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doppler.ajakes

Construct asymmetrical Doppler spectrum object

Syntax

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

Description

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 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 ${f}_{d}$, in Hz) frequencies ${f}_{norm}$ such that $-1\le {f}_{\mathrm{min},norm}\le {f}_{norm}\le {f}_{\mathrm{max},norm}\le 1$, where ${f}_{\mathrm{min},norm}$ is given by freqminmaxajakes(1) and ${f}_{\mathrm{max},norm}$ is given by freqminmaxajakes(2). The maximum Doppler shift ${f}_{d}$ is specified by the MaxDopplerShift property of the channel object. Analytically: ${f}_{\mathrm{min},norm}={f}_{\mathrm{min}}/{f}_{d}$ and ${f}_{\mathrm{max},norm}={f}_{\mathrm{max}}/{f}_{d}$, where ${f}_{\mathrm{min}}$ is the minimum Doppler shift (in hertz) and ${f}_{\mathrm{max}}$ is the maximum Doppler shift (in hertz).

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 freqminmaxajakes = [0 1]. This syntax is equivalent to constructing a Jakes Doppler spectrum that is nonzero only for positive frequencies.

Properties

The AJakes Doppler spectrum object contains the following properties.

PropertyDescription
SpectrumTypeFixed value, 'AJakes'
FreqMinMaxAJakesVector of minimum and maximum normalized Doppler shifts, two real finite numbers between -1 and 1

Theory and Applications

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 $-{f}_{d}$ to ${f}_{d}$, ${f}_{d}$ 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 $-{f}_{d}$ to ${f}_{d}$. The AJakes Doppler spectrum object covers the case of a power spectrum that is nonzero only for frequencies $f$ such that $-{f}_{d}\le {f}_{\mathrm{min}}\le f\le {f}_{\mathrm{max}}\le {f}_{d}$. It is an asymmetrical spectrum in the general case, but becomes a symmetrical spectrum if ${f}_{\mathrm{min}}=-{f}_{\mathrm{max}}$.

The normalized AJakes Doppler power spectrum is given analytically by:

where ${f}_{\mathrm{min}}$ and ${f}_{\mathrm{max}}$ 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.

Examples

The following MATLAB code first creates a Rayleigh channel object with a maximum Doppler shift of ${f}_{d}=10$ Hz. It then creates an AJakes Doppler object with minimum normalized Doppler shift ${f}_{\mathrm{min},norm}=-0.2$ and maximum normalized Doppler shift ${f}_{\mathrm{max},norm}=0.05$. 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 $f$ such that $-{f}_{d}\le {f}_{\mathrm{min}}\le f\le {f}_{\mathrm{max}}\le {f}_{d}$, where ${f}_{\mathrm{min}}={f}_{\mathrm{min},norm}×{f}_{d}=-2$ Hz and ${f}_{\mathrm{max}}={f}_{\mathrm{max},norm}×{f}_{d}=0.5$ 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]
```