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arxiv: 2603.03895 · v2 · pith:VVWRMJD7new · submitted 2026-03-04 · 📡 eess.SP

Constellation Selection and Power Control for OFDM-based ISAC: From Theory to Prototype

Kaitao Meng , Kawon Han , Christos Masouros , Fan Liu This is my paper

Pith reviewed 2026-05-25 07:18 UTC · model grok-4.3

classification 📡 eess.SP
keywords ISACOFDMconstellation selectionmatched filteringreciprocal filteringkurtosisPareto optimalitypower control
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The pith

Per-subcarrier constellation choice from standard alphabets tunes OFDM ISAC sidelobes through kurtosis sums and second moments without waveform changes.

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

The paper shows that matched-filter sidelobes in OFDM sensing equal a weighted sum of kurtosis values across chosen constellations, while reciprocal-filter noise enhancement equals the inverse second moment of the symbols. This link supplies a closed-form way to balance sensing quality against communication rate by swapping among off-the-shelf alphabets on each subcarrier. In flat channels any Pareto-optimal assignment uses at most three distinct constellations; a bilevel optimizer with closed inner steps reaches near-optimal performance on frequency-selective channels. The same statistics govern multi-symbol coherent integration and deliver the expected processing gain. Because the scheme needs no custom waveforms or frame changes it works with existing devices.

Core claim

Under any finite-alphabet constellation combination, MF sidelobes depend on the weighted sum of the kurtosis values of the per-subcarrier constellations, while RF noise enhancement depends on the inverse second moment of the transmit symbol, providing a tractable expression for tuning the sensing-communication trade-off. The analysis extends to multi-symbol coherent integration and achieves the expected processing gain. We prove that in flat-fading channels, any Pareto-optimal solution activates no more than three constellations. For frequency-selective channels, a bilevel algorithm with closed-form inner updates attains near-optimal performance while sharply reducing computational复杂度.

What carries the argument

Constellation selection over a finite off-the-shelf alphabet whose per-subcarrier kurtosis and second-moment statistics determine MF sidelobe level and RF noise enhancement.

If this is right

  • MF sidelobe level is predicted exactly from the weighted kurtosis sum of chosen constellations.
  • RF noise enhancement is predicted exactly from the inverse second moment of the transmit symbols.
  • In flat fading any Pareto-optimal assignment uses at most three distinct constellations.
  • Multi-symbol coherent integration yields the expected processing gain under the same constellation statistics.
  • A bilevel optimizer with closed-form inner steps yields near-optimal performance on frequency-selective channels at low complexity.

Where Pith is reading between the lines

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

  • Dynamic per-symbol constellation switching could adapt the sensing-communication balance on a frame-by-frame basis using only existing modulation tables.
  • The same kurtosis and second-moment relations may extend to other multicarrier formats that retain independent subcarrier symbols.
  • Power-control degrees of freedom already present in the framework could be combined with the constellation choice to further enlarge the achievable trade-off region.
  • Hardware prototypes could test whether real RF impairments preserve the predicted dependence on kurtosis and second moment.

Load-bearing premise

Receivers apply matched or reciprocal filtering to OFDM symbols whose data symbols are drawn independently from a finite off-the-shelf constellation set without any custom waveform or frame changes.

What would settle it

Measure MF range sidelobe height for two different mixed-constellation OFDM symbols whose kurtosis sums differ by a known factor; if the measured ratio deviates from the predicted ratio the kurtosis-sidelobe law is falsified.

Figures

Figures reproduced from arXiv: 2603.03895 by Christos Masouros, Fan Liu, Kaitao Meng, Kawon Han.

Figure 1
Figure 1. Figure 1: Scenarios of ranging measurements using same communication signals. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of constellation selection to balance sensing and communi [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Constellation proportions versus Rmin (Pave = 6). b) Outer layer update.: Let R = 1 N P n Rjn be the achieved average rate and Sy = P n κ ⋆ n the total power returned by (52). ψL and λL are updated by a projected subgradient, ψ (t+1) L = ψ (t) L + ψt [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Constellation results per subcarrier allocation with [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: illustrates that range RMSE versus SNR for both MF and RF. In [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Tradeoff between sensing and communications in (P1). [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Scenario of experiments (google maps). ing metrics, together with communication outcomes including throughput and bit error rate. This controlled protocol enables a fair comparison of ranging accuracy and communication quality and isolates the effect of constellation selection [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 12
Figure 12. Figure 12: Communication BER and throughput versus QPSK fraction (remaining [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
read the original abstract

Integrated sensing and communication (ISAC) techniques can leverage existing, wide-coverage communication networks to perform sensing tasks, enabling large-scale and low-cost target sensing. However, the inherent randomness of communication data payloads introduces undesired sidelobes in the ambiguity function that may degrade target detection and parameter estimation performance. This paper develops a communication-centric ISAC framework that is standards-compliant and compatible with existing devices. Specifically, we propose a low-complexity constellation selection scheme over a finite, off-the-shelf alphabet, achieving an efficient sensing-communication trade-off without custom waveforms or frame-structure changes. To this end, we analyze two classical sensing receivers including matched filtering (MF) and reciprocal filtering (RF) for ranging measurements, and derive closed-form sensing laws that link constellation statistics to sensing performance. Under any finite-alphabet constellation combination, MF sidelobes depend on the weighted sum of the kurtosis values of the per-subcarrier constellations, while RF noise enhancement depends on the inverse second moment of the transmit symbol, providing a tractable expression for tuning the sensing-communication trade-off. The analysis extends to multi-symbol coherent integration and achieves the expected processing gain. We prove that in flat-fading channels, any Pareto-optimal solution activates no more than three constellations. For frequency-selective channels, a bilevel algorithm with closed-form inner updates attains near-optimal performance while sharply reducing computational complexity. We validate the entire theoretical pipeline with numerical simulations as well as experimental results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper develops a standards-compliant, communication-centric ISAC framework for OFDM systems that performs constellation selection over a finite off-the-shelf alphabet together with power control. It derives closed-form sensing performance expressions for classical matched-filtering (MF) and reciprocal-filtering (RF) receivers, showing that MF sidelobe levels depend on a weighted sum of per-subcarrier kurtoses while RF noise enhancement depends on the inverse second moment of the transmit symbols. The analysis extends to multi-symbol coherent integration; a proof establishes that Pareto-optimal solutions in flat-fading channels activate at most three constellations; a bilevel algorithm with closed-form inner updates is proposed for frequency-selective channels; and the pipeline is validated by numerical simulations plus prototype experiments.

Significance. If the derivations hold, the work supplies explicit, tractable links between constellation statistics and the sensing-communication trade-off under unmodified OFDM frames and standard receivers, together with a sparsity result that limits the number of active constellations and a low-complexity algorithm. The explicit credit given to the closed-form sensing laws, the Pareto-optimality proof, and the experimental prototype validation strengthens the practical relevance of the contribution.

minor comments (3)
  1. [§4] §4 (or equivalent section presenting the bilevel algorithm): the description of the inner closed-form updates would benefit from an explicit statement of the optimality conditions used to obtain them.
  2. [Experimental results section] Figure captions for the prototype results should include the exact number of OFDM symbols used in coherent integration and the measured SNR range to allow direct comparison with the theoretical processing-gain claim.
  3. [Notation / §3] Notation table or early section: the weighting coefficients in the kurtosis sum for MF sidelobes should be defined once with a single symbol rather than re-introduced in multiple places.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment and the recommendation to accept the manuscript. The summary accurately captures the main contributions regarding closed-form sensing expressions, the Pareto-optimality result, the bilevel algorithm, and the experimental validation.

Circularity Check

0 steps flagged

Derivations self-contained from standard MF/RF models

full rationale

The paper derives MF sidelobe levels via fourth-moment expansion of the autocorrelation function and RF noise enhancement via E[1/|s|^2] directly from the definitions of matched and reciprocal filtering applied to independent draws from finite alphabets; these steps use only the receiver structures and symbol statistics as inputs and produce explicit closed-form links without redefining the outputs in terms of the optimization variables. The flat-fading Pareto result (at most three active constellations) follows from the algebraic structure of the resulting multi-objective program, while the frequency-selective bilevel procedure uses closed-form inner solutions; no load-bearing step reduces to a self-citation, fitted parameter renamed as prediction, or ansatz smuggled via prior work. The entire chain remains externally falsifiable against classical receiver analysis and is therefore non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities beyond standard OFDM and ISAC modeling assumptions.

pith-pipeline@v0.9.0 · 5796 in / 1143 out tokens · 31141 ms · 2026-05-25T07:18:38.213204+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Constellation-Independent Range Estimation in Payload-Based OFDM-ISAC

    eess.SP 2026-05 unverdicted novelty 6.0

    The ROI-MMF enables constellation-independent range estimation in OFDM-ISAC by suppressing sidelobes in a prescribed delay region, achieving near-CRB MSE performance with an efficient Woodbury-based implementation.

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