(To be removed) Construct restricted Jakes Doppler spectrum object
dop = doppler.rjakes
dop = doppler.rjakes(freqminmaxrjakes)
doppler.rjakes will be removed in a future release. Use
('Restricted Jakes', ...) instead.
doppler.rjakes function creates a restricted Jakes (RJakes)
Doppler spectrum object that is used for the
of a channel object (created with either the
rayleighchan or the
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
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).
dop is used as the
of a channel object,
freqminmaxrjakes(2) should be spaced by more than 1/50. Assigning
a smaller spacing results in
freqminmaxrjakes being reset to the
default value of
The RJakes Doppler spectrum object contains the following properties.
|Fixed value, |
|Vector of minimum and maximum normalized Doppler shifts (two real finite numbers between 0 and 1)|
The Jakes power spectrum is based on the assumption that the angles of arrival at the mobile receiver are uniformly distributed , 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 . 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:
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.
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]
 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.