On Diagonalizable Delay-Doppler Channels and Their Diagonalizing Waveforms
2026-08-31 • Information Theory
Information Theory
AI summaryⓘ
The authors study communication channels that change over time and frequency, which usually makes decoding signals complicated. They show that by carefully choosing the transmitted waveforms, it's possible to simplify the channel effects so that decoding requires just a simple operation. They identify all channel conditions where this simplification is possible and provide exact formulas for the waveforms to use. This work helps understand when and how a complex wireless channel can be made easier to handle.
doubly selective channelsdelay-Doppler dispersionequalizationwaveformscyclic prefixorthonormal basisblock transmissionchannel diagonalizationone-tap equalization
Authors
Sirui Li, Cheng Du, Yu Zhu
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.