Noise Figure in a Microwave Photonic Link

The standard definition for noise figure (NF) is the degradation of signal to noise ratio (SNR). That is, if the output noise power of the system is increased more than the output signal power, then this implies a significant noise figure and a degredation of SNR.

For an RF photonic link, there are a couple assumptions that result in a slightly altered definition and calculation for noise figure. One assumption is that the input noise is the thermal noise (kT), such as would be detected from an antenna receiver. It is also the case that RF photonic links may be employed in a case where the input signal power level is not defined. In simple telecommunications aplications, it is standard to expect a certain input power level, but as a communications system at a radar front end for instance, the input signal is not known. We can use the gain of the link as a relationship between output signal and input signal instead of a known input and output signal power.

It is a goal of the link designer in those cases to ensure that all true signals can be distinguished from noise. For these reasons, we may also think of noise figure in the following definition:

Noise figure (NF) is the difference between the total equivalent input noise and thermal background noise.

The equivalent input noise is the output noise without considering the gain of the link.

For the noise figure calculation, we have then:

NF = 10*log_10( EIN / GkT ),

where EIN is the equivalent input noise, G is the link gain, k is Boltzmann’s constant, and T is the temperature in Kelvin.

Equivalent input noise (EIN) is as follows:

EIN = GkT + <I^2>*Z_PD,

where <I^2> is the current noise power spectral density at the output of the link and Z_PD is the photodetector termination impedance.

These together, we have noise figure:

NF = 10*log_10(1+(<I^2*Z_PD)/GkT)

Noise Sources in RF Photonic Links

Identifying the noise sources in an RF Photonic link allows us to determine the performance of the link and helps us to identify critical components to link and device design to develop a high performance link. Below is an intensity modulated optical link. Other modulation schemes in RF photonic links may be discussed at a later point.

Since the output of the RF photonic link is the photocurrent generated by the photodetector, the noise sources are a current noise power spectral density.

Noise sources from the laser:

Laser RIN (relative intensity noise) is the fluctuation of optical power. Relative intensity noise is the noise of the optical power divided by the average optical power in a laser. RIN noise originates from spontaneous radiative carrier recombination and photon generation.

Noise sources from the modulator:

Noise in a modulator is due to thermal noise of electrode termination and ohmic loss in the electrodes.

Noise sources from the photodetector:

Shot noise occurs as a result of the quantization of discrete charges or photons. Noise is also generated by the photodetector termination.

Total current noise power spectral density of the RF photonic link:

Thermal Background Noise

Any object with a temperature above absolute zero (Kelvin) radiates electromagnetic energy, or thermal noise. Noise is generated by the earth and cosmos, and this is background thermal noise, which is received by an antenna.

Thermal background noise is the starting point for system performance. A signal of strength below the thermal background noise will be indistinguishable from noise.

The thermal background noise power is proportional to the temperature (P = kTB, k being Boltzmann’s constant, T the temperature in Kelvin, and B the bandwidth in hertz). The thermal background noise power spectral density is the fundamental noise minimum at -174 dBm/Hz at 300K.

The gain of the device or system further amplifies the thermal background noise. RF Photonic links most often use a low noise amplifier (LNA) directly before the modulator, amplifying the thermal background noise.

The definition of thermal noise applied to electronics is the movement of charge carriers caused by temperature in a conductor.

Mean Squared Noise Power

What does it mean when people say “mean squared”?

The average value of a noise waveform is zero. The square of the waveform mean is also equal to zero. The square of the noise signal and the mean of the square are non-zero. This is because the negative values associated with the zero-mean noise waveform are made positive by squaring, and the entire waveform is positive. Taking the root of the averaged square of the waveform yields the RMS.

The mean of the squared (“mean square”) noise waveform is the noise power with respect to a 1 Ohm resistor (units: V2/Ω=W, “power” if noise signal is a voltage signal, and units I2/Ω=W, also “power” if noise waveform is current).

The power spectral density is the power of the signal in a unit bandwidth.

What is a current noise power spectral density?

The correct definition of current noise spectral density is the mean of the squared current per hertz, <i2>. The units are A2/Hz.

The square of the mean is equal to zero, because the mean of the noise waveform is zero and squaring that number remains zero. The mean of the square is a non-zero number. Taking the square of a noise current results in a positive valued current waveform. Taking the average of the square is a non-zero number used for the spectral density.