Receiver Thermal Noise

Apply receiver thermal noise to complex signal

• 

Libraries:
Communications Toolbox / RF Impairments and Components

Description

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 the thermal noise based on the noise temperature, noise figure, or noise factor.

Examples

Apply Receiver Thermal Noise to QAM Modulated Signal

The cm_receiver_thermal_noise_qam model applies receiver thermal noise to a 16-QAM signal, and displays the signal in a constellation diagram. The model applies receiver thermal noise by specifying the noise figure in the Receiver Thermal Noise block.

Run the simulation at a sample rate of 1 kHz by setting the sample time to 1e-3 samples per second in the Random Integer Generator block. The Rectangular QAM Modulator Baseband block has the normalization method set to average power and the average power level set to 3e-13 watts (-92.5 dBm). Set the noise figure level in the Receiver Thermal Noise block to 20 dB, and display the constellation diagram of the 16-QAM signal.

Decreasing the noise figure will reduce the simulated receive noise level, and result in a tighter clustering of samples for the individual points in the constellation diagram. To demonstrate this, set the noise figure level to 10 dB and show the constellation diagram of the 16-QAM signal.

Add RF Impairments to DQPSK Signal

This example applies RF impairments to a signal modulated by the differential quadrature phase shift keying (DQPSK) method. To show the RF impairments, the example applies exaggerated levels that are not typical levels for modern radios.

In this example, the slex_rcvrimpairments_dqpsk model DQPSK-modulates a random signal and applies various RF impairments to the signal. The model uses impairment blocks from the RF Impairments library. The InitFun callback function initializes simulation variables. For more information, see Model Callbacks (Simulink).

After the impairment blocks, the signal forks into two paths. One path applies DC blocking, automatic gain control (AGC), and I/Q imbalance compensation to the signal before demodulation. The signal on the correction path is adjusted by the DC Blocker, AGC, and I/Q Imbalance Compensator blocks. Because the signal is DQPSK modulated, no carrier synchronization is required. The second path goes directly to demodulation. After demodulation, an error rate calculation is performed on both signals. The model includes Constellation Diagram blocks after modulation, before correction, and after correction so that you can analyze the constellation.

When the model runs, constellation diagrams plot the signal at these stages in the simulation:

• The After Modulation constellation diagram shows the reference DQPSK-modulated signal constellation.

• The Before Correction constellation diagram shows the attenuated and distorted signal constellation.

• The After Correction constellation diagram shows the signal has been amplified and improved after the correction blocks.

The error rate for the demodulated signal without AGC is primarily caused by free space path loss and I/Q imbalance. The QPSK modulation minimizes the effects of the other impairments.

Error rate for corrected signal:   0.000
Error rate for uncorrected signal: 0.042

To explore the model try:

• Adjusting RF impairment settings, rerun the model, and notice the changes to the constellation diagrams and error rates.

• Modifying the model to add an equalizer stage before the demodulation. Equalization has inherent ability to reduce some of the distortion caused by impairments. For more information, see Equalization.

Apply Thermal Noise To Multichannel Signal in Simulink

Apply thermal noise to a multichannel signal and compute the variance of each channel. Confirm the Receiver Thermal Noise block applies equivalent thermal noise to the individual channels by comparing the variances are approximately equal for each channel. The Receiver Thermal Noise block applies to confirm has the same noise floor by computing the variance of each channel.

The multichan_thermal_noise.slx model creates a multichannel signal with equal power per channel, and then applies receiver thermal noise to the multichannel signal.

Run the model to output the computed variance for each channel.

            Ch1   Ch2   Ch3
Variance: 10.347 10.015 9.905

Extended Examples

RF Satellite Link

Simulate a satellite link that models amplifier impairments by using a Memoryless Nonlinearity block.

• Open Script

Limitations

• To use this block in a For Each Subsystem (Simulink) you must set Random number source to Global Stream and the model to Normal or Accelerator simulation mode. This ensures that each run will generate independent noise samples.

Ports

Input

In1 — 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.

Data Types: double | single
Complex Number Support: Yes

Output

Out1 — 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.

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Specification method — Thermal noise specification method

Noise temperature (default) | Noise figure | Noise factor

Thermal noise specification method, specified as one of these options.

• Noise temperature specifies the noise in kelvins.

• Noise figure specifies the added receiver noise in dB relative to an input noise temperature of 290 K. The noise figure is the decibel equivalent of the noise factor.

• Noise factor specifies the added receiver noise relative to an input noise temperature of 290 K. The noise factor is the linear equivalent of the noise figure.

Noise temperature (K) — Noise temperature

290 (default) | scalar

Noise temperature in kelvins, specified as a scalar.

Tunable: Yes

Dependencies

This parameter applies when you set Specification method to Noise temperature.

Data Types: double | single

Noise figure (dB) — Receiver noise figure

3.0103 (default) | scalar

Receiver noise figure in dB relative to a noise temperature of 290 K, specified as a scalar.

Note

This parameter specifies the noise contribution of the receiver circuitry only. To add the effects of antenna noise, select Add 290K antenna noise.

Tunable: Yes

Dependencies

This parameter applies when you set Specification method to Noise figure.

Data Types: double | single

Noise factor — Receiver noise factor

2 (default) | scalar

Receiver noise factor relative to a noise temperature of 290 K, specified as a scalar.

Note

This parameter specifies the noise contribution of the receiver circuitry only. To add the effects of antenna noise, select Add 290K antenna noise.

Tunable: Yes

Dependencies

This parameter applies when you set Specification method to Noise factor.

Data Types: double | single

Add 290K antenna noise — Option to add 290 K antenna noise

off (default) | on

Select this parameter to add 290 K antenna noise to the signal.

Dependencies

This parameter applies when you set Specification method to Noise factor or Noise figure.

Reference load (ohm) — Reference load

1 (default) | scalar

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

Tunable: Yes

Data Types: double | single

Random number source — Source for random number stream

Global stream (default) | mt19937ar with seed

Source for random number stream, specified as Global stream or mt19937ar with seed.

Initial seed — Initial seed value

67987 (default) | scalar

Initial seed value for the random number generator, specified as a scalar.

Dependencies

This parameter applies when you set Random number source to mt19937ar with seed.

Data Types: double | single

Simulate using — Type of simulation to run

Code generation (default) | Interpreted execution

Type of simulation to run, specified as Code generation or Interpreted execution.

• Code generation — Simulate the model by using generated C code. The first time you run a simulation, Simulink generates C code for the block. The model reuses the C code for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than with the Interpreted execution option.

• Interpreted execution — Simulate the model by using the MATLAB^® interpreter. This option shortens startup time, but the speed of subsequent simulations is slower than with the Code generation option. In this mode, you can debug the source code of the block.

For more information, see Interpreted Execution vs. Code Generation (Simulink).

Block Characteristics

Data Types	double | single
Multidimensional Signals	no
Variable-Size Signals	yes

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

$$\begin{array}{c}F=\frac{S_i/N_i}{G{S}_i/\left(N_{ckt}+G{N}_i\right)}\\ =\frac{N_{ckt}+G{N}_i}{G{N}_i}.\end{array}$$

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

$$\begin{array}{c}F=\frac{N_{ckt}+G{N}_i}{G{N}_i}\\ =\frac{GkB{T}_{ckt}+GkB{T}_0}{GkB{T}_0}\\ =\frac{T_{ckt}+T_0}{T_0}.\end{array}$$

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

$$T_{ckt}=T_0(F-1).$$

The overall noise temperature of an antenna and receiver T_sys is

$$T_{sys}=T_{ant}+T_{ckt},$$

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

$$NF=10{\log }_{10}(F).$$

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

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

Version History

Introduced before R2006a

R2023b: Multichannel input support

The Receiver Thermal Noise 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: Variable-size support

This support enables you to vary the length of input signal each time the block executes in your simulation.

R2023b: Random number generator update

The Receiver Thermal Noise block updates the random number generator (RNG) source. You can now use the Random number source parameter to select Global stream or mt19937ar with seed as the RNG source. To use this block in a For Each Subsystem (Simulink) you must set Random number source to Global Stream. This ensures that each run will generate independent noise samples.

For simulations created before R2023b, the block defaults to legacy mode. In legacy mode, the block uses the Random Source block to generate noise and random numbers are generated using the Ziggurat method (V5 RANDN algorithm). The block reuses the same initial seeds every time you rerun the simulation, so that this block outputs the same signal each time you run a simulation.

To improve statistics when running simulations with pre-R2023b models that use the Receiver Thermal Noise block, run Update Model and convert the pre-R2023b model to use new the Receiver Thermal Noise block capability.

R2023b: Code Generation

Code generation is enabled by default. For more information, see Simulate using.

R2023b: Single data type support

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