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

TL;DR

This paper proposes the cyclic delay-Doppler shift (CDDS) technique to enhance transmit diversity in delay-Doppler waveforms for high-mobility doubly selective channels, applicable to OTFS and AFDM.

Contribution

Introduction of simple CDDS schemes (TD-CDDS and MD-CDDS) for MIMO delay-Doppler waveforms, providing full transmit diversity gain in high-mobility channels.

Findings

CDDS achieves full transmit diversity gain for OTFS and AFDM.

Theoretical and experimental validation of CDDS effectiveness.

Application of CDDS to multiple delay-Doppler waveforms.

Abstract

Delay-Doppler waveform design has been considered as a promising solution to achieve reliable communication under high-mobility channels for the space-air-ground-integrated networks (SAGIN). In this paper, we introduce the cyclic delay-Doppler shift (CDDS) technique for delay-Doppler waveforms to extract transmit diversity in doubly selective channels. Two simple CDDS schemes, named time-domain CDDS (TD-CDDS) and modulation-domain CDDS (MD-CDDS), are proposed in the setting of multiple-input multiple-output (MIMO). We demonstrate the applications of CDDS on two representative delay-Doppler waveforms, namely orthogonal time frequency space (OTFS) and affine frequency division multiplexing (AFDM), by deriving their corresponding CDDS matrices. Furthermore, we prove theoretically and experimentally that CDDS can provide OTFS and AFDM with full transmit diversity gain on most occasions.