Affine Frequency-Division Multiplexing (AFDM)

• AFDM is a chirp-based multicarrier waveform built on the discrete affine Fourier transform (DAFT) that replaces sinusoidal subcarriers with orthogonal chirps to mitigate delay and Doppler effects.
• Its design employs two tunable affine parameters to control chirp rate and phase, creating a sparse, quasi-diagonal channel representation that can achieve full diversity.
• AFDM supports efficient channel estimation, equalization, and joint sensing-communications functionality while maintaining compatibility with OFDM-based systems.

Affine Frequency-Division Multiplexing (AFDM) is a chirp-based multicarrier waveform built on the discrete affine Fourier transform (DAFT) and its inverse, proposed as a direct generalization of OFDM for high-mobility, doubly dispersive channels in which delay spread and Doppler spread jointly destroy the orthogonality of sinusoidal subcarriers. In AFDM, Fourier tones are replaced by orthogonal chirp subcarriers, a chirp-periodic prefix (CPP) replaces or generalizes the cyclic prefix, and two tunable affine parameters control how the waveform is embedded in the time-frequency plane. The resulting DAFT-domain channel is typically sparse, quasi-diagonal, and delay-Doppler structured, which under suitable parameter choices enables full diversity and makes AFDM simultaneously relevant to communications, sensing, and OFDM-compatible system evolution (Bemani et al., 2021, Yin et al., 7 Feb 2025, Luo et al., 11 Jun 2026).

1. Conceptual origin and relation to other waveforms

AFDM was introduced as a response to the central weakness of OFDM in linear time-varying and doubly dispersive channels: Doppler spread destroys subcarrier orthogonality and creates severe inter-carrier interference (ICI), so the frequency-domain channel no longer behaves as a simple diagonalizable multipath operator (Bemani et al., 2021, Bemani et al., 2022). The AFDM literature therefore redefines the multicarrier basis rather than abandoning multicarrier signaling. Data are still block-mapped and transformed, but the basis functions are chirps rather than stationary complex exponentials.

This positioning is important because AFDM is consistently presented not as an unrelated waveform family, but as an affine-transform extension of OFDM and related chirp systems. Standardization-oriented treatments describe OFDM as the special case $c_1=c_2=0$, and they also place OCDM inside the same affine-transform family as another special parameter setting, so AFDM functions as a unifying framework rather than a purely ad hoc construction (Luo et al., 11 Jun 2026, Rou et al., 8 Feb 2026). In the same literature, OTFS is treated as the main conceptual comparator: OTFS uses a two-dimensional delay-Doppler representation, whereas AFDM uses a one-dimensional DAFT-domain representation that retains FFT-centric implementation structure while still targeting delay-Doppler separability (Bemani et al., 2022, Yin et al., 7 Feb 2025).

A recurring misconception in the early discussion of AFDM is that it is merely “chirped OFDM.” The survey literature rejects that reduction. AFDM is OFDM-like in its use of block transforms, orthogonal multiplexing, and FFT/IFFT hardware reuse, but its defining feature is the affine-domain mapping that makes channel paths visible as structured DAFT-domain shifts rather than as diffuse ICI patterns (Yin et al., 7 Feb 2025, Rou et al., 29 Jul 2025). A second misconception is that AFDM is only a communications waveform. By 2024–2026, a substantial body of work had reframed it as a joint communication-sensing waveform with explicit ambiguity-function analysis, pilot-only sensing constructions, monostatic and bistatic processing modes, and compatibility arguments with FMCW-like processing (Bemani et al., 2024, Bedeer, 3 Apr 2025, Yin et al., 11 Jul 2025, Bemani et al., 6 Nov 2025).

2. Modulation kernel, chirp parameters, and transceiver structure

In its standard discrete formulation, AFDM maps a DAFT-domain symbol vector $\mathbf{x}=[x[0],\dots,x[N-1]]^T$ to the time domain by

$$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$

where $\mathbf{F}$ is the $N$-point DFT matrix and $\mathbf{A}_{c}$ is a diagonal chirp matrix (Yin et al., 7 Feb 2025). In elementwise form,

$$s[n]=\frac{1}{\sqrt{N}}\sum_{m=0}^{N-1} x_m e^{j2\pi\left(c_1 n^2+c_2 m^2+\frac{nm}{N}\right)}, \qquad n=0,\dots,N-1,$$

so the transmitted waveform is a superposition of orthogonal chirps whose phase contains quadratic terms in time index $n$ and subcarrier index $m$ (Bedeer, 3 Apr 2025).

The two affine parameters have distinct operational roles. The literature emphasizes that $c_1$ appears only in the quadratic time term $\mathbf{x}=[x[0],\dots,x[N-1]]^T$0, while $\mathbf{x}=[x[0],\dots,x[N-1]]^T$1 appears only in the quadratic subcarrier-index term $\mathbf{x}=[x[0],\dots,x[N-1]]^T$2. Accordingly, $\mathbf{x}=[x[0],\dots,x[N-1]]^T$3 controls the common chirp rate of all subcarriers, i.e. the frequency sweep versus time, whereas $\mathbf{x}=[x[0],\dots,x[N-1]]^T$4 controls the initial phase offset across subcarriers, i.e. how the chirps are staggered in phase (Yin et al., 7 Feb 2025). The mixed term $\mathbf{x}=[x[0],\dots,x[N-1]]^T$5 provides uniformly spaced initial frequencies across subcarriers and is the point at which AFDM most closely resembles OFDM-style multiplexing.

The transceiver architecture is one of AFDM’s most persistent selling points. Multiple papers note that the IDAFT can be implemented as an IFFT surrounded by diagonal chirp multiplications, and the DAFT as the corresponding FFT-surrounded inverse chirp operations, so the structural deviation from OFDM is lightweight digital pre- and post-processing rather than a new modem pipeline (Yin et al., 7 Feb 2025, Rou et al., 8 Feb 2026, Rou et al., 29 Jul 2025). Prefixing is handled by a CPP rather than a CP. The CPP length must be at least the maximum channel delay spread, and when $\mathbf{x}=[x[0],\dots,x[N-1]]^T$6 is an integer multiple of $\mathbf{x}=[x[0],\dots,x[N-1]]^T$7 with even $\mathbf{x}=[x[0],\dots,x[N-1]]^T$8, the CPP reduces to the conventional CP, reinforcing the backward-compatibility argument (Yin et al., 7 Feb 2025, Bemani et al., 2021).

A further feature developed in later standardization-oriented work is the continuous-time chirp interpretation and spectral wrapping. If $\mathbf{x}=[x[0],\dots,x[N-1]]^T$9, the instantaneous bandwidth of the chirp exceeds the Nyquist bandwidth, and digital sampling folds the spectrum periodically into $$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$0. This structured wrapping is treated not as a defect but as part of AFDM’s design space, with consequences for sensing, FMCW compatibility, and discrete-time implementation (Luo et al., 11 Jun 2026, Yin et al., 11 Jul 2025).

3. Delay-Doppler representation, diversity, and generalized channel models

The central analytical claim of AFDM is that the DAFT domain provides a full or near-full delay-Doppler representation of the channel. In the original integer-Doppler analysis, the effective DAFT-domain channel becomes sparse, with each path producing a structured shift whose location depends on path delay and Doppler (Bemani et al., 2021, Bemani et al., 2022). The location variable is typically written in terms of a delay-dependent affine shift, and the overviews emphasize the corresponding intuition: a unit Doppler shift corresponds to a unit shift in the DAFT domain, while a unit delay shift corresponds to a $$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$1-step shift (Yin et al., 7 Feb 2025).

This leads directly to the parameter-design problem. The canonical integer-Doppler choice is

$$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$2

with $$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$3 chosen as an irrational number or a sufficiently small rational number, so that paths with different delays and Dopplers do not overlap in the DAFT domain and the resulting path-dependent matrices remain linearly independent (Bemani et al., 2021, Bemani et al., 2022). A related overview formulation states that if

$$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$4

then a bijective relationship between the delay-Doppler domain and the DAFT domain is obtained (Yin et al., 7 Feb 2025). Under the associated underspread condition

$$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$5

AFDM achieves full diversity, meaning that the diversity order equals the number of separable paths $$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$6 (Bemani et al., 2021, Bemani et al., 2022).

The phrase “optimal diversity order” in the survey literature refers to this pathwise harvesting of channel diversity. Because each symbol effectively experiences all separable paths in the DAFT domain, the signal-channel interaction is described as “non-fading” in the sense that path energy can be coherently gathered rather than being lost to ICI-dominated interference (Yin et al., 7 Feb 2025). This is also the basis for the frequent comparison with OTFS: AFDM’s channel representation is treated as effectively one-dimensional in the DAFT domain, whereas OTFS’s native delay-Doppler representation is inherently two-dimensional (Yin et al., 7 Feb 2025, Tao et al., 2023).

Beyond the original narrowband integer-Doppler setting, later work broadened the model class substantially. Fractional Doppler and fractional delay were analyzed through generalized fractional-delay-fractional-Doppler channel models that include practical pulse shaping and inter-sample coupling (Rou et al., 8 Feb 2026). Underwater acoustic and other low-carrier-frequency settings motivated multi-scale multi-lag channel models in which Doppler time scaling cannot be ignored; there the AFDM channel frequency response was analyzed under DFS and DTS, leading to new estimators and theoretical comparisons via CFR overlap probability, mutual incoherence, and diversity gain (Cao et al., 2024). Wideband doubly dispersive channels with time-scaling effects motivated a further CPP/CPS extension, optimized chirp-parameter design for pulse widening and pulse shortening, and a sparsity analysis of the DAF-domain equivalent channel under scale-dependent Doppler geometry (Li et al., 4 Jul 2025). Collectively, these developments show that AFDM’s core affine design principle is being pushed well beyond the original narrowband LTV formulation.

4. Channel estimation, equalization, and detection

Because AFDM makes the effective channel sparse or quasi-diagonal in the DAFT domain, pilot-aided estimation can be organized around a small protected region rather than a two-dimensional pilot lattice. The foundational pilot-aided channel-estimation work proposed single-pilot aided (SPA) and multiple-pilots aided (MPA) schemes, in which pilot, guard, and data symbols are arranged in the DAFT domain and the receiver uses an estimation threshold and a mapping table to recover path delays, Dopplers, and gains (Yin et al., 2022). Embedded pilot-aided estimation within the same AFDM frame was then formalized in a broader transceiver treatment, where one pilot plus guard symbols is sufficient to estimate the effective channel while preserving the remaining DAFT-domain positions for data (Bemani et al., 2022).

The literature is explicit that sparse pilot-domain behavior is strongest when path shifts are integer-grid aligned. Fractional delay and fractional Doppler spread energy across the DAFT domain, degrading sparsity and pilot-data separability. One remedy proposed in the 2025 overview is pulse shaping and matched filtering in the DAFT domain, with lower-sidelobe windows such as Hamming or Dolph–Chebyshev recommended to suppress spreading and improve the normalized mean-square error of channel estimation (Yin et al., 7 Feb 2025). When pathwise parameter estimation becomes inaccurate because of limited delay-Doppler resolution, the same overview recommends estimating the effective channel matrix directly via a diagonal-reconstruction strategy, exploiting the fact that the AFDM ECM remains quasi-diagonal (Yin et al., 7 Feb 2025).

Detection follows the same structural logic. Since AFDM symbols are dispersed across the DAFT domain, sequence-wise detection is generally required, but low-complexity processing is enabled by the sparse or banded ECM. The original full-diversity paper proposed a weighted MRC-based DFE using zero padding, while later surveys summarize non-iterative ZF and LMMSE detectors that exploit matrix structure, alongside iterative message-passing detectors that improve BER in high-mobility doubly selective channels (Bemani et al., 2022, Yin et al., 7 Feb 2025). For robust index-modulated and multi-antenna settings, a double-layer message passing (DLMP) detector was developed to enforce activation constraints while preserving a better BER-complexity tradeoff than conventional low-complexity alternatives (Tao et al., 2024). In wideband time-scaled channels, a cross-domain distributed orthogonal approximate message passing detector (CD-D-OAMP) was introduced, with state evolution and parallelizable groupwise updates explicitly designed around AFDM’s cross-domain sparsity (Li et al., 4 Jul 2025).

Specialized channel-estimation regimes have also emerged. For multi-scale multi-lag underwater acoustic channels, AFDM-IMI was proposed for low-to-moderate DTS and AFDM-OMP for high DTS; the latter exploits sparse recovery on a delay-scale dictionary and is motivated by AFDM’s lower mutual incoherence relative to OFDM and OCDM in the same setting (Cao et al., 2024). These extensions are significant because they indicate that the AFDM estimation problem is not monolithic: the same affine structure supports threshold-based pilot mapping, banded linear estimation, sparse recovery, and message passing, depending on the propagation regime.

5. Integrated sensing and communication

AFDM’s sensing relevance follows from its chirp structure and from the fact that delay and Doppler are already the native variables of its communication-theoretic channel representation. An early ISAC letter showed that either the full AFDM signal or only its pilot part consisting of one DAFT-domain symbol and its guard interval can be used to identify all delay and Doppler components associated with the propagation medium, and that one pilot symbol achieves almost the same sensing performance as using the entire AFDM frame (Bemani et al., 2024). The same work highlighted a distinctive monostatic advantage: because the pilot is itself a chirp, analog dechirping and simple filtering support self-interference cancellation without expensive full-duplex methods (Bemani et al., 2024).

A more formal ambiguity-function analysis then established the sensing geometry of AFDM. For random $$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$7-ary QAM data, a closed-form normalized ambiguity function was derived,

$$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$8

together with mean and variance expressions and a Rice approximation for $$\mathbf{s}=\mathbf{A}_{c_2}^{H}\mathbf{F}^{H}\mathbf{A}_{c_1}^{H}\mathbf{x}, \qquad \mathbf{x}=\mathbf{A}_{c_1}\mathbf{F}\mathbf{A}_{c_2}\mathbf{s},$$9 (Bedeer, 3 Apr 2025). That work also derived a sensing-oriented chirp-rate condition,

$\mathbf{F}$0

to minimize delay/range sidelobes in the presence of random data symbols, and it reported that AFDM substantially outperforms OFDM in both PSLR and ISLR (Bedeer, 3 Apr 2025). An important nuance of this analysis is that $\mathbf{F}$1 is the dominant sensing-design parameter, whereas $\mathbf{F}$2 does not appear in the zero-delay response in a way that enables Doppler-sidelobe reduction (Bedeer, 3 Apr 2025).

Another 2025 sensing analysis recast the same behavior geometrically. It showed that the auto-ambiguity function of an AFDM chirp subcarrier has a “spike-like” local property and a “periodic-like” global property along rotated delay and Doppler dimensions, generating a parallelogram-shaped unambiguity region of area $\mathbf{F}$3 (Yin et al., 11 Jul 2025). The cross-ambiguity function between distinct chirp subcarriers has the same local and global structure with an additional Doppler shift, and inserting guard symbols around a pilot produces interference-free sensing within a smaller interference-free parallelogram (Yin et al., 11 Jul 2025). This formalizes the widespread intuition that AFDM is not merely sensing-capable because it is chirped, but because its chirp structure yields a predictable ambiguity lattice.

ISAC-oriented system papers then leveraged these properties in more architectural ways. Standardization and “communication to sensing” surveys describe AFDM as naturally compatible with FMCW-style dechirping, monostatic low-complexity SIC, and reduced-rate sampling. In monostatic sensing, analog dechirping can collapse the strong direct transmitter-receiver leakage to a DC component that is removable by simple filtering; in bistatic sensing, AFDM supports sub-Nyquist sampling while preserving delay resolution, with the tradeoff that the maximum unambiguous delay is reduced by the downsampling factor (Luo et al., 11 Jun 2026, Bemani et al., 6 Nov 2025). These works also emphasize that DAFT-domain resource assignment provides a mechanism for multiradar or multicell interference mitigation without forcing different cells to use different chirp rates (Bemani et al., 6 Nov 2025).

6. Compatibility, standardization, and RF/system considerations

From 2025 onward, a distinct AFDM literature emerged around standardization rather than only BER performance. Its main thesis is that AFDM can be inserted into legacy 4G/5G-style processing chains with limited modification because the waveform reuses FFT/IFFT engines, one-dimensional resource grids, and CP-like protection logic, adding only chirp-domain preprocessing and postprocessing (Luo et al., 11 Jun 2026, Rou et al., 8 Feb 2026). This claim is made both for downlink integration, via a cascaded IDAFT plus CP-OFDM-style mapping over NR resource blocks, and for uplink integration, via DFT-s-OFDM with frequency-domain spectral shaping (FDSS), where AFDM can be interpreted as an enhanced shaping mode rather than a wholly distinct uplink transmitter (Luo et al., 11 Jun 2026).

The same standardization literature extends compatibility arguments well beyond NR. For FMCW radar, a special AFDM setting with $\mathbf{F}$4 and the $\mathbf{F}$5-th subcarrier active produces a digital discrete-time counterpart of an FMCW chirp, with dechirped beat-frequency processing that approaches conventional FMCW sensing performance and near-CRLB behavior (Luo et al., 11 Jun 2026). For LoRa, a parameter setting exists in which a LoRa symbol is interpreted as a single-active-index AFDM symbol, so either the conventional LoRa receiver or a DAFT-domain AFDM receiver can be used (Luo et al., 11 Jun 2026). These are compatibility claims in the literal architectural sense, not only analogies.

Multiple access, MIMO, and RF metrics are treated as standardization-critical. AFDMA resource assignment can be organized around guard-symbol requirements $\mathbf{F}$6, reducing pilot-data interference and inter-user interference, while non-orthogonal access options such as SCMA on top of AFDM are also mentioned (Yin et al., 7 Feb 2025). MIMO-AFDM is formulated in a joint Spatial-Affine domain with end-to-end models of the form

$\mathbf{F}$7

and the literature points to LOS-based precoding in single-user settings and weighted MMSE extensions in multi-user settings (Luo et al., 11 Jun 2026). Pilot design, scalable MIMO scheduling, DMRS integration, waveform coexistence with CP-OFDM and DFT-s-OFDM, and higher-layer signaling of chirp parameters are all listed as open specification issues (Luo et al., 11 Jun 2026, Rou et al., 29 Jul 2025).

PAPR remains a practical concern. A 2024 letter identified high PAPR in AFDM as a crucial problem and proposed grouped pre-chirp selection (GPS), which varies the pre-chirp parameter across subcarrier groups without destroying orthogonality or the sparse effective-channel structure (Yuan et al., 2024). Simulations reported that AFDM with GPS can achieve better PAPR performance than OTFS while maintaining lower modulation complexity, and that adjacent grouping outperforms comb grouping, with the gap shrinking as the number of groups increases (Yuan et al., 2024). Later survey work broadened the point: AFDM can reuse OFDM-era PAPR techniques such as PTS and tone reservation, while its chirp parameters provide additional waveform-native flexibility (Luo et al., 11 Jun 2026).

Hardware impairments have also been analyzed directly. A 2026 overview modeled phase noise as a discrete Wiener process and CFO as a diagonal phase-rotation matrix, then compared the resulting distortion in OFDM and AFDM. In the reported simulations, OFDM lost about $\mathbf{F}$8 dB SNR at BER $\mathbf{F}$9 under CFO $N$0, whereas AFDM remained close to the ideal case; under phase noise at BER $N$1, AFDM gained about $N$2 dB over OFDM (Rou et al., 8 Feb 2026). These results are part of the argument that AFDM is not only mobility-robust but also comparatively resilient to high-frequency oscillator impairments.

7. Emerging variants, security, and open research directions

One of the most active AFDM subfields is index modulation. AFDM-IM uses activation states of DAF-domain subsymbols to carry information in addition to conventional constellation symbols, and early analyses derived asymptotically tight BER bounds under channel-estimation errors while showing that distributed grouping performs better than localized grouping (Tao et al., 2023). A notable result of that paper is that index bits have stronger diversity protection than modulated bits even when the full-diversity condition of AFDM is not satisfied (Tao et al., 2023). Pre-chirp-domain index modulation then pushed the idea further by using subcarrier-dependent $N$3 choices as implicit information carriers; the key analytical point was that changing $N$4 across subcarriers does not destroy orthogonality (Liu et al., 2024).

Subsequent variants diversified the same principle. Multiple-mode AFDM-IM uses multiple constellation alphabets, with mode activation patterns and chirp arrangement patterns jointly conveying additional bits; at equal spectral efficiency of $N$5 bit/s/Hz, the paper reports more than $N$6 dB SNR gain at BER $N$7 relative to its benchmark schemes (Liu et al., 17 Jul 2025). IM-AFDM-SS incorporates spread spectrum by letting spreading-code indices carry information, together with a low-complexity MRC detector; one reported result is about $N$8 dB gain at BER $N$9 over conventional IM-AFDM (Qian et al., 14 May 2025). For multiple-antenna transmission, CDD-AFDM-IM-I and CDD-AFDM-IM-II combine cyclic delay diversity with AFDM-IM and use a DLMP detector, with simulations reporting about $\mathbf{A}_{c}$0 dB improvement versus CDD-AFDM at BER $\mathbf{A}_{c}$1 in integer Doppler and about $\mathbf{A}_{c}$2 dB at BER $\mathbf{A}_{c}$3 in fractional Doppler (Tao et al., 2024). These extensions show that the affine/chirp domain has become an information-bearing design space in its own right.

Physical-layer security is another area where AFDM’s parameterization has been exploited directly. Secure AFDM (SE-AFDM) dynamically varies the pre-chirp parameter $\mathbf{A}_{c}$4 using a public codebook driven by a long-period pseudo-noise sequence, thereby implementing what the paper calls parameter-domain spreading rather than data-domain spreading (Wang et al., 2 Oct 2025). The core security claim is that an unsynchronized eavesdropper cannot eliminate the nonlinear impact of the time-varying parameter, while the legitimate receiver can cancel it after LPPN synchronization. In the reported high-mobility simulations, Bob’s BER remains essentially the same as conventional AFDM, Eve’s BER degrades toward $\mathbf{A}_{c}$5 as $\mathbf{A}_{c}$6 increases, and a hardware prototype validates the synchronization framework (Wang et al., 2 Oct 2025). More general surveys interpret this as evidence that AFDM’s chirp parameters are not merely tuning knobs but a new security degree of freedom (Rou et al., 29 Jul 2025, Rou et al., 8 Feb 2026).

Open problems remain substantial. The overviews repeatedly identify coded AFDM, joint detection/decoding, flexible numerology design, reference-signal and DMRS design, pilot overhead under fractional Doppler, timing-offset robustness, coexistence among CP-OFDM, AFDM, and DFT-s-OFDM, scalable MIMO scheduling, and benchmarking of hardware complexity and RF impairments as unresolved issues (Yin et al., 7 Feb 2025, Luo et al., 11 Jun 2026, Rou et al., 29 Jul 2025). The same papers also note a broader methodological gap: despite growing analytical maturity, extensive SDR prototyping, field trials, open reference implementations, and standardized benchmark suites are still limited (Rou et al., 29 Jul 2025). This suggests that AFDM has moved from waveform invention to system-level consolidation, but not yet to closure.