# Documentation

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# doppler.jakes

Construct Jakes Doppler spectrum object

## Description

`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.

## Properties

The Jakes Doppler spectrum object contains only one property, `SpectrumType`, which is read-only and has a fixed value of `'Jakes'`.

## Theory and Applications

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 $\left[-\pi ,\text{\hspace{0.17em}}\pi \right]$.

• 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:

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

## Examples

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```

## References

[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.