  In this paper, a reduced-complexity cross-domain iterative detection for
orthogonal time frequency space (OTFS) modulation is proposed, which exploits
channel properties in both time and delay-Doppler domains. Specifically, we
first show that in the time domain effective channel, the path delay only
introduces interference among samples in adjacent time slots, while the Doppler
becomes a phase term that does not affect the channel sparsity. This
``band-limited'' matrix structure motivates us to apply a reduced-size linear
minimum mean square error (LMMSE) filter to eliminate the effect of delay in
the time domain, while exploiting the cross-domain iteration for minimizing the
effect of Doppler by noticing that the time and Doppler are a pair of Fourier
dual. The state (MSE) evolution was derived and compared with bounds to verify
the effectiveness of the proposed scheme. Simulation results demonstrate that
the proposed scheme achieves almost the same error performance as the optimal
detection, but only requires a reduced complexity.
