## Noise in RF Systems

Noise in an RF system is generated internally by active components in the system or introduced externally like channel interference or antenna.

### White and Colored Noise

*White noise*: Noise with a flat frequency spectrum is called
`white noise`

. White noise has equal power across all
frequencies of the system band width.

*Colored noise*: Noise with power that varies according to
frequencies in an RF system bandwidth is called ```
colored
noise
```

.

To simulate white or colored noise in RF Blockset, use the Noise block.

### Thermal Noise

Thermal noise is the most common noise introduced in an RF system. This noise is generated internally by active components in the system or externally due to channel interference or antenna. Thermal noise is also known as Johnson or Nyquist noise. The equation for thermal noise is:

$${P}_{N}={k}_{B}TB$$

*k*is Boltzmann's constant, equal to 1.38065 × 10_{B}^{-23}J/K.*T*is the noise temperature, specified as 293.15 K in this example.*R*is the noise source impedance, specified as 50 Ω in this example to agree with the resistance value of the Resistor block labeled_{s}`R1`

.*B*is the bandwidth.

At room temperature, the thermal noise generated by system with a
band width of 1 Hz is `-174 dBm`

.

To generate thermal noise in a RF Blockset system use Resistor and Configuration block. You can also generate thermal noise using the S-Parameters block if the S-parameter is passive.

Thermal noise floor in RF Blockset is defined by the equation:

$${P}_{noise}=4{k}_{B}T{R}_{s}\Delta f$$

where:

*k*is Boltzmann's constant, equal to 1.38065 × 10_{B}^{-23}J/K.*T*is the noise temperature, specified as 293.15 K in this example.*R*is the noise source impedance, specified as 50 Ω in this example to agree with the resistance value of the Resistor block labeled_{s}`R1`

.Δ

*f*is the noise bandwidth.

### Phase Noise

Phase noise is a short-term fluctuation in the phase of an oscillator signal. This noise introduces uncertainty in the detection of digitally modulated signals. Phase noise is defined as the ratio of power ins one-phase modulation sideband to the total signal power per unit bandwidth. It is expressed in decibels relative to the carrier power per hertz of bandwidth (dBc/Hz). To know how to model LO phase noise in an oscillator see, Model LO Phase Noise.

### Noise Figure

Noise figure value determines the degradation of signal to noise ratio of a signal as it goes through the network. Noise figure is defined by the equation:

$${N}_{f}=\frac{\frac{Signal}{Noise}\text{attheinput}}{\frac{Signal}{Noise}\text{attheoutput}}$$

Excessive noise figure in the system causes the noise to overwhelm the signal, making the signal unrecoverable. Noise figure is a function of frequency but it is independent of the bandwidth of the system. Noise figure is expressed in dB.

In RF Blockset, you can specify noise figure for an RF system using the Amplifier or Mixer blocks.