Zak-OFDM: Low Complexity Joint Equalization of OFDM Carriers in Doubly-Spread Channels

2025-06-28

AI Summary

In doubly-dispersive channels, CP-OFDM suffers from severe inter-carrier interference (ICI) due to mobility-induced Doppler shifts and delay spread, while accurate frequency-domain channel estimation remains challenging; meanwhile, Zak-OTFS offers inherent delay-Doppler (DD) domain sparsity but incurs prohibitive computational complexity $mathcal{O}(M^3N^3)$ for direct equalization. To address these issues, this paper proposes a Zak-OFDM joint equalization framework that synergistically integrates Zak-OTFS’s DD-domain channel estimation capability with CP-OFDM’s waveform compatibility. By modeling the channel in the DD domain, the framework enables pilot-free, full-band frequency-domain channel reconstruction. Furthermore, a low-complexity joint subcarrier equalizer is designed, reducing complexity to $mathcal{O}(M^2N^2)$. Experimental results demonstrate that the proposed method significantly suppresses ICI, mitigates sensitivity of subcarrier spacing to Doppler shift, and enhances system robustness and performance in high-mobility scenarios—without compromising spectral efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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 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, the naive approach to equalization has complexity ${mathcal O}(M^3N^3)$ where $M$ and $N$ are respectively the number of delay and Doppler bins in an OTFS frame. We simplify equalization by transforming Zak-OTFS information symbols to CP-OFDM (cyclic prefix orthogonal frequency division multiplexing) modulation. Why not simply communicate with CP-OFDM? Inter-carrier interference (ICI) in CP-OFDM makes it is very challenging to acquire the complete frequency domain (FD) channel response between subcarriers in the presence of mobility and delay spread. We avoid this difficulty by estimating the effective channel in the DD domain from which we are able to reconstruct the complete FD channel response. We take advantage of CP-OFDM to design an ${mathcal O}(M^2N^2)$ low-complexity method of jointly equalizing all subcarriers, where $MN$ is the number of subcarriers. Our approach removes the need for traditional pilots in CP-OFDM and reduces the need to vary carrier spacing with mobility.

Problem

• Reducing complexity in joint OFDM carrier equalization
• Overcoming inter-carrier interference in CP-OFDM systems
• Enabling efficient channel estimation in doubly-spread channels

Innovation

• Transforms Zak-OTFS symbols to CP-OFDM modulation
• Estimates channel in delay-Doppler domain
• Reduces equalization complexity to O(M^2N^2)