comm.ThermalNoise

Add thermal noise to signal

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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

Syntax

noise = comm.ThermalNoise

noise = comm.ThermalNoise(Name=Value)

Description

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

noise = comm.ThermalNoise(Name=Value) sets properties using one or more name-value arguments. For example, SampleRate=2 sets the input signal sample rate to 2.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`NoiseMethod` — Method used to set noise power
`'Noise temperature'` (default) | `'Noise figure'` | `'Noise factor'`

Method used to set the noise power, specified as 'Noise temperature', 'Noise figure', or 'Noise factor'.

`NoiseTemperature` — Receiver noise temperature
`290` (default) | nonnegative scalar

Receiver noise temperature, specified in kelvins as a nonnegative scalar. Noise temperature is typically used to characterize receivers because the input noise temperature can vary and is often less than 290 K.

Tunable: Yes

Dependencies

This property applies when you set NoiseMethod to 'Noise temperature'.

Data Types: double | single

`NoiseFigure` — Noise figure
`3.01` (default) | nonnegative scalar

Noise figure in dB, specified as a nonnegative scalar. Noise figure describes the performance of a receiver and does not include the effect of the antenna. It is defined only for an input noise temperature of 290 K. The noise figure is the dB equivalent of the noise factor.

Tunable: Yes

Dependencies

This property applies when you set NoiseMethod to 'Noise figure'.

Data Types: double | single

`NoiseFactor` — Noise factor
`2` (default) | scalar ≥ 1

Noise factor, specified as a scalar greater than or equal to 1. Noise factor describes the performance of a receiver and does not include the effect of the antenna. It is defined only for an input noise temperature of 290 K. The noise factor is the linear equivalent of the noise figure.

Tunable: Yes

Dependencies

This property applies when you set NoiseMethod to 'Noise factor'.

Data Types: double | single

`ReferenceLoad` — Reference load
`1` (default) | positive scalar

Reference load in ohms, specified as a positive scalar. The reference load value is used to compute the voltage levels based on the signal and noise power levels.

Tunable: Yes

Data Types: double | single

`SampleRate` — Sample rate
`1` (default) | positive scalar

Sample rate in Hz, specified as a positive scalar. The object computes the variance of the noise added to the input signal as kT×SampleRate×ReferenceLoad. The value k is Boltzmann's constant and T is the noise temperature specified explicitly or implicitly via one of the noise methods.

Data Types: double | single

`Add290KAntennaNoise` — Option to add 290 K antenna noise
`false` or `0` (default) | `true` or `1`

Option to add 290 K antenna noise to the input signal, specified as a logical 0 (false) or 1 (true). To add 290 K antenna noise, set this property to true. The total noise applied to the input signal is the sum of the circuit noise and the antenna noise.

Dependencies

To enable this property, set the NoiseMethod property to 'Noise factor' or 'Noise figure'.

Data Types: logical

Usage

Syntax

outsignal = noise(insignal)

Description

outsignal = noise(insignal) adds thermal noise to the complex baseband input signal insignal and returns the result in outsignal.

Input Arguments

`insignal` — Baseband signal
scalar | column vector | matrix

Baseband signal, specified as a complex-valued scalar, N_S-element column vector, or N_S-by-N_C matrix. N_S is the number of samples and N_C is the number of channels.

This object accepts variable-size inputs. After the object is locked, you can change the size of each input channel, but you cannot change the number of channels. For more information, see Variable-Size Signal Support with System Objects.

Data Types: double | single
Complex Number Support: Yes

Output Arguments

`outsignal` — Output signal
scalar | column vector | matrix

Output signal, returned as a scalar, column vector, or matrix of complex values with the same length and data type as the input signal.

Data Types: double | single
Complex Number Support: Yes

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)

Specific to `comm.ThermalNoise`

info Characteristic information about thermal noise object

Common to All System Objects

`step`	Run System object algorithm
`release`	Release resources and allow changes to System object property values and input characteristics
`reset`	Reset internal states of System object

Examples

Add Thermal Noise to QPSK Signal

Open Live Script

Create a thermal noise object with a noise temperature of 290 K and a sample rate of 5 MHz.

thNoise = comm.ThermalNoise('NoiseTemperature',290,'SampleRate',5e6);

Generate QPSK modulated data with an output power of 20 dBm.

data = randi([0 3],1000,1);
modData = (10^((20-30)/20)) * pskmod(data,4,pi/4);

Attenuate the signal by the free space path loss assuming a 1000 m link distance and a carrier frequency of 2 GHz.

d = 1000;                    % m  
f = 2e9;                     % Hz
c = 3e8;                     % m/s 
fsl = (4*pi*d*f/c)^2;
rxData = modData/sqrt(fsl);

Add thermal noise to the signal. Plot the noisy constellation.

noisyData = thNoise(rxData);
scatterplot(noisyData)

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains a line object which displays its values using only markers. This object represents Channel 1.

Add Antenna and Receiver Thermal Noise to 16-QAM Signal

Open Live Script

Create a thermal noise object with a 5 dB noise figure and a 10 MHz sample rate. Include 290 K antenna noise.

thermalNoise = comm.ThermalNoise('NoiseMethod','Noise figure', ...
    'NoiseFigure',5, ...
    'SampleRate',10e6, ...
    'Add290KAntennaNoise',true);

Generate QPSK modulated data with an output power of 1 W.

data = randi([0 15],1000,1);
modSig = qammod(data,16,'UnitAveragePower',true);

Attenuate the signal by the free space path loss assuming a 1 km link distance and a 5 GHz carrier frequency.

d = 1000;                   % m
f = 5e9;                    % Hz
c = 3e8;                    % m/s
fsl = (4*pi*d*f/c)^2;
rxSig = modSig/sqrt(fsl);

Add thermal noise to the signal and plot its constellation.

noisySig = thermalNoise(rxSig);
scatterplot(noisySig)

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains a line object which displays its values using only markers. This object represents Channel 1.

Estimate the SNR.

mer = comm.MER;
snrEst1 = mer(rxSig,noisySig)

snrEst1 = 
22.6611

Decrease the noise figure to 0 dB and plot the resultant received signal. The signal is not completely noiseless because antenna noise is included.

thermalNoise.NoiseFigure = 0;
noisySig = thermalNoise(rxSig);
scatterplot(noisySig)

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains a line object which displays its values using only markers. This object represents Channel 1.

Estimate the SNR. The SNR is 5 dB higher than in the first case, which is expected given the 5 dB decrease in the noise figure.

snrEst2 = mer(rxSig,noisySig)

snrEst2 = 
27.8658

snrEst2 - snrEst1

ans = 
5.2047

Apply Thermal Noise to Multichannel Signal

Open Live Script

Apply thermal noise to a multichannel signal and confirm that each channel has the same noise floor as returned by the info object function.

Create a comm.ThermalNoise object.

tn = comm.ThermalNoise

tn = 
  comm.ThermalNoise with properties:

         NoiseMethod: 'Noise temperature'
    NoiseTemperature: 290
       ReferenceLoad: 1
          SampleRate: 1

Apply thermal noise to a multichannel signal and compute the signal variance for each channel.

x = tn(zeros(100000,3,'like',1i)); 
10*log10(var(x))

ans = 1×3

 -203.9973 -203.9684 -203.9802

Use the info object function to return the receiver thermal noise floor.

info(tn)

ans = struct with fields:
    NoiseFloor: -203.9752

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_i to the output signal-to-noise ratio, S_o/N_o, such that

$F = \frac{S_{i} / N_{i}}{S_{o} / N_{o}} .$

Given the receiver gain G and receiver noise power N_ckt, the noise factor can be expressed as

$\begin{matrix} F = \frac{S_{i} / N_{i}}{G S_{i} / (N_{c k t} + G N_{i})} \\ = \frac{N_{c k t} + G N_{i}}{G N_{i}} . \end{matrix}$

The IEEE^® defines the noise factor assuming that noise temperature at the input is T₀, where T₀ = 290 K. The noise factor is then

$\begin{matrix} F = \frac{N_{c k t} + G N_{i}}{G N_{i}} \\ = \frac{G k B T_{c k t} + G k B T_{0}}{G k B T_{0}} \\ = \frac{T_{c k t} + T_{0}}{T_{0}} . \end{matrix}$

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

$T_{c k t} = T_{0} (F - 1) .$

The overall noise temperature of an antenna and receiver T_sys is

$T_{s y s} = T_{a n t} + T_{c k t},$

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

$N F = 10 \log_{10} (F) .$

The noise power can be expressed as

$N = k T B = V^{2} / R,$

where V is the noise voltage expressed as

$V^{2} = k T B R,$

and R is the reference load.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2012a

R2023b: Multichannel input support

The comm.ThermalNoise System object accepts a matrix input baseband signal. Each column of the matrix represents a baseband signal from one channel of a multi-antenna system.

R2023b: Noise floor information

You can use the info object function to return the noise floor for a comm.ThermalNoise System object.

R2023b: Single data type support

If the input signal is of type single, then the object natively computes in single precision, and the returned output is also of type single.

See Also

Objects

comm.AWGNChannel | comm.IQImbalanceCompensator | comm.PhaseNoise | comm.MemorylessNonlinearity

Functions

fspl | frequencyOffset | iqimbal | iqcoef2imbal | iqimbal2coef

Blocks

Receiver Thermal Noise