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doppler.ajakes

Construct asymmetrical Doppler spectrum object

Syntax

dop = doppler.ajakes(freqminmaxajakes)
dop = doppler.ajakes

Description

The doppler.ajakes function creates an asymmetrical Jakes (AJakes) Doppler spectrum object. This object is to be used for the DopplerSpectrum property of a channel object created with the rayleighchan or the ricianchan functions.

dop = doppler.ajakes(freqminmaxajakes), where freqminmaxajakes is a row vector of two finite real numbers between -1 and 1, creates a Jakes Doppler spectrum that is nonzero only for normalized (by the maximum Doppler shift fd, in Hz) frequencies fnorm such that 1fmin,normfnormfmax,norm1, where fmin,norm is given by freqminmaxajakes(1) and fmax,norm is given by freqminmaxajakes(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, space freqminmaxajakes(1) and freqminmaxajakes(2) by more than 1/50. Assigning a smaller spacing results in freqminmaxarjakes being reset to the default value of [0 1].

dop = doppler.ajakes creates an asymmetrical Doppler spectrum object with a default freqminmaxajakes = [0 1]. This syntax is equivalent to constructing a Jakes Doppler spectrum that is nonzero only for positive frequencies.

Properties

The AJakes Doppler spectrum object contains the following properties.

PropertyDescription
SpectrumTypeFixed value, 'AJakes'
FreqMinMaxAJakesVector of minimum and maximum normalized Doppler shifts, two real finite numbers between -1 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]: the spectrum then covers the frequency range from fd to fd, fd being the maximum Doppler shift. When the angles of arrival are not uniformly distributed, then the Jakes power spectrum does not cover the full Doppler bandwidth from fd to fd. The AJakes Doppler spectrum object covers the case of a power spectrum that is nonzero only for frequencies f such that fdfminffmaxfd. It is an asymmetrical spectrum in the general case, but becomes a symmetrical spectrum if fmin=fmax.

The normalized AJakes Doppler power spectrum is given analytically by:

S(f)=Aaπfd1(f/fd)2,  fdfminffmaxfdAa=11π[sin1(fmaxfd)sin1(fminfd)]

where fmin and fmax denote the minimum and maximum frequencies where the spectrum is nonzero. You can determine these values from the probability density function of the angles of arrival.

Examples

The following MATLAB code first creates a Rayleigh channel object with a maximum Doppler shift of fd=10 Hz. It then creates an AJakes Doppler object with minimum normalized Doppler shift fmin,norm=0.2 and maximum normalized Doppler shift fmax,norm=0.05. The Doppler object is then assigned to the DopplerSpectrum property of the channel object. The channel then has a Doppler spectrum that is nonzero for frequencies f such that fdfminffmaxfd, where fmin=fmin,norm×fd=2 Hz and fmax=fmax,norm×fd=0.5 Hz.

chan = rayleighchan(1/1000, 10);
dop_ajakes = doppler.ajakes([-0.2 0.05]);
chan.DopplerSpectrum = dop_ajakes;
chan.DopplerSpectrum

This code returns:

        SpectrumType: 'AJakes'
    FreqMinMaxAJakes: [-0.2000 0.0500]

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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