Multicarrier Modulation on Delay-Doppler Plane: Achieving Orthogonality with Fine Resolutions

TL;DR

This paper introduces a novel orthogonal delay-Doppler division multiplexing (ODDM) modulation that achieves orthogonality on the delay-Doppler plane with fine resolutions, improving performance in doubly-selective channels.

Contribution

It proposes the ODDM modulation and designs a corresponding orthogonal transmit pulse, demonstrating its feasibility and advantages over existing methods.

Findings

Proves the existence of an orthogonal pulse on the DD plane.

Shows improved out-of-band radiation performance.

Achieves lower bit error rates in simulations.

Abstract

In this paper, we investigate the design of a novel multicarrier (MC) modulation on delay-Doppler (DD) plane, to couple the modulated signal with a doubly-selective channel having DD resolutions. A key challenge for the design of DD plane MC modulation is to find a realizable pulse orthogonal with respect to the DD plane's fine resolutions. To this end, we first indicate that a feasible DD plane MC modulation is essentially a type of staggered multitone modulation. Then, we propose an orthogonal delay-Doppler division multiplexing (ODDM) modulation, and design the corresponding transmit pulse. Most importantly, we prove that the proposed transmit pulse is orthogonal with respect to the DD plane's resolutions and therefore a realizable DD plane orthogonal pulse does exist. Finally, we demonstrate the superior performance of the proposed ODDM modulation in terms of out-of-band radiation and bit error rate.