Low-Complexity Frequency Domain Equalization of Zak-OTFS in Doubly-Spread Channels

TL;DR

This paper proposes a low-complexity frequency domain equalization method for Zak-OTFS in doubly-spread channels, significantly reducing computational complexity while maintaining effective channel prediction and spectral efficiency.

Contribution

It introduces a frequency domain equalization approach for Zak-OTFS that reduces complexity from cubic to quadratic order, and provides a method to reconstruct the FD channel from DD domain estimates.

Findings

Frequency domain equalization reduces complexity to ${ m O}(M^2 N^2)$.

Effective channel reconstruction from DD to FD domain is feasible.

No spectral efficiency loss with the proposed method.

Abstract

We communicate over wireless channels by first estimating and then equalizing the effective channel. In Zak-OTFS (orthogonal time frequency space) modulation the carrier waveform is a pulse in the delay-Doppler (DD) domain, formally a quasi-periodic localized function with specific periods along delay and Doppler. When the channel delay spread is less than the delay period, and the channel Doppler spread is less than the Doppler period, the response to a single Zak-OTFS carrier provides an image of the scattering environment and can be used to predict the effective channel at all other carriers. This makes DD domain channel estimation straightforward, and there is no loss in spectral efficiency since it is possible to design data and pilot signals that are mutually unbiased. However, equalization in the DD domain has high complexity ${\mathcal O}(M^3N^3)$ where $M$, $N$ are respectively the number of delay and Doppler bins in an OTFS frame, and $MN$ is the number of information symbols. We demonstrate that equalization in the frequency domain (FD) reduces complexity to only ${\mathcal O}(M^2 N^2)$ by taking advantage of the banded structure of the effective FD channel. We also derive a low-complexity method to reconstruct the effective FD channel from the estimated DD domain effective channel.