On the Zak Transform-based Interpretation of OTFS Modulation

Akshay S. Bondre, Christ D. Richmond

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In this paper, we present a Zak transform-based development of the recently proposed orthogonal time frequency space (OTFS) modulation scheme. Unlike previous works, we focus on the interpretation of the spreading function as the Zak transform of the 'impulse train response' for general underspread linear time-varying (LTV) channels. For an underspread channel, the Zak transform of the output signal is given by the twisted convolution of the spreading function with the Zak transform of the input signal. This twisted convolution relationship provides a Zak domain input-output relationship for general underspread LTV channels. We extend these results to the discrete case, by presenting a development of the discrete Zak transform (DZT) similar to the one provided by Mohammed for the continuous Zak transform. We argue that the discrete Zak domain twisted convolution relationship for LTV channels provides a simple and concise input-output relationship for OTFS modulation, analogous to the frequency domain multiplication relationship for orthogonal frequency division multiplexing (OFDM) over linear time invariant (LTI) channels. Lastly, we discuss the impact of adding a cyclic prefix and zero-padding in delay and Doppler in the discrete Zak domain.

Original languageEnglish (US)
Title of host publication56th Asilomar Conference on Signals, Systems and Computers, ACSSC 2022
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages715-721
Number of pages7
ISBN (Electronic)9781665459068
DOIs
StatePublished - 2022
Externally publishedYes
Event56th Asilomar Conference on Signals, Systems and Computers, ACSSC 2022 - Virtual, Online, United States
Duration: Oct 31 2022Nov 2 2022

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2022-October
ISSN (Print)1058-6393

Conference

Conference56th Asilomar Conference on Signals, Systems and Computers, ACSSC 2022
Country/TerritoryUnited States
CityVirtual, Online
Period10/31/2211/2/22

Keywords

  • Linear time-varying channels
  • OTFS modulation
  • Zak transform
  • spreading function
  • underspread channels

ASJC Scopus subject areas

  • Signal Processing
  • Computer Networks and Communications

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