  The orthogonal-time-frequency-space (OTFS) modulation has emerged as a
promising modulation scheme for high mobility wireless communications. To
harvest the time and frequency diversity promised by OTFS, some promising
detectors, especially message passing based ones, have been developed by taking
advantage of the sparsity of the channel in the delay-Doppler domain. However,
when the number of channel paths is relatively large or fractional Doppler
{shifts have} to be considered, the complexity of existing detectors is a
concern, and the message passing based detectors may suffer from performance
loss due to the short loops involved in message passing. In this work, we
investigate the design of OTFS detectors based on the approximate message
passing (AMP). In particular, {leveraging the unitary AMP (UAMP), we design new
detectors that enjoy} the structure of the channel matrix and allow efficient
implementation. In addition, the estimation of noise variance is incorporated
into the UAMP-based detectors. Thanks to the robustness of UAMP relative to
AMP, the UAMP-based detectors deliver superior performance, and outperform
state-of-the-art detectors significantly. We also investigate iterative joint
detection and decoding in a coded OTFS system, where the OTFS detectors are
integrated into a powerful turbo receiver, leading to considerable performance
gains.
