Construct restricted Jakes Doppler spectrum object
dop = doppler.rjakes
dop = doppler.rjakes(freqminmaxrjakes)
doppler.rjakes function creates a restricted
Jakes (RJakes) Doppler spectrum object that is used for the
of a channel object (created with either 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
MaxDopplerShift property of the channel object.
dop = doppler.rjakes(freqminmaxrjakes),
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
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,
be spaced by more than 1/50. Assigning a smaller spacing results in
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
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.