Low-complexity equalization of Zak-OTFS in the frequency domain

4G/5G wireless standards ustransfer domain ise orthogonal frequency division multiplexing (OFDM) which is robust to frequency selectivity. Equalization is possible with a single tap filter, and low-complexity equalization makes OFDM an attractive physical layer. However, the performance of OFDM degrades with mobility. Zak-transform based orthogonal time frequency space (Zak-OTFS) modulation has been shown to be robust to doubly selective channels. The received signal in Zak-OTFS is a superposition of many attenuated copies since the doubly selective channel introduces delay and Doppler shifts and are more difficult to equalize since they are subject to interference along both delay and Doppler axes. In this paper, we propose a low-complexity method of equalizing Zak-OTFS in the frequency domain (FD). We derive the FD system model and show that it is unitarily equivalent to the DD system model. We show that the channel matrix in the FD is banded, making it possible to apply conjugate gradient methods to reduce the complexity of equalization. We show that complexity of FD equalization is linear in the dimension of a Zak-OTFS frame while naive MMSE equalization incurs cubic complexity. Through numerical simulations we show that FD equalization of Zak-OTFS achieves similar performance as equalization in DD domain.