AFDM: Evolving OFDM Towards 6G+

TL;DR

This work proposes affine frequency division multiplexing (AFDM) as an evolutionary 6G+ waveform that preserves orthogonal frequency division multiplexing (OFDM) infrastructure while delivering robustness in doubly dispersive channels and enabling integrated sensing. It develops a generalized FDFD/DAFT channel model, derives AFDM and OFDM signal models, and shows that AFDM reuses the OFDM pipeline with lightweight chirp pre/post-processing, preserving hardware and software ecosystems. The paper analyzes AFDM across modulation complexity, channel estimation, detection architectures, MIMO extensions, and impairments (PHN/CFO), demonstrating superior resilience to Doppler, phase noise, and carrier offsets relative to OFDM, plus flexible chirp-domain functions like index modulation and physical-layer security. It also discusses multi-user coexistence with OFDM (AFDMA/Per-block and Per-subcarrier), pilot design, and practical deployment considerations, arguing that AFDM offers a low-risk path toward high-fidelity 6G+ communications with backward compatibility. Overall, AFDM stands out as an efficient, adaptable waveform that can support extreme mobility, integrated sensing, and security needs without a radical departure from existing OFDM architectures.

Abstract

As the standardization of sixth generation (6G) wireless systems accelerates, there is a growing consensus in favor of evolutionary waveforms that offer new features while maximizing compatibility with orthogonal frequency division multiplexing (OFDM), which underpins the 4G and 5G systems. This article presents affine frequency division multiplexing (AFDM) as a premier candidate for 6G, offering intrinsic robustness for both high-mobility communications and integrated sensing and communication (ISAC) in doubly dispersive channels, while maintaining a high degree of synergy with the legacy OFDM. To this end, we provide a comprehensive analysis of AFDM, starting with a generalized fractional-delay-fractional-Doppler (FDFD) channel model that accounts for practical pulse shaping filters and inter-sample coupling. We then detail the AFDM transceiver architecture, demonstrating that it reuses nearly the entire OFDM pipeline and requires only lightweight digital pre- and post-processing. We also analyze the impact of hardware impairments, such as phase noise and carrier frequency offset, and explore advanced functionalities enabled by the chirp-parameter domain, including index modulation and physical-layer security. By evaluating the reusability across the radio-frequency, physical, and higher layers, the article demonstrates that AFDM provides a low-risk, feature-rich, and efficient path toward achieving high-fidelity communications in the later versions of 6G and beyond (6G+).

Figures (12)

• Figure 1: Illustration of a single path within the channel matrix under IDID and FDFD scenarios, with $N=64$. (a) shows the conventional IDID sparse permutation model of eq. \ref{['eq:Hp_integerdelay']} with $\ell_p = 4$ and $f_p = 2$; (b) shows the proposed generalized FDFD formulation of eq. \ref{['eq:Hp_FDFD_generalized']} but under the same integer conditions; and (c) shows the proposed generalized FDFD formulation with fractional delay ($\ell_p = 4.3$) and fractional Doppler ($f_p = 2.1$), revealing the inter-sample coupling effects. The FDFD models in (b) and (c) are constructed based on the ideal band-limited pulse (Sinc interpolation).
• Figure 2: Impact of different transmit pulse shapes $g(\cdot)$ on the single-path FDFD channel matrix $\mathbf{H}_p$ ($N=64, \ell_p=4.3, f_p=2.1$), where the choice of the transmit filter governs the sparsity of the inter-sample coupling and the thickness of the diagonal band, while the main position of the shifted components remains unchanged and deterministic to the integer delay part $\lfloor \ell_p \rceil$.
• Figure 3: Effective channel matrices $\mathbf{\Xi}$ for OFDM and AFDM, respectively on the first and second rows, in a 3-path doubly dispersive scenario with $N=64$. The physical channel parameters are defined by path coefficients $\{1, 0.9, 0.8\}$, normalized delays $\{1.3, 3.25, 5.96\}$, and normalized digital Dopplers $\{1.1, -2.3, 0.85\}$, where for the IDID and IDFD cases, the delays and Dopplers are rounded to the nearest integers as relevant. For the AFDM implementation, chirp parameters are set to $c_1 = (2(f_{\max} + 1) + 1)/2N$, with $f_{\max} = 3$, and $c_2 = 1/2N$. It can be seen that on top of the discussed effects of the fraction taps in Section \ref{['sec:system_model']}-\ref{['subsec:matrix_form_IO']}, the different paths of the OFDM effective channel matrices are indistinguishable under Doppler shifts, leading to significant inter-carrier interference, while AFDM maintains a more distinguishable effective channel matrix, preserving better orthogonality.
• Figure 4: Comparison of OFDM and AFDM transceiver structures, which highlights that the only structural difference lies in the two element-wise chirp-phase rotations (pre- and post-multiplications) surrounding the IFFT/FFT blocks from the conventional OFDM transceivers.
• Figure 5: Transmitted pilot vector multiplexed with data $\mathbf{x}$ (as in \ref{['eq:pilotsap']}) in the affine-frequency domain and received signal $\mathbf{y}$.