# comm.ThermalNoise

Add thermal noise to signal

## Description

The `comm.ThermalNoise`

System object™ object simulates the effects of thermal noise on a complex baseband signal. For
more information, see Algorithms.

To add thermal noise to a complex baseband signal:

Create the

`comm.ThermalNoise`

object and set its properties.Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

## Creation

### Description

creates a receiver
thermal noise System object. This object adds thermal noise to the complex baseband input signal.`noise`

= comm.ThermalNoise

sets properties using one or more name-value arguments. For example,
`noise`

= comm.ThermalNoise(`Name`

=`Value`

)`SampleRate=2`

sets the input signal sample rate to 2.

## Properties

## Usage

### Description

### Input Arguments

### Output Arguments

## Object Functions

To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named `obj`

, use
this syntax:

release(obj)

## Examples

## Algorithms

Wireless receiver performance is often expressed as a noise factor or figure. The noise
factor, *F*, is defined as the ratio of the input signal-to-noise ratio,
*S _{i}*/

*N*to the output signal-to-noise ratio,

_{i}*S*/

_{o}*N*, such that

_{o}$$F=\frac{{S}_{i}/{N}_{i}}{{S}_{o}/{N}_{o}}\text{\hspace{0.17em}}.$$

Given the receiver gain *G* and receiver noise power
*N _{ckt}*, the noise factor can be expressed as

$$\begin{array}{c}F=\frac{{S}_{i}/{N}_{i}}{G{S}_{i}/\left({N}_{ckt}+G{N}_{i}\right)}\\ =\frac{{N}_{ckt}+G{N}_{i}}{G{N}_{i}}\text{\hspace{0.17em}}.\end{array}$$

The IEEE^{®} defines the noise factor assuming that noise temperature at the input is
*T _{0}*, where

*T*= 290 K. The noise factor is then

_{0}$$\begin{array}{c}F=\frac{{N}_{ckt}+G{N}_{i}}{G{N}_{i}}\\ =\frac{GkB{T}_{ckt}+GkB{T}_{0}}{GkB{T}_{0}}\\ =\frac{{T}_{ckt}+{T}_{0}}{{T}_{0}}\text{\hspace{0.17em}}.\end{array}$$

*k* is Boltzmann's constant. *B* is the signal bandwidth.
*T _{ckt}* is the equivalent input noise
temperature of the receiver and is expressed as

$${T}_{ckt}={T}_{0}(F-1)\text{\hspace{0.17em}}.$$

The overall noise temperature of an antenna and receiver
*T _{sys}* is

$${T}_{sys}={T}_{ant}+{T}_{ckt}\text{\hspace{0.17em}},$$

where *T _{ant}* is the antenna noise temperature.

The noise figure *NF* is the dB equivalent of the noise factor and can be
expressed as

$$NF=10{\mathrm{log}}_{10}(F)\text{\hspace{0.17em}}.$$

The noise power can be expressed as

$$N=kTB={V}^{2}/R,$$

where *V* is the noise voltage expressed as

$${V}^{2}=kTBR,$$

and *R* is the reference load.

## Extended Capabilities

## Version History

**Introduced in R2012a**