| Communications Toolbox™ | |
dop = doppler.bigaussian(property1,value1,...)
dop = doppler.bigaussian
The doppler.bigaussian function creates a bi-Gaussian Doppler spectrum object to be used for the DopplerSpectrum property of a channel object (created with either the rayleighchan function or the ricianchan function).
dop = doppler.bigaussian(property1,value1,...) creates a bi-Gaussian Doppler spectrum object with properties as specified by the property/value pairs. If you do not specify a value for a property, the property is assigned a default value.
dop = doppler.bigaussian creates a bi-Gaussian Doppler spectrum object with default properties. The constructed Doppler spectrum object is equivalent to a single Gaussian Doppler spectrum centered at zero frequency. The equivalent command with property/value pairs is:
dop = doppler.bigaussian(‘SigmaGaussian1', 1/sqrt(2), … ‘SigmaGaussian2', 1/sqrt(2), … ‘CenterFrequencyGaussian1', 0, … ‘CenterFrequencyGaussian2', 0, … ‘GainGaussian1', 0.5, … ‘GainGaussian2', 0.5)
The bi-Gaussian Doppler spectrum object contains the following properties.
| Property | Description |
|---|---|
| SpectrumType | Fixed value, 'BiGaussian' |
| SigmaGaussian1 | Normalized standard deviation of first Gaussian function (real positive finite scalar value) |
| SigmaGaussian2 | Normalized standard deviation of second Gaussian function (real positive finite scalar value) |
| CenterFreqGaussian1 | Normalized center frequency of first Gaussian function (real scalar value between -1 and 1) |
| CenterFreqGaussian2 | Normalized center frequency of second Gaussian function (real scalar value between -1 and 1) |
| GainGaussian1 | Power gain of first Gaussian function (linear scale, real nonnegative finite scalar value) |
| GainGaussian2 | Power gain of second Gaussian function (linear scale, real nonnegative finite scalar value) |
All properties are writable except for the SpectrumType property.
The properties SigmaGaussian1, SigmaGaussian2, GainGaussian1, and GainGaussian2 are normalized by the MaxDopplerShift property of the associated channel object.
Analytically, the normalized standard deviations of the first
and second Gaussian functions are determined as
and
, respectively, where
and
are the standard deviations
of the first and second Gaussian functions, and
is the maximum Doppler shift,
in hertz. Similarly, the normalized center frequencies of the first
and second Gaussian functions are determined as
and
, respectively, where
and
are the center frequencies of
the first and second Gaussian functions. The properties GainGaussian1 and GainGaussian2 correspond
to the power gains
and
, respectively, of the two Gaussian
functions.
The bi-Gaussian power spectrum consists of two frequency-shifted Gaussian spectra. The COST207 channel models ([1], [2], [3]) specify two distinct bi-Gaussian Doppler spectra, GAUS1 and GAUS2, to be used in modeling long echos for urban and hilly terrain profiles.
The normalized bi-Gaussian Doppler spectrum is given analytically by:
where
and
are standard deviations,
and
are center frequencies,
and
are power gains, and
is a normalization coefficient.
If either
or
, a frequency-shifted Gaussian
Doppler spectrum is obtained.
The following MATLAB code first creates a bi-Gaussian Doppler
spectrum object with the same parameters as that of a COST 207 GAUS2
Doppler spectrum. It then creates a Rayleigh channel object with a
maximum Doppler shift of
and
assigns the constructed Doppler spectrum object to its DopplerSpectrum property.
dop_bigaussian = doppler.bigaussian(‘SigmaGaussian1', 0.1, ... ‘SigmaGaussian2', 0.15, ‘CenterFreqGaussian1', 0.7, ... ‘CenterFreqGaussian2', -0.4, ‘GainGaussian1', 1, ... ‘GainGaussian2', 1/10^1.5) chan = rayleighchan(1e-3, 30); chan.DopplerSpectrum = dop_bigaussian;
[1] COST 207 WG1, Proposal on channel transfer functions to be used in GSM tests late 1986, COST 207 TD (86) 51 Rev. 3, Sept. 1986.
[2] COST 207, Digital land mobile radio communications, Office for Official Publications of the European Communities, Final report, Luxembourg, 1989.
[3] Pätzold, M., Mobile Fading Channels, Wiley, 2002.
doppler, doppler.ajakes, doppler.flat, doppler.gaussian, doppler.jakes, doppler.rjakes, doppler.rounded, rayleighchan, ricianchan, stdchan, and Fading Channels
| doppler.ajakes | doppler.flat | |
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