Main Content

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`

.

**Note**

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

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