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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 a0=1, a2=1.72, a4=0.785 (see Theory and Applications for the meaning of these coefficients). The maximum Doppler shift fd (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, a0, a2, a4, 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:

S(f)=Cr[a0+a2(ffd)2+a4(ffd)4]|f|fd

where

Cr=12fd[a0+a23+a45]

fd is the maximum Doppler shift, and a0, a2, a4 are real finite coefficients. The fixed wireless channel model of IEEE 802.16 [1] uses the following parameters: a0=1, a2=1.72, and a4=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 fd=10. It then creates a rounded Doppler spectrum object with polynomial coefficients a0=1.0, a2=0.5, a4=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;

More About

References

[1] IEEE 802.16 Broadband Wireless Access Working Group, "Channel models for fixed wireless applications," IEEE 802.16a-03/01, 2003-06-27.

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