Asymptotically Optimal Aperiodic and Periodic Sequence Sets with Low Ambiguity Zone Through Locally Perfect Nonlinear Functions
Zheng Wang, Zhengchun Zhou, Avik Ranjan Adhikary, Yang Yang, Sihem Mesnager, Pingzhi Fan
TL;DR
This work tackles the design of low ambiguity zone (LAZ) sequences for integrated sensing and communication (ISAC) by introducing locally perfect nonlinear functions (LPNFs) and leveraging interleaving. It presents three new classes of both periodic and aperiodic LAZ sequence sets with flexible parameters, showing that the periodic constructions are asymptotically optimal against the periodic AF bound, while the aperiodic constructions asymptotically meet the aperiodic bound for the first time. The results establish cyclic distinctness of the sequences and connect to prior constructions as special cases. The framework enables asymptotically optimal LAZ designs across multiple parameter regimes, potentially impacting practical JC/S sensing systems with limited Doppler-delay regions.
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.