Constant amplitude zero autocorrelation waveform: Difference between revisions

Revision as of 05:00, 19 March 2010

Latest revision as of 13:12, 25 August 2025

(22 intermediate revisions by 20 users not shown)

Line 1:

AIn [[signal processing]], a '''Constant Amplitude Zero AutoCorrelation waveform''' (abbreviated '''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 LTE[[3GPP Long Term Evolution]] for synchronisationsynchronization of mobile phones with base stations. [[Zadoff–Chu sequence|Zadoff-Chu sequences]]s are well -known CAZAC sequences with special properties.

{{Context|date=March 2009}}

{{Refimprove|date=March 2009}}

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

== Example CAZAC Sequence ==

CAZAC (constant amplitude with zero auto correlation)

In wireless cdma technology , the given data encoded and in transmitter side number users assign to unique codes with help comman codes ( ex.. PN sequences , psuedo random noice) . In cdma technology data transmitted under same range of frequency but the users are identified by the unique nomber , the codes are matched between the particular users than data will transmitted .

The matching between the users is called synchoronous cdma. The coded data sending with constant amplitude and zero auto correlation . The constant amplitude means the sending and receiving easily without any correption. Zero auto correlation means the correlative variance between the users is zero ,so no interaction between the users.

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.)|journal=IEEE Transactions on Information Theory|volume=18|issue=4|pages=531–532|doi=10.1109/TIT.1972.1054840|issn=1557-9654}}</ref>

CAZAC (constant amplitude with zero auto correlation)

In wireless cdma technology , the given data encoded and in transmitter side number users assign to unique codes with help comman codes ( ex.. PN sequences , psuedo random noice) . In cdma technology data transmitted under same range of frequency but the users are identified by the unique nomber , the codes are matched between the particular users than data will transmitted .

===Even N===

The matching between the users is called synchoronous cdma. The coded data sending with constant amplitude and zero auto correlation . The constant amplitude means the sending and receiving easily without any correption. Zero auto correlation means the correlative variance between the users is zero ,so no interaction between the users. (ccet odc ece DMD).

<math>u_k = \exp \left(j \frac{M \pi k^2}{N} \right)</math>

===Odd N===

<math>u_k = \exp \left(j \frac{M \pi k (k+1)}{N} \right)</math>

==Power Spectrum of CAZAC Sequence==

The power spectrum of a CAZAC sequence is flat.

If we have a CAZAC sequence the time ___domain autocorrelation is an impulse

: <math>r(\tau)=\delta(n)</math>

The discrete fourier transform of the autocorrelation is flat

: <math>R(f) = 1/N</math>

Power spectrum is related to autocorrelation by

: <math>R(f) = \left| X(f) \right|^2</math>

As a result the power spectrum is also flat.

: <math>\left| X(f) \right|^2 = 1/N</math>

==References==

{{Reflist}}

==External links==

* [httphttps://www.math.umd.edu/~jjb/cazac/ CAZAC Sequence Generator (Java applet)]

{{DEFAULTSORT:Constant Amplitude Zero Autocorrelation Waveform}}

Line 20 ⟶ 43:

{{signal-processing-stub}}

{{mathapplied-stub}}