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

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.