Resolving the Discontinuity of Continuous-Time AFDM Waveforms

2026-09-07

AI Summary

本文解决了连续时间AFDM波形的不连续性问题，该问题导致高带外发射。通过提出一种新的连续时间波形SFDM，保持频率在奈奎斯特采样间隔内不变，从而消除不连续性并减少OOBE。

Abstract

Continuous-time affine frequency division multiplexing (AFDM) waveforms, constructed via frequency wrapping and phase correction, are known to be sample-wise equivalent to the widely adopted discrete AFDM framework. In this paper, we uncover a fundamental and previously overlooked flaw in this construction: its complex envelope is inherently discontinuous for generic chirp parameters. We show that these discontinuities are the direct cause of the high out-of-band emission (OOBE). To resolve this issue, we propose a fundamentally different continuous-time waveform, termed stepped frequency division multiplexing (SFDM). Unlike conventional approaches that allow continuous frequency variation, SFDM freezes the instantaneous frequency at the midpoint of the underlying chirp trajectory within each Nyquist sampling interval. This design yields a complex envelope that is strictly continuous over the entire symbol duration while preserving exact sample-wise equivalence with discrete AFDM. A unified spectral analysis reveals that the superior OOBE performance of SFDM stems from the absence of internal jump discontinuities, which otherwise dominate the far-out spectral roll-off. Numerical results confirm that SFDM consistently achieves significantly lower OOBE across a wide range of chirp rates.

Problem

• Continuous-time AFDM
• discontinuity
• out-of-band emission
• chirp parameters

Innovation

• Stepped Frequency Division Multiplexing (SFDM)
• Continuous Envelope
• Out-of-Band Emission (OOBE)