  We investigate the relationship between Orthogonal Time Frequency Space
(OTFS) modulation and Orthogonal Short Time Fourier (OSTF) signaling. OTFS was
recently proposed as a new scheme for high Doppler scenarios and builds on
OSTF. We first show that the two schemes are unitarily equivalent in the
digital domain. However, OSTF defines the analog-digital interface with the
waveform domain. We then develop a critically sampled matrix-vector model for
the two systems and consider linear minimum mean-squared error (MMSE) filtering
at the receiver to suppress inter-symbol interference. Initial comparison of
capacity and (uncoded) probability of error reveals a surprising observation:
OTFS under-performs OSTF in capacity but over-performs in probability of error.
This result can be attributed to characteristics of the channel matrices
induced by the two systems. In particular, the diagonal entries of OTFS matrix
exhibit nearly identical magnitude, whereas those of the OSTF matrix exhibit
wild fluctuations induced by multipath randomness. It is observed that by
simply replacing the unitary matrix, relating OTFS to OSTF, by an arbitrary
unitary matrix results in performance nearly identical to OTFS. We then extend
our analysis to orthogonal frequency division multiplexing (OFDM) and also
consider a more extreme scenario of relatively large delay and Doppler spreads.
Our results demonstrate the significance of using OSTF basis waveforms rather
than sinusoidal ones in OFDM in highly dynamic environments, and also highlight
the impact of the level of channel state information used at the receiver.
