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)

autocorrelation Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable ...

s equal to zero. CAZAC sequences find application in wireless communication systems, for example in

3GPP Long Term Evolution In telecommunications, long-term evolution (LTE) is a standard for wireless broadband communication for mobile devices and data terminals, based on the GSM/EDGE and UMTS/HSPA standards. It improves on those standards' capacity and speed by usi ...

for synchronization of mobile phones with base stations.

Zadoff–Chu sequence A Zadoff–Chu (ZC) sequence, also referred to as Chu sequence or Frank–Zadoff–Chu (FZC) sequence, is a complex-valued mathematical sequence which, when applied to a signal, gives rise to a new signal of constant amplitude. When cyclically shi ...

s are well-known CAZAC sequences with special properties.

Example CAZAC Sequence

For a CAZAC sequence of length

N

where

M

is relatively prime to

N

the

k

th symbol

u_k

is given by:

Even N

u_k = \exp \left(j \frac \right)

Odd N

u_k = \exp \left(j \frac \right)

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 :

r(\tau)=\delta(n)

The discrete fourier transform of the autocorrelation is flat :

R(f) = 1/N

Power spectrum is related to autocorrelation by :

R(f) = \left,  X(f) \^2

As a result the power spectrum is also flat. :

\left,  X(f) \^2 = 1/N

References

External links

CAZAC Sequence Generator (Java applet)
Signal processing {{mathapplied-stub