Construct Jakes Doppler spectrum object

`dop = doppler.jakes`

creates a Jakes Doppler
spectrum object that is to be used for the `DopplerSpectrum`

property
of a channel object (created with either the `rayleighchan`

or
the `ricianchan`

function). The maximum
Doppler shift of the Jakes Doppler spectrum object is specified by
the `MaxDopplerShift`

property of the channel object.
By default, channel objects are created with a Jakes Doppler spectrum.

The Jakes Doppler spectrum object contains only one property, `SpectrumType`

,
which is read-only and has a fixed value of `'Jakes'`

.

The Jakes Doppler power spectrum model is actually due to Gans [2],
who analyzed the Clarke-Gilbert model ([1], [3], and [5]). The Clarke-Gilbert model is also
called the *classical model*.

The Jakes Doppler power spectrum applies to a mobile receiver. It derives from the following assumptions [6]:

The radio waves propagate horizontally.

At the mobile receiver, the angles of arrival of the radio waves are uniformly distributed over $$[-\pi ,\text{\hspace{0.17em}}\pi ]$$.

At the mobile receiver, the antenna is omnidirectional (i.e., the antenna pattern is circular-symmetrical).

The normalized Jakes Doppler power spectrum is given analytically by:

$$S(f)=\frac{1}{\pi {f}_{d}\sqrt{1-{(f/{f}_{d})}^{2}}},\text{}\left|f\right|\le {f}_{d}$$

where $${f}_{d}$$ is the maximum Doppler frequency.

Create a Rayleigh channel object with a maximum Doppler shift
of fd=10 Hertz. Then, create a Jakes Doppler spectrum object and assigns
it to the `DopplerSpectrum`

property of the channel
object.

chan = rayleighchan(1/1000,10); dop_gaussian = doppler.jakes; chan.DopplerSpectrum = dop_gaussian

[1] Clarke, R. H., "A Statistical Theory
of Mobile-Radio Reception," *Bell System Technical
Journal*, Vol. 47, No. 6, pp. 957–1000, July-August
1968.

[2] Gans, M. J., "A Power-Spectral
Theory of Propagation in the Mobile-Radio Environment," *IEEE
Trans. Veh. Technol.*, Vol. VT-21, No. 1, pp. 27–38,
Feb. 1972.

[3] Gilbert, E. N., "Energy Reception
for Mobile Radio," *Bell System Technical Journal*,
Vol. 44, No. 8, pp. 1779–1803, Oct. 1965.

[4] Jakes, W. C., Ed. *Microwave
Mobile Communications*, Wiley, 1974.

[5] Lee, W. C. Y., *Mobile Communications
Engineering: Theory and Applications*, 2nd Ed., McGraw-Hill,
1998.

[6] Pätzold, M., *Mobile Fading
Channels*, Wiley, 2002.

`doppler`

| `doppler.ajakes`

| `doppler.bell`

| `doppler.bigaussian`

| `doppler.flat`

| `doppler.gaussian`

| `doppler.rjakes`

| `doppler.rounded`

| `rayleighchan`

| `ricianchan`

| `stdchan`

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