ZC
Table of Contents
Introduction
The Zadoff-Chu (ZC) sequence1 is named after Solomon A. Zadoff and D. C. Chu, which is a constant amplitude zero auto-correlation (CAZAC) sequence2 with its cylically shifted versions are zero correlated, i.e. orthogonal to each other. A ZC sequence without cyclic shift is termed a root sequence, which can be expressed as
where
Properties
- The auto-correlation of a ZC sequence is delta function, i.e. zero correlated.
- ZC sequences with odd length are periodic, i.e.
. - For a ZC sequence with odd length, its DFT is another ZC sequence.
- The cross-correlation between two prime length ZC sequences,
and , is constant , provided that is relative prime to .
Applications
ZC sequences are widely used in 3GPP LTE/LTE-Advanced system3
- Primary synchronization signal (PSS)
- Random access preamble
- Uplink demodulation reference signal (DMRS)
- Sounding reference signal (SRS)