Multiple-Mode Affine Frequency Division Multiplexing with Index Modulation

Guangyao Liu; Jingjing Zhao; Tianqi Mao; Yanqun Tang; Zhenyu Xiao

REVIEW 5 major objections 5 minor 20 references

Multiple-Mode Affine Frequency Division Multiplexing with Index Modulation

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read MM-AFDM-IM, an index-modulation layer for AFDM, claims over 1.5 dB SNR gain at BER 10^-3 over three prior schemes by hiding bits in constellation-mode and chirp-arrangement patterns.

desk verdict Sound incremental extension of MM-OFDM-IM to AFDM, with a real but modest gain and a theoretical bound whose tightness claim needs a geometry-averaging caveat. read the letter →

arxiv 2507.13037 v1 pith:7XFPUVSA submitted 2025-07-17 eess.SP

Guangyao Liu , Tianqi Mao , Yanqun Tang , Jingjing Zhao , Zhenyu Xiao This is my paper · ORCID

classification eess.SP

keywords affinefrequencydivisionmultiplexingindexmodulationmultiple-modeconstellationsmodeactivationpatternchirparrangementdoubly-dispersivechannelspairwiseerrorprobabilitymaximum-likelihooddetection

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Affine frequency division multiplexing (AFDM) sends data on chirp-based subcarriers and is built to survive the time- and frequency-spreading channels of high-mobility links. This paper proposes MM-AFDM-IM, a variant that adds an index-modulation layer: each AFDM sub-block chooses which constellation alphabets (modes) are active on its chirps and how those modes are arranged, so extra bits ride in the mode-activation and chirp-arrangement patterns without spending extra power or bandwidth. At equal spectral efficiency of 2.25 bit/s/Hz on a three-path doubly dispersive channel, the paper reports more than 1.5 dB SNR gain at a bit error rate of $10^{-3}$ over AFDM-IM, distributed AFDM-IM, and super-mode OFDM-IM. It also derives a closed-form union bound on average bit error probability from pairwise error probabilities averaged over the channel, and shows by simulation that the bound is tight at high SNR. If the scheme works as claimed, AFDM gains a low-cost extra axis of information in the index domain, improving reliability without sacrificing spectral efficiency.

What carries the argument

The central object is the joint mode-activation/chirp-arrangement pattern (MAP/CAP) per AFDM sub-block: index bits select a combination of $k$ mode alphabets out of $M$ and a permutation of those modes over $n$ chirps, so the activation-and-arrangement pattern itself is an information carrier while all chirps stay active. The analytic result is carried by expressing a pairwise error event as a quadratic form $\delta = h^\dagger \Upsilon h$ of the channel vector $h$, where $\Upsilon = (\Phi(\hat{x})-\Phi(x))^\dagger(\Phi(\hat{x})-\Phi(x))$; the moment-generating function of this form is a product over the nonzero eigenvalues of $\Upsilon$, which converts the conditional pairwise error probability into a closed-form upper bound that can be summed over all pairwise events.

What would settle it

Run the same comparison at BER $10^{-3}$ on the $P=3$ doubly dispersive channel but feed the ML detector an imperfect estimated channel matrix; if the more-than-1.5 dB gain over the benchmarks shrinks or disappears, the central performance claim is falsified. Alternatively, push the $P=3$ and $P=4$ simulations in Fig. 3 to very low BER and check whether the union bound of eq. (27) ever falls below the simulated BER, which would falsify the claim that it is an upper bound.

Watch

Extended reading notes

Core claim

The paper's central claim is that a multiple-mode index-modulation layer can be inserted into AFDM without deactivating any chirps. In each sub-block of $n$ chirps, $k$ of $M$ possible disjoint constellation modes are selected by an index pattern, and the selected modes are permuted across the chirps by a second pattern; the index bits therefore encode both the mode activation pattern (MAP) and the chirp arrangement pattern (CAP), while every chirp carries a constellation symbol. The number of index bits per sub-block is $\lfloor \log_2(\binom{M}{k} n!/((n/k)!)^k) \rfloor$, and the symbol bits number $n\log_2 U$. Under maximum-likelihood detection with perfect channel state information, the paper bounds the pairwise error probability via the moment-generating function of a quadratic form in the channel vector, then unions over all pairwise events to obtain the average bit error probability upper bound of eq. (27). Simulation validates the bound as tight at high SNR and shows the proposed scheme exceeding the three benchmark schemes by more than 1.5 dB in SNR at BER $10^{-3}$ under the simulated doubly dispersive channel.

Load-bearing premise

The load-bearing premise is that the receiver has perfect channel state information and performs exhaustive maximum-likelihood detection over the full joint space of mode patterns, chirp arrangements, and symbols; with imperfect channel knowledge or a reduced-complexity detector, the claimed SNR gains are not established.

Editorial extensions

If this is right

At the simulated $P=3$ doubly dispersive channel and equal spectral efficiency of 2.25 bit/s/Hz, MM-AFDM-IM beats AFDM-IM, AFDM-IM-distributed, and SuM-OFDM-IM by more than 1.5 dB in SNR at BER $10^{-3}$.
The upper bound of eq. (27) is tight in the high-SNR regime for $P=3$ and $P=4$ path channels, so it can replace Monte Carlo simulations for performance prediction in that regime.
BER improves when the number of channel paths grows from 3 to 4, since the AFDM full-diversity design harvests more diversity from independent paths.
Because all chirps carry symbols, the scheme avoids the spectral waste of sparse index modulation that deactivates chirps; its gain is not simply a higher-order modulation effect.
Shifting a larger share of bits into the index domain moves information away from the constellation points that are most damaged by delay and Doppler spread, which is the paper's stated reason for the reliability gain.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper does not test what happens with imperfect channel estimation or with a reduced-complexity detector; whether the 1.5 dB gain survives practical reception is an open question the paper leaves implicit.
The mode-selection analysis suggests the QAM-based partition has larger inter-mode distance for most $MU>4$; extending the comparison to higher $M$ and $U$ could reveal whether the gain scales beyond the single simulated parameter set.
The analytical bound relies on a Gaussian channel vector, so measured high-mobility channels with correlated Doppler or non-Gaussian statistics would require re-deriving the quadratic-form moment-generating function.
A natural extension is to apply the same joint MAP/CAP philosophy to OTFS or other full-diversity waveforms, although the paper does not address such cross-waveform comparisons.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here's my read of arXiv:2507.13037. The paper takes the well-known MM-OFDM-IM machinery (mode activation patterns, chirp arrangement patterns, joint selection) and transplants it into AFDM. What's genuinely new is the AFDM-specific input-output model, the PEP/MGF/union-bound analysis, and the numerical evaluation. The construction is not a breakthrough, but it's a clean, competent piece of incremental work: all chirps remain active, so it avoids the spectral waste of sparse IM schemes, and the equal-spectral-efficiency comparison against AFDM-IM, AFDM-IM-distributed, and SuM-OFDM-IM shows a consistent >1.5 dB SNR gain at BER 10^-3. That gain is believable given the index-domain bit shift.

The analytical part is internally consistent: the CPEP, the Q-function approximation, the MGF step, and the union bound all follow. I see no circularity; the bound is derived, not fitted, and Fig. 3 shows it is tight for N=4, P=3,4 at high SNR. Credit where it's due: the derivations are standard but the execution is careful.

Now the soft spots. The biggest one concerns the tightness claim. The PEP in eq. (26) averages only over the Gaussian channel vector h, treating the delay and Doppler geometry (d_p, alpha_p) as fixed. But Sec. IV says the Doppler is generated per Jakes as alpha_p = alpha_max cos(theta_p), and the paper never states whether theta_p and d_p are held fixed across Monte Carlo trials. If they are resampled per frame, then the analytical bound is conditional on geometry and is not the average ABEP plotted in Fig. 3; the tightness shown could be an artifact of one geometry. If they are fixed, the bound is correct for that geometry, but then the claim of an 'average' bound is overstated. Either way, the paper needs one sentence to clarify, and ideally a bound averaged over geometry or a statement that geometry is fixed in both analysis and simulation.

Second, the closest baseline — dual-mode AFDM-IM [19] — is missing from Fig. 4. The whole point is to generalize from two modes to multiple modes, so a reader cannot see what the generalization actually buys. Third, the receiver is exhaustive ML with perfect CSI; there is no channel estimator or low-complexity detector, so the practical relevance is unproven. Fourth, the tightness validation is only for a toy system (N=4); fine for a first check, but not enough to claim 'asymptotically tight' broadly.

The citation pattern looks fine; the self-citation [20] is a standard MGF result, not a red flag. No code or data, but for this subfield that's not disqualifying.

Who's this for? Researchers working on IM-aided AFDM for 6G. It's a solid incremental paper that deserves a serious referee, provided the authors address the geometry issue and add the missing baseline. I'd send it to review, not desk-reject.

Referee Report

5 major / 5 minor

Summary. The paper proposes MM-AFDM-IM, an index-modulation scheme for affine frequency division multiplexing in which each sub-block activates k out of M constellation modes and arranges them over n chirps, so that index bits are carried by both the mode-activation pattern and the chirp-arrangement pattern while all chirps remain active. A mode-selection strategy based on MIAD/MIRD is discussed, and an approximate average bit error probability (ABEP) bound is derived through conditional PEP, a two-exponential Q-function approximation, MGFs, and a union bound. Simulations for a doubly dispersive channel are presented for N=4 to support the bound and for N=8 to compare against AFDM-IM, AFDM-IM-distributed, and SuM-OFDM-IM at equal spectral efficiency, claiming more than 1.5 dB SNR gain at BER 10^-3.

Significance. If the performance claim holds, MM-AFDM-IM is a useful extension of multiple-mode index modulation to AFDM, achieving full chirp utilization and an additional index-domain information dimension without extra energy. The analytical chain in eqs. (19)-(27) is internally consistent, the Q-function approximation and MGF step are standard, and the small-system validation in Fig. 3 suggests the high-SNR bound can be tight. The scheme is clearly specified with a look-up table example, and the benchmark comparison is made at a common spectral efficiency. However, the generality of the theoretical bound, the ideal-reception assumption, and the absence of the closest prior-work baseline limit the strength of the current claims.

major comments (5)

[Sec. III-B and Sec. IV] The PEP derivation in eqs. (20)-(26) treats the delay/Doppler geometry as deterministic: the matrices H_p and the quadratic form Υ depend on fixed d_p and α_p, and only h is averaged in eq. (23). Section IV, however, states that α_p = α_max cos(θ_p) with θ_p uniformly distributed, and it does not state that d_p and θ_p are held fixed across Monte Carlo trials. If the geometry is resampled per frame, the theoretical curve in Fig. 3 is not the average ABEP of the simulated system. Please either fix the delay/Doppler geometry in the simulation and state this explicitly, or extend the UPEP derivation to average over the geometry distribution.
[Sec. III-B, eq. (27), and abstract] The result is described as an 'upper bound' on ABEP, but eq. (21) is not a strict upper bound for the Q-function (at x=0 the right-hand side is 1/3, below Q(0)=1/2). Consequently eqs. (24)-(26) are approximations, and the wording 'asymptotically tight upper bound' in the abstract and Section V should be qualified accordingly.
[Sec. IV, Fig. 3] The tightness of the analytical bound is validated only for the tiny system (N=4, G=1, P=3,4). The main comparison in Fig. 4 uses (N,M,n,G,k,U)=(8,4,4,2,2,2), for which no theoretical curve is provided. Please add a validation at the N=8 configuration or justify why the small-system validation is sufficient to support the general tightness claim.
[Sec. II-B, eq. (15)] The receiver in eq. (15) is exhaustive maximum-likelihood detection with perfect CSI, and the paper provides no complexity analysis or reduced-complexity alternative. The index bits are precisely the components most sensitive to imperfect channel knowledge, and the ML search space is exponential in the number of bits, so the practical significance of the claimed SNR gains under ideal reception is not established. Please add a complexity discussion and, ideally, an evaluation under imperfect CSI or with a suboptimal detector.
[Sec. IV, Fig. 4] The paper cites the dual-mode AFDM-IM scheme [19] as the most relevant previous extension of distinguishable modes to AFDM, but [19] is not included in the benchmark comparison in Fig. 4. Without this closest baseline, the claim of superiority over 'conventional benchmark schemes' is incomplete.

minor comments (5)

[Eq. (16)] The notation d_PSK_MIAD(M U) is ambiguous; please clarify whether this is the minimum distance of the parent M·U-ary PSK constellation or the actual intra-mode distance after partitioning.
[Sec. II-A] The condition M1 ∩ M2 ∩ ... ∩ MM = ∅ should be stated as pairwise disjointness; the current formulation only requires the intersection of all modes to be empty.
[Eq. (27)] Please define e(x → xhat) explicitly as the Hamming distance between the bit mappings of x and xhat.
[Table I] The notation S_i^(j) is somewhat compact; a short explanation of the superscript (j) before the table would improve readability.
[References] Reference [14] contains a typo ('Cmmun.' instead of 'Commun.'), and reference [9] contains 'V e h.' instead of 'Ve h.'; these should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ABEP bound is derived from the stated channel model and validated against external benchmarks; the only self-citation is a general MGF lemma.

full rationale

Walked the claimed derivation chain. The ABEP derivation in Sec. III-B is not fitted to the simulated curves: the CPEP in eq. (20), the MGF-based UPEP in eqs. (23)-(26), and the union bound in eq. (27) follow algebraically from the stated Gaussian channel-coefficient model and the Q-function approximation. The only self-citation is [20, Theorem 2], used to evaluate the MGF of a Hermitian quadratic form of a zero-mean complex Gaussian vector; this is a general, parameter-free lemma whose stated assumptions do not include the target BER result, so under the independence rule it does not make the derivation circular. The performance claim in Fig. 4 is tested against three external benchmark schemes (AFDM-IM, AFDM-IM-distributed, SuM-OFDM-IM) at equal spectral efficiency, so the central claim has independent content. The reviewer concern that eq. (26) averages only over the channel coefficients h while Sec. IV randomizes Doppler geometry according to the Jakes model is a correctness/completeness issue about the tightness of the bound for the simulated channel, not a circularity, because no fitted parameter and no self-referential definition is involved. No step in the paper reduces by construction to its own input, so no circularity steps are reported.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The theory uses no data-fitted numbers and postulates no new physical entities. The central claim rests on standard math (MGF and union bounds), the doubly-dispersive channel model of the AFDM literature, and an idealized receiver (perfect CSI, exhaustive ML detection). The main ledger cost is the idealized receiver assumption and the unstated averaging of the PEP bound over randomized delay and Doppler geometry.

assumptions (5)

domain assumption The effective channel matrices H_p = A Γ_p^CPP Δ_νp Π^{d_p} A^H with the CPP matrix of eq. (12) model the doubly-dispersive channel in the DAF domain.
Invoked in Sec. II-B, eqs. (10)-(14); the phase terms are taken from the AFDM literature and not re-derived here.
domain assumption Perfect CSI at the receiver and ML detection over all MAP, CAP, and symbol realizations (eq. 15).
Stated in Sec. III-B; the entire analysis and simulation assume ideal reception, and no channel estimator is proposed.
domain assumption Path gains h_p are i.i.d. CN(0,1/P) and independent of the normalized delays and Doppler shifts, enabling the MGF-based PEP of eqs. (25)-(26).
Used in Sec. III-B to write δ as a quadratic form of a zero-mean complex Gaussian with covariance (1/P)I; consistent with the Jakes-based simulation but not stated as a separate assumption there.
standard math MGF of a Hermitian quadratic form of a zero-mean complex Gaussian vector, cited to [20, Theorem 2] (eq. 25).
Standard result; cited to the authors' own paper but externally checkable.
standard math Q-function bound (eq. 21) and union bound (eq. 27).
Both are standard; the paper itself notes the union bound is loose at low SNR (Sec. IV), matching the gap in Fig. 3.

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Cite this review

Pith. "Pith review of Multiple-Mode Affine Frequency Division Multiplexing with Index Modulation." pith.science (2026). https://pith.science/paper/7XFPUVSA

@misc{pith2026250713037,
  author       = {Pith},
  title        = {Pith review of: Multiple-Mode Affine Frequency Division Multiplexing with Index Modulation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7XFPUVSA}},
  note         = {Machine review of arXiv:2507.13037}
}

read the original abstract

Affine frequency division multiplexing (AFDM), a promising multicarrier technique utilizing chirp signals, has been envisioned as an effective solution for high-mobility communication scenarios. In this paper, we develop a multiple-mode index modulation scheme tailored for AFDM, termed as MM-AFDM-IM, which aims to further improve the spectral and energy efficiencies of AFDM. Specifically, multiple constellation alphabets are selected for different chirp-based subcarriers (chirps). Aside from classical amplitude/phase modulation, additional information bits can be conveyed by the dynamic patterns of both constellation mode selection and chirp activation, without extra energy consumption. Furthermore, we discuss the mode selection strategy and derive an asymptotically tight upper bound on the bit error rate (BER) of the proposed scheme under maximum-likelihood detection. Simulation results are provided to demonstrate the superior performance of MM-AFDM-IM compared to conventional benchmark schemes.

Figures

Figures reproduced from arXiv: 2507.13037 by the authors.

**Figure 2.** An example for 8-mode constellation, which constitutes a 16-QAM [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Comparison of the theoretical ABEP upper bound and the simulated [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Performance comparison between the proposed MM-AFDM-IM and [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

20 extracted references · 19 canonical work pages

[19]

Dual- mode index modulation based on affine frequency division multiplex- ing,

A. Anoop, C. K. Thomas, S. Kala, J. B. Benifa, and W. Saad, “Dual- mode index modulation based on affine frequency division multiplex- ing,” Phys. Commun. , vol. 70, p. 102628, Jun. 2025

work page 2025
[20]

Pre-chirp-domain index modulation for full-diversity affine frequency division multiplexing towards 6G,

G. Liu, T. Mao, Z. Xiao, M. Wen, R. Liu, J. Zhao, E. Basar, Z. Wang, and S. Chen, “Pre-chirp-domain index modulation for full-diversity affine frequency division multiplexing towards 6G,” IEEE Trans. Wireless Commun., early access, Apr. 2025, DOI: 10.1109/TWC.2025.3559997

work page arXiv 2025
[1]

LEO satellite access network (LEO-SAN) toward 6G: Challenges and approaches,

Z. Xiao, J. Yang, T. Mao, C. Xu, R. Zhang, Z. Han, and X.-G. Xia, “LEO satellite access network (LEO-SAN) toward 6G: Challenges and approaches,” IEEE Wireless Commun. , vol. 31, no. 2, pp. 89–96, Apr. 2024

work page 2024
[2]

On the road to 6G: Visions, requirements, key technologies, and testbeds,

C.-X. Wang et al. , “On the road to 6G: Visions, requirements, key technologies, and testbeds,” IEEE Commun. Surv. Tuts. , vol. 25, no. 2, pp. 905–974, Feb. 2023

work page 2023
[3]

AFDM: A full diversity next generation waveform for high mobility communications,

A. Bemani, N. Ksairi, and M. Kountouris, “AFDM: A full diversity next generation waveform for high mobility communications,” in Proc. IEEE Int. Conf. Commun. Workshops (ICC Workshops) , Montreal, QC, Canada, Jun. 2021, pp. 1–6

work page 2021
[4]

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. Wireless Commun., vol. 22, no. 11, pp. 8214 – 8229, Nov. 2023

work page 2023
[5]

AFDM-SCMA: A promising waveform for massive connectivity over high mobility channels,

Q. Luo, P. Xiao, Z. Liu, Z. Wan, N. Thomos, Z. Gao, and Z. He, “AFDM-SCMA: A promising waveform for massive connectivity over high mobility channels,” IEEE Trans. Wireless Commun., vol. 23, no. 10, pp. 14 421–14 436, Oct. 2024

work page 2024
[6]

AFDM- based bistatic integrated sensing and communication in static scatterer environments,

J. Zhu, Y . Tang, F. Liu, X. Zhang, H. Yin, and Y . Zhou, “AFDM- based bistatic integrated sensing and communication in static scatterer environments,” IEEE Wireless Commun. Lett. , vol. 13, no. 8, pp. 2245– 2249, Aug. 2024

work page 2024

Show all 20 references

[7]

AFDM-enabled integrated sensing and communication: Theoretical framework and pilot design,

F. Zhang, Z. Wang, T. Mao, T. Jiao, Y . Zhuo, M. Wen, W. Xi- ang, S. Chen, and G. K. Karagiannidis, “AFDM-enabled integrated sensing and communication: Theoretical framework and pilot design,” arXiv:2502.14203, 2025

2025 arXiv
[8]

Diagonally reconstructed channel estimation for MIMO-AFDM with inter-doppler interference in doubly selective channels,

H. Yin, X. Wei, Y . Tang, and K. Yang, “Diagonally reconstructed channel estimation for MIMO-AFDM with inter-doppler interference in doubly selective channels,” IEEE Trans. Wireless Commun. , vol. 23, no. 10, pp. 14 066–14 079, Oct. 2024

2024
[9]

Channel estimation for AFDM with superimposed pilots,

K. Zheng, M. Wen, T. Mao, L. Xiao, and Z. Wang, “Channel estimation for AFDM with superimposed pilots,” IEEE Trans. V eh. Technol. , vol. 74, no. 2, pp. 3389–3394, Feb. 2025

2025
[10]

Orthogonal frequency division multiplexing with index modulation,

E. Bas ¸ar, ¨U. Ayg ¨ol¨u, E. Panayırcı, and H. V . Poor, “Orthogonal frequency division multiplexing with index modulation,” IEEE Trans. Signal Process., vol. 61, no. 22, pp. 5536–5549, Nov. 2013

2013
[11]

Index-modulation- aided terahertz communications with reconfigurable intelligent surface,

T. Mao, Z. Zhou, Z. Xiao, C. Han, and Z. Wang, “Index-modulation- aided terahertz communications with reconfigurable intelligent surface,” IEEE Trans. Wireless Commun., vol. 23, no. 7, pp. 8059–8070, Jul. 2024

2024
[12]

Novel index modulation techniques: A survey,

T. Mao, Q. Wang, Z. Wang, and S. Chen, “Novel index modulation techniques: A survey,” IEEE Commun. Surv. Tuts. , vol. 21, no. 1, pp. 315–348, 1st Quart. 2019

2019
[13]

Terahertz wireless communications with flexible index modulation aided pilot design,

T. Mao and Z. Wang, “Terahertz wireless communications with flexible index modulation aided pilot design,” IEEE J. Sel. Areas Commun. , vol. 39, no. 6, pp. 1651–1662, Jun. 2021

2021
[14]

Design and performance analysis of index modulation empowered AFDM system,

J. Zhu, Q. Luo, G. Chen, P. Xiao, and L. Xiao, “Design and performance analysis of index modulation empowered AFDM system,”IEEE Wireless Cmmun. Lett. , vol. 13, no. 3, pp. 686–690, Mar. 2024

2024
[15]

Affine frequency division multiplexing with index modulation,

Y . Tao, M. Wen, Y . Ge, and J. Li, “Affine frequency division multiplexing with index modulation,” in Proc. IEEE Wireless Commun. Netw. Conf. (WCNC), Dubai, United Arab Emirates, Apr. 2024, pp. 1–6

2024
[16]

Dual-mode index modulation aided OFDM,

T. Mao, Z. Wang, Q. Wang, S. Chen, and L. Hanzo, “Dual-mode index modulation aided OFDM,” IEEE Access , vol. 5, pp. 50–60, Feb. 2017

2017
[17]

Multiple-mode orthogonal frequency division multiplexing with index modulation,

M. Wen, E. Basar, Q. Li, B. Zheng, and M. Zhang, “Multiple-mode orthogonal frequency division multiplexing with index modulation,” IEEE Trans. Commun. , vol. 65, no. 9, pp. 3892–3906, Sep. 2017

2017
[18]

Super-mode OFDM with index modula- tion,

A. T. Dogukan and E. Basar, “Super-mode OFDM with index modula- tion,” IEEE Trans. Wireless Commun. , vol. 19, no. 11, pp. 7353–7362, Nov. 2020

2020

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [19]

Dual- mode index modulation based on affine frequency division multiplex- ing,

A. Anoop, C. K. Thomas, S. Kala, J. B. Benifa, and W. Saad, “Dual- mode index modulation based on affine frequency division multiplex- ing,” Phys. Commun. , vol. 70, p. 102628, Jun. 2025

work page 2025

[2] [20]

Pre-chirp-domain index modulation for full-diversity affine frequency division multiplexing towards 6G,

G. Liu, T. Mao, Z. Xiao, M. Wen, R. Liu, J. Zhao, E. Basar, Z. Wang, and S. Chen, “Pre-chirp-domain index modulation for full-diversity affine frequency division multiplexing towards 6G,” IEEE Trans. Wireless Commun., early access, Apr. 2025, DOI: 10.1109/TWC.2025.3559997

work page arXiv 2025

[3] [1]

LEO satellite access network (LEO-SAN) toward 6G: Challenges and approaches,

Z. Xiao, J. Yang, T. Mao, C. Xu, R. Zhang, Z. Han, and X.-G. Xia, “LEO satellite access network (LEO-SAN) toward 6G: Challenges and approaches,” IEEE Wireless Commun. , vol. 31, no. 2, pp. 89–96, Apr. 2024

work page 2024

[4] [2]

On the road to 6G: Visions, requirements, key technologies, and testbeds,

C.-X. Wang et al. , “On the road to 6G: Visions, requirements, key technologies, and testbeds,” IEEE Commun. Surv. Tuts. , vol. 25, no. 2, pp. 905–974, Feb. 2023

work page 2023

[5] [3]

AFDM: A full diversity next generation waveform for high mobility communications,

A. Bemani, N. Ksairi, and M. Kountouris, “AFDM: A full diversity next generation waveform for high mobility communications,” in Proc. IEEE Int. Conf. Commun. Workshops (ICC Workshops) , Montreal, QC, Canada, Jun. 2021, pp. 1–6

work page 2021

[6] [4]

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. Wireless Commun., vol. 22, no. 11, pp. 8214 – 8229, Nov. 2023

work page 2023

[7] [5]

AFDM-SCMA: A promising waveform for massive connectivity over high mobility channels,

Q. Luo, P. Xiao, Z. Liu, Z. Wan, N. Thomos, Z. Gao, and Z. He, “AFDM-SCMA: A promising waveform for massive connectivity over high mobility channels,” IEEE Trans. Wireless Commun., vol. 23, no. 10, pp. 14 421–14 436, Oct. 2024

work page 2024

[8] [6]

AFDM- based bistatic integrated sensing and communication in static scatterer environments,

J. Zhu, Y . Tang, F. Liu, X. Zhang, H. Yin, and Y . Zhou, “AFDM- based bistatic integrated sensing and communication in static scatterer environments,” IEEE Wireless Commun. Lett. , vol. 13, no. 8, pp. 2245– 2249, Aug. 2024

work page 2024