arxiv: 2604.26778 · v1 · submitted 2026-04-29 · 💻 cs.IT · eess.SP· math.IT

Recognition: unknown

Input Distribution Design for Ranging-Oriented OFDM-ISAC Systems Under Frequency-Selective Fading

Weijiang Zhao , Yifeng Xiong

Authors on Pith no claims yet

Pith reviewed 2026-05-07 11:22 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT

keywords OFDM-ISACinput distribution designkurtosis allocationfrequency-selective fadingcapacity-distortion frameworkranging performanceconstellation design

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The pith

Under practical sensing constraints, optimal input distribution for OFDM-ISAC allocates kurtosis of constellations appropriately over subcarriers.

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

The paper develops a method for designing input distributions in OFDM-based integrated sensing and communication systems that operate over frequency-selective fading channels. It uses the capacity-distortion framework to shape transmitted signals for a good balance between communication rates and sensing capabilities. The central idea is to treat the kurtosis of the constellations as a resource that can be allocated differently across individual subcarriers to optimize performance under realistic sensing requirements.

Core claim

Following the theoretical framework of capacity distortion, we propose a computationally efficient input distribution design approach for OFDM-ISAC under frequency-selective channels. We highlight that under practical sensing constraints, the optimal strategy is to treat the kurtosis of constellations as a resource, and allocate it appropriately over subcarriers.

What carries the argument

Capacity-distortion framework in which kurtosis of input constellations is treated as an allocatable resource across OFDM subcarriers.

If this is right

The resulting design is computationally efficient and suitable for real-time implementation in OFDM systems.
It produces a favorable balance between achievable communication rate and ranging performance.
The allocation rule applies directly to frequency-selective channels without requiring exhaustive search over distributions.
Systems can adjust the kurtosis distribution to meet varying sensing priorities while preserving communication quality.

Where Pith is reading between the lines

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

Uniform kurtosis across subcarriers may be near-optimal only when the channel is frequency-flat.
The same resource-allocation view could extend to multi-user or time-varying ISAC scenarios.
Adaptive implementations could recompute the kurtosis map from real-time channel estimates.

Load-bearing premise

The capacity-distortion framework directly yields the optimal kurtosis allocation for ranging-oriented OFDM-ISAC under frequency-selective fading without additional unstated constraints or approximations that would alter the allocation rule.

What would settle it

Numerical simulations or experiments showing that an alternative allocation strategy achieves a strictly superior communication-rate versus ranging-accuracy trade-off under the same practical sensing constraints would disprove the claim.

Figures

Figures reproduced from arXiv: 2604.26778 by Weijiang Zhao, Yifeng Xiong.

**Figure 1.** Figure 1: The numerically computed partial derivative ∂h(z) ∂E{|z| 2} , which equals to zero when the kurtosis is around 1.57. more beneficial. However, in the presence of the EISL constraint, the derivative is not necessarily nonnegative. In particular, we are interested in the partial derivative ∂h(z) ∂E{|z| 2} , the rate of change of h(z) with respect to E{|z| 2}, given a specific value of the kurtosis κ = E{|z… view at source ↗

**Figure 2.** Figure 2: The rate-kurtosis tradeoff of the proposed method, compared to that of the uniform kurtosis allocation strategy. -30 -20 -10 0 10 20 30 Delay Index -40 -35 -30 -25 -20 -15 -10 -5 0 view at source ↗

**Figure 5.** Figure 5: Observe that the kurtosis distribution resembles the “water-filling” strategy, which assigns the smallest possible kurtosis (namely, 1) to subcarriers having a channel gain less than a certain threshold. For abovethreshold subcarriers, larger kurtoses are assigned to those that have a larger gain. Finally, we demonstrate the input distribution obtained by solving the deconvolution equation (24), 5 10 15 … view at source ↗

**Figure 6.** Figure 6: Input distribution obtained by solving the deconvolution problem (40). reconstructed PDF of p|˜x+ni|(|x˜ + ni |) (obtained by convolving p˜x(˜x) with pni (ni) and taking the magnitude) closely approximates the original output distribution p opt z (z), implying that the accuracy of the deconvolution is satisfactory. VII. CONCLUSIONS In this treatise, we have proposed a computationally efficient approac… view at source ↗

read the original abstract

The implementation of the \ac{isac} feature in \ac{6g} networks is most likely to be based on the framework of \ac{ofdm}. Input distribution design, or constellation design, is a crucial technique in \ac{ofdm}-\ac{isac} systems enabling a favorable balance between communication rate and sensing performance. In this treatise, we propose a computationally efficient input distribution design approach for \ac{ofdm}-\ac{isac} under frequency-selective channels, following the theoretical framework of capacity distortion. We highlight that under practical sensing constraints, the optimal strategy is to treat the kurtosis of constellations as a resource, and allocate it appropriately over subcarriers.

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.

Desk Editor's Note private letter to a colleague

The paper adapts capacity-distortion ideas to OFDM-ISAC by treating kurtosis as an allocatable resource across subcarriers, but the abstract leaves the derivations and handling of cross-subcarrier coupling unshown.

read the letter

The main point is that this work takes the existing capacity-distortion framework and applies it to input distribution design in OFDM-ISAC systems under frequency-selective fading, with the central move being to treat constellation kurtosis as the resource that gets allocated over subcarriers to balance ranging performance against communication rate. That framing is the actual new piece: it is not just a routine application but a specific choice of what to optimize under practical sensing constraints. The authors claim this yields a computationally efficient approach, which is a reasonable target for 6G waveform work where OFDM is the expected carrier. If the full derivations and any accompanying simulations back that up, it gives designers a concrete handle they can tune. The paper does a clean job of stating the problem and linking it to the prior theoretical framework without overclaiming. On the soft spots, the abstract supplies no optimization formulation, closed-form results, or numerical checks, so the central claim about optimality cannot be verified yet. The stress-test concern about subcarrier coupling is worth watching: ranging distortion depends on the composite waveform across the full bandwidth and the frequency-selective channel, which introduces dependence that may not separate neatly into independent per-subcarrier kurtosis terms. If the paper invokes an unstated separability approximation there, the allocation rule could shift. No error analysis or validation data appears in the text provided. This is aimed at researchers already working on ISAC optimization and waveform design who know the capacity-distortion literature. A reader looking for practical handles in integrated sensing and communications would get value once the math is checked. It deserves a serious referee to examine the derivations, confirm whether the coupling is handled, and see the supporting results.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a computationally efficient input distribution design approach for ranging-oriented OFDM-ISAC systems operating under frequency-selective fading channels. Following the capacity-distortion theoretical framework, it claims that the optimal strategy is to treat the kurtosis of the constellations as an allocatable resource and distribute it across subcarriers to achieve a favorable balance between communication rate and ranging performance.

Significance. If the derivations and numerical results hold, the work offers a practical method for constellation design in 6G ISAC systems by reframing kurtosis as a design degree of freedom. This could simplify optimization in frequency-selective environments and strengthen the applicability of capacity-distortion ideas to integrated sensing and communication. The approach is computationally efficient by design, which is a positive attribute for real-world deployment.

major comments (2)

[Central derivation / capacity-distortion application] The central claim that kurtosis can be allocated independently per subcarrier follows directly from the capacity-distortion framework without extra approximations. However, ranging distortion metrics (such as CRLB on delay estimation or ambiguity function properties) depend on the composite waveform across the full occupied bandwidth and the frequency-selective channel response. This introduces cross-subcarrier coupling that is not automatically separable; the manuscript must explicitly derive or justify the separability assumption in the optimization step (likely around the formulation of the distortion function and the resulting allocation rule).
[Abstract and optimization formulation] The abstract states the framework and the kurtosis-allocation insight but supplies no closed-form expressions, optimization problem statement, or error analysis. Without these, the claim that the method is both optimal and computationally efficient cannot be verified; the full derivation (including how the capacity-distortion objective is adapted to OFDM-ISAC ranging) is load-bearing for the contribution.

minor comments (2)

[Abstract] Clarify the precise definition of 'practical sensing constraints' used to motivate the kurtosis focus; this term appears in the abstract but is not expanded.
[Numerical results] Ensure that any numerical validation includes comparisons against both uniform kurtosis allocation and conventional constellation designs (e.g., QAM) under the same frequency-selective channel realizations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the detailed review and constructive feedback on our manuscript. We have carefully considered the major comments and will revise the paper to address the concerns regarding the derivation of separability and the clarity of the optimization formulation. Below we provide point-by-point responses.

read point-by-point responses

Referee: The central claim that kurtosis can be allocated independently per subcarrier follows directly from the capacity-distortion framework without extra approximations. However, ranging distortion metrics (such as CRLB on delay estimation or ambiguity function properties) depend on the composite waveform across the full occupied bandwidth and the frequency-selective channel response. This introduces cross-subcarrier coupling that is not automatically separable; the manuscript must explicitly derive or justify the separability assumption in the optimization step (likely around the formulation of the distortion function and the resulting allocation rule).

Authors: We thank the referee for highlighting this important point on potential cross-subcarrier dependencies. In adapting the capacity-distortion framework to OFDM-ISAC, the ranging distortion is expressed through the effective kurtosis allocation per subcarrier, with the frequency-selective channel incorporated into the per-subcarrier weights. The separability is justified by the OFDM subcarrier orthogonality and the structure of the CRLB for time-delay estimation, which decomposes into a sum over subcarriers. We will include an explicit derivation of this in the revised manuscript to clarify the assumption without introducing extra approximations. revision: yes
Referee: The abstract states the framework and the kurtosis-allocation insight but supplies no closed-form expressions, optimization problem statement, or error analysis. Without these, the claim that the method is both optimal and computationally efficient cannot be verified; the full derivation (including how the capacity-distortion objective is adapted to OFDM-ISAC ranging) is load-bearing for the contribution.

Authors: We agree that the abstract could better convey the technical details. The manuscript presents the optimization problem in Section II and derives the closed-form allocation rule in Section III under the capacity-distortion framework adapted for ranging. Error analysis is provided via numerical validation and theoretical bounds in Section IV. We will update the abstract to include a brief statement of the optimization formulation and the key closed-form result. We will also ensure the adaptation of the capacity-distortion objective is more explicitly outlined in the introduction and methods sections. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation builds on external capacity-distortion framework without self-referential reduction.

full rationale

The paper explicitly follows the external theoretical framework of capacity-distortion to derive an input distribution design for ranging-oriented OFDM-ISAC under frequency-selective fading. The central claim—that kurtosis should be treated as an allocatable resource over subcarriers—is presented as a direct consequence of applying that framework under practical sensing constraints, without evidence of self-definition, fitted inputs renamed as predictions, or load-bearing self-citations that reduce the result to the paper's own inputs by construction. The derivation chain remains independent of the target allocation rule itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of the capacity-distortion framework to the OFDM-ISAC setting and on the standard frequency-selective fading channel model; no new free parameters or invented entities are introduced in the abstract.

axioms (2)

domain assumption Capacity-distortion framework accurately captures the communication-sensing trade-off for OFDM-ISAC
Paper states it follows this framework; no independent derivation or validation supplied.
domain assumption Frequency-selective fading model is appropriate for the target 6G scenarios
Invoked implicitly by the problem statement.

pith-pipeline@v0.9.0 · 5418 in / 1270 out tokens · 38246 ms · 2026-05-07T11:22:57.621034+00:00 · methodology

discussion (0)

Reference graph

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