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REVIEW 2 major objections 4 minor 32 references

In multi-cell OFDM-ISAC, closed-form delay–Doppler SINR expressions turn constellation selection and per-subcarrier power allocation into tractable design.

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2026-08-01 07:28 UTC pith:S4OW3KYB

load-bearing objection Solid closed-form multi-cell ISAC SINR framework with a real caveat: the MF SINR is an offset-averaged quantity, not a true per-bin worst-case, so the derived power allocations optimize an average. the 2 major comments →

arxiv 2607.21418 v1 pith:S4OW3KYB submitted 2026-07-23 eess.SP

Constellation Selection and Power Allocation for Multi-Cell OFDM-ISAC: Managing Inter-Cell Interference and Sensing Sidelobes

Kaitao Meng , Kawon Han , Christos Masouros , Lajos Hanzo This is my paper
classification eess.SP
keywords OFDM-ISACintegrated sensing and communicationmulti-cell interferencedelay–Doppler SINRmatched filteringreciprocal filteringconstellation selectionpower allocation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tries to prove that the sensing performance of a multi-cell OFDM integrated-sensing-and-communication system can be captured by two closed-form delay–Doppler SINR expressions, one for matched filtering and one for reciprocal filtering. It shows that the two receivers see interference in opposite ways: matched filtering is driven by fourth-order constellation moments and power overlap between cells, while reciprocal filtering is driven by inverse-symbol-power moments and per-subcarrier power ratios. From these expressions, the authors derive two simple power-allocation laws — ramped water-filling for matched filtering and square-root compensation for reciprocal filtering — and a tractable mixed-integer convex formulation that selects a standard constellation and power level on every subcarrier subject to communication rate and reliability constraints. If correct, a network can manage inter-cell interference and sensing sidelobes using existing constellations and per-subcarrier power control, without bespoke waveform redesign. The paper also characterises when cells should share or orthogonalise spectrum and how beyond-CP delays merely redistribute, not add, interference energy.

Core claim

The central discovery: the delay–Doppler sensing SINR in multi-cell OFDM-ISAC has closed forms. Matched filtering (Eq. 22) is set by fourth-order constellation moments, inter-cell power-overlap terms, and noise; reciprocal filtering (Eq. 25) by inverse-symbol-power moments and interfering-to-sensing power ratios. Maximizing them gives opposite power laws — avoid interfered tones under MF, reinforce them under RF — and joint constellation/power selection becomes mixed-integer convex. A two-cell benchmark shows MF's sharing-versus-orthogonalization threshold; masked RF always prefers minimal overlap. Beyond-CP interference conserves energy, redistributing it via a Dirichlet-squared leakage ker

What carries the argument

The load-bearing object is the per-DD-bin SINR identity. It is built from the DD-domain cross-ambiguity kernel χ(ℓ,0)[k,p], evaluated with receive weight V_m[n] equal to the conjugate data symbol (matched filtering) or its reciprocal (reciprocal filtering). Constellation geometry enters only through two moments, µ4 = E|s|^4 and µ−2 = E|s|^−2. The derivation uses Parseval's theorem plus a maximum-entropy uniform-offset approximation that replaces the per-bin sidelobe level by an average over all non-peak bins, yielding Eq. (22) and Eq. (25); the beyond-CP extension is carried by the effective interference spectrum P_eff[n].

Load-bearing premise

The load-bearing premise is the maximum-entropy uniform-offset approximation of Appendix A (after Eq. 53): undesired monostatic target and clutter offsets are treated as equally likely, so one averaged sidelobe power represents the MF interference floor; the on-grid integer-delay model and the masked-RF footnote (which sets aside active-tone-pattern sidelobes) are related idealizations — if clutter concentrates at particular offset bins, the closed-form SINR and allocations a

What would settle it

Run the MF receiver of Section II in a scenario with exactly one strong stationary clutter point (zero Doppler, fixed delay) and one weak target at a different DD bin; compare the measured SINR at the weak-target bin to Eq. (22) using the true path powers. If the discrepancy grows as the clutter's offset distance varies while the averaged sidelobe power stays constant, the uniform-offset assumption is falsified. An even more direct check is to compute the per-bin sidelobe power E|χ_MF[k,p]|^2 from Eq. (49) and compare its peak over all non-peak bins to the average ρ̄_MF used in Eq. (22).

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A base station can jointly pick, per subcarrier, a standard constellation and a power level to lower the DD-domain interference floor; simulations show weak-target peaks become visible under both filters.
  • MF and RF need opposite power strategies: MF should reduce power on heavily interfered tones, RF should increase power there; both laws are closed-form and require only one-dimensional bisection or a square-root normalisation.
  • The threshold in the two-cell benchmark tells cells when full spectral overlap is better than orthogonalization for MF; masked RF, by contrast, always reduces overlap when inter-cell coupling exists.
  • Beyond-CP propagation delays do not create new interference energy; they redistribute it, so the derived MF/RF allocation laws survive by replacing the nominal inter-cell spectrum with the delay-distorted effective spectrum.
  • Communication rate and reliability constraints can be traded against sensing SINR in a computable way, giving an explicit sensing–communication tradeoff curve.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that, because the SINRs depend only on two constellation moments, other signal formats with known moments could plug into the same allocation framework without re-derivation.
  • The uniform-offset approximation makes Eq. (22) an average-SINR statement; a natural extension is to re-derive or numerically check the per-bin SINR under concentrated clutter, where the power allocations could differ.
  • The beyond-CP leakage kernel suggests a coordination idea the paper does not pursue: deliberately place interferer subcarriers so that leaked Dirichlet-squared sidelobes fall on sensing tones where the victim's weight is small.
  • Since MF and RF prefer opposite spectrum-sharing structures, a mixed-filter network might split shared and orthogonalized tones between RF and MF cells rather than applying one policy globally.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper develops a modulation- and receive-filter-aware framework for multi-cell OFDM-ISAC. It derives closed-form DD-domain sensing SINR expressions for matched filtering (MF) and reciprocal filtering (RF), showing that MF depends on fourth-order constellation moments and power-overlap inter-cell terms while RF depends on inverse-symbol-power moments and ratio-type interference. Based on these expressions, it proposes MF and RF power-allocation laws (ramped water-filling and square-root), formulates joint constellation-selection and power-allocation problems as mixed-integer convex programs, analyzes spectrum-overlap coordination in a symmetric two-BS benchmark, and extends the interference model to beyond-CP delays with an effective spectrum characterization. The analytical formulas are validated by Monte Carlo simulations in Fig. 3, and the optimized profiles are shown to lower the DD-interference floor and improve weak-target visibility.

Significance. If the results are accepted, the paper provides a useful analytical bridge between finite-alphabet modulation, receive filtering, and multi-cell interference management in OFDM-ISAC. The closed-form SINR expressions (22) and (25) are credible and supported by the appendices and simulation; the identification of opposing MF/RF power-allocation behaviors (interference avoidance vs. compensation) is a valuable design insight. The mixed-integer convex reformulations are a practical step toward standards-compliant constellation selection and per-subcarrier power control. The beyond-CP leakage analysis, including the delay-distorted effective spectrum and the conservation of total interference energy, is a useful extension. The paper is generally self-contained and transparent about its approximations, though the per-bin interpretation of the MF SINR and one spectrum-coordination result need qualification.

major comments (2)
  1. [Section III-A / Appendix A, Eqs. (22), (53)-(55)] Equation (22) is presented as the 'per-bin' MF SINR, but the proof in Appendix A replaces every undesired monostatic path's DD offset by the offset-averaged sidelobe power rho_bar_MF. After Eq. (53), the relative DD offsets are modeled as i.i.d. uniform over G\{(0,0)}, so Eq. (22) is the SINR averaged over the offset distribution, not the SINR of a specified DD bin. This is a modeling choice, but the abstract's 'each range-Doppler bin' and Prop. 1's 'per-bin SINR' overstate what is proven. In a scene with strong stationary clutter near zero Doppler, or clutter sharing the target's bin, the true per-bin interference floor can be far above rho_bar_MF, and the MF power allocations (Prop. 3, Problem (33)) derived from this average are not necessarily optimal for that bin. Please rephrase Eq. (22) as an average SINR under the uniform-offset model and add a per-bin worst-case caveat.
  2. [Section III-E2 / Appendix D, Prop. 6 and Remark 3] The minimum-overlap conclusion for masked RF is derived from a surrogate that includes the mainlobe gain and the denominator terms in (37), but it omits active-tone-pattern-induced sidelobes and ambiguity peaks, as the footnote in Section III-E2 acknowledges. Since masked RF zeroes out subcarriers, the comb pattern inevitably creates additional DD responses that can dominate the overlap-versus-noise tradeoff. As stated, Remark 3 ('masked RF favours the minimum feasible overlap whenever inter-cell coupling is present') is stronger than the analysis supports. Please qualify Prop. 6 and Remark 3 to the considered mainlobe/denominator surrogate and discuss how tone-pattern sidelobes could affect the overlap choice.
minor comments (4)
  1. [Contributions bullet 2 / Prop. 3] The contributions list says 'closed-form optimal power allocation laws,' but Prop. 3 is explicitly a denominator-minimization surrogate with the numerator's profile-dependent term treated as negligible. The proposition itself is correctly labeled, but the contributions and conclusions should consistently use 'surrogate-optimal' to avoid overstatement.
  2. [Section II / Notational clarity] The symbol EISL is used in Section IV and in the introduction but is formally defined only in Appendix A (Eq. (52)). Consider defining it in the main text when it first appears.
  3. [Appendix B, Eq. (57)] The derivation of E[|χ^{(ℓ,0)}_{RF}[k,p]|^2] is only stated; a one-line expansion showing how the reciprocal filter 1/X leads to μ_{-2,n}/P_n would improve readability.
  4. [General / Typos] There are minor typographical issues, e.g., in Eq. (22) the large parentheses in the sidelobe term are not visually balanced, and in Appendix A the phrase 'the main peak[k, p] = (0,0)' should be '[k,p]=(0,0)' for consistency.

Circularity Check

0 steps flagged

No significant circularity: the SINR and power-allocation derivations are self-contained given the paper's explicit model assumptions.

full rationale

The paper's central derivations do not reduce to their inputs by construction. The MF SINR in Eq. (22) is obtained in Appendix A by direct expansion of the ambiguity-function kernel, Parseval's identity, and a clearly stated uniform-offset approximation for undesired monostatic scatterer offsets (after Eq. 53). That approximation turns the per-offset sidelobe powers into an averaged value rho_bar_MF, which is a modeling assumption about scatterer statistics, not a fitted input or a definitional restatement of the SINR. The RF SINR in Eq. (25) is likewise derived from the reciprocal-filter weight and elementary symbol moments. Propositions 3 and 4 are KKT-derived closed forms for the denominator surrogates, and Propositions 5 and 6 are explicit optimizations for symmetric benchmarks. The references to the authors' prior work [13], [15], [17] supply constellation-moment and BER-threshold building blocks that are independently introduced in Eq. (4) and are not the paper's novel multi-cell interference result. The skeptical concern that the uniform-offset averaging makes Eq. (22) an average rather than a per-bin SINR is a legitimate robustness caveat, but it concerns the fidelity of an explicit assumption, not circular reasoning. No fitted parameter is relabeled as a prediction, no uniqueness theorem is imported from self-citation, and no load-bearing ansatz is smuggled in via a self-reference. The derivation chain is therefore not circular; at most it relies on minor, non-load-bearing reuse of the authors' earlier, independently derivable moment/threshold results.

Axiom & Free-Parameter Ledger

0 free parameters · 9 axioms · 0 invented entities

The paper introduces no fitted free parameters and no invented physical entities. Its load-bearing assumptions are modeling choices about the propagation environment, the sidelobe statistics, and the coordination abstraction. The most consequential is the uniform-offset sidelobe model, which converts a worst-case per-bin quantity into an average and thus underpins the closed-form MF SINR and all derived allocation laws.

axioms (9)
  • domain assumption On-grid DD model: paths within CP with integer sample-spaced delays and Doppler aligned to the processing grid.
    Section III opening; gives the circular shift property (17) used to compute kernel powers.
  • ad hoc to paper Uniform-offset/maximum-entropy sidelobe model: relative DD offsets of undesired monostatic paths are uniformly distributed over non-peak bins.
    Appendix A after Eq. (53); introduced to obtain the closed-form average sidelobe level rho_bar_MF that becomes the MF denominator term in (22). Not empirically justified.
  • domain assumption Path phases are independent random phases; path powers are fixed.
    Section III; removes all cross-path terms in E|Λ|^2 and makes the SINR a ratio of averages.
  • domain assumption Full-band RF with P_n>0 on all N subcarriers.
    Section III-B; RF weight 1/X requires every tone active; the masked-RF variant relaxes this but is analyzed separately.
  • domain assumption Inter-cell interference profiles and path powers are known over the design interval.
    Sections I-II; the local optimization at BS-0 treats other BS power profiles as fixed known inputs.
  • domain assumption Beyond-CP analysis: integer excess delay d in {1,...,N-1}, at most one-symbol ISI, and no Doppler/CFO on quasi-static inter-cell links.
    Section IV; the leakage matrices G0, G1 and the total-energy preservation (41) rely on these restrictions.
  • domain assumption Symmetric homogeneous twin-BS abstraction for spectrum-overlap results.
    Section III-E; Props. 5-6 restrict to equal powers on shared tones, identical moments, equal interference coupling; conclusions may not generalize to asymmetric networks.
  • domain assumption Masked-RF active-tone-pattern sidelobes are ignored.
    Footnote 1 in Section III-E-2; the minimum-overlap conclusion of Prop. 6 omits these sidelobes, which can be significant for sparse active sets.
  • domain assumption Communication thresholds Gamma_j taken from standard BER-vs-SINR curves of the selected constellations.
    Section II-D; the QoS model (16c) assumes these thresholds are known and accurate.

pith-pipeline@v1.3.0-alltime-deepseek · 21784 in / 15119 out tokens · 129441 ms · 2026-08-01T07:28:37.245312+00:00 · methodology

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read the original abstract

Future integrated sensing and communication (ISAC) networks are expected to operate in dense multi-cell environments, where multiple base stations (BSs) share their time-frequency resources for communication and sensing. In such scenarios, the delay--Doppler (DD) sensing performance is strongly affected by random finite-alphabet orthogonal frequency-division multiplexing (OFDM) symbols, power allocation, receive filtering, and interference. This paper develops a modulation- and receive-filter-aware framework for the sensing-interference management in multi-cell OFDM-ISAC systems. Starting from a discrete-time OFDM sensing model, we derive closed-form signal-to-interference-plus-noise ratio (SINR) expressions for each range--Doppler bin under matched filtering (MF) and reciprocal filtering (RF). The analysis reveals distinct interference structures: MF depends on fourth-order constellation moments and power-overlap terms, whereas RF is governed by inverse-symbol-power and ratio-type interference terms. Based on these expressions, we obtain sensing-oriented power allocation structures, including a ramped water-filling solution for MF and a square-root allocation rule for RF. Furthermore, we jointly optimize the finite-alphabet constellation selection and power allocation under realistic communication and power constraints, and obtain tractable mixed-integer convex formulations for both MF and RF. Additionally, we study spectrum-overlap coordination in multi-cell scenarios and reveal the distinct MF/RF preferences for shared and orthogonalized tones. Furthermore, we extend the interference model to inter-cell propagation delays exceeding the cyclic prefix (CP), and show how the resultant delay violation redistributes the nominal interference spectrum into a delay-distorted effective spectrum...

Figures

Figures reproduced from arXiv: 2607.21418 by Christos Masouros, Kaitao Meng, Kawon Han, Lajos Hanzo.

Figure 1
Figure 1. Figure 1: Multi-cell OFDM-ISAC interference management with constellation [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Timing structure of within-CP and beyond-CP inter-cell interference. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Analytical and Monte Carlo sensing SINR versus the average transmit () [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Optimized power and constellation allocation across subcarriers under [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: MF sensing profiles with optimized power allocation [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: Sensing SINR and MSE versus communication payload requirement. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: Impact of communication payload requirements on sensing profiles. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

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