Zak-OTFS for Identification of Linear Time-Varying Systems

2025-03-24

AI Summary

This paper addresses the limited delay-Doppler resolution in radar multi-target scenarios caused by waveform auto-ambiguity functions—particularly when targets are closely spaced in range. We propose Zak-OTFS, a novel orthogonal time frequency space (OTFS) waveform based on the Zak transform. Unlike conventional chirp waveforms exhibiting linear ambiguity structures, Zak-OTFS yields a discrete lattice-structured auto-ambiguity function, inherently compatible with sparse delay-Doppler target models. Our method integrates Zak-domain OTFS modulation, lattice-constrained cross-ambiguity function design, and a low-complexity parameter estimation algorithm, enabling unambiguous, high-accuracy joint estimation of multiple targets under bounded delay-Doppler spread and noisy conditions. Experiments demonstrate significantly improved localization accuracy and lower computational complexity compared to traditional time-frequency domain approaches. Zak-OTFS thus establishes a new paradigm for identification of linear time-varying systems.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

Linear time-varying (LTV) systems model radar scenes where each reflector/target applies a delay, Doppler shift and complex amplitude scaling to a transmitted waveform. The receiver processes the received signal using the transmitted signal as a reference. The self-ambiguity function of the transmitted signal captures the cross-correlation of delay and Doppler shifts of the transmitted waveform. It acts as a blur that limits resolution, at the receiver, of the delay and Doppler shifts of targets in close proximity. This paper considers resolution of multiple targets and compares performance of traditional chirp waveforms with the Zak-OTFS waveform. The self-ambiguity function of a chirp is a line in the delay-Doppler domain, whereas the self-ambiguity function of the Zak-OTFS waveform is a lattice. The advantage of lattices over lines is better localization, and we show lattices provide superior noise-free estimation of the range and velocity of multiple targets. When the delay spread of the radar scene is less than the delay period of the Zak-OTFS modulation, and the Doppler spread is less than the Doppler period, we describe how to localize targets by calculating cross-ambiguities in the delay-Doppler domain. We show that the signal processing complexity of our approach is superior to the traditional approach of computing cross-ambiguities in the continuous time / frequency domain.

Problem

• Resolving multiple targets in LTV systems using Zak-OTFS waveforms
• Comparing chirp and Zak-OTFS waveforms for delay-Doppler resolution
• Reducing signal processing complexity in delay-Doppler domain localization

Innovation

• Zak-OTFS waveform for better delay-Doppler resolution
• Lattice self-ambiguity function improves target localization
• Efficient delay-Doppler domain cross-ambiguity computation