Rician Noise Generator

(Has been removed) Generate Rician distributed noise

Rician Noise Generator has been removed. Use the MATLAB Function (Simulink) block and randn function instead.

Library

Noise Generators sublibrary of Comm Sources

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Description

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

$$f(x)=\{\begin{array}{cc}\frac{x}{{\sigma }^2}{I}_0\left(\frac{mx}{{\sigma }^2}\right)\exp \left(-\frac{x^2+m^2}{2{\sigma }^2}\right)& x\ge 0\\ 0& x<0\end{array}$$

where:

• σ is the standard deviation of the Gaussian distribution that underlies the Rician distribution noise

• m² = m_I²+m_Q², where m_I and m_Q are the mean values of two independent Gaussian components

• I₀ is the modified 0th-order Bessel function of the first kind given by

  $$I_0(y)=\frac{1}{2\pi }{\displaystyle {\int }_{-\pi }^{\pi }{e}^{y\cos t}dt}$$

Note that m and σ are not the mean value and standard deviation for the Rician noise.

You must specify the Initial seed for the random number generator. When it is a constant, the resulting noise is repeatable. The vector length of the Initial seed parameter should equal the number of columns in a frame-based output or the number of elements in a sample-based output. The set of numerical parameters above the Initial seed parameter in the dialog box can consist of vectors having the same length as the Initial seed, or scalars.

Initial Seed

The scalar Initial seed parameter initializes the random number generator that the block uses to generate its Rician-distributed complex random process. When multiple blocks in a model have the Initial seed parameter, you can choose different initial seeds for each block to ensure different random streams are used in each block. Set Initial seed to an integer value for repeatable results or use the randi function to randomize your results.

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 Communications Toolbox™ User's Guide for more details.

The number of elements in the Initial seed and Sigma parameters 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 and Sigma parameters becomes the shape of a sample-based two-dimensional output signal.

Parameters

Specification method

Either K-factor or Quadrature components.

Rician K-factor

K = m²/(2σ²), where m is as in the Rician probability density function. This field appears only if Specification method is K-factor.

In-phase component (mean), Quadrature component (mean)

The mean values m_I and m_Q, respectively, of the Gaussian components. These fields appear only if Specification method is Quadrature components.

Sigma

The variable σ in the Rician 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.

References

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