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

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 and aperiodic LAZ sequence sets are asymptotically optimal with respect to the periodic and aperiodic lower AF bounds, respectively, which were proposed recently in [IEEE J. Sel. Areas Commun. 40 (6): 1809-1822]. Notably, the aperiodic LAZ sequence sets are the first such sequence sets in the literature that satisfy the bound. Finally, we demonstrate that the proposed sequence sets are cyclically distinct.