Constant amplitude zero autocorrelation waveform

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In signal processing, a Constant Amplitude Zero AutoCorrelation waveform (CAZAC) is a periodic complex-valued signal with modulus one and out-of-phase periodic (cyclic) autocorrelations 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 sequences are well-known CAZAC sequences with special properties.

Example CAZAC Sequence

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For a CAZAC sequence of length   where   is relatively prime to   the  th symbol   is given by:[1]

Even N

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Odd N

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Power Spectrum of CAZAC Sequence

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The power spectrum of a CAZAC sequence is flat.

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

 

The discrete fourier transform of the autocorrelation is flat

 

Power spectrum is related to autocorrelation by

 

As a result the power spectrum is also flat.

 

References

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  1. ^ Chu, D. (July 1972). "Polyphase codes with good periodic correlation properties (Corresp.)". IEEE Transactions on Information Theory. 18 (4): 531–532. doi:10.1109/TIT.1972.1054840. ISSN 1557-9654.
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