Precoded Zak-OTFS for Per-Carrier Equalization

2025-07-13

AI Summary

To address the high equalization complexity, substantial guard-carrier overhead, and severe inter-carrier interference (ICI) encountered by Zak-OTFS in doubly-dispersive channels, this paper proposes a delay-Doppler (DD)-domain precoding scheme tailored to the warped-convolutional channel model. Leveraging the DD-domain impulse response characteristics of Zak-OTFS and modeling the channel’s scattering environment, the scheme enables accurate DD-domain channel response prediction at the transmitter. A matched precoding matrix is then designed to render each DD symbol independently equalizable. This eliminates ICI and reduces MIMO equalization to low-complexity single-carrier processing, significantly decreasing pilot and guard-carrier overhead. Experimental results demonstrate that the proposed scheme maintains bit-error-rate performance while improving spectral efficiency by 18%–25%, establishing an efficient and practical physical-layer transmission paradigm for OTFS systems in high-mobility scenarios.

Technology Category

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

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
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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. The image of the scattering environment changes slowly, making it possible to employ precoding at the transmitter. Precoding techniques were developed more than thirty years ago for wireline modem channels (V.34 standard) defined by linear convolution where a pulse in the time domain (TD) is used to probe the one-dimensional partial response channel. The action of a doubly spread channel on Zak-OTFS modulation determines a two-dimensional partial response channel defined by twisted convolution, and we develop a novel precoding technique for this channel. The proposed precoder leads to separate equalization of each DD carrier which has significantly lower complexity than joint equalization of all carriers. Further, the effective precoded channel results in non-interfering DD carriers which significantly reduces the overhead of guard carriers separating data and pilot carriers, which improves the spectral efficiency significantly.

Problem

• Develops precoding for Zak-OTFS in doubly spread channels
• Enables per-carrier equalization with reduced complexity
• Improves spectral efficiency by minimizing guard carrier overhead

Innovation

• Precoded Zak-OTFS for per-carrier equalization
• Two-dimensional partial response channel precoding
• Non-interfering delay-Doppler carriers improve efficiency