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A Novel ISAC Waveform Based on Orthogonal Delay-Doppler Division Multiplexing with FMCW

Kehan Huang, Akram Shafie, Min Qiu, Elias Aboutanios, Jinhong Yuan

TL;DR

This work introduces a low-PAPR ISAC waveform by embedding a square-root Nyquist filtered FMCW (SRN-FMCW) into orthogonal delay-Doppler division multiplexing (ODDM) as a DD-domain embedded SRN-FMCW (DD-SRN-FMCW). By transmitting an ODDM frame superimposed with a DD-SRN-FMCW pilot, and using DD chirp compression, the approach achieves efficient sensing and channel estimation while maintaining data throughput. A data-aided sensing (DAS) and joint channel estimation and data detection (JCEDD) framework based on OMP with grid evolution and soft SIC-MMSE is developed, with comprehensive performance analyses on PAPR, spectrum, ambiguity function, and Cramér-Rao bounds, supported by numerical results showing BER improvements and sensing accuracy close to theoretical limits. Overall, the proposed ODDM-FMCW scheme offers a practical, high-performance ISAC solution for doubly-selective channels, combining low out-of-band emissions with strong DD-domain processing advantages.

Abstract

In this work, we propose the orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation with frequency modulated continuous wave (FMCW) (ODDM-FMCW) waveform to enable integrated sensing and communication (ISAC) with a low peak-to-average power ratio (PAPR). We first propose a square-root-Nyquist-filtered FMCW (SRN-FMCW) waveform to address limitations of conventional linear FMCW waveforms in ISAC systems. To better integrate with ODDM, we generate SRN-FMCW by embedding symbols in the DD domain, referred to as a DD-SRN-FMCW frame. A DD chirp compression receiver is designed to obtain the channel response efficiently. Next, we construct the proposed ODDM-FMCW waveform for ISAC by superimposing a DD-SRN-FMCW frame onto an ODDM data frame. A comprehensive performance analysis of the ODDM-FMCW waveform is presented, covering peak-to-average power ratio, spectrum, ambiguity function, and Cramer-Rao bound for delay and Doppler estimation. Numerical results show that the proposed ODDM-FMCW waveform delivers excellent ISAC performance in terms of root mean square error for sensing and bit error rate for communications.

A Novel ISAC Waveform Based on Orthogonal Delay-Doppler Division Multiplexing with FMCW

TL;DR

This work introduces a low-PAPR ISAC waveform by embedding a square-root Nyquist filtered FMCW (SRN-FMCW) into orthogonal delay-Doppler division multiplexing (ODDM) as a DD-domain embedded SRN-FMCW (DD-SRN-FMCW). By transmitting an ODDM frame superimposed with a DD-SRN-FMCW pilot, and using DD chirp compression, the approach achieves efficient sensing and channel estimation while maintaining data throughput. A data-aided sensing (DAS) and joint channel estimation and data detection (JCEDD) framework based on OMP with grid evolution and soft SIC-MMSE is developed, with comprehensive performance analyses on PAPR, spectrum, ambiguity function, and Cramér-Rao bounds, supported by numerical results showing BER improvements and sensing accuracy close to theoretical limits. Overall, the proposed ODDM-FMCW scheme offers a practical, high-performance ISAC solution for doubly-selective channels, combining low out-of-band emissions with strong DD-domain processing advantages.

Abstract

In this work, we propose the orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation with frequency modulated continuous wave (FMCW) (ODDM-FMCW) waveform to enable integrated sensing and communication (ISAC) with a low peak-to-average power ratio (PAPR). We first propose a square-root-Nyquist-filtered FMCW (SRN-FMCW) waveform to address limitations of conventional linear FMCW waveforms in ISAC systems. To better integrate with ODDM, we generate SRN-FMCW by embedding symbols in the DD domain, referred to as a DD-SRN-FMCW frame. A DD chirp compression receiver is designed to obtain the channel response efficiently. Next, we construct the proposed ODDM-FMCW waveform for ISAC by superimposing a DD-SRN-FMCW frame onto an ODDM data frame. A comprehensive performance analysis of the ODDM-FMCW waveform is presented, covering peak-to-average power ratio, spectrum, ambiguity function, and Cramer-Rao bound for delay and Doppler estimation. Numerical results show that the proposed ODDM-FMCW waveform delivers excellent ISAC performance in terms of root mean square error for sensing and bit error rate for communications.
Paper Structure (27 sections, 3 theorems, 57 equations, 18 figures, 1 table, 4 algorithms)

This paper contains 27 sections, 3 theorems, 57 equations, 18 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Motivations
  3. Doubly-Selective LTV Channel
  4. ODDM Modulation
  5. ODDM Transmitter
  6. ODDM Receiver
  7. FMCW Radar and Stretch Processing
  8. Chirp-based Pulsed Radar and Chirp Compression
  9. Challenges and Motivations
  10. From Linear FMCW to DD-SRN-FMCW
  11. SRN-Filtered Chirp with Chirp Compression
  12. SRN-Filtered FMCW
  13. DD-Domain Embedded SRN-Filtered FMCW
  14. Proposed ODDM-FMCW System for ISAC
  15. ODDM-FMCW Waveform
  16. ...and 12 more sections

Key Result

Lemma 1

If $\frac{\epsilon T^2}{M}\in\mathbb{Z}$ and $\gcd\left(\frac{\epsilon T^2}{M},M\right)=1$, then $\dot{c}[m]$ satisfies the zero linear autocorrelation (ZLA) property: for $\zeta\in\mathbb{Z}$.

Figures (18)

  • Figure 1: Considered ISAC scenario.
  • Figure 2: Delay ambiguity (chirp compression output) of chirps.
  • Figure 3: Time-domain transmitted sequences: ODDM, SRN-FMCW, and DD-SRN-FMCW. ($M=8,N=4$)
  • Figure 4: DD frame structure for ODDM-FMCW signals.
  • Figure 5: Construction of a sub-channel matrix for SIC-MMSE.
  • ...and 13 more figures

Theorems & Definitions (4)

  • Lemma 1
  • Proposition 1
  • Remark 1
  • Corollary 1