Contents

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 fd, in Hz) σG,norm=1/2. The maximum Doppler shift fd is specified by the MaxDopplerShift property of the channel object. Analytically, σG,norm=σG/fd=1/2, where σG is the standard deviation of the Gaussian Doppler spectrum.

dop = doppler.gaussian(sigmagaussian) creates a Gaussian Doppler spectrum object with a normalized fd (by the maximum Doppler shift fd, in Hz) σG,norm 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:

SG(f)=12πσG2exp(f22σG2)

An alternate representation is [4]:

SG(f)=1fcln2πexp((ln2)(ffc)2)

where fc=σG2ln2 is the 3 dB cutoff frequency. If you set fc=fdln2, where fd is the maximum Doppler shift, or equivalently σG=fd/2, 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:

σD=f2S(f)dfS(f)df

Examples

The following code creates a Rayleigh channel object with a maximum Doppler shift of fd=10. It then creates a Gaussian Doppler spectrum object with a normalized standard deviation of σG,norm=0.5, 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;

More About

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.

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