What are the units of RSSI, noise and SNR as defined by IEEE 802.11?

Question

I'm a CS graduate, but to my shame have very limited knowledge of electrical engineering and especially antenna theory.

As far as I understand, RSSI determines quality of how measurer "hears" the object being measured. Noise determines environment conditions that affects measurer. And SNR is simply how much RSSI is better than Noise. This theory (assuming I got the basics right) raises only single question:

• How is it even possible for a single fixed measurer to determine both RSSI and Noise?

Now some practice. Let's say measurer is my Macbook Air running builtin Wireless Diagnostic tool. And the object being measured is my WiFi Router. Observed values are −60 dBm for RSSI and −92 dBm for Noise. Therefore SNR is 32 dB. What I completely cannot understand is:

• Why both values are negative and measured in dBm?

As far as I understand, −60 dBm means 10⁻⁹ W while −92 dBm means 10⁻¹² W. But who radiate that power? Maybe that theory represents Noise as another "antenna"? But why is its value so small then? Or I miss some very key points here? I'll be thankful for an intuitive explanation of this stuff.

Answer 1

"How is it even possible for a single fixed measurer to determine both RSSI and Noise?" - very good question. The noise they are talking about is receiver noise and not interfering signal. At very low powers, the noise is mostly the thermal noise of the receiver: ie, if you were to disconnect the antenna and replace it with a 50 Ohm load (most RF systems are 50 Ohm) you will measure a certain level of noise. So, even if you had all the ideal components, your noise power would be P = k*T*B*G, where k is the Boltzmann's constant, T is the temperature in K, B is the bandwidth in Hz, and G is the gain of your system. In reality, every component adds noise as specified by its noise figure (listed in the datasheet of every RF component). If you look again at the noise power equation, you will see that by reducing bandwidth, you also reduce the noise. However, high bandwidth is necessary for high data rates, which explains why you need good SNR for high data rates.

"Why both values are negative and measured in dBm" - 0 dBm means the power is 1 mW. -20 dbm means the power is .01 mW. The minus indicates the number of dB below 0 dBm. Without the minus, it would have been above 0 dBm

"But who radiate that power?" - in case of noise, it is internal, in case of signal, the transmitter. However, fundamentally it doesn't matter.

"But why is its value so small then?" - it comes from what is called Friis transmission formula. So, with several simplifications, imagine that my transmit antenna radiates power isotropically in all directions. So, your power is uniformly distributed on the surface of a sphere of radius r (and surface area 4*pi*r^2), where r is the distance from the transmit antenna. In Imagine, that your receive antenna is about 1 m^2 and it can capture all the radiation that hits its surface. Now, it can only capture 1/(4*pi*r^2) of all the radiation, making the receive power very tiny and RF engineering a complex field :). This is a very hand wavy explanation but I hope it makes sense

Answer 2

They're negative because they are really small. The dB scale is a logarithmic scale, with 0 dBm referenced to 1 mW. Negative values are smaller and positive values are larger. Like you said -60 dBm is 1 nanowatt and -90 dBm is 1 picowatt. I'm actually not sure where the noise measurement is coming from offhand. The radio receiver does generate some noise internally that prevents it from receiving an arbitrarily small signal just due to the nature of how the receiver is built. It contains lots of electrons bouncing around and generating noise, and it's not sitting at absolute zero so things are wiggling around and generating thermal noise. Think about how small 1 picowatt is. It is 100 trillion times smaller than your standard 100 watt light bulb.

It's possible that the noise figure represents the signal level on adjacent channels in some way. Have you noticed the noise value varying at all, or is it always -92 dBm? If it is fixed at -92 dBm, then that would be considered the noise floor of the receiver, and it is not capable of receiving signals that do not have a sufficient margin above the noise floor. In this case the noise level is not being measured, it is simply a characteristic of the receiver.

If the noise value varies, then it is probably a measurement of the noise on the channel when none of the wifi radios are transmitting. In a wifi system, all nodes in a network transmit on the same frequency in a shared channel. When no nodes are transmitting, the receiver can measure the signal level on the channel for a measure of the background environmental noise. Noise in the band might be caused by other wifi networks, bluetooth devices, zigbee, microwave ovens operating at 2.4 GHz, etc.

Answer 3

The work Friis did on developing a simple formula for received power makes a basic assumption about distance - all bets are off if the transmitter and receiver are up-close. This is called the near-field and the standard equation of: -

LinkLoss (dB) = \$ 32.45 + 20 log_{10}(F) + 20 log_{10}(D)\$

..... doesn't work up-close because you are not really measuring (or receiving) a true electromagnetic wave - you'll have the E field and the H field at all sorts of odd phase angles to each other and you'll actually be loading the transmit antenna. In the far field, (several wavelengths away) you'll get something like this: -

Once you're in the far field, EM wave power quarters with distance doubling. So, plugging your numbers into the equation (where F is in MHz and D is in kilometres) we get this at 300m: -

linkloss = 32.45 + 20log(2450 for wifi) + 20log(0.3) = 32.45dB + 67.8dB -10.5dB = 89.75dB.

This is a free-space link loss and as a rough guide folk tend to add 30dB to this figure to account for fade margin giving you a link loss of 119.8dB. Your antennas steal a little back to bring it down to about 116dB and your +30dBm transmission power means that at 300m you might expect to receive: -

86dBm.

Your receiver needs more received power for a bigger bandwidth (because noise power is proportional to bandwidth) and another good rule of thumb is minimum received power required is \$-154dBm + 10log_{10} (data rate) dBm\$.

If data rate is 10Mbps, then your minimum receiver power is -154dBm + 70dBm = 84dBm which is pretty close I'd say. You might want to replicate the calculations at (say) 2.45m (10 wavelengths away) to see if the numbers start to tally.

See also my answers on these : -

How to know (or estimate) the range of a transceiver?

Calculate distance from RSSI

Long range (~15 km) low baud-rate wireless communication in a mountain environment (no LOS)