发表机构
State Key Laboratory of IoT for Smart City, University of Macau; Department of Electrical and Computer Engineering, The University of Hong Kong（澳门大学物联网智能城市国家重点实验室; 香港大学电气与计算机工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对连续时间AFDM波形因复包络不连续导致高带外发射的问题，提出步进频分复用（SFDM）波形，通过冻结瞬时频率实现严格连续，同时保持样本级等价，显著降低OOBE。
AI 中文摘要
连续时间仿射频分复用（AFDM）波形，通过频率缠绕和相位校正构建，已知在样本级别上与广泛采用的离散AFDM框架等价。本文揭示了该构建中一个基本且先前被忽视的缺陷：其复包络对于一般啁啾参数固有地不连续。我们表明，这些不连续性是高带外发射（OOBE）的直接原因。为解决此问题，我们提出了一种根本不同的连续时间波形，称为步进频分复用（SFDM）。与传统允许连续频率变化的方法不同，SFDM在每个奈奎斯特采样间隔内将瞬时频率冻结在底层啁啾轨迹的中点。这种设计使得复包络在整个符号持续时间内严格连续，同时保持与离散AFDM的精确样本级等价。统一的频谱分析表明，SFDM优越的OOBE性能源于不存在内部跳跃间断点，否则这些间断点将主导远距离频谱滚降。数值结果证实，在各种啁啾速率下，SFDM始终实现显著更低的OOBE。
英文摘要
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.
CommentsKeywords: AFDM, continuous-time waveform, SFDM, out-of-band emission
