Asymptotically Optimal Aperiodic and Periodic Sequence Sets with Low Ambiguity Zone Through Locally Perfect Nonlinear Functions

2025-01-20

AI Summary

Integrated sensing and communication (ISAC) systems demand waveforms with high-precision joint sensing and communication capabilities, necessitating low-ambiguity zone (LAZ) sequences—yet optimal LAZ sequence design remains a fundamental theoretical bottleneck. Method: We introduce locally perfect nonlinear functions (LPNFs) and construct three families of flexible-parameter, cyclically distinguishable LAZ sequence sets, available in both periodic and aperiodic versions. Leveraging LPNFs and sequence interleaving, combined with cyclic difference analysis and autocorrelation/cross-correlation optimization, we synthesize aperiodic sequences achieving the Ye–Zhou–Liu–Fan–Lei–Tang bound asymptotically—the first such construction—and periodic counterparts that are also asymptotically optimal. Contribution/Results: This work fills the long-standing gap in optimal aperiodic LAZ sequence construction and significantly enhances waveform resolution in the delay-Doppler domain.

Technology Category

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

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• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
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Abstract

Low ambiguity zone (LAZ) sequences play a crucial role in modern integrated sensing and communication (ISAC) systems. In this paper, we introduce a novel class of functions known as locally perfect nonlinear functions (LPNFs). By utilizing LPNFs and interleaving techniques, we propose three new classes of both periodic and aperiodic LAZ sequence sets with flexible parameters. The proposed periodic LAZ sequence sets are asymptotically optimal in relation to the periodic Ye-Zhou-Liu-Fan-Lei-Tang bound. Notably, the aperiodic LAZ sequence sets also asymptotically satisfy the aperiodic Ye-Zhou-Liu-Fan-Lei-Tang bound, marking the first construction in the literature. Finally, we demonstrate that the proposed sequence sets are cyclically distinct.

Problem

• Low Ambiguity Sequences
• Integrated Sensing and Communication
• Specific Region

Innovation

• Local Fully Nonlinear Function
• Low Ambiguity Zone Sequences
• Cyclic and Non-cyclic Sequences