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On Diagonalizable Delay-Doppler Channels and Their Diagonalizing Waveforms

Sirui Li, Cheng Du and Yu Zhu

Published
Source
OpenAlex
DOI
10.48550/arxiv.2608.30717
Original
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Topics
Signal Processing

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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