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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'.

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 [π,π].

  • 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)=1πfd1(f/fd)2, |f|fd

where fd 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.

Introduced in R2007a

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