Low-Complexity Linear Equalizers for OTFS Exploiting Two-Dimensional Fast Fourier Transform

TL;DR

This paper introduces low-complexity linear equalizers for OTFS modulation that leverage the doubly block circulant structure of the channel, enabling efficient implementation with 2D FFTs and maintaining performance.

Contribution

It reveals the doubly block circulant feature of OTFS channels and proposes ZF and MMSE equalizers that significantly reduce computational complexity using 2D FFTs.

Findings

Complexity reduced from O((NM)^3) to O(NM log2(NM))

Equalizers achieve similar performance to existing methods

Efficient implementation with 2D FFTs

Abstract

Orthogonal time frequency space (OTFS) modulation can effectively convert a doubly dispersive channel into an almost non-fading channel in the delay-Doppler domain. However, one critical issue for OTFS is the very high complexity of equalizers. In this letter, we first reveal the doubly block circulant feature of OTFS channel represented in the delay-Doppler domain. By exploiting this unique feature, we further propose zero-forcing (ZF) and minimum mean squared error (MMSE) equalizers that can be efficiently implemented with the two-dimensional fast Fourier transform. The complexity of our proposed equalizers is gracefully reduced from $\mathcal{O}\left(\left(NM\right)^{3}\right)$ to $\mathcal{O}\left(NM\mathrm{log_{2}}\left(NM\right)\right)$, where $N$ and $M$ are the number of OTFS symbols and subcarriers, respectively. Analysis and simulation results show that compared with other existing linear equalizers for OTFS, our proposed linear equalizers enjoy a much lower computational complexity without any performance loss.