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REVIEW 4 major objections 6 minor 1 cited by

AFBM, an affine chirp-precoded filter-bank waveform for 6G ISAC, is claimed to jointly deliver low PAPR, low out-of-band emission, and delay-Doppler resilience, with about 2 dB BER gain over AFDM at 10^-3.

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2026-08-05 05:14 UTC pith:UZIOGN47

load-bearing objection A novel AFDM/FBMC hybrid worth a serious referee, but the headline BER/RMSE gains rest on a visually-supported Gram-matrix diagonal claim and an O=4 vs O<=1.5 tension that need real evidence. the 4 major comments →

arxiv 2509.05683 v1 pith:UZIOGN47 submitted 2025-09-06 eess.SP

Affine Filter Bank Modulation (AFBM): A Novel 6G ISAC Waveform with Low PAPR and OOBE

Kuranage Roche Rayan Ranasinghe , Henrique L. Senger , Gustavo P. Gon\c{c}alves , Hyeon Seok Rou , Bruno S. Chang , Giuseppe Thadeu Freitas de Abreu , Didier Le Ruyet This is my paper
classification eess.SP
keywords AFBM6G ISACAFDMfilter bank multicarrierPAPRout-of-band emissionGaussian belief propagationprobabilistic data association
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.

The paper proposes a new waveform, affine filter bank modulation (AFBM), for integrated sensing and communications (ISAC) in 6G, and claims it is the first cited design to combine three qualities at once: low peak-to-average power ratio (PAPR), strong out-of-band emission (OOBE) suppression, and reliable operation over doubly-dispersive delay-Doppler channels. AFBM is built by inserting a pruned discrete affine Fourier transform (DAFT) precoder and a filter-compensation stage into an AFDM-style chirp modulator, so that each subcarrier becomes a chirp-filtered pulse shaped by an FBMC prototype filter. For communications the paper designs a Gaussian belief propagation (GaBP) detector that uses only element-wise scalar operations and reports roughly 2 dB gain over conventional AFDM at a bit error rate of 10^-3; for sensing it designs an EM-assisted probabilistic data association (PDA) estimator that reads target ranges and velocities off a sparse delay-Doppler grid. Both receivers rest on one claimed structural property: the Gram matrix of AFBM's hybrid filtered time-domain channel approaches a diagonal form at scale, so matched-filter message passing is well conditioned. Evidence is analytical and numerical across PAPR, OOBE, ambiguity function, BER, and radar RMSE metrics.

Core claim

AFBM replaces the rectangle-windowed chirp subcarriers of AFDM with chirp-filtered subcarriers: data are placed only in the outer quarters of the time-frequency grid, multiplied by a diagonal compensation stage that cancels intrinsic filter interference and restores complex orthogonality, spread by a pruned DAFT whose chirp parameters set the diagonal spreading of the delay-Doppler channel, and convolved with a localized prototype filter (Hermite or PHYDYAS, with tunable overlap factor O). The paper argues that the payoffs follow from this single construction: an ambiguity function nearly identical to AFDM's, PAPR about 2 dB lower, and spectral sidelobes at FBMC levels, so no cited predecess

What carries the argument

The central construction is the AFBM modulator chain s = G (I_K ⊗ Q_P C_f) Ξ x: a placement map Ξ that reserves the middle half of the band as guard space, a diagonal compensation filter C_f (chosen so the cascade C_f^H Q_P^H G^T G Q_P C_f is a unit diagonal, cancelling intrinsic interference for overlap O ≤ 1.5), a pruned IDAFT Q_P that spreads channel diagonals in delay-Doppler, and a block-Toeplitz prototype-filter matrix G that supplies spectral localization. The receiver-supporting mechanism is the hybrid filtered time-domain Gram matrix Ḡ_FTD = H̄^H H̄ of equation (27b), which the paper claims approaches a diagonal form in high-dimensional AFBM systems; near-diagonality is what lets G

Load-bearing premise

Both low-complexity receivers assume the Gram matrix of AFBM's hybrid filtered time-domain channel is nearly diagonal in practice; the paper supports this with a single visual inspection and then builds the GaBP and EM-PDA estimators on it, so if diagonality weakens at realistic dimensions the reported BER and RMSE gains lose their stated support.

What would settle it

Compute the squared off-diagonal mass of Ḡ_FTD = H̄^H H̄ from equation (27b) relative to its diagonal for the Figure 9-11 settings (L=128, N=256, K=8, three paths, ℓmax=16, fmax=2) over many random channel draws; if the ratio does not shrink with system size, run the GaBP detector with the true (non-diagonal) Gram matrix and check whether its error floor moves well above the 10^-4 regime, which would contradict the claimed ~2 dB edge over AFDM at 10^-3.

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

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If this is right

  • One AFBM transceiver could carry both the data and radar functions of a 6G ISAC node: the ambiguity function tracks AFDM's for sensing while the low PAPR relaxes power-amplifier back-off and the low OOBE permits fragmented-spectrum operation.
  • The reported ~2 dB BER advantage at 10^-3 transposes into lower transmit power or longer range for equal reliability, delivered by a detector whose per-iteration cost is element-wise scalar operations rather than a cubic matrix inversion.
  • The sensing receiver's O(N^3) cost is independent of the delay-Doppler grid size, so target range and velocity resolution can be refined without increasing the dominant algorithmic cost.
  • The filter-compensation design shows the classical FBMC orthogonality toolkit (guarded subcarriers, O ≤ 1.5 overlap, compensation coefficients) survives transplantation into chirp-domain modulation, making the pattern available to the wider DAFT waveform family.

Where Pith is reading between the lines

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

  • My read: the near-diagonality of Ḡ_FTD is the hinge of the paper, yet it is supported by visual inspection of one Gram-matrix figure; a quantitative scan of the off-diagonal-to-diagonal energy ratio across L, N, K and many channel realizations would show whether the claimed property is generic or specific to the displayed parameters.
  • My read: the reported PAPR advantage is fragile with respect to the chirp parameter c2, since it vanishes as c2,L grows from 1/πL² to 50/πL²; a joint optimization of chirp parameters, prototype filter, and the IDAFT length P (currently chosen heuristically) is the obvious next lever for widening the low-PAPR operating region.
  • My read: because the same pruned-DAFT-plus-compensation recipe could be grafted onto DAFT-s-AFDM or zero-padded chirp modulations, the cleanest test of the paper's thesis is whether the 2 dB gain is a property of the AFBM construction specifically or of giving any chirp waveform a filter-bank front end.
  • My read: reserving half the subcarriers as guard space and demanding P > L carries a spectral-efficiency cost the paper does not quantify; a net spectral-efficiency comparison against OFDM and AFDM would sharpen the tradeoff the waveform actually offers.

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

4 major / 6 minor

Summary. The paper proposes affine filter bank modulation (AFBM), a waveform that inserts a pruned DAFT precoder and an FBMC-type filter bank into the AFDM framework. The authors claim that AFBM simultaneously achieves low PAPR, low OOBE, and quasi-orthogonality in doubly-dispersive channels, and they develop two receivers: a GaBP-based data detector and an EM-PDA-based sensing/radar parameter estimator. Numerical results report an approximately 2 dB BER gain over conventional AFDM at BER 10^{-3} and sensing RMSE comparable to AFDM. The transmitter algebra (compensation, pruned DAFT, filtering) is presented in detail, and the GaBP/PDA update structures are standard. However, the load-bearing premises—especially the approximate diagonality of the filtered time-domain Gram matrix and the validity of the compensation stage for the simulated overlap factors—are not established quantitatively, and there is a dimension inconsistency in the channel model at Eq. (19).

Significance. If the claims are substantiated, AFBM would address a real gap in the ISAC waveform literature: no cited waveform simultaneously provides robustness to doubly-dispersive channels, intrinsically low PAPR, and good spectral containment. The paper gives a concrete transmitter structure, a clear receiver architecture, and reproducible-looking algorithms; these are useful contributions. The significance is conditional, however: the central performance claims rest on a visually demonstrated Gram-diagonality assumption and on hand-picked chirp parameters, so the results as presented are not yet at the standard of a definitive waveform proposal.

major comments (4)
  1. [Section II-B, Eq. (19)-(25)] There is a serious dimension inconsistency. The channel matrix is defined as H = I_{K-1} ⊗ \check H ∈ C^{(K-1)M × (K-1)M}, while G ∈ C^{M × NK}. For K > 2, the product H G in (19) and G^H H G in (24) are not defined. Consequently \bar H in (25), the I/O relation (29), and the receiver derivations in Sections V and VI are based on an undefined object as printed. This must be corrected; if a block-channel structure is intended, it should be specified explicitly and all dimensions rechecked.
  2. [Section III-B, Fig. 4] The claim that the hybrid filtered time-domain Gram matrix \bar G_FTD approaches a diagonal form is load-bearing for the GaBP receiver (Section V) and the PDA sensing receiver (Section VI), but it is supported only by visual inspection of one figure with a single parameter set. No diagonal-dominance metric, no dimension sweep, and no statistics over channel realizations are given. Since \bar H = G^H H G(I⊗Q_P C_f)Ξ is a structured product of Toeplitz/diagonal/sparse matrices and not an i.i.d. random matrix, the asserted concentration is not self-evident. The authors should provide a quantitative measure (e.g., normalized off-diagonal energy) as a function of L,N,K and over channel realizations before the BER/RMSE results can be attributed to well-conditioned matched-filter processing.
  3. [Section II-A1 and Figs. 6, 9, 10] Section II-A1 states that correct compensation via (7)-(9) is guaranteed only when the overlap factor satisfies O ≤ 1.5, and that for larger O the off-diagonal interference reduces the signal-to-interference ratio. However, the OOBE and BER simulations with the PHYDYAS filter use O = 4. The paper never quantifies the resulting SIR loss or explains why the compensation and the Gram analysis remain valid at O = 4. This is an internal inconsistency that affects the generality of the OOBE and BER claims; it should be addressed explicitly.
  4. [Section IV-A, Fig. 5] The low-PAPR claim is demonstrated only for the specific choice c_{2,L} = 1/(πL^2). The text itself notes that raising c_{2,L} to 50/(πL^2) makes AFBM's PAPR higher than that of AFDM. Since c_2 is a free design parameter and the paper provides no optimization or feasible-region analysis over the AFDM orthogonality constraint, the claimed 'remarkably low PAPR' is not established as a robust property of AFBM. A systematic characterization of PAPR versus admissible chirp parameters, or a constrained optimization, is needed to support the headline claim.
minor comments (6)
  1. [Figures 7 and 8] The captions read 'AbuguityFunction' — should be 'Ambiguity Function'.
  2. [Equation (7)] The matrix \tilde G appears in (7) before G is defined in (17); please define \tilde G (presumably the per-symbol filtering matrix) at first use.
  3. [Section II-C] The complexity discussion mentions K-point (I)DFTs and assumes K log K multiplications, but the displayed complexity expression does not include a K log K term. Align the text with the equation or explain the omission.
  4. [Figure 4] Please specify the parameters used in each panel of Figure 4 (L, N, K, P, O, filter type) and add a quantitative color scale; the visual claim would also benefit from a numerical off-diagonal energy caption.
  5. [Section IV-C] The AF parameters 'c_{2,\bar M}=3e100' should be clarified: this appears to be a garbled scientific notation. Also, the heuristic selection of ambiguity-function parameters is stated but not justified; a short explanation of the chosen values would improve reproducibility.
  6. [Section II-A] The paper reserves half the subcarriers as guard bands and transmits at twice the rate. Please state explicitly how the spectral efficiency compares with the AFDM/OFDM benchmarks in the BER and OOBE simulations, so that the comparisons are not inadvertently affected by different occupied bandwidths.

Circularity Check

0 steps flagged

No load-bearing circularity; the Gram-diagonal premise is weakly supported and some benchmarks use hand-picked chirp parameters or self-cited implementations, but no derivation reduces to its own inputs.

full rationale

The AFBM transmit chain (equations (1)-(24)) is a closed-form construction: the compensation filter is defined via (8) so that (7) holds, and the quasi-orthogonality in the noiseless case follows from that definition. This is a design property, not a prediction obtained from the thing it is supposed to predict. The GaBP and PDA receivers are derived from the linear model (29) with standard message-passing equations; they do not fit a parameter and then report that parameter as a result. The diagonal-Gram premise in Section III-B is a support gap: it is justified only by visual inspection of Figure 4 and an appeal to 'increased randomness,' with no quantitative diagonal-dominance metric or dimension sweep. This is a correctness/evidence weakness, not circularity, because the BER and RMSE simulations would fail if the premise were false. Similarly, the PAPR and AF comparisons use explicitly disclosed chirp-parameter choices (Section IV-C: 'heuristic values were selected for each waveform to ensure the best performance'), and Section IV-A shows the PAPR advantage reverses at other c_2 values; this makes the claims conditional, not circular. The paper cites the authors' own prior work (AFBM in [41], AFDM baseline in [16], filter-bank designs in [38]-[40]), but those citations supply a construction and a benchmark, not a uniqueness theorem or an unverified ansatz that forces the present conclusions. The internal tension between the O<=1.5 compensation condition (Section II-A1) and the PHYDYAS O=4 simulations is a consistency concern, not a circular reduction. Overall, no equation or fitted parameter is renamed as a prediction; the central claims still depend on independent simulations and standard derivations.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

No new physical entities are introduced; AFBM is a signal construction, not a postulated entity, so the invented-entities ledger is empty. The assumption load is carried by six model choices: the circular affine channel model from [22] applied to a prefix-free filtered signal; the block-constant channel stated in footnote 1; the numerically motivated Gram-matrix diagonality; the Gaussianity and independence approximations of message passing; the single-coefficient interference condition (O <= 1.5) that the O = 4 simulations violate; and perfect knowledge of prototype filter coefficients. Free parameters include the hand-chosen chirp rates that set the headline PAPR and AF numbers, the unstated guard width xi, the damping factors, the assumed target count in the sensing prior, and heuristic baseline chirp values for the AF comparison.

free parameters (5)
  • Chirp parameter c2 (c2,L, c2,P, c2,N) = c2,L=1/(pi L^2), c2,P=1/(pi P^2), c2,N=1/(pi N^2) for PAPR plots; c2,L=pi/L^2, c2,P=0, c2,N=0 for AF plots
    The headline low-PAPR and AF results are obtained at hand-selected chirp rates; Section IV-A states the selection is critical and that raising c2,L to 5/(pi L^2) or 50/(pi L^2) erases or reverses the PAPR advantage. Footnote 2 concedes optimization is left for future work.
  • Guard width xi (free integer in chirp orthogonality condition) = not specified in the text
    In the condition 2(f_max+xi)(l_max+1)+l_max <= P stated in Section V-C, xi is a free parameter controlling Doppler guard width; its value is never given, leaving the simulation operating point underspecified.
  • Damping factors beta_x and beta_h = beta_x = 0.5; beta_h not specified numerically
    Hand-chosen algorithmic hyperparameters introduced to avoid convergence to local minima (Section V-A3 and Algorithm 2); the sensing damping value is absent from the text.
  • Number of targets/paths P for the sensing prior = R = 3 in simulations (Figure 11)
    Algorithm 2 requires the sparsity rate rho^(0) = P/(K_tau D_nu), so the target count is treated as known input rather than estimated, a strong assumption for a radar parameter estimation task.
  • AF baseline chirp values for DAFT-s-AFDM = c2,Mbar = 3e100 and c2,Dbar = 0 as printed
    Heuristic values selected to make the ambiguity-function comparison favorable (Section IV-C); the printed value '3e100' is likely a typo, and its effect is unquantified.
axioms (6)
  • domain assumption The doubly-dispersive channel is represented by the circular affine convolution matrix H = sum_r h_r Phi_r Z^{f_r} Pi^{l_r} from [22], applied directly to the prefix-free overlapped filter-bank signal.
    Invoked in equations (19)-(20). For AFDM this model corresponds to a chirp-periodic prefix; AFBM has no such prefix, and the text does not justify circular convolution for the overlapped filter-bank transmit signal.
  • domain assumption The doubly-dispersive channel remains constant over the K time slots.
    Footnote 1 states: 'the doubly-dispersive channel remains constant during the K time slots.' The authors flag this as a limitation enabling N_bar = NK; it is tension with the high-mobility motivation of the waveform.
  • ad hoc to paper The Gram matrix of the hybrid filtered TD channel is approximately diagonal in high-dimensional AFBM systems.
    Section III-B: the premise that 'the hybrid filtered TD Gram matrix approaches a diagonal form in high-dimensional AFBM systems' is supported only by visual inspection of Figure 4; it is load-bearing for both receiver designs.
  • domain assumption Scalar Gaussian (SGA) and vector Gaussian (VGA/CLT) approximations with independence of estimation errors hold for the message-passing receivers.
    Section V-A2 and VI-A1. Standard large-system message-passing assumptions, but the independence claim is unverified for the specific filtered channel structure of AFBM.
  • standard math Interference during compensation is limited to a single filter coefficient, which requires overlap factor O <= 1.5.
    Section II-A1, citing [38]: off-diagonal interference and SIR loss appear for O > 1.5. Yet the main BER results (Figures 9-10) use PHYDYAS with O = 4; the effect of this violation is not quantified.
  • domain assumption Prototype filter coefficients are known at both transmitter and receiver.
    Section II-A1: 'the coefficients are derived from a pre-defined prototype filter... they are assumed to be known.' This bypasses channel and filter estimation, which the conclusion defers to future work.

pith-pipeline@v1.3.0-alltime-deepseek · 20405 in / 31271 out tokens · 293197 ms · 2026-08-05T05:14:14.674679+00:00 · methodology

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Cite this review

Pith. "Pith review of Affine Filter Bank Modulation (AFBM): A Novel 6G ISAC Waveform with Low PAPR and OOBE." pith.science (2026). https://pith.science/paper/UZIOGN47

@misc{pith2026250905683,
  author       = {Pith},
  title        = {Pith review of: Affine Filter Bank Modulation (AFBM): A Novel 6G ISAC Waveform with Low PAPR and OOBE},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UZIOGN47}},
  note         = {Machine review of arXiv:2509.05683}
}
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read the original abstract

We propose the affine filter bank modulation (AFBM) waveform for enhanced integrated sensing and communications (ISAC) in sixth generation (6G), designed by drawing on concepts from classical filter bank multicarrier modulation (FBMC) theory and recent advances in chirp-domain waveforms, particularly affine frequency division multiplexing (AFDM). Specifically, AFBM exhibits several desirable properties, with emphasis on its remarkably low peak-to-average power ratio (PAPR) and reduced out-of-band emission (OOBE) when benchmarked against the conventional AFDM waveform under doubly-dispersive (DD) channel conditions. In the communications setting, reliable symbol detection is achieved using a tailored low-complexity Gaussian belief propagation (GaBP)-based algorithm, while in the sensing setting, a range and velocity estimation approach is developed that integrates an expectation maximization (EM)-assisted probabilistic data association (PDA) framework to accurately identify surrounding targets. The highlighted performance and benefits of AFBM are validated through analytical and numerical evaluations, including conventional metrics such as ambiguity function (AF), bit error rate (BER), and root mean square error (RMSE), consolidating its position as a promising waveform for next-generation wireless systems.

Figures

Figures reproduced from arXiv: 2509.05683 by Bruno S. Chang, Didier Le Ruyet, Giuseppe Thadeu Freitas de Abreu, Gustavo P. Gon\c{c}alves, Henrique L. Senger, Hyeon Seok Rou, Kuranage Roche Rayan Ranasinghe.

Figure 1
Figure 1. Figure 1: Illustration of an AFBM-ISAC scenario, where the ISAC-RX either [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Visualization of the AFBM modulation procedure. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: 3D illustration of a three-path AFBM intermediate effective channel [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of the Gram matrix structure of the two effective channels with various prototype filter types computed via equations (27a) and (27b). [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: illustrates the PAPR performance of the considered systems. It can be observed that, due to its single-carrier￾like structure, the proposed AFBM waveform achieves an advantage of approximately 2 dB compared with regular AFDM, which exhibits the same high PAPR levels as conven￾tional OFDM-based schemes. Furthermore, since the proposed waveform can be regarded as an affine extension of the pruned DFT-spread … view at source ↗
Figure 6
Figure 6. Figure 6: OOBE performance of AFDM and AFBM with the Hermite and [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Doppler AF performance of AFDM and AFBM with the Hermite and [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: BER performance of the proposed GaBP technique for both the AFDM [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: BER performance of the proposed GaBP technique for both the [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Radar parameter estimation performance of the proposed AFBM [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗

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Cited by 1 Pith paper

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

  1. AFDM: Evolving OFDM Towards 6G+

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    AFDM is presented as an OFDM-backward-compatible 6G+ waveform whose added transceiver cost is two O(N) chirp rotations, supported by a generalized pulse-shaped FDFD channel formulation.

Reference graph

Works this paper leans on

52 extracted references · 43 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    Low- complexity receiver design for affine filter bank modulation,

    K. R. R. Ranasinghe, B. S. Chang, and G. T. F. de Abreu, “Low- complexity receiver design for affine filter bank modulation,” inIEEE 10th International Workshop on Computational Advances in Multi- Sensor Adaptive Processing (CAMSAP), 2025

    work page 2025

  2. [2]

    Terahertz communications and sensing for 6g and beyond: A comprehensive review,

    W. Jiang, Q. Zhou, J. He, M. A. Habibi, S. Melnyk, M. El-Absi, B. Han, M. D. Renzo, H. D. Schotten, F.-L. Luo, T. S. El-Bawab, M. Juntti, M. Debbah, and V . C. M. Leung, “Terahertz communications and sensing for 6g and beyond: A comprehensive review,”IEEE Communications Surveys & Tutorials, vol. 26, no. 4, pp. 2326–2381, 2024

    work page 2024

  3. [3]

    Cellular wireless networks in the upper mid-band,

    S. Kang, M. Mezzavilla, S. Rangan, A. Madanayake, S. B. Venkatakrish- nan, G. Hellbourg, M. Ghosh, H. Rahmani, and A. Dhananjay, “Cellular wireless networks in the upper mid-band,”IEEE Open Journal of the Communications Society, vol. 5, pp. 2058–2075, 2024

    2058

  4. [4]

    A survey on high mobility wireless communications: Challenges, opportunities and solutions,

    J. Wu and P. Fan, “A survey on high mobility wireless communications: Challenges, opportunities and solutions,”IEEE Access, vol. 4, pp. 450– 476, 2016

    work page 2016

  5. [5]

    Enabling data-driven otfs modulation for 6g hyper reliable high-mobility commu- nications,

    J. Xue, T. Jiang, H. Huang, Z. Zhang, H. Zhou, and X. Shen, “Enabling data-driven otfs modulation for 6g hyper reliable high-mobility commu- nications,”IEEE Wireless Communications, vol. 32, no. 3, pp. 196–203, 2025

    work page 2025

  6. [6]

    Closer twins model: Consistent design of modem scheme and channel esti- mation under high-mobility scenarios,

    H. Zhang, X. Wang, J. Tan, J. Wang, Z. Yang, and B. Ai, “Closer twins model: Consistent design of modem scheme and channel esti- mation under high-mobility scenarios,”IEEE Transactions on Wireless Communications, vol. 24, no. 6, pp. 4564–4580, 2025

    work page 2025

  7. [7]

    Slepian function-based windowed ofdm systems with high mobility,

    H. Mu, J. Wang, M. Jiang, and Q. Zhang, “Slepian function-based windowed ofdm systems with high mobility,”IEEE Wireless Communi- cations Letters, vol. 14, no. 6, pp. 1643–1647, 2025

    work page 2025

  8. [8]

    Flexible delay-doppler domain multiple access for massive connectivity with high mobility,

    X. Wang, H. Zhang, J. Wang, Z. Yang, H. Lin, and J. Song, “Flexible delay-doppler domain multiple access for massive connectivity with high mobility,”IEEE Transactions on Wireless Communications, vol. 24, no. 6, pp. 5050–5065, 2025

    work page 2025

  9. [9]

    From theory to reality: A design framework for integrated communication and computing receivers,

    K. R. Rayan Ranasinghe, K. Ando, and G. T. Freitas de Abreu, “From theory to reality: A design framework for integrated communication and computing receivers,” in2025 International Conference on Computing, Networking and Communications (ICNC), 2025, pp. 865–870

    2025

  10. [10]

    A flexible design framework for integrated communication and computing receivers,

    K. R. R. Ranasinghe, K. Ando, H. S. Rou, G. T. F. de Abreu, T. Takahashi, M. D. Renzo, and D. G. G, “A flexible design framework for integrated communication and computing receivers,” 2025. [Online]. Available: https://arxiv.org/abs/2506.05944

    Pith/arXiv arXiv 2025

  11. [11]

    Beamforming design for active ris-aided over-the-air computation,

    D. Zhang, M. Xiao, C. Shi, M. Skoglund, Y . Li, and H. Vincent Poor, “Beamforming design for active ris-aided over-the-air computation,” IEEE Transactions on Communications, pp. 1–1, 2025. 13

    work page 2025

  12. [12]

    Remac: Digital multiple access computing by repeated transmissions,

    X. Yan, S. Razavikia, and C. Fischione, “Remac: Digital multiple access computing by repeated transmissions,”IEEE Transactions on Communications, pp. 1–1, 2025

    work page 2025

  13. [13]

    Digital over-the-air computation: Achieving high reliability via bit-slicing,

    J. Liu, Y . Gong, and K. Huang, “Digital over-the-air computation: Achieving high reliability via bit-slicing,”IEEE Transactions on Wire- less Communications, vol. 24, no. 5, pp. 4101–4114, 2025

    work page 2025

  14. [14]

    Integrated sensing and communication signals toward 5G-A and 6G: A survey,

    Z. Wei, H. Qu, Y . Wang, X. Yuan, H. Wu, Y . Du, K. Han, N. Zhang, and Z. Feng, “Integrated sensing and communication signals toward 5G-A and 6G: A survey,”IEEE Internet of Things Journal, vol. 10, no. 13, pp. 11 068–11 092, 2023

    2023

  15. [15]

    The integrated sensing and communication revolution for 6G: Vision, techniques, and applications,

    N. Gonz ´alez-Prelcic, M. Furkan Keskin, O. Kaltiokallio, M. Valkama, D. Dardari, X. Shen, Y . Shen, M. Bayraktar, and H. Wymeersch, “The integrated sensing and communication revolution for 6G: Vision, techniques, and applications,”Proceedings of the IEEE, vol. 112, no. 7, pp. 676–723, 2024

    2024

  16. [16]

    Joint channel, data, and radar parameter estimation for afdm systems in doubly-dispersive channels,

    K. R. R. Ranasinghe, H. Seok Rou, G. Thadeu Freitas de Abreu, T. Taka- hashi, and K. Ito, “Joint channel, data, and radar parameter estimation for afdm systems in doubly-dispersive channels,”IEEE Transactions on Wireless Communications, vol. 24, no. 2, pp. 1602–1619, 2025

    2025

  17. [17]

    Terahertz integrated sensing and communication-empowered uavs in 6g: A transceiver design perspective,

    R. Zhang, W. Wu, X. Chen, Z. Gao, and Y . Cai, “Terahertz integrated sensing and communication-empowered uavs in 6g: A transceiver design perspective,”IEEE V ehicular Technology Magazine, pp. 2–11, 2025

    work page 2025

  18. [18]

    Emerging trends in radar: Otfs-based radar for integrated sensing and communications systems,

    A. Correas-Serrano, N. Petrov, M. Gonzalez-Huici, and A. Yarovoy, “Emerging trends in radar: Otfs-based radar for integrated sensing and communications systems,”IEEE Aerospace and Electronic Systems Magazine, vol. 40, no. 6, pp. 102–107, 2025

    work page 2025

  19. [19]

    Integrated sensing and communication enabled multiple base stations cooperative sensing towards 6g,

    Z. Wei, W. Jiang, Z. Feng, H. Wu, N. Zhang, K. Han, R. Xu, and P. Zhang, “Integrated sensing and communication enabled multiple base stations cooperative sensing towards 6g,”IEEE Network, vol. 38, no. 4, pp. 207–215, 2024

    work page 2024

  20. [20]

    Comparison of CP-OFDM and OFDM/OQAM in doubly dispersive channels,

    J. Du and S. Signell, “Comparison of CP-OFDM and OFDM/OQAM in doubly dispersive channels,” inFuture Generation Communication and Networking (FGCN 2007), vol. 2, 2007, pp. 207–211

    work page 2007

  21. [21]

    Ofdm-rsma: Robust transmission under inter-carrier interference,

    M. M. S ¸ahin, O. Dizdar, B. Clerckx, and H. Arslan, “Ofdm-rsma: Robust transmission under inter-carrier interference,”IEEE Transactions on Communications, vol. 73, no. 7, pp. 4602–4615, 2025

    work page 2025

  22. [22]

    H. S. Rou, G. T. F. de Abreu, J. Choi, D. Gonz ´alez G., M. Kountouris, Y . L. Guan, and O. Gonsa, “From orthogonal time–frequency space to affine frequency-division multiplexing: A comparative study of next- generation waveforms for integrated sensing and communications in doubly dispersive channels,”IEEE Signal Process. Mag., vol. 41, no. 5, pp. 71–86, 2024

    work page 2024

  23. [23]

    Orthogonal time frequency space modu- lation,

    R. Hadani, S. Rakib, M. Tsatsanis, A. Monk, A. J. Goldsmith, A. F. Molisch, and R. Calderbank, “Orthogonal time frequency space modu- lation,” in2017 IEEE Wireless Communications and Networking Con- ference (WCNC), 2017, pp. 1–6

    work page 2017

  24. [24]

    On the effective- ness of otfs for joint radar parameter estimation and communication,

    L. Gaudio, M. Kobayashi, G. Caire, and G. Colavolpe, “On the effective- ness of otfs for joint radar parameter estimation and communication,” IEEE Transactions on Wireless Communications, vol. 19, no. 9, pp. 5951–5965, 2020

    work page 2020

  25. [25]

    On the diversity of uncoded otfs modulation in doubly-dispersive channels,

    G. D. Surabhi, R. M. Augustine, and A. Chockalingam, “On the diversity of uncoded otfs modulation in doubly-dispersive channels,” IEEE Transactions on Wireless Communications, vol. 18, no. 6, pp. 3049–3063, 2019

    work page 2019

  26. [26]

    Affine frequency division multiplexing (afdm) for 6g: Properties, features, and challenges,

    H. S. Rou, K. R. R. Ranasinghe, V . Savaux, G. T. F. de Abreu, C. Ma- souroset al., “Affine frequency division multiplexing (afdm) for 6g: Properties, features, and challenges,”arXiv preprint arXiv:2507.21704, 2025

    work page arXiv 2025

  27. [27]

    Orthogonal delay-doppler division multiplexing (oddm) over general physical channels,

    J. Tong, J. Yuan, H. Lin, and J. Xi, “Orthogonal delay-doppler division multiplexing (oddm) over general physical channels,”IEEE Transactions on Communications, vol. 72, no. 12, pp. 7938–7953, 2024

    work page 2024

  28. [28]

    Affine frequency division multiplexing for next generation wireless communications,

    A. Bemani, N. Ksairi, and M. Kountouris, “Affine frequency division multiplexing for next generation wireless communications,”IEEE Trans- actions on Wireless Communications, vol. 22, no. 11, pp. 8214–8229, 2023

    2023

  29. [29]

    Affine frequency division multiplexing with index modulation: Full diversity condition, performance analysis, and low-complexity detection,

    Y . Tao, M. Wen, Y . Ge, J. Li, E. Basar, and N. Al-Dhahir, “Affine frequency division multiplexing with index modulation: Full diversity condition, performance analysis, and low-complexity detection,”IEEE Journal on Selected Areas in Communications, vol. 43, no. 4, pp. 1041– 1055, 2025

    work page 2025

  30. [30]

    Affine frequency division multiplexing for 6g networks: Fundamentals, oppor- tunities, and challenges,

    Q. Li, J. Li, M. Wen, X. Dang, H. Arslan, and N. Al-Dhahir, “Affine frequency division multiplexing for 6g networks: Fundamentals, oppor- tunities, and challenges,”IEEE Network, pp. 1–1, 2025

    work page 2025

  31. [31]

    DAFT-spread affine frequency division multiple access for downlink transmission,

    Y . Tao, M. Wen, Y . Ge, T. Mao, L. Xiao, and J. Li, “DAFT-spread affine frequency division multiple access for downlink transmission,” in GLOBECOM 2024 - 2024 IEEE Global Communications Conference, 2024, pp. 2991–2996

    work page 2024

  32. [32]

    Spectrum design for orthogonal chirp division multiplexing transmissions,

    M. S. Omar and X. Ma, “Spectrum design for orthogonal chirp division multiplexing transmissions,”IEEE Wireless Communications Letters, vol. 9, no. 11, pp. 1990–1994, 2020

    work page 1990

  33. [33]

    Special cases of DFT-based modulation and demodulation for affine frequency division multiplexing,

    V . Savaux, “Special cases of DFT-based modulation and demodulation for affine frequency division multiplexing,”IEEE Transactions on Com- munications, vol. 72, no. 12, pp. 7627–7638, 2024

    work page 2024

  34. [34]

    Spectrum efficient, localized, orthogonal waveforms: Closing the gap with the balian-low theorem,

    C. W. Korevaar, A. B. J. Kokkeler, P.-T. d. Boer, and G. J. M. Smit, “Spectrum efficient, localized, orthogonal waveforms: Closing the gap with the balian-low theorem,”IEEE Transactions on Communications, vol. 64, no. 5, pp. 2155–2165, 2016

    work page 2016

  35. [35]

    A novel filter-bank multicarrier scheme to mitigate the intrinsic interference: Application to mimo systems,

    R. Zakaria and D. Le Ruyet, “A novel filter-bank multicarrier scheme to mitigate the intrinsic interference: Application to mimo systems,”IEEE Transactions on Wireless Communications, vol. 11, no. 3, pp. 1112– 1123, 2012

    work page 2012

  36. [36]

    Pruned DFT-spread FBMC: Low PAPR, low la- tency, high spectral efficiency,

    R. Nissel and M. Rupp, “Pruned DFT-spread FBMC: Low PAPR, low la- tency, high spectral efficiency,”IEEE Transactions on Communications, vol. 66, no. 10, pp. 4811–4825, 2018

    work page 2018

  37. [37]

    A novel DFT precoded filter bank system with iterative equalization,

    R. P. Junior, C. A. F. d. Rocha, B. S. Chang, and D. Le Ruyet, “A novel DFT precoded filter bank system with iterative equalization,”IEEE Wireless Communications Letters, vol. 10, no. 3, pp. 478–482, 2021

    work page 2021

  38. [38]

    A generalized DFT precoded filter bank system,

    ——, “A generalized DFT precoded filter bank system,”IEEE Wireless Communications Letters, vol. 11, no. 6, pp. 1176–1180, 2022

    work page 2022

  39. [39]

    A two-dimensional FFT precoded filter bank scheme,

    R. P. Junior, C. A. F. da Rocha, B. S. Chang, and D. Le Ruyet, “A two-dimensional FFT precoded filter bank scheme,”IEEE Transactions on Wireless Communications, vol. 22, no. 11, pp. 8366–8377, 2023

    work page 2023

  40. [40]

    A generalized two-dimensional fft precoded filter bank scheme with low complexity equalizers in time-frequency domain,

    R. P. Junior, C. A. F. Da Rocha, B. S. Chang, and D. Le Ruyet, “A generalized two-dimensional fft precoded filter bank scheme with low complexity equalizers in time-frequency domain,”IEEE Access, vol. 11, pp. 112 414–112 428, 2023

    work page 2023

  41. [41]

    Affine filter bank modulation: A new waveform for high mobility communications,

    H. L. Senger, G. P. Gonc ¸alves, B. S. Chang, H. S. Rou, K. R. R. Ranasinghe, G. T. F. de Abreu, and D. L. Ruyet, “Affine filter bank modulation: A new waveform for high mobility communications,”

    work page

  42. [42]

    Joint channel estimation and data detection for afdm receivers with oversampling,

    K. R. Rayan Ranasinghe, Y . Ge, G. T. Freitas de Abreu, and Y . Liang Guan, “Joint channel estimation and data detection for afdm receivers with oversampling,” in2025 International Conference on Computing, Networking and Communications (ICNC), 2025, pp. 823– 828

    work page 2025

  43. [43]

    Low-complexity large mimo detection via layered belief propagation in beam domain,

    T. Takahashi, A. T ¨olli, S. Ibi, and S. Sampei, “Low-complexity large mimo detection via layered belief propagation in beam domain,”IEEE Transactions on Wireless Communications, vol. 21, no. 1, pp. 234–249, 2022

    work page 2022

  44. [44]

    Design of adaptively scaled belief in multi-dimensional signal detection for higher-order modulation,

    T. Takahashi, S. Ibi, and S. Sampei, “Design of adaptively scaled belief in multi-dimensional signal detection for higher-order modulation,” IEEE Transactions on Communications, vol. 67, no. 3, pp. 1986–2001, 2019

    1986

  45. [45]

    On convergence conditions of gaussian belief propagation,

    Q. Su and Y .-C. Wu, “On convergence conditions of gaussian belief propagation,”IEEE Transactions on Signal Processing, vol. 63, no. 5, pp. 1144–1155, 2015

    work page 2015

  46. [46]

    Data- Aided CSI Estimation Using Affine-Precoded Superimposed Pilots in Orthogonal Time Frequency Space Modulated MIMO Systems,

    A. Mehrotra, S. Srivastava, A. K. Jagannatham, and L. Hanzo, “Data- Aided CSI Estimation Using Affine-Precoded Superimposed Pilots in Orthogonal Time Frequency Space Modulated MIMO Systems,”IEEE Transactions on Communications, vol. 71, no. 8, pp. 4482–4498, 2023

    work page 2023

  47. [47]

    Bayesian Joint Channel and Data Estimation for Correlated Large MIMO with Non-orthogonal Pi- lots,

    K. Ito, T. Takahashi, S. Ibi, and S. Sampei, “Bayesian Joint Channel and Data Estimation for Correlated Large MIMO with Non-orthogonal Pi- lots,” inICC 2021 - IEEE International Conference on Communications, 2021, pp. 1–6

    work page 2021

  48. [48]

    Bilinear Generalized Ap- proximate Message Passing—Part I: Derivation,

    J. T. Parker, P. Schniter, and V . Cevher, “Bilinear Generalized Ap- proximate Message Passing—Part I: Derivation,”IEEE Transactions on Signal Processing, vol. 62, no. 22, pp. 5839–5853, 2014

    work page 2014

  49. [49]

    Expectation-maximization gaussian-mixture approximate message passing,

    J. P. Vila and P. Schniter, “Expectation-maximization gaussian-mixture approximate message passing,”IEEE Transactions on Signal Processing, vol. 61, no. 19, pp. 4658–4672, 2013

    work page 2013

  50. [50]

    C. M. Bishop,Pattern Recognition and Machine Learning (Information Science and Statistics). Berlin, Heidelberg: Springer-Verlag, 2006

    2006

  51. [51]

    Fast and Efficient Sequential Radar Parameter Estimation in MIMO-OTFS Systems,

    K. R. R. Ranasinghe, H. S. Rou, and G. T. F. de Abreu, “Fast and Efficient Sequential Radar Parameter Estimation in MIMO-OTFS Systems,” inICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2024, pp. 8661– 8665

    work page 2024

  52. [2025]

    Affine Filter Bank Modulation: A New Waveform for High Mobility Communications

    [Online]. Available: https://arxiv.org/abs/2505.03589

    work page internal anchor Pith review Pith/arXiv arXiv