On the Diversity of Uncoded OTFS Modulation in Doubly-Dispersive Channels

Orthogonal time-frequency space (OTFS) is a two-dimensional (2D) modulation technique designed in the delay-Doppler domain. A key premise behind OTFS is the transformation of a time-varying multipath channel into an almost non-fading 2D channel in the delay-Doppler domain such that all symbols in a transmission frame experience the same channel gain. It has been suggested in the recent literature that the OTFS can extract full diversity in the delay-Doppler domain, where full diversity refers to the number of multipath components separable in either the delay or Doppler dimension, but without formal analysis. In this paper, we present a formal analysis of the diversity achieved by the OTFS modulation along with supporting simulations. Specifically, we prove that the asymptotic diversity order of the OTFS (as SNR \rightarrow \infty ) is one. However, in the finite SNR regime, the potential for a higher order diversity is witnessed before the diversity one regime takes over. Also, the diversity one regime is found to start at lower BER values for increased frame sizes. We also propose a phase rotation scheme for the OTFS using transcendental numbers and show that the OTFS, with this proposed scheme, extracts full diversity in the delay-Doppler domain.