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Agile Affine Frequency Division Multiplexing

Yewen Cao, Yulin Shao

TL;DR

This work introduces Agile-AFDM, a data-aware extension of Affine Frequency Division Multiplexing (AFDM) that optimizes the chirp parameters $(c_1,c_2)$ on a per-transmission-block basis using real-time CSI and transmitted data. The approach enables concurrent improvements in power efficiency (PAPR), communication reliability (ICI/SIR), and sensing accuracy (CRLB) by exploiting analytical relations between chirp parameters and performance metrics, plus tailored optimization algorithms: a PAPR-focused fine-grained search for $c_2$, FP-based SIR optimization with Adam updates, and PSO for CRLB minimization. Simulations show Agile-AFDM significantly outperforms OFDM and static AFDM across PAPR reduction, SIR gains, and Doppler-delay CRLB improvements, validating its potential for agile waveform design in 6G and ISAC contexts. The framework also highlights the practicality of dynamic, block-level waveform adaptation with manageable complexity, and suggests avenues for multi-objective optimization and broader applicability to other parameterized waveforms.

Abstract

The advancement to 6G calls for waveforms that transcend static robustness to achieve intelligent adaptability. Affine Frequency Division Multiplexing (AFDM), despite its strength in doubly-dispersive channels, has been confined by chirp parameters optimized for worst-case scenarios. This paper shatters this limitation with Agile-AFDM, a novel framework that endows AFDM with dynamic, data-aware intelligence. By redefining chirp parameters as optimizable variables for each transmission block based on real-time channel and data information, Agile-AFDM transforms into an adaptive platform. It can actively reconfigure its waveform to minimize peak-to-average power ratio (PAPR) for power efficiency, suppress inter-carrier interference (ICI) for communication reliability, or reduce Cramer-Rao bound (CRLB) for sensing accuracy. This paradigm shift from a static, one-size-fits-all waveform to a context-aware signal designer is made practical by efficient, tailored optimization algorithms. Comprehensive simulations demonstrate that this capability delivers significant performance gains across all metrics, surpassing conventional OFDM and static AFDM. Agile-AFDM, therefore, offers a crucial step forward in the design of agile waveforms for 6G and beyond.

Agile Affine Frequency Division Multiplexing

TL;DR

This work introduces Agile-AFDM, a data-aware extension of Affine Frequency Division Multiplexing (AFDM) that optimizes the chirp parameters on a per-transmission-block basis using real-time CSI and transmitted data. The approach enables concurrent improvements in power efficiency (PAPR), communication reliability (ICI/SIR), and sensing accuracy (CRLB) by exploiting analytical relations between chirp parameters and performance metrics, plus tailored optimization algorithms: a PAPR-focused fine-grained search for , FP-based SIR optimization with Adam updates, and PSO for CRLB minimization. Simulations show Agile-AFDM significantly outperforms OFDM and static AFDM across PAPR reduction, SIR gains, and Doppler-delay CRLB improvements, validating its potential for agile waveform design in 6G and ISAC contexts. The framework also highlights the practicality of dynamic, block-level waveform adaptation with manageable complexity, and suggests avenues for multi-objective optimization and broader applicability to other parameterized waveforms.

Abstract

The advancement to 6G calls for waveforms that transcend static robustness to achieve intelligent adaptability. Affine Frequency Division Multiplexing (AFDM), despite its strength in doubly-dispersive channels, has been confined by chirp parameters optimized for worst-case scenarios. This paper shatters this limitation with Agile-AFDM, a novel framework that endows AFDM with dynamic, data-aware intelligence. By redefining chirp parameters as optimizable variables for each transmission block based on real-time channel and data information, Agile-AFDM transforms into an adaptive platform. It can actively reconfigure its waveform to minimize peak-to-average power ratio (PAPR) for power efficiency, suppress inter-carrier interference (ICI) for communication reliability, or reduce Cramer-Rao bound (CRLB) for sensing accuracy. This paradigm shift from a static, one-size-fits-all waveform to a context-aware signal designer is made practical by efficient, tailored optimization algorithms. Comprehensive simulations demonstrate that this capability delivers significant performance gains across all metrics, surpassing conventional OFDM and static AFDM. Agile-AFDM, therefore, offers a crucial step forward in the design of agile waveforms for 6G and beyond.

Paper Structure

This paper contains 26 sections, 6 theorems, 95 equations, 4 figures, 4 tables, 3 algorithms.

Key Result

Proposition 1

The effective communication channel matrix $\bm{H}_{\text{eff}}^{\text{comm}}$ and the effective sensing channel matrix $\bm{H}_{\text{eff}}^{\text{sens}}$ are periodic functions of the chirp parameters $c_1$ and $c_2$ with period $1$. Specifically, for any integers $k, m \in \mathbb{Z}$, the follow

Figures (4)

  • Figure 1: Architecture of the Agile-AFDM transceiver, showcasing the signal processing flow and its adaptive configuration for three objectives: minimizing PAPR, mitigating ICI, and lowering CRLB for sensing.
  • Figure 2: CCDF achieved by various PAPR reduction techniques under different modulation formats: (a) complex Gaussian signals, (b) 64QAM, (c) 128QAM. We highlight that AFDM with static chirp parameters exhibits the same PAPR performance with OFDM.
  • Figure 3: SIR Performance Comparison of OFDM, static (but parameter-optimized) AFDM and Agile-AFDM in Rayleigh Fading Channels: (a) CDF, (b) Average SIR Comparison, (c) Statistical Distribution Analysis.
  • Figure 4: Percentage improvement of the Agile-AFDM in terms of CRLB reduction versus $\ell$ and $\nu$. (a) Agile-AFDM vs. OFDM: CRLB on channel delay estimation. (b) Agile-AFDM vs. OFDM: CRLB on Doppler shift estimation. (c) Agile-AFDM vs. AFDM: CRLB on channel delay estimation. (d) Agile-AFDM vs. AFDM: CRLB on Doppler shift estimation.

Theorems & Definitions (20)

  • Definition 1
  • Remark 1
  • Proposition 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 4
  • proof
  • ...and 10 more