A Primer on Orthogonal Delay-Doppler Division Multiplexing (ODDM)

TL;DR

This paper tackles waveform design for linear time-varying channels by introducing Orthogonal Delay-Doppler Division Multiplexing ($\text{ODDM}$), a multicarrier scheme built on the delay-Doppler domain orthogonal pulse ($\text{DDOP}$). It develops the DDOP representation, clarifies how ODDM differs from conventional MF schemes and OTFS/OFDM, and proposes two practical implementations: a pulse-shaped OFDM (PS-OFDM) and a wideband filtered-OFDM approach, supported by waveform-level simulations. The key contributions are the local (bi)orthogonality concept for finite Weyl–Heisenberg subsets, the alternative DDOP representations, and the demonstration that DDOP-based ODDM can achieve fine delay-Doppler resolution within a practical TF framework. Overall, ODDM offers a principled way to exploit the delay-Doppler structure of LTV channels with two concrete, implementable pathways, suggesting a promising direction for robust waveform design in dynamic wireless environments.

Abstract

As a new type of multicarrier (MC) scheme built upon the recently discovered delay-Doppler domain orthogonal pulse (DDOP), orthogonal delay-Doppler division multiplexing (ODDM) aims to address the challenges of waveform design in linear time-varying channels. In this paper, we explore the design principles of ODDM and clarify the key ideas underlying the DDOP. We then derive an alternative representation of the DDOP and highlight the fundamental differences between ODDM and conventional MC schemes. Finally, we discuss and compare two implementation methods for ODDM.

Figures (3)

• Figure 1: The DDOP $u(t)$.
• Figure 2: Frequency domain representation $U(f)$ of the DDOP $u(t)$.
• Figure 3: NMSE of approximate ODDM waveform, $M=512$, $N=32$.