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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, fd, in Hertz), fnorm, such that 0fmin,norm|fnorm|fmax,norm1, where fmin,norm is given by freqminmaxrjakes(1) and fmax,norm is given by freqminmaxrjakes(2). The maximum Doppler shift fd is specified by the MaxDopplerShift property of the channel object. Analytically, fmin,norm=fmin/fd and fmax,norm=fmax/fd, where fmin is the minimum Doppler shift (in Hertz) and fmax 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.

PropertyDescription
SpectrumTypeFixed value, 'RJakes'
FreqMinMaxRJakesVector 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 fd to fd, fd 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 fd to fd. 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 0fmin|f|fmaxfd.

The normalized RJakes Doppler power spectrum is given analytically by:

S(f)=Arπfd1(f/fd)2, 0fmin|f|fmaxfd

where

Ar=12π[sin1(fmaxfd)sin1(fminfd)]

fmin and fmax 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.

Examples

The following code first creates a Rayleigh channel object with a maximum Doppler shift of fd=10. It then creates an RJakes Doppler object with minimum normalized Doppler shift fmin,norm=0.14 and maximum normalized Doppler shift fmax,norm=0.9.

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 0fmin|f|fmaxfd, where fmin=fmin,norm×fd=1.4 Hz and fmax=fmax,norm×fd=9 Hz.

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]

More About

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.

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