A Primer on Zadoff Chu Sequences
This paper addresses the widespread neglect by communication engineers of the critical role of Zadoff–Chu (ZC) sequences in cellular system overhead channels. We systematically uncover their universal design principles across LTE and 5G NR—spanning synchronization, random access, uplink control, sounding reference signals (SRS), and pilot design. Leveraging complex unit-magnitude modeling, DFT symmetry analysis, and rigorous derivation of zero autocorrelation and ideal cross-correlation properties, we establish the mathematical necessity and engineering superiority of ZC sequences over PN or Walsh sequences. For the first time, we unify the construction principles, time–frequency mapping rules, and robustness foundations of ZC sequences from a practical implementation perspective, bridging a long-standing gap between theoretical properties and physical-layer realization. The work provides a reusable theoretical framework and design guidelines for low-overhead, high-reliability sequence design in 6G systems.