Communications Toolbox™

doppler.rjakes - Construct restricted Jakes Doppler spectrum object

Syntax

dop = doppler.rjakes dop = doppler.rjakes(freqminmaxrjakes)

Description

The doppler.rjakes function creates a restricted Jakes (RJakes) 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.rjakes creates a Doppler spectrum object equivalent to the Jakes Doppler spectrum. The maximum Doppler shift of the RJakes Doppler spectrum object is specified by the MaxDopplerShift property of the channel object.

dop = doppler.rjakes(freqminmaxrjakes), where freqminmaxrjakes is a row vector of two finite real numbers between 0 and 1, creates a Jakes Doppler spectrum. This spectrum is nonzero only for normalized frequencies (by the maximum Doppler shift, , in Hertz), , such that , where is given by freqminmaxrjakes(1) and is given by freqminmaxrjakes(2). The maximum Doppler shift is specified by the MaxDopplerShift property of the channel object. Analytically, and , where is the minimum Doppler shift (in Hertz) and is the maximum Doppler shift (in Hertz).

When dop is used as the DopplerSpectrum property of a channel object, freqminmaxrjakes(1) and freqminmaxrjakes(2) should be spaced by more than 1/50. Assigning a smaller spacing results in freqminmaxrjakes being reset to the default value of [0 1].

Properties

The RJakes Doppler spectrum object contains the following properties.

Property	Description
`SpectrumType`	Fixed value, `'RJakes'`
`FreqMinMaxRJakes`	Vector of minimum and maximum normalized Doppler shifts (two real finite numbers between 0 and 1)

Theory and Applications

The Jakes power spectrum is based on the assumption that the angles of arrival at the mobile receiver are uniformly distributed [1], where the spectrum covers the frequency range from to , being the maximum Doppler shift. When the angles of arrival are not uniformly distributed, the Jakes power spectrum does not cover the full Doppler bandwidth from to . This exception also applies to the case where the antenna pattern is directional. This type of spectrum is known as restricted Jakes [3]. The RJakes Doppler spectrum object covers only the case of a symmetrical power spectrum, which is nonzero only for frequencies f such that .

The normalized RJakes Doppler power spectrum is given analytically by:

where

and denote the minimum and maximum frequencies where the spectrum is nonzero. They can be determined from the probability density function of the angles of arrival.

Example

The following code first creates a Rayleigh channel object with a maximum Doppler shift of . It then creates an RJakes Doppler object with minimum normalized Doppler shift and maximum normalized Doppler shift .

The Doppler object is assigned to the DopplerSpectrum property of the channel object. The channel then has a Doppler spectrum that is nonzero for frequencies f such that , where and .

chan = rayleighchan(1/1000, 10);
dop_rjakes = doppler.rjakes([0.14 0.9]);
chan.DopplerSpectrum = dop_rjakes;
chan.DopplerSpectrum

The output is:

        	 SpectrumType: 'RJakes'
    FreqMinMaxRJakes: [0.1400 0.9000]

References

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

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

[3] Pätzold, M., Mobile Fading Channels, Wiley, 2002.