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A Primer on Zadoff Chu Sequences. (arXiv:2211.05702v2 [cs.IT] UPDATED)

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Zadoff Chu (ZC) sequences are a principal manifestation of spread spectrum in
modern cellular systems including LTE and 5G NR, largely displacing PN and
Walsh sequences which were the mainstays of 3G cellular (WCDMA and cdma2000)
and the 2G-era 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 $\pm1$ when used in communication systems.


ZC sequences have a number of remarkable and desirable properties that we
define in the next section. Because of these properties, they are used for many
key functions in current cellular systems, and are likely to be prevalent in
future cellular systems as well. In LTE and 5G NR, they are widely used for a
number of important initial access and overhead channel functions that are
often overlooked by engineers who focus on data transmission. For example, ZC
sequences are used for initial access in both the downlink (synchronization)
and uplink (random access), uplink control information, uplink channel
sounding, and for the reference symbols (pilots) used for fine-grained channel
estimation. It is not an exaggeration to say that most types of signals other
than the data transmissions in modern cellular standards utilize ZC sequences.

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