# Orthogonal Delay-Doppler Division Multiplexing Modulation

arXiv: https://arxiv.org/abs/2206.13999 · HTML: https://mlsanity.com/paper/2206.13999/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2022.

## Built on by (most cited first, 1 of 1)

- [OFDM-Standard Compatible SC-NOFS Waveforms for Low-Latency and Jitter-Tolerance Industrial IoT Communications](https://mlsanity.com/paper/2406.04776/) (2024)

## Abstract (arXiv)

Inspired by the orthogonal time frequency space (OTFS) modulation, in this paper, we consider designing a 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 investigate whether a realizable pulse orthogonal with respect to the DD plane's fine resolutions exists or not. To this end, we first indicate that a feasible DD plane MC modulation is essentially a type of staggered multitone modulation. Then, analogous to orthogonal frequency division multiplexing, we propose an orthogonal delay-Doppler division multiplexing (ODDM) modulation, and design the corresponding transmit pulse. Furthermore, 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. The orthogonality of this particular pulse significantly eases the derivation of the ODDM's DD domain channel input-output relation, and yields a channel matrix with an elegant block-circulant-like structure. We demonstrate that the ODDM outperforms the OTFS in terms of out-of-band emission and bit error rate, by achieving perfect coupling between the modulated signal and the DD channel.