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

TL;DR

This paper introduces a simple, efficient transmit diversity technique called cyclic delay-Doppler shift (CDDS) for AFDM and OTFS waveforms, enhancing ultra-reliable communications in doubly selective channels with lower complexity and latency.

Contribution

The paper proposes two novel CDDS schemes that can be implemented via sparse phase-compensated permutation matrices, providing optimal transmit diversity gain in high-mobility scenarios.

Findings

Both CDDS schemes achieve optimal transmit diversity gain.

CDDS reduces channel estimation overhead and implementation complexity.

The schemes are suitable for ultra-reliable high-mobility communications.

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.