Orthogonal time frequency space (OTFS) can resist the Doppler effect and guarantee reliable communication in high-speed scenarios. However, the Doppler rate induced by the relative acceleration between the transmitter and receiver degrades the performance of the OTFS. So far, the impact of the Doppler rate on OTFS systems has not been addressed. In this paper, we first introduce the Doppler rate in the OTFS system and derive the delay-Doppler domain input-output relation. In addition, the impact of the Doppler rate on the effective delay-Doppler domain channel is characterized by utilizing the first mean value theorem for definite integrals to avoid complicated integrals. To mitigate the effect of the Doppler rate, a large-scale antenna array is arranged at the receiver to separate each path of the multi-path channel through a high-resolution spatial matched filter beamformer. Next, the Doppler rate estimation scheme for an arbitrary order Doppler rate is proposed based on the successive interference cancellation pattern and the maximization of the spectrum of the ratio of high-order moments between the received samples in the identified branch and the transmitted samples. Finally, the estimation accuracy of the Doppler rate and the error performance of the proposed transceiver are validated by the numerical results.

The application of the orthogonal time frequency space (OTFS) modulation in multiple-antenna systems is investigated. The diversity and/or the multiplexing gain can be achieved by deploying various multiple-antenna techniques, and thus the reliability and/or the spectral efficiency are improved correspondingly. We provide two classes of OTFS-based multiple-antenna approaches for both the open-loop and the closed-loop systems. Specifically, in the open-loop system, a transmitting diversity approach, which resembles the space-time coding technique, is proposed by allocating the information symbols appropriately in the delay-Doppler domain. In the closed-loop system, we adopt the Tomlinson-Harashima precoding in our derived delay-Doppler equivalent transmission model. Numerical evaluations demonstrate the advantages of applying the multiple-antenna techniques to the OTFS. At last, several challenges and opportunities are presented.