  This paper presents a linear complexity iterative rake detector for the
recently proposed orthogonal time frequency space (OTFS) modulation scheme. The
basic idea is to extract and coherently combine the received multipath
components of the transmitted symbols in the delay-Doppler grid using maximal
ratio combining (MRC) to improve the SNR of the combined signal. We reformulate
the OTFS input-output relation in simple vector form by placing guard null
symbols or zero padding (ZP) in the delay-Doppler grid and exploiting the
resulting circulant property of the blocks of the channel matrix. Using this
vector input-output relation we propose a low complexity iterative decision
feedback equalizer (DFE) based on MRC. The performance and complexity of the
proposed detector favorably compares with the state of the art message passing
detector. An alternative time domain MRC based detector is also proposed for
even faster detection. We further propose a Gauss-Seidel based over-relaxation
parameter in the rake detector to improve the performance and the convergence
speed of the iterative detection. We also show how the MRC detector can be
combined with outer error-correcting codes to operate as a turbo DFE scheme to
further improve the error performance. All results are compared with a baseline
orthogonal frequency division multiplexing (OFDM) scheme employing a single tap
minimum mean square error (MMSE) equalizer.
