Accelerating the pace of engineering and science

# Documentation Center

• Trial Software

# 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 , in Hz) frequencies such that , where is given by freqminmaxajakes(1) and is given by freqminmaxajakes(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, 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 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.

## Examples

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]
```