Derivation of OTFS Modulation from First Principles

TL;DR

This paper rigorously derives OTFS modulation from first principles using the ZAK representation, explaining its robustness to Doppler shifts and the trade-offs involved in its implementation.

Contribution

It provides the first first-principles derivation of OTFS modulation, clarifying its localization properties and robustness to Doppler effects in high mobility channels.

Findings

OTFS basis signals are localized in delay-Doppler domain.

Robustness of OTFS to Doppler shift is due to basis signal localization.

Trade-off exists between robustness and latency based on signal duration.

Abstract

Orthogonal Time Frequency Space (OTFS) modulation has been recently proposed to be robust to channel induced Doppler shift in high mobility wireless communication systems. However, to the best of our knowledge, none of the prior works on OTFS have derived it from first principles. In this paper, using the ZAK representation of time-domain (TD) signals, we rigorously derive an orthonormal basis of approximately time and bandwidth limited signals which are also localized in the delay-Doppler (DD) domain. We then consider DD domain modulation based on this orthonormal basis, and derive OTFS modulation. To the best of our knowledge, this is the first paper to rigorously derive OTFS modulation from first principles. We show that irrespective of the amount of Doppler shift, the received DD domain basis signals are localized in a small interval of size roughly equal to the inverse time duration along the Doppler domain and of size roughly equal to the inverse bandwidth along the delay domain (time duration refers to the length of the time-interval where the TD transmit signal has been limited). With sufficiently large time duration and bandwidth, there is little interference between information symbols modulated on different basis signals, which allows for joint DD domain equalization of all information symbols. This explains the inherent robustness of DD domain modulation to channel induced Doppler shift when compared with Orthogonal Frequency Division Multiplexing (OFDM). The degree of localization of the DD domain basis signals is inversely related to the time duration of the transmit signal, which explains the trade-off between robustness to Doppler shift and latency.