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Cyclic Delay-Doppler Shift: A Simple Transmit Diversity Technique for Ultra-Reliable Communications in Doubly Selective Channels

Haoran Yin, Yu Zhou, Yanqun Tang, Di Zhang, Chi Zhang, Xizhang Wei, Jiaojiao Xiong, Fan Liu, Marwa Chafii, Mérouane Debbah

Abstract

Affine frequency division multiplexing (AFDM) and orthogonal time frequency space (OTFS) are two promising advanced waveforms proposed for reliable communications in high-mobility scenarios. In this paper, we introduce a simple transmit diversity technique, termed cyclic delay-Doppler shift (CDDS), for these two advanced waveforms to achieve ultra-reliable communications in doubly selective channels (DSCs). Two simple CDDS schemes, named modulation-domain CDDS (MD-CDDS) and time-domain CDDS (TD-CDDS), are proposed, which perform CDDS in advance at the transmitter before and after the modulation, respectively. We demonstrate that both of the two proposed CDDS schemes can be implemented efficiently and flexibly by multiplying the transmit vector with a well-designed precoding matrix, which is nothing but a sparse phase-compensated permutation matrix. Moreover, we theoretically and numerically prove that CDDS can provide MIMO-AFDM and MIMO-OTFS with optimal transmit diversity gain when a proper CDDS step is adopted. Compared to the conventional transmit diversity techniques, the proposed CDDS scheme enjoys the advantages of lower channel estimation overhead, implementation complexity, and signal processing latency, making it particularly suitable for ultra-reliable communications in high-mobility scenarios.

Cyclic Delay-Doppler Shift: A Simple Transmit Diversity Technique for Ultra-Reliable Communications in Doubly Selective Channels

Abstract

Affine frequency division multiplexing (AFDM) and orthogonal time frequency space (OTFS) are two promising advanced waveforms proposed for reliable communications in high-mobility scenarios. In this paper, we introduce a simple transmit diversity technique, termed cyclic delay-Doppler shift (CDDS), for these two advanced waveforms to achieve ultra-reliable communications in doubly selective channels (DSCs). Two simple CDDS schemes, named modulation-domain CDDS (MD-CDDS) and time-domain CDDS (TD-CDDS), are proposed, which perform CDDS in advance at the transmitter before and after the modulation, respectively. We demonstrate that both of the two proposed CDDS schemes can be implemented efficiently and flexibly by multiplying the transmit vector with a well-designed precoding matrix, which is nothing but a sparse phase-compensated permutation matrix. Moreover, we theoretically and numerically prove that CDDS can provide MIMO-AFDM and MIMO-OTFS with optimal transmit diversity gain when a proper CDDS step is adopted. Compared to the conventional transmit diversity techniques, the proposed CDDS scheme enjoys the advantages of lower channel estimation overhead, implementation complexity, and signal processing latency, making it particularly suitable for ultra-reliable communications in high-mobility scenarios.
Paper Structure (22 sections, 1 theorem, 54 equations, 14 figures, 2 tables)

This paper contains 22 sections, 1 theorem, 54 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Fundamental of MIMO-AFDM and MIMO-OTFS
  3. AFDM Modulation and Demodulation
  4. OTFS Modulation and Demodulation
  5. MIMO-AFDM and MIMO-OTFS Systems
  6. Cyclic Delay-Doppler Shift
  7. TD-CDDS
  8. MD-CDDS
  9. MD-CDDS-OTFS
  10. MD-CDDS-AFDM
  11. Graphic Interpretation of CDDS
  12. Comparison between TD-CDDS and MD-CDDS
  13. Performance Analysis of CDDS
  14. Transmit Diversity
  15. EPA Channel Estimation Overhead
  16. ...and 7 more sections

Key Result

Proposition 1

Optimal transmit diversity gain quivalent to the number of transmit antennas $N_{t}$ can be achieved by MIMO-AFDM and MIMO-OTFS with CDDS in doubly selective channels if

Figures (14)

  • Figure 1: General modulation/demodulation block diagrams of baseband MIMO-AFDM and MIMO-OTFS systems.
  • Figure 2: Block diagrams of the transmitter in a TD-CDDS system.
  • Figure 3: Block diagrams of the transmitter in an MD-CDDS system.
  • Figure 4: The bijective relation between DD-domain (left) and DAFT-domain (right) channel representations ($k_{\max}=2$ and $k_{\text{space}}=1$).
  • Figure 5: An example of the equivalent DD-domain channel after CDDS with six TAs.
  • ...and 9 more figures

Theorems & Definitions (6)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Proposition 1
  • proof