  Orthogonal time frequency space (OTFS) modulation was shown to provide
significant error performance advantages over orthogonal frequency division
multiplexing (OFDM) in delay--Doppler channels. In order to detect OTFS
modulated data, the channel impulse response needs to be known at the receiver.
In this paper, we propose embedded pilot-aided channel estimation schemes for
OTFS. In each OTFS frame, we arrange pilot, guard, and data symbols in the
delay--Doppler plane to suitably avoid interference between pilot and data
symbols at the receiver. We develop such symbol arrangements for OTFS over
multipath channels with integer and fractional Doppler shifts, respectively. At
the receiver, channel estimation is performed based on a threshold method and
the estimated channel information is used for data detection via a message
passing (MP) algorithm. Thanks to our specific embedded symbol arrangements,
both channel estimation and data detection are performed within the same OTFS
frame with a minimum overhead. We compare by simulations the error performance
of OTFS using the proposed channel estimation and OTFS with ideally known
channel information and observe only a marginal performance loss. We also
demonstrate that the proposed channel estimation in OTFS significantly
outperforms OFDM with known channel information. Finally, we present extensions
of the proposed schemes to MIMO and multi-user uplink/downlink.
