Polyphase Sequences With Flexible Zero-Ambiguity-Zone Configurations for Integrated Sensing and Communications

This paper explores the design and theoretical framework of polyphase sequences with zero-ambiguity-zone (ZAZ) for the better efficiency and functionality of integrated sensing and communication (ISAC) systems. We first prove that a polyphase sequence with an optimal rectangular auto-ZAZ must be a member of some uncorrelated optimal ZCZ sequence family, and conversely, any member of an uncorrelated optimal ZCZ sequence family has an optimal rectangular auto-ZAZ (Theorems 1, 2 and 3). We generalize the optimality condition on the rectangular ZAZ into that on the centrally symmetric convex ZAZ in general (Theorem 4). We propose some constructions of families of polyphase sequences with a strictly or asymptotically optimal rectangular ZAZ (Theorem 1), dual asymptotically optimal rectangular ZAZs (Theorems 5 and 6), and asymptotically optimal rhombic or hexagonal ZAZ (Remarks 4 and 5) from the flexible ZAZ configuration.