Constant amplitude zero autocorrelation waveform: Difference between revisions

Revision as of 18:10, 3 December 2021

Revision as of 06:25, 27 January 2022

Line 1:

In [[signal processing]], a '''Constant Amplitude Zero AutoCorrelation waveform''' ('''CAZAC''') is a periodic [[complex number|complex]]-valued [[signal (electrical engineering)|signal]] with modulus one and out-of-phase periodic (cyclic) [[autocorrelation]]s equal to zero. CAZAC sequences find application in wireless communication systems, for example in [[3GPP Long Term Evolution]] for synchronization of mobile phones with base stations. [[Zadoff–Chu sequence]]s are well-known CAZAC sequences with special properties.

== Example CAZAC Sequence ==

== Example CAZAC Sequence <ref>{{Cite journal|last=Chu|first=D.|date=July 1972|title=Polyphase codes with good periodic correlation properties (Corresp.)|url=https://ieeexplore.ieee.org/document/1054840|journal=IEEE Transactions on Information Theory|volume=18|issue=4|pages=531–532|doi=10.1109/TIT.1972.1054840|issn=1557-9654}}</ref> ==

For a CAZAC sequence of length <math>N</math> where <math>M</math> is relatively prime to <math>N</math> the <math>k</math>th symbol <math>u_k</math> is given by:<ref>{{Cite journal|last=Chu|first=D.|date=July 1972|title=Polyphase codes with good periodic correlation properties (Corresp.)|url=https://ieeexplore.ieee.org/document/1054840|journal=IEEE Transactions on Information Theory|volume=18|issue=4|pages=531–532|doi=10.1109/TIT.1972.1054840|issn=1557-9654}}</ref>

===Even N===