  In this work, we derive a equivalent delay-Doppler channel matrix of the
Orthogonal Time Frequency Space (OTFS) modulation that has not been studied in
previous literature. It has the similar structure as the banded channel matrix
of OFDM systems over rapidly time-varying channels. However, the band in the
equivalent channel matrix will no longer spread with the increase of the
Doppler spread once the length of maximum channel delay spread and the OTFS
frame duration are deter- mined. Furthermore, the equivalent channel matrix can
simplify the OTFS modulation in the transmitter side. Incorporating the
equivalent channel matrix, we propose a simple two-stage equal- izer in 1
dimensional operations for OTFS modulation. First, the receive signal is
equalized using the conventional OFDM single- tap equalizer in the frequency
domain. The multipath effects can be removed. In the second stage, another low
complexity delay- Doppler domain equalizer is employed to eliminate the effects
of the residual interference caused by the Doppler spread with the equivalent
channel matrix. The simulation results demonstrate that the proposed method is
superior to the conventional single- tap equalizer and full minimum mean
squared error (MMSE) equalizer of OFDM systems in terms of BER in high Doppler
spread scenarios.
