# Documentation

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# Rayleigh Noise Generator

Generate Rayleigh distributed noise

## Library

Noise Generators sublibrary of Comm Sources

## Description

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

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

where σ2 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.

### Initial Seed

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.

### Attributes of Output Signal

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.

## Parameters

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™)

## References

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