Accelerating the pace of engineering and science

# doppler.rounded

Construct rounded Doppler spectrum object

## Syntax

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

## 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
SpectrumTypeFixed value, 'Rounded'
CoeffRoundedVector 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 [1]. 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 [1] 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;```