# Documentation

Generate root Zadoff-Chu sequence of complex symbols

## Syntax

• `SEQ = lteZadoffChuSeq(R,N)`

## Description

````SEQ = lteZadoffChuSeq(R,N)` generates the `R`th root Zadoff-Chu sequence with length `N`, as defined in the LTE specifications [1]. The output SEQ is an `N`-length column vector of complex symbols.The function generates the actual sequence using the following algorithm:$seq\left(m+1\right)=\mathrm{exp}\left(-j\cdot \pi \cdot R\cdot m\cdot \left(m+1\right)/N\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}for\text{\hspace{0.17em}}\text{\hspace{0.17em}}m=0,...,N-1$This function uses a negative polarity on the argument of the exponent or a clockwise sequence of phases.```

## Examples

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### Examine the Correlation Properties of a Zadoff-Chu Sequence

Generate the 25th root length-139 Zadoff-Chu sequence.

Use `lteZadoffChuSeq` to generate the sequence and then plot its absolute values.

```seq = lteZadoffChuSeq(25,139); plot(abs(xcorr(seq)./length(seq))) ```

## Input Arguments

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### `R` — Root of the Zadoff-Chu sequencepositive integer scalar

Example: `25`

Data Types: `single` | `double`
Complex Number Support: Yes

### `N` — Length of the Zadof-Chu sequencepositive integer scalar

Example: `139`

Data Types: `single` | `double`
Complex Number Support: Yes

## Output Arguments

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### `SEQ` — Zadoff-Chu output sequencecomplex double-type column vector

The output sequence is a complex-valued column vector that contains the `R`th root Zadoff-Chu sequence of length `N`.

## References

[1] 3rd Generation Partnership Project: Technical Specification Group Radio Access Network. "Evolved Universal Terrestrial Radio Access (E-UTRA)," Physical Channels and Modulation, Release 10, 2010–2012, TS 36.211, Vol. 10.0.0.