Model System Noise Figure

RF receivers amplify signals and translate them to lower frequencies. The receiver itself introduces noise that degrades the received signal. The signal-to-noise ratio (SNR) at the receiver output ultimately determines the usability of the receiver.

The preceding figure illustrates the effect of the receiver on the signal. The receiver amplifies a low-power RF signal at the carrier f_RF with a high SNR and downconverts the signal to f_IF. The noise figure (NF) of the system determines the difference between the SNR at the output and the SNR at the input:

where the difference is calculated in decibels. Excessive noise figure in the system causes the noise to overwhelm the signal, making the signal unrecoverable.

Create a Low-IF Receiver Model

The model

ex_simrf_snr

simulates a simplified IF receiver architecture. A Sinusoid block and a Noise block model a two-tone input centered at f_RF and low-level thermal noise. The RF system amplifies the signal and mixes it with the local oscillator f_LO down to an intermediate frequency f_IF. A voltage sensor recovers the signal at the IF.

The amplifier contributes 40 dB of gain and a 15-dB noise figure, and the mixer contributes 0 dB of gain and a 20-dB noise figure, which are values characteristic of a relatively noisy, high-gain receiver. The two-tone input has a specified level of .1 μV. A 1-V level in the local oscillator ensures consistency with the formulation of the conversion gain of the mixer.

To run the model:

1. Open the model by clicking the link or by typing the model name at the Command Window prompt.

2. Select Simulation > Start.

Models that contain SimRF™ Amplifier and Mixer blocks generate files at update time. Before you can successfully update and run models with these blocks, you have to set up a compiler by running mex -setup.

By default, SimRF software generates files in the current MATLAB^® folder. However, you can change the output location for these files by specifying a cache folder in the Simulink^® Preferences dialog box. To specify a cache folder:

1. Open the Simulink Preferences dialog box (File > Preferences).

2. Specify a location for the Simulink cache folder parameter.

For more information about the Simulink interface, see Simulink Preferences Window.

Set Up the SimRF Environment

The model simulates according to the following settings:

• In the SimRF Parameters Block Parameters dialog box, the Carrier frequencies parameter specifies the carriers of the SimRF environment:

  • f_RF, the carrier of the desired signal, equal to 2 GHz.

  • f_LO, the frequency of the LO in the first mixing stage, equal to 1.9999 GHz.

  • f_IF, the intermediate frequency, equal to f_RF – f_LO, or 100 kHz.

  This example uses the variable car_env, defined in the initialization function, to specify the carriers.

• In the Solver Configuration Block Parameters dialog box, the Use local solver box is selected. This setting causes the SimRF environment to simulate with a local solver with the following settings:

  • The Solver type is set to Trapezoidal rule.

  • The Sample time parameter is set to 1/64.

  Since the model uses a local solver, the global solver settings do not affect the simulation within the SimRF environment. For more information on global and local solvers, see Choosing Simulink and Simscape™ Solvers.

View Simulation Output

The model uses subsystems with a MATLAB Coder™ implementation of a fast Fourier transform (FFT) to generate two plots. The FFT uses 64 bins, so for a sampling frequency of 64 Hz, the bandwidth of each bin is 1 Hz. Subsequently, the power levels shown in the figures also represent the power spectral density (PSD) of the signals in dBm/Hz.

• The Input Display plot shows the power spectrum of the signal and noise at the input of the receiver.

  

  The measured power of each tone is consistent with the expected power level of a 0.1-μV two-tone envelope:

  

  A factor of 1/2 is due to voltage division across source and load resistors, and another factor of 1/2 is due to envelope scaling. See the demo Two-Tone Envelope Analysis Using Real Signals for more discussion on scaling envelope signals for power calculation.

  The measured noise floor at -177 dBm/Hz is reduced by 3 dB from the specified -174 dBm/Hz noise floor. The difference is due to power transfer from the source to the input of the amplifier. The amplifier also models a thermal noise floor, so although this decrease is unrealistic, it does not affect accuracy at the output stage.

• The Output Display plot shows the power spectrum of the signal and noise at the output of the receiver.

  

  The measured PSD of -102 dBm/Hz for each tone is consistent with the 40-dB combined gain of the amplifier and mixer. The noise PSD in the figure is shown to be approximately 50 dB higher at the output, due to the gain and noise figure of the system.

If you have DSP System Toolbox™ software installed, you can replace the MATLAB Coder subsystems with Vector Scope or Spectrum Scope blocks.

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Simulate a Thermal Noise Floor

Thermal noise power can be modeled according to the equation

where:

• k_B is Boltzmann's constant, equal to 1.38065 × 10^-23 J/K.

• T is the noise temperature, specified as 293.15 K in this example.

• R_s is the noise source impedance, specified as 50 Ω in this example to agree with the resistance value of the Resistor block labeled R1.

• Δf is the noise bandwidth.

To model the noise floor on the RF signal at the resistor, the model uses a combination of settings in two different blocks.

• In the Noise block dialog box:

  • The Noise Power Spectral Density (Watts/Hz) parameter is calculated as .

  • The Carrier frequencies parameter, set to carriers.RF, places noise on the RF carrier only.

• In the SimRF Parameters block dialog box:

  • The Simulate Noise box is selected. When this box is cleared, the model simulates without noise.

  • The Noise bandwidth type parameter is set to Absolute bandwidth.

  • The Noise bandwidth is 1/sample_time, where sample_time is the discrete sample time used by the local solver. This setting matches the Sample time parameter in the Solver Configuration dialog box. This value specifies Δf in the preceding expressions.

  The Temperature parameter of the SimRF Parameters block only applies the specified thermal noise to Amplifier and Mixer blocks.

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Computing System Noise Figure

To model RF noise from component noise figures:

1. Select Simulate noise in the SimRF Parameters block dialog box, if it is not already selected.

2. Specify a value for the Noise figure (dB) parameter of an Amplifier and Mixer blocks.

The noise figures are not strictly additive. The amplifier contributes more noise to the system than the mixer because it appears first in the cascade. To calculate the total noise figure of the RF system with n stages, use the Friis equation:

where F_i and G_i are the noise factor and gain of the ith stage, and NF_i = 10log₁₀(F_i).

In this example, the noise figure of the amplifier is 10 dB, and the noise figure of the mixer is 15 dB, so the noise figure of the system is:

The Friis equation shows that although the mixer has a higher noise figure, the amplifier contributes more noise to the system.

For more information on RF system noise figure, see the demo Impact of RF Receiver on Communcations System Performance.

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Sensitivity

Designing a Receiver with an ADC

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