Generate Rayleigh distributed noise

Noise Generators sublibrary of Comm Sources

The Rayleigh Noise Generator block generates Rayleigh distributed noise. The Rayleigh probability density function is given by

$$f(x)=\{\begin{array}{ll}\frac{x}{{\sigma}^{2}}\mathrm{exp}\left(-\frac{{x}^{2}}{2{\sigma}^{2}}\right)\hfill & x\ge 0\hfill \\ 0\hfill & x<0\hfill \end{array}$$

where σ^{2} is known as the *fading
envelope* of the Rayleigh distribution.

The block requires you to specify the **Initial seed** for
the random number generator. If it is a constant, then the resulting
noise is repeatable. The **sigma** parameter can
be either a vector of the same length as the **Initial seed**,
or a scalar. When **sigma** is a scalar, every element
of the output signal shares that same value.

The **Initial seed** parameter initializes
the random number generator that the Rayleigh Noise Generator block
uses to add noise to the input signal. For best results, the **Initial
seed** should be a prime number greater than 30. Also, if
there are other blocks in a model that have an **Initial seed** parameter,
you should choose different initial seeds for all such blocks.

You can choose seeds for the Rayleigh Noise Generator block
using the Communications System Toolbox™ randseed function.
At the MATLAB^{®} prompt, enter

randseed

This returns a random prime number greater than 30. Entering `randseed`

again
produces a different prime number. If you supply an integer argument, `randseed`

always
returns the same prime for that integer. For example, `randseed(5)`

always
returns the same answer.

The output signal can be a frame-based matrix, a sample-based
row or column vector, or a sample-based one-dimensional array. These
attributes are controlled by the **Frame-based outputs**, **Samples
per frame**, and **Interpret vector parameters as
1-D** parameters. See Sources and Sinks in the Control System Toolbox™ documentation
for more details.

The number of elements in the **Initial seed** parameter
becomes the number of columns in a frame-based output or the number
of elements in a sample-based vector output. Also, the shape (row
or column) of the **Initial seed** parameter becomes
the shape of a sample-based two-dimensional output signal.

**Sigma**Specify σ as defined in the Rayleigh probability density function.

**Initial seed**The initial seed value for the random number generator.

**Sample time**The period of each sample-based vector or each row of a frame-based matrix.

**Frame-based outputs**Determines whether the output is frame-based or sample-based. This box is active only if

**Interpret vector parameters as 1-D**is unchecked.**Samples per frame**The number of samples in each column of a frame-based output signal. This field is active only if

**Frame-based outputs**is checked.**Interpret vector parameters as 1-D**If this box is checked, then the output is a one-dimensional signal. Otherwise, the output is a two-dimensional signal. This box is active only if

**Frame-based outputs**is unchecked.**Output data type**The output can be set to

`double`

or`single`

data types.

Multipath Rayleigh Fading Channel; `raylrnd`

(Statistics and Machine
Learning Toolbox™)

[1] Proakis, John G., *Digital Communications*,
Third edition, New York, McGraw Hill, 1995.

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