(To be removed) Construct asymmetrical Doppler spectrum object
dop = doppler.ajakes(freqminmaxajakes)
dop = doppler.ajakes
doppler.ajakes will be removed in a future release. Use
('Asymmetric Jakes', ...) instead.
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
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 , in Hz) frequencies such that , where is given by
freqminmaxajakes(1) and is given by
freqminmaxajakes(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).
dop is used as the
of a channel object, space
freqminmaxajakes(2) by more than 1/50. Assigning a smaller
spacing results in
freqminmaxarjakes being reset to the default value
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
The AJakes Doppler spectrum object contains the following properties.
|Fixed value, |
|Vector of minimum and maximum normalized Doppler shifts, two real finite numbers between -1 and 1|
The Jakes power spectrum is based on the assumption that the angles of arrival at the mobile receiver are uniformly distributed : the spectrum then covers the frequency range from to , 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 to . The AJakes Doppler spectrum object covers the case of a power spectrum that is nonzero only for frequencies such that . It is an asymmetrical spectrum in the general case, but becomes a symmetrical spectrum if .
The normalized AJakes Doppler power spectrum is given analytically by:
where and 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.
The following MATLAB code first creates a Rayleigh channel object with a maximum
Doppler shift of Hz. It then creates an AJakes Doppler object with minimum normalized
Doppler shift and maximum normalized Doppler shift . 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 such that , where Hz and 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]
 Jakes, W. C., Ed., Microwave Mobile Communications, Wiley, 1974.
 Lee, W. C. Y., Mobile Communications Engineering: Theory and Applications, 2nd Ed., McGraw-Hill, 1998.
 Pätzold, M., Mobile Fading Channels, Wiley, 2002.