rf

WN Blog 024 – RF Math

Hey!

Welcome to our latest blog – this time we are taking it back to some RF fundamentals and more specific – RF Math!

Since we started our Podcast & Blog, we have had requests from people to cover beginner level WiFi basics, which we will be doing with a series of blogs & podcasts coming up in the future but today let’s make a start with understanding some RF Maths.

You might be wondering why do I need to learn RF maths? I had enough of Maths when I was at school – I don’t want to have to do it all again! Well RF maths is important in WiFi because we typically measure WiFi in dBm & dBm means dB scale relative to mW. For example, when looking at your RSSI (Received Signal Strength Indicator) in dBm it would look something like this “-50dBm”.

WinFi RSSI

Now I am no maths expert at all, so luckily there is a relatively simple rule we can follow to pretty much work out all RF maths.

This is the rule of “10s & 3s”

Below is a table, on one side we have dBm and on the other we have mW. Now whatever we do on one side of the table we must do on the other side of the table. If you + (add) in dBs, then we X (times) in mW. If we – (minus) in dBs, then we / (divide) in mW. 10 in dBs is 10 in mW and the only thing that is a little bit tricky to remember is 3 in dBs is 2 in mW.

dBm mW
+ X
/
10 10
3 2

This table below might help paint a bit of clearer picture, for example if we increase the signal strength by +3dBs we then have 2 x the power. If our signal strength decreases by -10dBs we then have 1/10th of the power that we had.  

dBm Power
+3dB 2x Power
-3dB ½ Power
-10dB 1/10th Power
+10dB 10x Power

Starting to make a bit of sense? If not, do not worry as we have plenty more examples below that will help you have a better understanding of how this works & we have even thrown in a little quiz for you guys!

When we are doing RF math, we always start with 0dBm & 1mW at our starting point.

In the example below, we are converting dBm to mW & our aim is to work out what 13dBm would be in mW.

Remembering that we always start from 0dBm, we first would add +10db and then add another +3dBs to get to 13dBm. Now to convert that to mW & remembering that we always start from 1mW, we first x 10 and then x 2. Which would mean our calculation would be “1 x 10 x 2” and then equals 20mW.

RF Math Example 1

Let’s move on to another example. This time, how do we convert 36dBm into mW. See in the image below, in dB we +10 +10 +10 +3 +3 to get to 36 so that means in mW we x10 x10 x10 x2 x2 which = 4000mW.

RF Math Example 2

A very strong signal in WiFi & typically the highest you will see is -30dBm. Let’s work out in mW what is considered a very high RSSI if WiFi. Remember we start from 0dBm, so -10 -10 -10 will get us to -30dBm. Which means in mW we / 10 / 10 / 10 – so our calculations will be 1 / 10 / 10 / 10 which equals 0.001mW! Wow, so an extremely good strong signal in WiFi has a power level of 0.001mW?! That’s impressive!

RF Math Example 3

Let’s move on to another example, this time -53dBm (still a very good signal strength in WiFi). To get to -53 from 0 we need to – 10 – 10 – 10 – 10 – 10 – 3. Which in mW would be / 10 / 10 / 10 / 10 / 10 / 2. That means our calculations would 1 / 10 / 10 / 10 / 10 / 10 / 2 which equals 0.000005mW.

RF Math Example 4

Are you starting to see why we do not measure RSSI in mW? Imagine having to go back to the customer and say, “oh yes Mr. Customer your signal strength here is very good, its actually 0.000005mW!” I think being able to say that the RSSI is -53dBm is much easier ????

I have put together another table below of some additional dBm conversions to mW and to Watts for your comparison.  

RF Math Examples Table

Hopefully after those few conversions we have worked out together you guys are ready for a little quiz & to work out some dBm to mW yourselves! Now, I will put the answers to the dBm levels below at the bottom of the blog but do not cheat! Work these ones out yourself using the 10s & 3s rule as well at the examples above and see what answers you come up with!

Quiz dBm to mW:

RF Math Quiz

Now that we are all RF Math WiFi Ninjas lets take this another step & take into consideration what happens when WiFi passes through walls. Some typical wall type materials we see in the wild & how they attenuate the WiFi signal.

If we first look at what wall is most commonly used internally in buildings, which is “drywall”. On average typically drywall will have an attenuation level of 3dBs. So that means when WiFi signals pass through the drywall we will lose -3dBs & losing -3dBs means that we now have half the power we originally did. Looking at the image below we can see an AP on the left-hand side where client A has an RSSI of -49dBm, but on the other side of the drywall, client B has an RSSI of -52dBm.

RF Math Dry Wall Example

Moving on to another type of wall that is commonly used on the exterior of buildings, “brick wall”. A brick wall typically has an attenuation of 10dBs, so this means when WiFi signals pass through a brick wall they will lose -10dBs, therefore we will now have 1/10th of the power we originally had before passing through the brick wall. Looking at the image below we can see an AP on the left-hand side where client A has an RSSI of -49dBm, but on the other side of the brick wall client B has an RSSI of -50dBm. 

RF Math Brick Wall Example

The final concept that we would like to explain to you is something called “Free Space Path Loss) aka – FSPL. What we need to remember with FSPL is that when you double the distance, you quarter the power. That will mean at double the distance we will need to half the original power and then half it again. To half the power in WiFi, we need to -3dB.

In the example image below, we are using the example of at 1m distance from the AP, we have an RSSI of -30dBm, we then move to 2m distance which is double 1m so we need to quarter the power which means -3 + -3 so at 2m our RSSI should be -36dBm. You can see / work out for yourself how we got to that RSSI at 4m & 8m ????

Free Space Path Loss Example

Here are the calculations and answers to the quiz above:

27dBm = 0 +10 + 10 + 10 – 3 = 27 so 1 x 10 x 10 x 10 / 2 = 500mW

45dBm = 0 +10 + 10 + 10 + 3 + 3 + 3 + 3 + 3 = 45 so 1 x 10 x 10 x 10 x 2 x 2 x 2 x 2 x 2 = 32,000 mW

39dBm = 0 – 10 – 10 – 10 – 3 – 3 – 3 = 39 so 1 / 10 / 10 / 10 / 2 / 2 / 2 = 0.000125mW

57dBm = 0 – 10 – 10 – 10 – 10 – 10 – 10 + 3 = 57 so 1 / 10 / 10 / 10 / 10 / 10 / 10 x 2 = 0.000002mW

How many did you get right? Let us know 😀

That concludes our RF Maths blog, we hope you found it useful if you are a WiFi beginner or even if you are more experienced and just needed a little refresh ????

Tons of Love,

WiFi Ninjas x

WN Blog 022 – Distance Between 802.11 Radios – How Close Is Too Close?

We have recently come across few production networks, where distance between two APs or APs and a client stations was much closer than I was comfortable with.

Natural reaction was to suggest moving radios at least few metres apart. But why exactly? What happens when two or more transmitting radios are too close to one another? How would placing a laptop next to the AP affect wireless network quality?

Intrigued and eager to answer questions that, interestingly, no one was asking, I have decided to lab it up, research it more deeply and document my findings. I quickly realised that there is not one, but two issues potentially affecting wireless transmission, where distances between radios were too short. Let’s discuss Channel Leakage and Near-Field Interference.

Structure:

  • Channel Leakage
  • Near-Field Interference
  • Literature

Channel Leakage

Few months after a successful design and refresh of a WiFi estate for a financial institution in London, I came back to work on a periodic wireless survey and to assess if there is anything that would be potentially stopping them from introducing more agile working heavily relying on the new WiFi deployment.

I was told that there is a separate company that is working closely with my client in the same offices and that they use their own, separate WiFi network. They have decided to put their own APs next (few inches away) to our APs convinced that since it worked perfectly for my client, it would continue working when two overlaid networks operate simultaneously. This is how the new original vs new deployment looked like:

Having completed the survey, we have concluded that city centre location inside a multi-tenant building with multiple WiFi networks leaking from the outside and adjacent floors combined with two separate, overlaid WiFi networks contributed to very high CCI averaging at 10 or sometimes more. RF tuning across both networks has helped a lot with the contention but the overall quality of the WiFi was still not great. It felt slow despite having strong underlying infrastructure, little CCI and fast Internet pipe. Quick wireless capture has revealed excessive retransmissions rates peaking at 30% in some areas even when there were not too many clients (maybe 10 per radio, often less) competing for the airtime, channel utilisation peaking at 10% and with no obvious faults with the configuration.

Lab

Next step was to reproduce the issue in the lab, where I wanted to show how channel separation and AP-to-AP distance impacts percentage of retries in the wireless transmission.

Setup

  • 2x Cisco 3702i APs registered to C9800-CL WLC broadcasting separate BSSIDs on 5GHz only
  • 20MHz static non-overlapping, clean channels (100 & 104 and 100 & 140) and max Tx power (1) set
  • One mobile station associated to each BSSID, running external speed test in the loop
  • Ekahau Sidekick used for wireless captures

Tests

4 different tests were performed, each test involved wireless capture over 30 seconds and was repeated 5 times to minimise measurement errors:

  • Channels 100 & 104 (no channel spacing)
    • Test 1: APs 0 metres away from one another
    • Test 2: APs 3 metres away from one another
  • Channels 100 & 140 (200MHz channel spacing)
    • Test 3: APs 0 metres away from one another
    • Test 4: APs 3 metres away from one another

Conclusion

We can clearly see in Test 1, that close physical distance between radios combined with no channel separation resulted in 15.4% retries.

Introducing 200MHz channel separation (Test 3) without extending distance between radios has reduced retries ratio by about half, to 8.2%.

Moving APs 3 metres away from one another has further reduced the retries to 3.9% (Test2; no channel separation) and 2.3% (Test 4; 200MHz channel separation).

Unplanned channel leakage really is an adjacent-channel interference, even though our channels theoretically don’t overlap. ACI will naturally cause increased number of retries, and therefore decrease the throughput and contribute to the slow WiFi perception.

Note: we used flagship Cisco APs with great quality of components providing great RF accuracy. Using cheaper APs that pack cheaper antennas and radios would result in less stellar performance of spectral masks (algorithms applied to the levels of radio transmissions used to reduce main channel leaking to adjacent channels) and amplify the effects of intermodulation (signal modulation on two or more different, non-harmonic, frequencies), increasing effects of ACI and percentage of retries when reasonable channel separation and physical distance between AP radios are not maintained.

Near-Field Interference

Another distance issue that I have frequently seen in an enterprise environment is placing receivers too close to transmitters.

Let’s start with a quick definition of what near-field is in wireless.

Near-field is a 1 wavelength region, where electromagnetic field EM charges and electric charge effects are extensively produced, potentially negatively affecting quality of the received transmission within this region.

Near-field interference decreases drastically, in a logarithmic fashion, when the receiver is moved farther away from the transmitter. It is normally considered enough to be 1 wavelength away from the transmitter to negate the impact of near-field interference. Near-field also affects reflected signal for Rx antennas.

Based on the above, we can conclude that:

  • Radios should never be positioned closer than 1 wavelength apart from one another
  • Receive antennas should not be positioned closer than one wavelength to any reflecting obstacle due to reflection indicted multi-path phase cancellation

How far is 1 wavelength? It depends on the frequency. The higher the frequency the shorter the wavelength. Here are the wavelength calculations for our beloved 802.11 bands:

2.4GHz frequency wavelength = 12.5cm

5GHz frequency wavelength = 6cm

Now we know, that when we position 2.4GHz radios closer than 12.5cm away from one another (or 6cm in 5GHz) we would suffer from extensive near-field interference and that the situation would improve greatly when we start increasing this distance. Bear in mind, that unwanted channel leakage might contribute to packets corruption here too, so it typically is recommended to keep at least few metres distance between the radios!

Couple of examples, where near-field interference can affect quality of WiFi transmission:

  • Enterprise-class AP placed on a small desk with few people sitting around it and their laptops virtually adjacent to the AP; note, that external antennas can increase the negative effect of a near-field interference
  • Capturing wireless packets with a capturing device positioned to close to a client or an AP

We must remember that WiFi is not NFC! ????

Lab

In this test I targeted impact of near-field interference on wireless receive quality, where receiver (AP in a sniffing mode) was within 1 wavelength of a transmitter (AP serving clients).

Setup

  • 2x Cisco 3702i APs registered to Cisco 3504 WLC and one test client associated to client serving AP
  • AP with blue LED is serving clients
  • AP with green LED is running as a sniffer and capturing packets on the same channel as the AP serving clients
  • Below tests are based on 5GHz, but in my tests I could have easily reproduced them across both 5GHz and 2.4GHz bands

Tests

It was enough to perform a very simple test here – check captured packets integrity in two scenarios:

  • Test 1: AP sniffer placed 60 centimetres away from a client-serving AP (more than 1 wavelength distance between radios)
  • Test 2: AP sniffer placed on top of a client-serving AP (less than 1 wavelength distance between radios)

Here are the results:

Test 1 captures, where APs are fairly far away from one another, are clean. Putting transmitting and receiving radios very close together (Test 2) results in corruption of almost all packets transmitted by client-serving AP.

Conclusion

When receiver is placed too close to transmitter (especially true when the distance is less than 1 wavelength apart), near field interference will cause packets to lose integrity and result in failed Frames Check Sequence (FCS).

Summary

As shown in the above tests, unwanted channel leakage can seriously affect the transmission quality over distances less than few metres, especially without proper channel separation on the neighbouring BSSIDs. Near-field interference can cause corruption of most of the transmitted frames, where distance between transmitting and receiving radios is less than 1 wavelength apart. Finally, after having a chat with my friend Nigel (Twitter @WiFiNigel), we have concluded that the Rx overdrive might also play a role in the frames corruption. Unfortunately, it is difficult to ascertain which phenomena impacts the frames corruption most using the home lab, so I’ll just conclude with this: don’t stack APs! 🙂 And put them away from strong reflectors. All above issues can be easily avoided by using good quality enterprise equipment, solid RF design and having a high-level understanding of how the distance induced interference can affect the quality of the wireless transmission.

Literature