A link budget is the arithmetic to keep track of all the gains and losses of power between a transmitter and a receiver. A typical transmitter may output 1W. The power travels through the transmission line, to the the antenna, and is radiated through space. Only tiny fraction of that power, maybe one nanowatt, ends up being delivered to the receiver.
Link budget came up recently when my colleagues were discussing a system with a 1mW body-worn transmitter. The system is mostly reliable but has “dead spots” where the link is lost, sometimes when the transmitter is facing the receiver at 3 meters distance. We looked into why the receiver occasional misses messages from a transmitter that should have more than enough power.
How could a good receiver not hear a 1mW transmitter at a distance of 3m?
To answer we work out a link budget.
| Link Budget Item | Power | Explanation |
|---|---|---|
| Output Power | 0 dBm (1mW) | Power kept low to conserve batt power. |
| TX Antenna Loss | 6dB (25%) | Device was smaller than 1/2 wavelength, making antenna inefficient. |
| Free-Space Path Loss (FSPL) | 41 dB | FSPL equation for 3m distance at 915MHz |
| RX Antenna Loss | 0dB | Receiver was a basestation large enough for a decent antenna. |
| Loss due to absorption and detuning from proximity to human body | 10dB | Device is worn very close to the body. |
| Received Signal Strength | -57dBm | This is a nice strong signal. |
The receiver needs only -85dBm to work reliably. The predicted signal strength (-57dBm) is 28dB greater than what’s needed, so at first you would think this system should be very reliable.
It’s actually not 100% reliable, though, because this calculation does not take into account fade margin. Fade margin is extra power to cover fluctuations in signal strength as you move around maintaining the same distance. Because of reflections that sometimes interfere constructively and sometimes destructively, signal strength varies as you move around. You have heard this if you’re listening to a weak FM radio station in a car. You may stop at a traffic light and the signal gets weak. If you inch the car forward even a small fraction of one wavelength (one wavelength is 3 meters at 100MHz), the signal quality may change. The more buildings for signals to reflect off, the more fading you will observe. This same process happens to a strong FM radio signal, but you can’t hear it because despite the fading the signal stays strong enough for the receiver to recover a clear signal.
So how do we predict the effects of fading?
It’s impractical to calculate strength of all the reflections of a radio wave in a real-world setting with many objects. (In an empty field you can calculate it because the only thing to consider is reflections off the ground.) In anything more populated than an empty field, we turn to statistical models to work out the probability of the signal strength at any one point. A mobile phone company, for example, doing this calculation will know at a given distance from the tower, what percentage of the time the signal will be above a certain threshold.
Many processes in nature can be modelled well by the Gaussian distribution, also called “the bell curve”. Fading is best modeled by a Rician distribution. The sigma and nu parameters of the distribution depend on the environment. There will be much more fading, and much more broadly spread probability distribution function, in dense urban environments and indoors.
In a dense environment, it is common to see fades that are 30dB deep or deeper in 1% of locations.
How does this affect the real-world wireless system we talked about above?
Earlier we talked about a system proven to provide -57dBm of signal strength in an outdoor environment. The receiver’s packet error rate is low (i.e. it works reliably) until the signal falls below -85dBm.
In an rich-fading indoor environment, however, the signal fades by 30dB 1% of the time. During these occasions, the signal strength drops below -87dBm. In rare unlucky stops it may fall as long as -97dBm. In extremely rare “lottery-jackpot winning” locations (i.e. much rarer than 1 in 100), the signal made fade to zero. What we care about is that packet error rate beceoms high enough to make the system noticeably unreliably at -85dBm. In this environment, 1% of the locations will experience packet loss.
What can we do about these deep fades?
- Increase fading margin: The easiest thing to do, if it’s an option, is to crank up the power. If you have 40dB more power than you need (i.e. 40dB of fade margin), it will cover all but the most lottery-winning fades.
- Antenna diversity: In the scenario above we said 1% of locations experience 30dB fades. But it’s much less likely (ideally 0.01^2 = 0.01%) that two locations will experience deep fades at the same time. This is why you see wireless equipment with more than one antenna.
- Frequency diversity: Fading environments are “frequency selective”, meaning the locations of “dead spots” due to fading change with frequency. If the system can change frequency when a fade occurs, it may not experience fading at the new frequency.
- Higher-Level Protocols: The higher level protocols must be able to tolerate some loss of information at the physical layer. Layer 2 should acknowledge messages and retry messages that are not acknowledged. Maybe the user will have moved out of a “dead spot” by the time the retry occurs. Even if retries fail, the layers above should handle the loss gracefully. If the system is a voice phone call, maybe it would choose to maintain the connection for a second or two even though there is no signal in case the connection improves. This way the user will experience the audio breaking up but not lose the call altogether.
Can all this be fun? (De gustibus non disputandum est)
Back when wireless was an avocation for me, I found it exciting when a frequency band that normally didn't support communication to a certain location allowed communication briefly due to unusual atmospheric conditions. Friends would call each other, "Go get on the 6m band. It's totally open. I just worked a station 600 miles away on 25W!" Even back then it occured to me that I could easily have the same contact on the 15m band, but this was rare because it was 6m. The conditions could change fast, and sometimes I would wear headphones and close my eyes to pull out the sounds as the signals faded in and out.
Just a few years ago I worked my first system that used MIMO. MIMO puts the time-delayed reflections that cause fading to good use. It allows systems to transmit two independent streams of data at the same time and same frequency. When the fading is deep enough to go into the noise floor, it falls back to single stream and listens to the same stream on multiple antennas to reconstruct signals too weak to be received on any one antenna. In all the technology I have worked with, MIMO ona a $50 radio car, is absolutely the most amazing technology I have seen.
I try to keep this in mind when fades are causing problems on a system that needs reliability.
