Noise floor

The noise floor is the level a detector, receiver or analyzer reports when no signal is applied: the combined noise of the system, integrated over the bandwidth in which it is observed. A signal well below the floor cannot be distinguished from noise, and one at the floor has a signal-to-noise ratio near one. Because white noise power grows in proportion to bandwidth, a floor is meaningful only with its bandwidth stated. The reference value for electrical systems is the thermal noise available from a matched source at 290 K, $k_BT = -174$ dBm/Hz, which is $-114$ dBm in 1 MHz and $-84$ dBm in 1 GHz.

The floor in three kinds of instrument

Photodetectors and receivers. The floor of a photoreceiver is usually quoted through its noise-equivalent power, the input optical power that gives SNR = 1 in a 1 Hz bandwidth. In a bandwidth $B$ the floor referred to the optical input is

$$P_\text{floor} = \text{NEP}\,\sqrt{B}$$

A receiver with an NEP of 3 pW/√Hz has a floor of 0.30 µW ($-35.2$ dBm) in 10 GHz and 95 pW ($-70.2$ dBm) in 1 kHz. The 35 dB between them is the factor $\sqrt{10^7}$ in power: optical power enters the photocurrent linearly, so the floor in optical units scales as $\sqrt{B}$, while the electrical noise power scales as $B$.

Electrical spectrum analyzers. The displayed average noise level is the thermal floor plus the analyzer's noise figure, scaled to the resolution bandwidth (RBW):

$$N = -174 + \text{NF} + 10\log_{10}(\text{RBW}/\text{Hz})$$

in dBm. With a 15 dB noise figure, the floor is $-129$ dBm at 1 kHz RBW and $-139$ dBm at 100 Hz RBW. Narrowing the RBW tenfold lowers the floor by 10 dB and, on a swept analyzer, lengthens the sweep about a hundredfold, since sweep time scales as span/RBW².

Optical spectrum analyzers. An optical spectrum analyzer reports power in dBm per resolution bandwidth, so its floor and any broadband noise it measures change with the RBW setting: a broadband noise level of $-40$ dBm read in 0.05 nm is $-37.0$ dBm in 0.1 nm. Grating analyzers specify their sensitivity, the lowest level they detect, at a stated wavelength range and sweep speed; slower sweeps with longer detector integration reach lower levels. For an amplified optical signal the floor that matters is usually the amplified spontaneous emission level between channels, which sets the OSNR. The OSA fundamentals article covers the RBW and dynamic-range settings.

Contributions and how they add

Independent noise sources add in power. In a photoreceiver the floor combines thermal noise of the load or feedback resistor, amplifier input noise, the shot noise of dark current and, once light is present, the shot noise of the signal itself. These are comparable at round numbers: the shot noise of 1 mA of photocurrent, $\sqrt{2eI} = 17.9$ pA/√Hz, equals the thermal noise current $\sqrt{4k_BT/R}$ of a 50 Ω resistor at 290 K. Above that photocurrent a 50 Ω receiver is shot-noise limited and its floor rises with the signal, which is why the no-signal floor does not fully describe a strong-signal measurement.

Averaging, bandwidth and detection below the floor

Averaging and bandwidth reduction act differently. Averaging $N$ power readings or traces reduces the scatter of the noise by $\sqrt{N}$, so 100 averages give a trace 10 times smoother, but the mean noise level stays where it was: a weak line becomes easier to see against a steadier floor without the floor itself moving. Reducing the noise bandwidth does lower the floor. A narrower RBW, a longer integration time, or a lock-in amplifier with a millihertz equivalent bandwidth all exclude noise, which is how signals far below a broadband floor are recovered. Synchronous averaging of a repetitive waveform in the time domain is a bandwidth reduction of this kind: noise that is uncorrelated with the trigger averages toward zero, while the signal adds coherently.

Pitfalls

Spectrum analyzers that average a logarithmic (dB) display underread Gaussian noise by 2.51 dB relative to power averaging; noise markers correct for this, plain trace averaging in log mode does not. A floor quoted in dBm/Hz must be converted with $10\log_{10}B$ before it is compared with a reading in dBm. And an instrument's floor is often set by the stage after the detector: the NEP of a fast photoreceiver is normally set by its amplifier.

Common questions

What is a good noise floor?

It depends on the bandwidth. For electrical systems the comparison is with $-174$ dBm/Hz plus the noise figure; a system within a few dB of that is near the thermal limit. For optical receivers the comparison is with receiver sensitivity at the required error ratio, which lies several dB above the SNR = 1 floor.

Does averaging lower the noise floor?

Averaging power readings lowers the fluctuation of the floor, not its mean level. Coherent averaging of a triggered waveform, or narrowing the bandwidth, lowers the floor itself.

Why is thermal noise −174 dBm/Hz?

$k_BT$ at 290 K is $4.0 \times 10^{-21}$ W/Hz, and $10\log_{10}$ of that power in milliwatts is $-174.0$ dBm/Hz. At 300 K it is $-173.8$ dBm/Hz.

References: P. Horowitz and W. Hill, The Art of Electronics, 3rd ed. (Cambridge University Press, 2015), chapter 8; B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010), chapter 4.