## Documentation Center |

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

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

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

The AJakes Doppler spectrum object contains the following properties.

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

SpectrumType | Fixed value, 'AJakes' |

FreqMinMaxAJakes | 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 [1]: 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]

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

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