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

xu(n)=ejπun(n+1+2q)L,n=0,1,,L1,

where u is the index of the root sequence, L is the length and qZ.

Properties

  • The auto-correlation of a ZC sequence is delta function, i.e. zero correlated.
  • ZC sequences with odd length are periodic, i.e. xu(n+L)=xu(n).
  • For a ZC sequence with odd length, its DFT is another ZC sequence.
  • The cross-correlation between two prime length ZC sequences, xu1(n) and xu2(n), is constant L, provided that u1u2 is relative prime to L.

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)

Footnotes: