It is something that we can calculate by applying this mathematical formula (

*d*in km and

*f*in GHz):

In a Wi-Fi environment, FSPL refers to the amount of power a Wi-Fi signal losses as it travels away from the transmitter (it can be an AP or a station).

This loss is relative to 2 main components:

**Frequency****Distance**

The following diagram shows exactly how much energy a Wi-Fi wave will lose as it travels away from an AP:

## Frequency

**frequency**. Here, we are talking about the frequency of the radio wave. As you can see in the formula above, the higher the frequency is, the higher the loss will be. In Wi-Fi, this means that a 2.4GHz signal is less prone to loss than a 5GHz signal. We commonly say that 2.4GHz travels further away than 5GHz.

Another factor is affecting « how far » a Wi-Fi signal is travelling. And this is related to a specific receive characteristic. Any dual band receivers will need 1 antenna to listen to 2.4GHz signals and another one to listen to 5GHz signals. Because the wavelength of a 2.4GHz signal (12 cm) is longer that the one of a 5GHz signal (6 cm), the size of the antenna needs to be bigger. This means that the 2.4GHz receiver will have a larger

**receive aperture**and will be able to better "hear" the incoming signal.

The FSPL formula in Wi-Fi defines that, in the first meter:

- A 2.4GHz signal is loosing about
**40dB**- Calculation for channel 1: 20log(0.001) + 20log(2.412) + 92.45 = 40.09dB
- Calculation for channel 11: 20log(0.001) + 20log(2.462) + 92.45 = 40.28dB
- Calculation for channel 13: 20log(0.001) + 20log(2.472) + 92.45 = 40.31dB

- A 5GHz signal is loosing about
**47dB**- Calculation for channel 36: 20log(0.001) + 20log(5.180) + 92.45 = 46.74dB
- Calculation for channel 52: 20log(0.001) + 20log(5.260) + 92.45 = 46.87dB
- Calculation for channel 100: 20log(0.001) + 20log(5.500) + 92.45 = 47.26dB
- Calculation for channel 149: 20log(0.001) + 20log(5.745) + 92.45 = 47.64dB
- Calculation for channel 165: 20log(0.001) + 20log(5.825) + 92.45 = 47.76dB

## Distance

The FSPL formula tells us exactly by how much following the

**inverse square law**.

The inverse square law tells us that as the distance from the source doubles, the energy is spread out over 4 times the area. This results in the signal loosing 4 times it's original amplitude. In other words, the Wi-Fi signal is loosing 6dB every time the distance from the source is doubled (This is represented in red in the diagram above).

So, if we know the power of our signal leaving the access point, we can calculate how far this signal will go. This is assuming there is no source of attenuation between the transmitter and the receiver.

What happens when we introduce a wall between the transmitter and the receiver?

## Introducing a wall

Here is an example if we have an AP using an EIRP of 14dBm (or 25mW) for band frequency bands:

In order to obtain the same cell size for both frequency bands, we can offset the EIRP of the 2.4GHz by 7dB. The way we can do it is by decreasing the 2.4GHz transmit power by 7dB. Most Wi-Fi system will only let us increase or decrease transmit power by an increment of 3dB. Therefore, the best we can do it decreasing the 2.4GHz transmit power by 6dB:

## Ressources on FSPL

- Wikipedia article on Free Space Path Loss: https://en.wikipedia.org/wiki/Free-space_path_loss
- Effect of Transmit power changes on AP by Nigel Bowden: http://wifinigel.blogspot.ca/2014/11/effect-of-transmit-power-changes-on-ap.html
- Wi-Fi Free Space Loss Calculator by Nigel Bowden: http://wifinigel.blogspot.ca/2014/05/wifi-free-space-loss-calculator.html
- FSPL diagram by Devin Akin: http://divdyn.com/so-called-ghost-frames-not-exist/

written by

**François Vergès**