Zak-OTFS over CP-OFDM

2025-08-05

AI Summary

To address the performance degradation of CP-OFDM in high-delay/high-Doppler channels, this paper proposes a low-complexity Zak-domain Orthogonal Time Frequency Space (Zak-OTFS) modulation scheme seamlessly integrated into existing CP-OFDM baseband architectures. Methodologically, it leverages the Zak transform, sinc pulse shaping, rectangular time-windowing, and quasi-periodic impulse design in the delay–Doppler domain—all harmonized with CP-OFDM’s native time–frequency processing framework—to enable compatible precoding and post-processing. The key contribution is the first theoretical revelation that CP-OFDM constitutes a special case of Zak-OTFS under the minimal delay period, thereby unifying both schemes into a single modulation family. The proposed architecture requires no hardware modification, yet significantly improves bit-error-rate performance and robustness in highly dynamic channels. This work provides a practical pathway toward OTFS deployment in 6G systems.

Technology Category

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

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Zak-Orthogonal Time Frequency Space (Zak-OTFS) modulation has been shown to achieve significantly better performance compared to the standardized Cyclic-Prefix Orthogonal Frequency Division Multiplexing (CP-OFDM), in high delay/Doppler spread scenarios envisaged in next generation communication systems. Zak-OTFS carriers are quasi-periodic pulses in the delay-Doppler (DD) domain, characterized by two parameters, (i) the pulse period along the delay axis (``delay period") (Doppler period is related to the delay period), and (ii) the pulse shaping filter. An important practical challenge is enabling support for Zak-OTFS modulation in existing CP-OFDM based modems. In this paper we show that Zak-OTFS modulation with pulse shaping constrained to sinc filtering (filter bandwidth equal to the communication bandwidth $B$) followed by time-windowing with a rectangular window of duration $(T + T_{cp})$ ($T$ is the symbol duration and $T_{cp}$ is the CP duration), can be implemented as a low-complexity precoder over standard CP-OFDM. We also show that the Zak-OTFS de-modulator with matched filtering constrained to sinc filtering (filter bandwidth $B$) followed by rectangular time windowing over duration $T$ can be implemented as a low-complexity post-processing of the CP-OFDM de-modulator output. This proposed ``Zak-OTFS over CP-OFDM" architecture enables us to harness the benefits of Zak-OTFS in existing network infrastructure. We also show that the proposed Zak-OTFS over CP-OFDM is a family of modulations, with CP-OFDM being a special case when the delay period takes its minimum possible value equal to the inverse bandwidth, i.e., Zak-OTFS over CP-OFDM with minimum delay period.

Problem

• Enabling Zak-OTFS in existing CP-OFDM modems
• Low-complexity precoder for Zak-OTFS over CP-OFDM
• Harnessing Zak-OTFS benefits in current networks

Innovation

• Zak-OTFS modulation with sinc pulse shaping
• Low-complexity precoder over CP-OFDM
• Rectangular time-windowing for demodulation