Parallel minimum mean square error equalization for reduced-zero-padding orthogonal time frequency space with the aid of unitary precoding

This work studies the equalization method for the reduced-prefix version of the orthogonal time frequency space (OTFS) modulation in which one zero-padding (ZP) is inserted in each frame. We focus on applications in low data rate scenarios such as the Internet of Things, and will consider the case where the number of subcarriers and time slots are small. The idea of this work is to retain the large singular values of the channel matrix through linear transformations, while discarding the remaining small singular values. This makes it possible to avoid performance degradation due to small singular values when inverting the matrix in the minimum mean square error (MMSE) equalization. Specifically, a joint unitary precoding and signal linear transformation method is proposed for the reduced-ZP OTFS modulation which decomposes the whole system into parallel subsystems. Then, the receiver can perform parallel MMSE equalization, where the singular values of each branch are not small. Simulation results show that the proposed method can achieve better bit error rate performance than the state-of-the-art methods like message passing, unitary approximate message passing, and variational unitary approximate message passing.