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arXiv · 2301.06721

On Delay-Doppler Plane Orthogonal Pulse

Hai Lin·Jinhong Yuan
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Abstract

In this paper, we analyze the recently discovered delay-Doppler plane orthogonal pulse (DDOP), which is essential for delay-Doppler plane multi-carrier modulation waveform. In particular, we introduce a local orthogonality property of pulses corresponding to Weyl-Heisenberg (WH) subset and justify the DDOP's existence, in contrast to global orthogonality corresponding to WH set governed by the WH frame theory. Then, sufficient conditions for locally-orthogonal pulses are presented and discussed. Based on the analysis, we propose a general DDOP design. We also derive the frequency domain representation of the DDOP, and compare the DDOP-based orthogonal delay-Doppler division multiplexing (ODDM) modulation with other modulation schemes, in terms of TF signal localization. Interestingly, we show perfect local orthogonality property of the DDOP with respect to delay-Doppler resolutions using its ambiguity function.

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Hai Lin, Jinhong Yuan. 2023-01-17. On Delay-Doppler Plane Orthogonal Pulse. https://doi.org/10.1109/globecom48099.2022.10001406

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