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# doppler.gaussian

Construct Gaussian Doppler spectrum object

## Syntax

dop = doppler.gaussian
dop = doppler.gaussian(sigmagaussian)

## Description

The doppler.gaussian function creates a Gaussian Doppler spectrum object that is to be used for the DopplerSpectrum property of a channel object (created with either the rayleighchan or the ricianchan function).

dop = doppler.gaussian creates a Gaussian Doppler spectrum object with a default standard deviation (normalized by the maximum Doppler shift , in Hz) . The maximum Doppler shift is specified by the MaxDopplerShift property of the channel object. Analytically, , where is the standard deviation of the Gaussian Doppler spectrum.

dop = doppler.gaussian(sigmagaussian) creates a Gaussian Doppler spectrum object with a normalized (by the maximum Doppler shift , in Hz) of value sigmagaussian.

## Properties

The Gaussian Doppler spectrum object contains the following properties.

PropertyDescription
SpectrumTypeFixed value, 'Gaussian'
SigmaGaussianNormalized standard deviation of the Gaussian Doppler spectrum (a real positive number)

## Theory and Applications

The Gaussian power spectrum is considered to be a good model for multipath components with long delays in UHF communications [3]. It is also proposed as a model for the aeronautical channel [2]. A Gaussian Doppler spectrum is also specified in some cases of the ANSI J-STD-008 reference channel models for PCS applications, for both outdoor (wireless loop) and indoor (residential, office) [1]. The normalized Gaussian Doppler power spectrum is given analytically by:

An alternate representation is [4]:

where is the 3 dB cutoff frequency. If you set , where is the maximum Doppler shift, or equivalently , the Doppler spread of the Gaussian power spectrum becomes equal to the Doppler spread of the Jakes power spectrum, where Doppler spread is defined as:

## Examples

The following code creates a Rayleigh channel object with a maximum Doppler shift of . It then creates a Gaussian Doppler spectrum object with a normalized standard deviation of , and assigns it to the DopplerSpectrum property of the channel object.

```chan = rayleighchan(1/1000,10);
dop_gaussian = doppler.gaussian(0.5);
chan.DopplerSpectrum = dop_gaussian;```

## References

[1] ANSI J-STD-008, Personal Station-Base Station Compatibility Requirements for 1.8 to 2.0 GHz Code Division Multiple Access (CDMA) Personal Communications Systems, March 1995.

[2] Bello, P. A., "Aeronautical channel characterizations," IEEE Trans. Commun., Vol. 21, pp. 548–563, May 1973.

[3] Cox, D. C., "Delay Doppler characteristics of multipath propagation at 910 MHz in a suburban mobile radio environment," IEEE Transactions on Antennas and Propagation, Vol. AP-20, No. 5, pp. 625–635, Sept. 1972.

[4] Pätzold, M., Mobile Fading Channels, Wiley, 2002.