ranging sidelobe and ISL trade-off framework that the paper generalizes to the multi-user OFDMA case.","marker":"[17]"},{"why":"Gives the correlation operator used in Eq. (2) for aperiodic ranging correlation.","marker":"[21]"},{"why":"Defines the Dirichlet kernel that forms the matrices B^(1), B^(2), whose eigen-structure determines where inter-band leakage concentrates.","marker":"[22]"},{"why":"Shows that the primary eigenvectors of the discretized Dirichlet kernel minimize leakage, the direct basis for the proposed P-DPSS spreading matrices.","marker":"[23]"},{"why":"Supplies the continuous-time leakage-minimization analogue that motivates using a truncated eigenvector subspace for the spreading layer.","marker":"[24]"}],"fun_headline_variants":["Spreading kills cross-user sidelobe leak in OFDM ISAC ranging","Orthogonal spreading flattens multi-user OFDM ranging sidelobes","Spread to stop cross-user sidelobe blow-up in ISAC","Spreading layer cuts inter-band interference in ISAC ranging","DPSS spreading tames multi-user OFDM sensing sidelobes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The interference path is modeled as a single delay-free, frequency-flat, noiseless scaled copy alpha times the other user's signal added to the sensing user's received signal; real multipath, delay, or frequency-selective interference would change the correlation-leakage structure and is not covered by the analysis.","fun_headline_variants_meta":{"raw":{"variants":["Spreading kills cross-user sidelobe leak in OFDM ISAC ranging","Orthogonal spreading flattens multi-user OFDM ranging sidelobes","Spread to stop cross-user sidelobe blow-up in ISAC","Spreading layer cuts inter-band interference in ISAC ranging","DPSS spreading tames multi-user OFDM sensing sidelobes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00019,"raw_usage":{"total_tokens":1424,"prompt_tokens":1115,"completion_tokens":309,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":731,"completion_tokens_details":{"reasoning_tokens":219}},"tokens_in":731,"tokens_out":309,"duration_ms":4159,"temperature":1.0,"reasoning_tokens":219,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T01:00:18.766007+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"In a two-user OFDMA ISAC experiment or simulation, pass user-2's signal through a multipath channel with two or more taps at different delays instead of a single scaled copy, then measure EISL versus alpha with and without P-DPSS spreading. If spreading no longer keeps EISL flat as alpha grows, or if the measured leakage energy no longer tracks Eq. (17), the paper's central claim is contradicted.","supporting_citations":[{"cited_title":"Conflict and trade-off of waveform uncertainty in joint com- munication and sensing systems,","cited_arxiv_id":null,"evidence_quote":"Provides the single-user ranging sidelobe and ISL trade-off framework that the paper generalizes to the multi-user OFDMA case."},{"cited_title":"Frequency multiplexing and waveform synthesis in joint com- munications and sensing,","cited_arxiv_id":null,"evidence_quote":"Gives the correlation operator used in Eq. (2) for aperiodic ranging correlation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Dirichlet kernel that forms the matrices B^(1), B^(2), whose eigen-structure determines where inter-band leakage concentrates."},{"cited_title":"On the periodic discrete prolate spheroidal sequences,","cited_arxiv_id":null,"evidence_quote":"Shows that the primary eigenvectors of the discretized Dirichlet kernel minimize leakage, the direct basis for the proposed P-DPSS spreading matrices."}],"review_version":1}