Continuous waveform design reduces interference in communication signals
Resolving the Discontinuity of Continuous-Time AFDM Waveforms
Information Theory
Summary
Communication signals need to be smooth to avoid interfering with other signals. The authors found that a common method creates sudden jumps in the waveform, causing unwanted noise outside the main signal range. They introduced a new method called SFDM that keeps the waveform smooth and continuous, which reduces this interference. Their tests show this method works better across different signal settings.
What this means in practice
- •For wireless communication engineers: Improve signal design to reduce interference caused by out-of-band emissions, enhancing wireless channel quality.
- •For satellite communication teams: Design transmission waveforms with lower spectral leakage to meet strict bandwidth regulations in satellite links.
Authors
Yewen Cao, Yulin Shao
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.