A Primer on Zadoff Chu Sequences

Zadoff Chu (ZC) sequences are the primary manifestation of spread spectrum in modern cellular systems including LTE and 5G NR, displacing PN and Walsh sequences which were the mainstays of 3G cellular (WCDMA and cdma2000) and IS-95. ZC sequences are complex sequences with unit amplitude and particular phase shifts, as opposed to Walsh and PN codes which are real and binary valued, most commonly $\pm 1$ when used in communication systems. ZC sequences have a number of remarkable and desirable properties. Because of these uniquely desirable properties, they are used for many key functions in current cellular systems, and are likely to be prevalent in future cellular systems as well.