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James Scott

Noise Floor

Updated: Aug 1, 2020

Lets talk about the noise floor, what it is, and contributors.


The noise floor is the sum of all background noise sources. Background noise is any signal / RF energy, that we don't want, that is layered on top of the signal that we do want.


So what is noise? In WIFI noise is any RF transmission on the channel in question, that cannot be demodulated. What is noise for one device, might be a valid transmission for another. We'll leave a discussion about the collision domain in WIFI for another post.


The noise floor is composed of several sources generally, and those sources can vary from one environment to another. But there is one source that is constant in nearly every case. Thankfully two gentleman have helped us define this constant in noise that will be present in nearly all channels. One John B Johnson, at Bell Labs in 1926, discovered and measure Thermal Noise for the first time. He didn't actually know what he was seeing. Until Harry Nquist, also working at Bell Labs, was able to explain the results. Thermal Noise is generated when heat is absorbed by any particle. If an infrared wave is of the correct electron voltage, it can be absorbed by an electron. The electron then elevates to a new orbital, it will then begin vibrating, this cannot be sustained, and thus the electron re-emits the energy, and drops back to its original orbital. Some of this energy is released as infrared energy, and some of it at other wavelengths, such as in the RF spectrum.


Thermal Noise = -174 + 10* LOG10 (F)

Where F = Width of the channel in use, in Hz.


An example may help. Lets provide an example of a 20 MHz wide channel.


Thermal Noise = -174 + 10*LOG10 (20,000,000) = ‭-100.98970004336018804786261105276‬ dBm


Commonly rounded to -101 dBm of Thermal Noise present. If you are curious like I am. You may wonder where the -174 comes from. This number is based on temperature and Boltzmanns constant. Specifically an average temperature of 300 Kelvin / 80.33 Fahrenheit. So this can actually change depending on temperature. Created by a Ludwig Boltzmann, surprise surprise. I think we are seeing a pattern here right? I will further explain the formula for those that enjoy math, and specifically want to truly understand the impact temperature has on Thermal Noise.


The full formula for Thermal Noise is the following.


Thermal Noise = 10*LOG10 (1000*K*T*B)


Where:

1000 = a constant to help us convert to milliwatts

K = Boltzmanns constant = 1.38*10^-23

T = Temperature in Kelvin

B = Channel width in Hertz


So we've seen what 300 kelvin gives us in Thermal Noise. What about a cooler temperature. Lets say 20 degrees Fahrenheit / 266.5 Kelvin.


Thermal Noise = 10*LOG10 (1000*(1.38*10^-23)*266.5*20,000,000) = -101.4 dBm


We can see that as temperature drops, Thermal Noise decreases. We can also see that a temperature change makes such a small difference, that you would need to be near -202 Fahrenheit before we would see a 3 dBm decrease in the Thermal Noise. And we would need to be near 572 Fahrenheit before we would see a 3 dBm increase in Thermal Noise. It's possible one of us could deploy APs in an environment like this. But doubtful.


Okay we are past the really hard math. Now we can talk about other contributing factors in the noise floor. Your main contributing factors will be co-channel interference (CCI), and adjacent channel interference (ACI). Something you may not have known, is that you can get ACI from non-overlapping but adjacent channels.


The noise floor is just part of the equation in determining your Signal-to-noise ratio (SNR). And the SNR is paramount in determining what modulation method is can be used. Specifically SNR at the receiver.


Let's take a look visually at the noise floor. Figure 1 demonstrates a very weak and very low noise floor, the purple box shows this noise floor. Right around what we would expect from our Thermal Noise calculations from earlier.



Figure 1

Other environments may have a noise floor that looks much more intimidating, like Figure 2. Of note, the noise floor in Figure 2 was created by ACI, from the SSID: Homeland Security in the picture.



Figure 2

Let's talk about non WI-FI interference as well. The most commonly talked about source of this, is a microwave oven. Although a plethora of things can cause interference in either the 2.4 GHz or 5 GHz bands. Figure 3 shows a baseline of my home WIFI over the course of 30 seconds. You can see from the real-time FFT in the top half and the swept spectrogram in the bottom half that there isn't a lot going on.



Figure 3

Figure 4 shows the same exact environment but with a microwave running, about 2.14 meters away. You can see significant interference in both the real-time FFT and swept spectrogram.



Figure 4

After speaking with Nigel Bowden and Devin Akin about this blog post. I realized I left a few things out that I wanted to cover.


The first is the impact channel width has on the amount of Thermal noise introduced. If we complete the same Thermal Noise formula from above using a 40 MHz channel we get the following.


Thermal Noise = -174 + 10*LOG10 (40,000,000) = -98 dBm


You can see that we have now gained 3 dB of noise. This happens each time you double the bandwidth. If you recall, your logarithmic math, that means we are doubling the amount of noise present in the channel, and reducing your SNR. That increase in noise could very well be enough to push you back down to a lower modulation rate. So take that into consideration when moving to wider channels.


The second thing I wanted to add, is in concerns to using the noise floor during a WLAN design phase. The amount of noise different radios might see in the exact same spot, is dependent on RX sensitivity, and polarization of the antenna of the radio chain. Let's touch lightly on RX sensitivity. This is greatly impacted by the LNA chosen ( Low Noise Amplifier ). This is typically the first amplifier that your received signal goes through. It's goal is to increase the received signal of interest as much as possible, while providing as little gain to noise as possible. This includes introducing little noise as well, poorly designed or low budget radios can generate noise that impacts the signal it is trying to receive. We will take a deeper dive on RX sensitivity another day. This means that different LNAs might have a higher amount of noise that makes it into the final signal.


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