  We elaborate on the recently proposed orthogonal time frequency space (OTFS)
modulation technique, which provides significant advantages over orthogonal
frequency division multiplexing (OFDM) in Doppler channels. We first derive the
input--output relation describing OTFS modulation and demodulation (mod/demod)
for delay--Doppler channels with arbitrary number of paths, with given delay
and Doppler values. We then propose a low-complexity message passing (MP)
detection algorithm, which is suitable for large-scale OTFS taking advantage of
the inherent channel sparsity. Since the fractional Doppler paths (i.e., not
exactly aligned with the Doppler taps) produce the inter Doppler interference
(IDI), we adapt the MP detection algorithm to compensate for the effect of IDI
in order to further improve performance. Simulations results illustrate the
superior performance gains of OTFS over OFDM under various channel conditions.
