Apply receiver thermal noise to complex signal
Communications Toolbox / RF Impairments
The Receiver Thermal Noise block applies receiver thermal noise to a complex signal. The block simulates the effects of thermal noise on a complex signal. The Specification method parameter enables specification of thermal noise based on noise temperature, noise figure, or noise factor.
Data Types 

Multidimensional Signals 

VariableSize Signals 

Wireless receiver performance is often expressed as a noise factor or figure. The noise factor is defined as the ratio of the input signaltonoise ratio, S_{i}/N_{i} to the output signaltonoise ratio, S_{o}/N_{o}, such that
$$F=\frac{{S}_{i}/{N}_{i}}{{S}_{o}/{N}_{o}}\text{\hspace{0.17em}}.$$
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 T_{0} = 290 K. The noise factor is then
$$\begin{array}{c}F=\frac{{N}_{ckt}+G{N}_{i}}{G{N}_{i}}\\ =\frac{GkB{T}_{ckt}+GkB{T}_{0}}{GkB{T}_{0}}\\ =\frac{{T}_{ckt}+{T}_{0}}{{T}_{0}}\text{\hspace{0.17em}}.\end{array}$$
T_{ckt} is the equivalent input noise temperature of the receiver and is expressed as
$${T}_{ckt}={T}_{0}(F1)\text{\hspace{0.17em}}.$$
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
$$NF=10{\mathrm{log}}_{10}(F)\text{\hspace{0.17em}}.$$