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

paper develops the theory and constructions of polyphase zero-ambiguity-zone (ZAZ) sequences for ISAC waveforms, enabling the ZAZ shape to be designed over delay–Doppler regions of interest and supporting flexible (including multi-mode) sensing–communication operation. 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 to that on centrally symmetric convex ZAZs 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 5 and 6) from the flexible ZAZ configuration