## Documentation Center |

`dop = doppler.rjakesdop = doppler.rjakes(freqminmaxrjakes)`

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,
, 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).

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]`.

The RJakes Doppler spectrum object contains the following properties.

Property | Description |
---|---|

SpectrumType | Fixed value, 'RJakes' |

FreqMinMaxRJakes | 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 [1], 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* [3].
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:

where

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]

[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.

`doppler` | `doppler.ajakes` | `doppler.bell` | `doppler.bigaussian` | `doppler.flat` | `doppler.gaussian` | `doppler.jakes` | `doppler.rounded` | `rayleighchan` | `ricianchan` | `stdchan`

Was this topic helpful?