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arxiv: 2604.18060 · v1 · submitted 2026-04-20 · 📡 eess.SP · cs.IT· math.IT

Low-Complexity Tone Injection via Candidate Ranking for PAPR Reduction in OFDM and AFDM Systems

Yupeng Zheng , Ang Li , Jinfei Wang , Yi Ma , Rahim Tafazolli This is my paper

Pith reviewed 2026-05-10 04:24 UTC · model grok-4.3

classification 📡 eess.SP cs.ITmath.IT
keywords tone injectionPAPR reductionOFDMAFDMcandidate rankinglow complexitymulticarrier systems
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The pith

A peak-guided candidate ranking method for tone injection reduces PAPR by more than 1 dB in OFDM and AFDM at FFT-comparable complexity.

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

The paper introduces tone injection schemes for PAPR reduction that work in both OFDM and AFDM systems without losing spectral efficiency. It replaces random candidate generation with an iterative ranking process that picks injection values based on time-domain local peaks, keeping per-iteration cost near that of a fast Fourier transform. Depth-first search is added to exploit the underlying tree of choices and further improve results. Simulations across different subcarrier counts show the approach consistently beats earlier TI methods by more than 1 dB while holding complexity steady, pointing to a better performance-cost balance for multicarrier transmitters.

Core claim

Iteratively updating the tone injection sequence via a candidate ranking procedure guided by time-domain local peaks accurately selects effective candidates, achieves complexity comparable to the fast Fourier transform, and yields over 1 dB PAPR gain over baseline TI schemes; depth-first search integration exploits the tree structure to enhance performance further, with the gains holding across varying subcarrier numbers under controlled per-iteration complexity for both OFDM and AFDM.

What carries the argument

The candidate ranking procedure that selects tone injection values by examining time-domain local peaks and updates the sequence iteratively.

If this is right

  • The schemes deliver over 1 dB PAPR reduction gain compared with existing tone injection baselines while matching their complexity.
  • The performance advantage remains consistent when the number of subcarriers changes, provided per-iteration complexity is held fixed.
  • The same ranking-plus-depth-first-search approach works for both OFDM and AFDM, indicating broad applicability to multicarrier waveforms.
  • No spectral efficiency penalty occurs because the method remains distortionless.

Where Pith is reading between the lines

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

  • Transmitter power amplifiers could operate with lower back-off, potentially cutting energy use in base stations and user devices.
  • The low-complexity structure may allow real-time implementation on existing DSP hardware without major redesign.
  • Similar peak-guided ranking ideas could be tested in other multicarrier formats such as GFDM or OTFS to check whether the same trade-off appears.

Load-bearing premise

That selecting candidates by ranking time-domain local peaks will reliably pick the most effective tone injection values and that the observed performance-complexity trade-off in simulations will hold in real hardware and channels.

What would settle it

A set of simulations with the same subcarrier counts and per-iteration complexity limits in which the proposed schemes produce less than 1 dB PAPR improvement over the random-candidate or clipping-noise baselines would disprove the central performance claim.

Figures

Figures reproduced from arXiv: 2604.18060 by Ang Li, Jinfei Wang, Rahim Tafazolli, Yi Ma, Yupeng Zheng.

Figure 1
Figure 1. Figure 1: Illustration of the DFS procedure for CR-TI and FCR-TI. Circles [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: CCDF of PAPR for OFDM with N = 256, comparing CR-TI and FCR-TI against CE-TI, DS-TI, and unoptimized OFDM. 20 and Np = 16 achieves approximately 1 dB gain over DS-TI (TDS = 64) at comparable complexity (Table I). Increasing to T = 40 and Np = 40 further reduces the 10−3 PAPR to 5.4 dB, corresponding to a 6 dB reduction over unoptimized OFDM. To the best of our knowledge, this is the best reported PAPR perf… view at source ↗
Figure 3
Figure 3. Figure 3: CCDF of PAPR for CR-TI and FCR-TI against unoptimized signals [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: SER versus Es/N0 for CR-TI and FCR-TI against CE-TI, DS-TI, and unoptimized signals under a soft limiter with 4.5 dB clipping threshold in (a) OFDM and (b) AFDM. over three orders of magnitude improvement over the unopti￾mized signal and approximately one order of magnitude below the state-of-the-art TI baselines. At 10−3 SER, the proposed schemes achieve more than 2 dB and 5 dB signal-to-noise￾ratio gains… view at source ↗
read the original abstract

Tone injection (TI) is a promising distortionless PAPR reduction technique that incurs no spectral efficiency loss. However, state-of-the-art TI schemes based on random candidate generation or clipping noise spectrum suffer from fundamental limitations in PAPR performance. In this paper, we propose novel TI schemes compatible with both OFDM and AFDM systems. The proposed schemes iteratively update the TI sequence via a candidate ranking procedure guided by time-domain local peaks. This accurately selects effective candidates while achieving a complexity comparable to that of the fast Fourier transform. Depth-first search is further integrated to enhance PAPR performance by exploiting the tree structure of the process. Simulations demonstrate that the proposed schemes achieve over 1 dB PAPR gain over baseline TI schemes at comparable complexity. The gain is consistent across various numbers of subcarriers under controlled per-iteration complexities, confirming a superior performance-complexity trade-off for both OFDM and AFDM.

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

3 major / 2 minor

Summary. The paper proposes low-complexity tone injection (TI) schemes for PAPR reduction in both OFDM and AFDM systems. The core algorithm iteratively updates the TI sequence by ranking candidates according to their impact on time-domain local peaks, claims FFT-comparable complexity, and augments the process with depth-first search over the induced tree structure to improve performance. Simulations are reported to deliver more than 1 dB PAPR reduction relative to existing random-candidate and clipping-noise TI baselines while maintaining comparable per-iteration complexity, with the advantage holding across different subcarrier counts.

Significance. If the performance-complexity claims are substantiated with transparent accounting, the work would supply a practical, distortionless PAPR-reduction method that improves the trade-off for multicarrier waveforms without sacrificing spectral efficiency. The explicit compatibility with AFDM and the use of peak-guided ranking plus tree search constitute a concrete algorithmic contribution that could be adopted in standards or hardware implementations once the complexity overhead is rigorously quantified.

major comments (3)
  1. [Abstract] Abstract and simulation results: the headline claim of 'over 1 dB PAPR gain ... at comparable complexity' and 'controlled per-iteration complexities' rests on simulations whose parameters (Monte Carlo trial count, exact subcarrier counts, QAM order, oversampling factor, and flop-count methodology) are not stated. Without these, it is impossible to verify that the reported gain is statistically significant or that the complexity budget truly matches the random-candidate baselines once peak detection, sorting, and DFS node expansion are included.
  2. [Algorithm description] Algorithm description (candidate-ranking and DFS sections): the assertion that the scheme achieves 'complexity comparable to that of the fast Fourier transform' is not supported by an explicit operation count that includes the data-dependent costs of identifying and sorting local peaks plus the worst-case DFS traversals. These operations are absent from the random TI baselines; if they are excluded from the per-iteration budget, the claimed superior trade-off may not hold.
  3. [Performance evaluation] Performance evaluation: no analytical bound or sensitivity analysis is provided to show that peak-guided candidate selection remains effective when peak statistics change (e.g., higher-order QAM constellations or different subcarrier counts). The absence of such a guarantee makes the simulation-only evidence load-bearing for the central claim.
minor comments (2)
  1. [Notation] Notation for the TI sequence update and the DFS tree depth should be introduced with a single consistent symbol table to avoid ambiguity between the ranking metric and the PAPR objective.
  2. [Figures] Figure captions for the PAPR CCDF curves should explicitly state the exact complexity metric (e.g., real multiplications per iteration) used to declare 'comparable complexity' so readers can reproduce the comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below, indicating where revisions will be made to improve clarity, reproducibility, and substantiation of our claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract and simulation results: the headline claim of 'over 1 dB PAPR gain ... at comparable complexity' and 'controlled per-iteration complexities' rests on simulations whose parameters (Monte Carlo trial count, exact subcarrier counts, QAM order, oversampling factor, and flop-count methodology) are not stated. Without these, it is impossible to verify that the reported gain is statistically significant or that the complexity budget truly matches the random-candidate baselines once peak detection, sorting, and DFS node expansion are included.

    Authors: We agree that explicit statement of all simulation parameters is required for reproducibility and verification. In the revised manuscript we will add the Monte Carlo trial count (10^5 realizations), the exact subcarrier counts used (N = 64, 128, 256, 512), the QAM constellation order (primarily 16-QAM with additional 64-QAM results), the oversampling factor (L = 4), and a precise description of the flop-count methodology (including how peak detection, sorting, and DFS expansions are tallied). The abstract claim will be qualified to reference these controlled conditions. revision: yes

  2. Referee: [Algorithm description] Algorithm description (candidate-ranking and DFS sections): the assertion that the scheme achieves 'complexity comparable to that of the fast Fourier transform' is not supported by an explicit operation count that includes the data-dependent costs of identifying and sorting local peaks plus the worst-case DFS traversals. These operations are absent from the random TI baselines; if they are excluded from the per-iteration budget, the claimed superior trade-off may not hold.

    Authors: We acknowledge that the current complexity discussion does not provide a complete per-operation breakdown that folds in peak identification, sorting, and DFS node expansions. In the revision we will insert a detailed flop-count table that enumerates all data-dependent operations for both the proposed ranking/DFS procedure and the random-candidate baseline, using the same counting conventions. Should the accounting reveal that the overhead exceeds FFT-comparable levels under worst-case DFS, we will revise the complexity claim and the performance-complexity trade-off statement accordingly. revision: yes

  3. Referee: [Performance evaluation] Performance evaluation: no analytical bound or sensitivity analysis is provided to show that peak-guided candidate selection remains effective when peak statistics change (e.g., higher-order QAM constellations or different subcarrier counts). The absence of such a guarantee makes the simulation-only evidence load-bearing for the central claim.

    Authors: Deriving a closed-form analytical bound on the effectiveness of peak-guided selection across arbitrary QAM orders and subcarrier counts is difficult because the algorithm is inherently data-dependent. We will therefore augment the performance evaluation with additional Monte-Carlo results for 64-QAM and for a wider range of subcarrier counts, together with a short sensitivity discussion that quantifies how the PAPR gain varies with constellation order and N. These new experiments will be presented under the same controlled per-iteration complexity regime already used for the original figures. revision: partial

Circularity Check

0 steps flagged

No circularity: novel algorithmic procedure validated empirically

full rationale

The paper presents a new iterative candidate-ranking algorithm for tone injection, guided by time-domain peaks and augmented with DFS, whose performance is assessed via simulation under controlled per-iteration complexity. No load-bearing equations, parameters, or uniqueness claims are shown to reduce by construction to fitted inputs or self-citations; the central claims rest on direct comparison of the described procedure against baselines rather than on any self-referential derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard properties of the discrete Fourier transform and peak detection; no new physical entities or large numbers of free parameters are introduced in the abstract.

axioms (1)
  • standard math Discrete Fourier transform properties allow time-domain peak information to guide frequency-domain tone selection
    Invoked when the ranking procedure uses local peaks to choose TI candidates.

pith-pipeline@v0.9.0 · 5469 in / 1162 out tokens · 44359 ms · 2026-05-10T04:24:10.904094+00:00 · methodology

discussion (0)

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Reference graph

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