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Construct rounded Doppler spectrum object

`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`

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