FM Capture Effect and LoRa "Capture Effect" - They're Different!
by Jon Adams, N7UV
You've heard of the FM capture effect, where an FM receiver will favor one station over the other so long as there's just enough receive signal strength difference between the two transmitters. If you're old enough to remember listening to FM broadcast radio while doing a road trip, and starting your trip listening to the favorite in your town, as you drove away from your town and closer to the town which had an FM station on the same channel, the FM capture effect would cause your car stereo to switch back and forth (sometimes called "picket fencing" or "mobile flutter") between the two broadcast stations depending on which was stronger at that moment. It all depends on the quality of the FM receiver discriminator function.
This is quite different from AM, used by medium-wave and shortwave broadcast, aviation and old-school 27 MHz (11 m) Citizen Band operators, where the receiver will demodulate both signals at the same time producing a carrier mix squeal, and while you may or may not be able to understand either transmission, you'd know that there was another station out there and you could ask for a repeat.
FM Receiver Signal Discrimination
For the regular old FM receiver, we'll start with a mobile and a single DIGI A. In all of the below, the mobile unit is temporarily stationary (stopped at a traffic signal, parked, whatever).
Figure 1
The grid is in either km or miles, it doesn't matter. we assume the world is flat and there are no buildings, trees, or any other stuff to get in the way of the radio waves, and there's no interaction with the earth. This is just free space! Maybe the car is that Tesla on its way to Mars or wherever and the digi A is another spacecraft. Yes, on and around the ground, the results are more variable, but the principles are the same.
So long as the mobile is in radio range of DIGI A, we all expect that the mobile can hear all packets transmitted by DIGI A. Whether a few km/mi apart or 50, so long as there's sufficient signal received at the mobile, it all works.
I found a neat graphing tool desmos that is easy to use and hopefully will help tell the story.
Figure 2
DIGI A is at location -50,0 (km or miles, doesn't matter for now) and can be heard by the mobile no matter what position the mobile is at (MOB A through MOB F). In this scenario, even at the MOB E position (+40, -6; MOB E is ~93 units away from DIGI A) there's plenty of signal from DIGI A to have successful reception.
Figure 3
Likewise, there could be only DIGI B (+50,0), and all the mobile positions MOB A through MOB F are in range of DIGI B.
Figure 4
Figure 5 makes the situation more interesting and typical by having overlapping coverage from DIGI A and DIGI B. We've already stated that every mobile position is in range of each digi. With 2 digis, the potential for overlapping transmission can cause situations where they interfere with one another at the receiver.
Figure 5
There will be regions where, due to the FM capture effect, the mobile can successfully hear one digi over the other, but there are also places where the signal strength difference between the 2 digis is small enough that the mobile cannot successfully discriminate between the two and any packets transmitted are lost.
In the following analysis, we will ignore the observation that in most digipeater hardware/firmware/software there are mechanisms to detect channel activity. It's not flawless, but works pretty well so long as it's configured properly. Figure 6 shows 3 different scenarios: 1 where there is no overlap between either transmitted signal; 2 where A starts transmitting before B, and B overlaps the end of the A frame; and 3 where B starts first, and A begins to transmit later and overlaps the end of B's frame. There's another one, which is more likely, where both overlap one another almost completely.
Figure 6
The analysis will assume scenario 2 or 3, where there is at least a partial temporal overlap as seen by the receiver.
While FM capture effect can approach zero in an ideal receiver, a typical ham-grade two-way radio FM receiver likely has an FM capture ratio (the difference in received signal strength (RSS) at the mobile between two competing transmitters) between 1.5 and 3 dB. A lower number is a better receiver. There may be some receivers out there that are worse than 3 dB, but that's not a spec that any manufacturer AFAIK publishes.
In Figure 5, MOB A position is exactly equidistant from DIGI A and DIGI B, causing the DIGI A and DIGI B RSSes to be exactly equal, and so MOB A cannot successfully discriminate between either digipeater, so it won't decode anything, no matter how good the receiver is. What about MOB C, which is somewhat closer to DIGI B than A? If our mobile unit has a high-performance FM discriminator and can successfully discriminate at a 1.5 dB RSS difference, that means so long as the mobile is closer to one digi than the other by a certain ratio, the mobile will successfully receive that closer digi. For a 1.5 dB difference, that ratio is ~1.188. How is this derived? Remember, we've assumed the two digipeaters are identical in all ways.
The formula to convert dB into linear power ratio is
The receiver performs successfully when one signal is stronger by 1.5 dB.
Thus, the winning transmitted signal must be ~1.413x stronger than the other. Now we know the square of the distance ratio.
Taking the square root of the above to get the direct ratio of the distances, we get
So long as the ratio of the distances to the two digis from the mobile is equal to or greater than 1.188, the receiver will successfully decode the stronger signal.
We already can deduce that a mobile at position MOB A will be unsuccessful in decoding either digi. What about position MOB C? It's obviously closer to DIGI B than A, but is the ratio of the distances enough to make the RSS from DIGI B at least 1.5 dB better than from DIGI A? And what about MOB D? Or any of the other potential mobile positions?
What we've described above is the basis of the Circles of Apollonius!
Figure 7
For the mobile receiver, if it's at any position between the red arc and DIGI A, the receiver will receive DIGI A successfully. If the mobile is at any position between the purple arc and DIGI B it will receive DIGI B successfully. If it's not in one of those two zones, it's unlikely to decode either! Look at all that highlighted space in-between the two arcs - the RSS for each digi at the receiver is not sufficiently different to discriminate between either. Let's zoom in.
Figure 8
As we already assumed, position MOB A will always be unsuccessful. We also see that position MOB C is not close enough to DIGI B to allow a 1.5 dB RSS difference, so the receiver will be unable to discriminate successfully. But the receiver at positions MOB B and MOB D will always successfully decode DIGI A, and at positions MOB E and MOB F will always decode DIGI B.
Figure 9
Figure 9 highlights the overlap zone for an FM receiver with a 3 dB capture ratio. Significantly larger than for the 1.5 dB capture ratio in Figure 8, and so the receiver suffers.
LoRa Receiver Discrimination
LoRa receivers aren't traditional FM receivers. While the LoRa signal is a form of FM, LoRa is a chirp spread spectrum modulation method. The LoRa receiver employs fast Fourier transforms (FFT) to detect and demodulate a valid signal. Much more sophisticated and complicated than an FM receiver, but more sensitive to signals close in received power level.
What this also means is that the traditional FM receiver can almost always have better receiver discrimination performance than a LoRa receiver. According to the Semtech literature and many industry papers and studies, the best their LoRa receiver can do is between 6 and 10 dB difference between competing signals of same bandwidth and spreading factor.
I'm sure it depends on a lot of things, but since we assumed a really high performing standard FM receiver and a 1.5 dB discriminator performance, let's choose the best case of 6 dB for the LoRa receiver.
Figure 10
Now the destructive overlap zone is quite large. Even position MOB D, which was firmly within the range of DIGI A, can no longer discriminate DIGI A from DIGI B if both transmitters overlap, and so the packet will most likely be lost. Position MOB F is approaching the edge of not working. We also now see that the zones of always-successful reception are circles! Every position outside of the two circles can suffer from co-digipeater interference. It's almost non-intuitive that position MOB G (upper right) suffers from destructive interference, but it does!
Conclusion
Part of the reason we set up the Arizona LoRa network was to see exactly how overlapping coverage impacts link performance. There are mitigating factors - mobile path fade changes the RSS at a receiver - this can allow the native LoRa receiver processing to recover a signal that is momentarily less than 6 dB stronger. Remember, for legacy FM AFSK APRS, even a single bit lost can mean the loss of the entire frame. LoRa is at least an order of magnitude more robust in error correction than FM AFSK.
Figure 11
We've seen the impact of destructive overlap zones. Figure 11 shows the frame type distribution as seen from N7UV-44 at my QTH. I see regular CRC errors due to overlaps between distant digis with generally non-overlapping coverage that are only a few dB different in RSS. The decision to make frames shorter by increasing the over-the-air data rate has not only allowed shorter channel occupancy time and thus increased capacity, but also reduced the probability that two digis with overlapping coverage transmit at the same time. We've also worked to manage the density of digis over what typical FM APRS uses. That has helped to make the received signal difference that much greater, improving the receiver's ability to discriminate. Note that Figure 11 doesn't give a clue as to the overall channel occupancy time, only the the frame type distribution when the receiver is actively receiving.
The LoRa network in Arizona, now with Southern California, is demonstrating every day that high-speed LoRa works as well as or better than legacy FM AFSK APRS, and carries over well 4x the traffic load. Join us!
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Cheers and 73 - Jon N7UV