On Delay-Doppler Plane Orthogonal Pulse

TL;DR

This paper analyzes the delay-Doppler plane orthogonal pulse (DDOP), introduces local orthogonality properties, proposes a general design, and compares its performance with other modulation schemes in delay-Doppler communication systems.

Contribution

It introduces a local orthogonality property for DDOP, provides conditions for designing such pulses, and compares DDOP-based modulation with existing schemes.

Findings

DDOP exhibits perfect local orthogonality in delay-Doppler domain.

The paper derives the frequency domain representation of DDOP.

DDOP-based ODDM shows improved TF localization compared to other schemes.

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.