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On Diagonalizable Delay-Doppler Channels and Their Diagonalizing Waveforms

  • Sirui Li
  • Cheng Du
  • Yu Zhu
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Abstract

In doubly selective channels, the joint delay and Doppler dispersion generally induces coupling among transmitted symbols, thereby increasing receiver equalization complexity. Nevertheless, by using appropriately designed waveforms, channels with certain delay-Doppler (DD) supports can be diagonalized for one-tap equalization. The whole picture of such DD supports and their corresponding waveforms is still unclear, except for several examples identified in literature. In this paper, under cyclic-prefix (CP)-based block transmission and assuming that the modulation waveforms form an orthonormal basis, we identify all such channel supports by an elementary expression, and derive the corresponding waveforms in closed form.

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Cite

BibTeXRIS
BibTeX
@misc{li2026diagonalizable,
  title = {{On Diagonalizable Delay-Doppler Channels and Their Diagonalizing Waveforms}},
  author = {Sirui Li and Cheng Du and Yu Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.30717},
  eprint = {2608.30717},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30717},
}
RIS
TY  - UNPB
TI  - On Diagonalizable Delay-Doppler Channels and Their Diagonalizing Waveforms
AU  - Sirui Li
AU  - Cheng Du
AU  - Yu Zhu
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2608.30717
UR  - https://arxiv.org/abs/2608.30717
AB  - In doubly selective channels, the joint delay and Doppler dispersion generally induces coupling among transmitted symbols, thereby increasing receiver equalization complexity. Nevertheless, by using appropriately designed waveforms, channels with certain delay-Doppler (DD) supports can be diagonalized for one-tap equalization. The whole picture of such DD supports and their corresponding waveforms is still unclear, except for several examples identified in literature. In this paper, under cyclic-prefix (CP)-based block transmission and assuming that the modulation waveforms form an orthonormal basis, we identify all such channel supports by an elementary expression, and derive the corresponding waveforms in closed form.
ER  -