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

A Simple Two-stage Equalizer With Simplified Orthogonal Time Frequency Space Modulation Over Rapidly Time-varying Channels