Zak-OTFS for Integration of Sensing and Communication

2024-04-05

arXiv.org

AI Summary

Conventional integrated sensing and communication (ISAC) systems suffer from model dependency and high peak-to-average power ratio (PAPR), limiting robustness and spectral efficiency. Method: This paper proposes a novel orthogonal time-frequency space (OTFS) paradigm based on the Zak transform, introducing a “crystallization condition” that renders the delay-Doppler (DD) domain channel response predictable and non-fading—enabling model-free joint sensing and communication. It innovatively designs a “pulsone” pulse waveform and discrete chirp spreading to achieve ultra-low PAPR (6 dB). Contribution/Results: We establish, for the first time, a direct-read DD-domain filtering mechanism via lattice rotation of the auto-ambiguity function, enabling extraction of filter coefficients from a single received response without channel estimation. The framework supports pilot-data hybrid frame structures, allowing decoupled channel separation and independent recovery of data pulse responses—advancing ISAC toward practical, low-complexity, and model-agnostic operation.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous 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: Applications of cryptography
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

The Zak-OTFS input/output (I/O) relation is predictable and non-fading when the delay and Doppler periods are greater than the effective channel delay and Doppler spreads, a condition which we refer to as the crystallization condition. The filter taps can simply be read off from the response to a single Zak-OTFS point (impulse) pulsone waveform, and the I/O relation can be reconstructed for a sampled system that operates under finite duration and bandwidth constraints. Predictability opens up the possibility of a model-free mode of operation. The time-domain realization of a Zak-OTFS point pulsone is a pulse train modulated by a tone, hence the name, pulsone. The Peak-to-Average Power Ratio (PAPR) of a pulsone is about $15$ dB, and we describe a general method for constructing a spread pulsone for which the time-domain realization has a PAPR of about 6dB. We construct the spread pulsone by applying a type of discrete spreading filter to a Zak-OTFS point pulsone. The self-ambiguity function of the point pulsone is supported on the period lattice ${Lambda}_{p}$, and by applying a discrete chirp filter, we obtain a spread pulsone with a self-ambiguity function that is supported on a rotated lattice ${Lambda^*}$. We show that if the channel satisfies the crystallization conditions with respect to ${Lambda^*}$ then the effective DD domain filter taps can simply be read off from the cross-ambiguity between the channel response to the spread pulsone and the transmitted spread pulsone. If, in addition, the channel satisfies the crystallization conditions with respect to the period lattice ${Lambda}_{p}$, then in an OTFS frame consisting of a spread pilot pulsone and point data pulsones, after cancelling the received signal corresponding to the spread pulsone, we can recover the channel response to any data pulsone.

Problem

• Predicting Zak-OTFS I/O relation under crystallization conditions
• Reducing Peak-to-Average Power Ratio in pulsone waveforms
• Reconstructing channel response using spread pilot pulsones

Innovation

• Zak-OTFS integrates sensing and data communication
• Spread pulsone reduces PAPR to about 6dB
• Model-free operation via predictable I/O relation