  Orthogonal time frequency space (OTFS) is a 2-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 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 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 a formal
analysis. In this paper, we present a formal analysis of the diversity achieved
by OTFS modulation along with supporting simulations. Specifically, we prove
that the asymptotic diversity order of OTFS (as SNR $\rightarrow \infty$) is
one. However, in the finite SNR regime, potential for a higher order diversity
is witnessed before the diversity one regime takes over. Also, the diversity
one regime starts at lower BER values for increased frame sizes. We also
propose a phase rotation scheme for OTFS using transcendental numbers. We show
that OTFS with this proposed scheme extracts the full diversity in the
delay-Doppler domain.
