  The recent emergence of orthogonal time frequency space (OTFS) modulation as
a novel PHY-layer mechanism is more suitable in high-mobility wireless
communication scenarios than traditional orthogonal frequency division
multiplexing (OFDM). Although multiple studies have analyzed OTFS performance
using theoretical and ideal baseband pulseshapes, a challenging and open
problem is the development of effective receivers for practical OTFS systems
that must rely on non-ideal pulseshapes for transmission. This work focuses on
the design of practical receivers for OTFS. We consider a fractionally spaced
sampling (FSS) receiver in which the sampling rate is an integer multiple of
the symbol rate. For rectangular pulses used in OTFS transmission, we derive a
general channel input-output relationship of OTFS in delay-Doppler domain
without the common reliance on impractical assumptions such as ideal
bi-orthogonal pulses and on-the-grid delay/Doppler shifts. We propose two
equalization algorithms: iterative combining message passing (ICMP) and turbo
message passing (TMP) for symbol detection by exploiting delay-Doppler channel
sparsity and the frequency diversity gain via FSS. We analyze the convergence
performance of TMP receiver and propose simplified message passing (MP)
receivers to further reduce complexity. Our FSS receivers demonstrate stronger
performance than traditional receivers and robustness to the imperfect channel
state information knowledge.
