Documentation

# doppler.rounded

(To be removed) Construct rounded Doppler spectrum object

## Syntax

```dop = doppler.rounded dop = doppler.rounded(coeffrounded) ```

`doppler.rounded` will be removed in a future release. Use `doppler``('Rounded', ...)` instead.

## Description

The `doppler.rounded` function creates a rounded Doppler spectrum object that is used for the `DopplerSpectrum` property of a channel object (created with either the `rayleighchan` or the `ricianchan` function).

`dop = doppler.rounded` creates a rounded Doppler spectrum object with default polynomial coefficients ${a}_{0}=1$, ${a}_{2}=-1.72$, ${a}_{4}=0.785$ (see Theory and Applications for the meaning of these coefficients). The maximum Doppler shift ${f}_{d}$ (in Hertz) is specified by the `MaxDopplerShift` property of the channel object.

`dop = doppler.rounded(coeffrounded)`, where `coeffrounded` is a row vector of three finite real numbers, creates a rounded Doppler spectrum object with polynomial coefficients, , given by `coeffrounded(1)`, `coeffrounded(2)`, and `coeffrounded(3)`, respectively.

## Properties

The rounded Doppler spectrum object contains the following properties.

PropertyDescription
`SpectrumType`Fixed value, `'Rounded'`
`CoeffRounded`Vector of three polynomial coefficients (real finite numbers)

## Theory and Applications

A rounded spectrum is proposed as an approximation to the measured Doppler spectrum of the scatter component of fixed wireless channels at 2.5 GHz . However, the shape of the spectrum is influenced by the center carrier frequency.

The normalized rounded Doppler spectrum is given analytically by a polynomial in f of order four, where only the even powers of f are retained:

where

`${C}_{r}=\frac{1}{2{f}_{d}\left[{a}_{0}+\frac{{a}_{2}}{3}+\frac{{a}_{4}}{5}\right]}$`

${f}_{d}$ is the maximum Doppler shift, and are real finite coefficients. The fixed wireless channel model of IEEE 802.16  uses the following parameters: ${a}_{0}=1$, ${a}_{2}=-1.72$, and ${a}_{4}=0.785$. Because the channel is modeled as Rician fading with a fixed line-of-sight (LOS) component, a Dirac delta is also present in the Doppler spectrum at $f=0$.

## Examples

The following code creates a Rician channel object with a maximum Doppler shift of ${f}_{d}=10$. It then creates a rounded Doppler spectrum object with polynomial coefficients ${a}_{0}=1.0$, ${a}_{2}=-0.5$, ${a}_{4}=1.5$, and assigns it to the `DopplerSpectrum` property of the channel object.

```chan = ricianchan(1/1000,10,1); dop_rounded = doppler.rounded([1.0 -0.5 1.5]); chan.DopplerSpectrum = dop_rounded;```

## References

 IEEE 802.16 Broadband Wireless Access Working Group, “Channel models for fixed wireless applications,” IEEE 802.16a-03/01, 2003-06-27.