Note: This page has been translated by MathWorks. Click here to see

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Add thermal noise to signal

The `ThermalNoise`

object simulates the effects
of thermal noise on a complex, baseband signal.

To add thermal noise to a complex, baseband signal:

Define and set up your thermal noise object. See Construction.

Call

`step`

to add thermal noise according to the properties of`comm.ThermalNoise`

.

Starting in R2016b, instead of using the `step`

method
to perform the operation defined by the System
object™, you can
call the object with arguments, as if it were a function. For example, ```
y
= step(obj,x)
```

and `y = obj(x)`

perform
equivalent operations.

`tn = comm.ThermalNoise`

creates a receiver
thermal noise System
object, `H`

. This object
adds thermal noise to the complex, baseband input signal.

`tn = comm.ThermalNoise(`

creates
a receiver thermal noise object, `Name`

,`Value`

)`H`

, with each specified
property set to the specified value. You can specify additional name-value
pair arguments in any order as (`Name1`

,`Value1`

,...,`NameN`

,`ValueN`

).

step | Add receiver thermal noise |

Common to All System Objects | |
---|---|

`release` | Allow System object property value changes |

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

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

Given 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

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

*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

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