Does 6G Need a New Waveform: Comparing Zak-OTFS with CP-OFDM

TL;DR

The paper investigates whether 6G should adopt a new waveform by comparing CP-OFDM and Zak-OTFS across a full range of propagation environments. It treats the choice as an architectural decision: CP-OFDM aims to avoid interference by operating on a coarse grid, while Zak-OTFS embraces interference and enables joint equalization via a fine delay-Doppler grid and twisted-convolution channel modeling. The authors derive and leverage the crystallization condition ($\tau_p>\tau_s$ and $\nu_p>\nu_s$) to enable efficient I/O relation acquisition with minimal pilot overhead, and they optimize Zak-OTFS operating points (delay/Doppler periods, pulse shaping, pilot/guard regions, and PDR) over Veh-A channel scenarios. Across 35 Doppler-delay scenarios at $SNR=12$ dB, Zak-OTFS matches CP-OFDM in low-mobility small cells but offers substantial spectral efficiency gains in high-mobility and/or large-cell settings, demonstrating Zak-OTFS as a viable and advantageous 6G waveform in challenging channels.

Abstract

Across the world, there is growing interest in new waveforms, Zak-OTFS in particular, and over-the-air implementations are starting to appear. The choice between OFDM and Zak-OTFS is not so much a choice between waveforms as it is an architectural choice between preventing inter-carrier interference (ICI) and embracing ICI. In OFDM, once the Input-Output (I/O) relation is known, equalization is relatively simple, at least when there is no ICI. However, in the presence of ICI the I/O relation is non-predictable and its acquisition is non-trivial. In contrast, equalization is more involved in Zak-OTFS due to inter-symbol-interference (ISI), however the I/O relation is predictable and its acquisition is simple. {Zak-OTFS exhibits superior performance in doubly-spread 6G use cases with high delay/Doppler channel spreads (i.e., high mobility and/or large cells), but architectural choice is governed by the typical use case, today and in the future. What is typical depends to some degree on geography, since large delay spread is a characteristic of large cells which are the rule rather than the exception in many important wireless markets.} This paper provides a comprehensive performance comparison of cyclic prefix OFDM (CP-OFDM) and Zak-OTFS across the full range of 6G propagation environments. The performance results provide insights into the fundamental architectural choice.

Figures (15)

• Figure 1: A quasi-periodic DD domain pulse and its TD (FD) realization, referred to as TD (FD) pulsone.
• Figure 2: Allocation of TF resources.
• Figure 3: An illustrative Zak-OTFS sub-frame with pilot, guard and data regions. $k_{max} \stackrel {\Delta} {=} \lceil B \tau_s \rceil$ and the fractional overhead of the pilot and guard regions is $(2 k_{max} + 3)/M \approx 2 \tau_s /\tau_p$. Note that with $\tau_p \gg \tau_s$, the pilot overhead is small, and the I/O relation can be acquired efficiently.
• Figure 4: A fundamental architectural choice. CP-OFDM operates on a coarse information grid to avoid ISI and ICI. Zak-OTFS operates on a fine information grid with carrier waveforms designed to enable joint equalization.
• Figure 5: Effect of (a) channel Doppler spread and (b) delay spread on CP-OFDM overheads, for a CP-OFDM sub-frame of duration $1$ ms and $48$ sub-carriers.