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dop = doppler.rounded
dop = doppler.rounded(coeffrounded)
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, $${a}_{0},\text{\hspace{0.17em}}\text{}{a}_{2},\text{\hspace{0.17em}}\text{}{a}_{4}$$, given by coeffrounded(1), coeffrounded(2), and coeffrounded(3), respectively.
The rounded Doppler spectrum object contains the following properties.
Property | Description |
---|---|
SpectrumType | Fixed value, 'Rounded' |
CoeffRounded | Vector of three polynomial coefficients (real finite numbers) |
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:
$$S(f)={C}_{r}\left[{a}_{0}+{a}_{2}{\left(\frac{f}{{f}_{d}}\right)}^{2}+{a}_{4}{\left(\frac{f}{{f}_{d}}\right)}^{4}\right]\text{,}\left|f\right|\le {f}_{d}$$
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 $${a}_{0},\text{\hspace{0.17em}}\text{}{a}_{2},\text{\hspace{0.17em}}\text{}{a}_{4}$$ 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 $$f=0$$.
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;
[1] IEEE 802.16 Broadband Wireless Access Working Group, "Channel models for fixed wireless applications," IEEE 802.16a-03/01, 2003-06-27.
doppler | doppler.ajakes | doppler.bell | doppler.bigaussian | doppler.flat | doppler.gaussian | doppler.jakes | doppler.rjakes | rayleighchan | ricianchan | stdchan