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