doppler

Construct Doppler spectrum structure

Syntax

s = doppler(specType)

s = doppler(specType, fieldValue)

s = doppler('BiGaussian', Name,Value)

Description

s = doppler(specType) constructs a Doppler spectrum structure of type specType for use with a fading channel System object. The returned structure, s, has default values for its dependent fields.

example

s = doppler(specType, fieldValue) constructs a Doppler spectrum structure of type specType for use with a fading channel System object. The returned structure, s, has its dependent field specified to fieldValue.

example

s = doppler('BiGaussian', Name,Value) constructs a BiGaussian Doppler spectrum structure for use with a fading channel System object. The returned structure, s, has dependent fields specified by Name,Value pair arguments.

Examples

collapse all

Construct a Flat Doppler Spectrum Structure

Open Live Script

Construct a flat Doppler structure variable for use with channel objects such as comm.RayleighChannel.

Invoke the doppler function to create a flat Doppler structure variable.

s = doppler('Flat')

s = struct with fields:
    SpectrumType: 'Flat'

Create a Bell Doppler Structure Variable

Open Live Script

Use the doppler function to create a Doppler structure variable having the Bell spectrum.

s = doppler('Bell')

s = struct with fields:
    SpectrumType: 'Bell'
     Coefficient: 9

Construct a Rounded Doppler Spectrum Structure with Specified Polynomial

Open Live Script

Specify the coefficients of the Doppler spectrum structure variable.

Construct a Rounded Doppler spectrum structure with coefficients a0, a2, and a4 set to 2, 6, and 1, respectively.

s = doppler('Rounded', [2, 6, 1])

s = struct with fields:
    SpectrumType: 'Rounded'
      Polynomial: [2 6 1]

Construct a BiGaussian Doppler Spectrum Structure with Specified Field Values

Open Live Script

Use the doppler function to create a Doppler spectrum structure with the parameters specified for a BiGaussian spectrum.

s = doppler('BiGaussian','NormalizedCenterFrequencies', ...
    [.1 .85],'PowerGains',[1 2])

s = struct with fields:
                    SpectrumType: 'BiGaussian'
    NormalizedStandardDeviations: [0.7071 0.7071]
     NormalizedCenterFrequencies: [0.1000 0.8500]
                      PowerGains: [1 2]

The NormalizedStandardDeviations field is set to the default value. The NormalizedCenterFrequencies, and PowerGains fields are set to the values specified from the input arguments.

Input Arguments

collapse all

`specType` — Spectrum type of Doppler spectrum structure for use with fading channel System object
`'Jakes'` | `'Flat'` | `'Rounded'` | `'Bell'` | `'Asymmetric Jakes'` | `'Restricted Jakes'` | `'Gaussian'` | `'BiGaussian'`

The spectrum type of a Doppler spectrum structure for use with a fading channel System object. Specify this value as a character vector.

The analytical expression for each Doppler spectrum type is described in the Algorithms section.

Data Types: char

`fieldValue` — Value of dependent field of Doppler spectrum structure
scalar | vector

The value of the dependent field of the Doppler spectrum structure, specified as a scalar or vector of built-in data type. If you do not specify fieldValue , the dependent fields of the spectrum type use the default values.

Spectrum Type	Dependent Field	Description	Default Value
Jakes	—	—	—
Flat	—	—	—
Rounded	`Polynomial`	1-by-3 vector of real finite values, representing the polynomial coefficients, `a0, a2` and `a4`	`[1 -1.72 0.785]`
Bell	`Coefficient`	Nonnegative, finite, real scalar representing the Bell spectrum coefficient	`9`
Asymmetric Jakes	`NormalizedFrequencyInterval`	1-by-2 vector of real values between –1 and 1, inclusive, representing the minimum and maximum normalized Doppler shifts	`[0 1]`
Restricted Jakes	`NormalizedFrequencyInterval`	1-by-2 vector of real values between 0 and 1, inclusive, representing the minimum and maximum normalized Doppler shifts	`[0 1]`
Gaussian	`NormalizedStandardDeviation`	Normalized standard deviation of the Gaussian Doppler spectrum, specified as a positive, finite, real scalar	`0.7071`
BiGaussian	`NormalizedStandardDeviations`	Normalized standard deviations of the BiGaussian Doppler spectrum, specified as a positive, finite, real 1-by-2 vector	`[0.7071 0.7071]`
	`NormalizedCenterFreqencies`	Normalized center frequencies of the BiGaussian Doppler spectrum specified as a real 1-by-2 vector whose elements fall between –1 and 1	`[0 0]`
	`PowerGains`	Linear power gains of the BiGaussian Doppler spectrum specified as a real nonnegative 1-by-2 vector	`[0.5 0.5]`

Data Types: double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example:

s=doppler('BiGaussian', 'NormalizedStandardDeviations',
[.8 .75], 'NormalizedCenterFrequencies', [-.8 0], 'PowerGains', [.6
.6])

`'NormalizedStandardDeviations'` — Normalized standard deviations of first and second Gaussian functions
`[1/sqrt(2) 1/sqrt(2)]` (default) | 1-by-2 positive numeric vector

The normalized standard deviation of the first and second Gaussian functions. You can specify this value as a 1-by-2 positive numeric vector, of built-in data types.

When you do not specify this dependent field, the default value is [1/sqrt(2) 1/sqrt(2)].

Data Types: double

`'NormalizedCenterFrequencies'` — Normalized center frequencies of first and second Gaussian functions
`[0 0]` (default) | 1-by-2 numeric vector

The normalized center frequencies of the first and second Gaussian functions. You can specify this value as a 1-by-2 numeric vector of real values between –1 and 1, of built-in data types.

When you do not specify this dependent field, the default value is [0 0].

Data Types: double

`'PowerGains'` — Power gains of first and second Gaussian functions
`[0.5 0.5]` (default) | 1-by-2 numeric vector

The power gains of the first and second Gaussian functions. You can specify this value as a 1-by-2 nonnegative numeric vector of built-in data types.

When you do not specify this dependent field, the default value is [0.5 0.5].

Data Types: double

Algorithms

collapse all

The following algorithms represent the analytical expressions for each Doppler spectrum type. In each case, $f_{d}$ denotes the maximum Doppler shift (MaximumDopplerShift property) of the associated fading channel System object.

Jakes

The theoretical Jakes Doppler spectrum, S(f) has the analytic formula

$S (f) = \frac{1}{π f_{d} \sqrt{1 - {(f / f_{d})}^{2}}}, | f | \leq f_{d}$

Flat

The theoretical Flat Doppler spectrum, S(f) has the analytic formula

$S (f) = \frac{1}{2 f_{d}}, | f | \leq f_{d}$

Rounded

The theoretical Rounded Doppler spectrum, S(f) has the analytic formula

$S (f) = C_{r} [a_{0} + a_{2} {(\frac{f}{f_{d}})}^{2} + a_{4} {(\frac{f}{f_{d}})}^{4}], | f | \leq f_{d}$

where

$C_{r} = \frac{1}{2 f_{d} [a_{0} + \frac{a_{2}}{3} + \frac{a_{4}}{5}]}$

and you can specify [ $a_{0}, a_{2}, a_{4}$ ] in the dependent field, polynomial.

Bell

The theoretical Bell Doppler spectrum, S(f) has the analytic formula

$S (f) = \frac{C_{b}}{1 + A {(\frac{f}{f_{d}})}^{2}}$

$| f | \leq f_{d}$

where

$C_{b} = \frac{\sqrt{A}}{π f_{d}}$

You can specify A in the dependent field, coefficient.

Asymmetric Jakes

The theoretical Asymmetric Jakes Doppler spectrum, S(f) has the analytic formula

$\begin{matrix} S (f) = \frac{A_{a}}{π f_{d} \sqrt{1 - {(f / f_{d})}^{2}}}, - f_{d} \leq f_{\min} \leq f \leq f_{\max} \leq f_{d} \\ A_{a} = \frac{1}{\frac{1}{π} [\sin^{- 1} (\frac{f_{\max}}{f_{d}}) - \sin^{- 1} (\frac{f_{\min}}{f_{d}})]} \end{matrix}$

where you can specify $f_{\min}$ / $f_{d}$ and $f_{\max}$ / $f_{d}$ in the dependent field, NormalizedFrequencyInterval.

Restricted Jakes

The theoretical Restricted Jakes Doppler spectrum, S(f) has the analytic formula

$S (f) = \frac{A_{r}}{π f_{d} \sqrt{1 - {(f / f_{d})}^{2}}}, 0 \leq f_{\min} \leq | f | \leq f_{\max} \leq f_{d}$

where

$A_{r} = \frac{1}{\frac{2}{π} [\sin^{- 1} (\frac{f_{\max}}{f_{d}}) - \sin^{- 1} (\frac{f_{\min}}{f_{d}})]}$

where you can specify $f_{\min}$ / $f_{d}$ and $f_{\max}$ / $f_{d}$ in the dependent field, NormalizedFrequencyInterval.

Gaussian

The theoretical Gaussian Doppler spectrum, S(f) has the analytic formula

$S_{G} (f) = \frac{1}{\sqrt{2 π σ_{G}^{2}}} \exp (- \frac{f^{2}}{2 σ_{G}^{2}})$

You can specify $σ_{G} / f_{d}$ in the dependent field, NormalizedStandardDeviation.

BiGaussian

The theoretical BiGaussian Doppler spectrum, S(f) has the analytic formula

$S_{G} (f) = A_{G} [\frac{C_{G 1}}{\sqrt{2 π σ_{G 1}^{2}}} \exp (- \frac{{(f - f_{G 1})}^{2}}{2 σ_{G 1}^{2}}) + \frac{C_{G 2}}{\sqrt{2 π σ_{G 2}^{2}}} \exp (- \frac{{(f - f_{G 2})}^{2}}{2 σ_{G 2}^{2}})]$

where $A_{G} = \frac{1}{C_{G 1} + C_{G 2}}$ is a normalization coefficient.

You can specify $σ_{G 1}$ / $f_{d}$ and $σ_{G 2}$ / $f_{d}$ in the NormalizedStandardDeviations dependent field.

You can specify $f_{G 1}$ / $f_{d}$ and $f_{G 2}$ / $f_{d}$ in the NormalizedCenterFrequencies dependent field.

$C_{G 1}$ and $C_{G 2}$ are power gains that you can specify in the PowerGains dependent field.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

All inputs must be constants. Expressions or variables are allowed if their values do not change.

Documentation

doppler

Syntax

Description

Examples

Construct a Flat Doppler Spectrum Structure

Create a Bell Doppler Structure Variable

Construct a Rounded Doppler Spectrum Structure with Specified Polynomial

Construct a BiGaussian Doppler Spectrum Structure with Specified Field Values

Input Arguments

`specType` — Spectrum type of Doppler spectrum structure for use with fading channel System object
`'Jakes'` | `'Flat'` | `'Rounded'` | `'Bell'` | `'Asymmetric Jakes'` | `'Restricted Jakes'` | `'Gaussian'` | `'BiGaussian'`

`fieldValue` — Value of dependent field of Doppler spectrum structure
scalar | vector

Name-Value Pair Arguments

`'NormalizedStandardDeviations'` — Normalized standard deviations of first and second Gaussian functions
`[1/sqrt(2) 1/sqrt(2)]` (default) | 1-by-2 positive numeric vector

`'NormalizedCenterFrequencies'` — Normalized center frequencies of first and second Gaussian functions
`[0 0]` (default) | 1-by-2 numeric vector

`'PowerGains'` — Power gains of first and second Gaussian functions
`[0.5 0.5]` (default) | 1-by-2 numeric vector

Algorithms

Jakes

Flat

Rounded

Bell

Asymmetric Jakes

Restricted Jakes

Gaussian

BiGaussian

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

Communications Toolbox Documentation

Support

Documentation

doppler

Syntax

Description

Examples

Construct a Flat Doppler Spectrum Structure

Create a Bell Doppler Structure Variable

Construct a Rounded Doppler Spectrum Structure with Specified Polynomial

Construct a BiGaussian Doppler Spectrum Structure with Specified Field Values

Input Arguments

specType — Spectrum type of Doppler spectrum structure for use with fading channel System object 'Jakes' | 'Flat' | 'Rounded' | 'Bell' | 'Asymmetric Jakes' | 'Restricted Jakes' | 'Gaussian' | 'BiGaussian'

fieldValue — Value of dependent field of Doppler spectrum structure scalar | vector

Name-Value Pair Arguments

'NormalizedStandardDeviations' — Normalized standard deviations of first and second Gaussian functions [1/sqrt(2) 1/sqrt(2)] (default) | 1-by-2 positive numeric vector

'NormalizedCenterFrequencies' — Normalized center frequencies of first and second Gaussian functions [0 0] (default) | 1-by-2 numeric vector

'PowerGains' — Power gains of first and second Gaussian functions [0.5 0.5] (default) | 1-by-2 numeric vector

Algorithms

Jakes

Flat

Rounded

Bell

Asymmetric Jakes

Restricted Jakes

Gaussian

BiGaussian

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

See Also

Communications Toolbox Documentation

Support

`specType` — Spectrum type of Doppler spectrum structure for use with fading channel System object
`'Jakes'` | `'Flat'` | `'Rounded'` | `'Bell'` | `'Asymmetric Jakes'` | `'Restricted Jakes'` | `'Gaussian'` | `'BiGaussian'`

`fieldValue` — Value of dependent field of Doppler spectrum structure
scalar | vector

`'NormalizedStandardDeviations'` — Normalized standard deviations of first and second Gaussian functions
`[1/sqrt(2) 1/sqrt(2)]` (default) | 1-by-2 positive numeric vector

`'NormalizedCenterFrequencies'` — Normalized center frequencies of first and second Gaussian functions
`[0 0]` (default) | 1-by-2 numeric vector

`'PowerGains'` — Power gains of first and second Gaussian functions
`[0.5 0.5]` (default) | 1-by-2 numeric vector

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.