Interesting read. I’m already familiar with these concepts, so I’m not really the target audience. I think mentioning (and showing) some antenna radiation patterns would help the viewer. The transceivers are not point sources. Their 3D orientation matters quite a lot, especially when multipath is a dominant factor (ie inside).
Also don’t be fooled by the last sentence. There is no way to cheat Shannon’s limit. These are all just tricks to try to get closer to Shannon’s limit. TANSTAAFL. You need lots of transistors to implement these complicated tricks and you are always limited by the channel (the signal from transmitter to receiver, including all antenna, multipath, noise, and circuitry effects).
Your point is a good one, and I don’t think you should get down-voted. I’ve seen many people appeal to Shannon’s law for SINGLE channel as an argument to why things like MIMO or Starlink are limited to low amounts of bandwidth. More channels is absolutely an important way to get around the “but there’s only so much bandwidth” argument, and by increasing number of channels (and increasing size of reciever and transmitter), you absolutely can just keep increasing throughput for the same frequency bandwidth allocation.
The case of StarLink (in difference to (indoor) 802.11n/ac) won't give you more than polarization duplex (capped at 2x, in practice you'd get up to (iirc) ~30dB isolation) for any individual point-to-point connection. Yes, including the satellite <=> ground-facility "backhaul".
Theoretically it _should_ be possible to get like 10x bandwidth via spatial MIMO when using <3μm (likely <1μm) wavelengths, but that might require optical heterodyne detection to get the MIMO streams separated from another in the speckle pattern the atmosphere caused.
I'd like to read that paper about optical heterodyne detection spatial MIMO for the link to/from a satellite in an 200~1000km orbit.
One terminal (which has beamforming capability on both ends with hundreds of elements) can connect to multiple satellites with the same frequency band.
Oh sure, that's a massive effect. It's just that for a single p2p link, there'd be at most minimal benefit from MIMO. As soon as there are either multiple satellites or multiple user terminals (or dare both), i'd expect nothing worse than the bandwidth scaling with the square root of the antenna count.
Not sure what you mean by that, but Shannon's law applies with MIMO as much as anything else. A single channel is still limited by the Shannon capacity, but you can do tricks to constructively interfere on different paths, or use multiple antennas to create multiple new channels.
But you get diminishing returns from around 1bit/s/Hz if you just turn up the power. Your energy efficiency will go down, a lot. The more you can get spatial multiplexing to keep you away from that border, the less energy you'd need to dump into the air. And as computing get's cheaper, that energy tradeoff moves more and more towards MIMO. Back in 2005 we didn't have a need to think of 8x8 MIMO (Laptop <=> AP). Now it becomes realistic, so we got it specified and standardized in 802.11ac to allow everyone to join in the testing/experimental setups.
As an aspiring speculative-fiction author always on the hunt for a new premise, I’d love to know, what would be possible if we could “cheat entropy” in this sense?
(This doesn’t have to be possible in our universe; posit a universe where it is possible—maybe one inside a Matrix-like simulation inside our own universe, if you like.)
The statement that we cannot cheat entropy is basically a statement that the volume of an evolving quantum system (in phase space) stays constant over time, but gets more complex.
Entropy increases because our maps of that volume increase in volume, because we can't follow all the little eddies and crinulations.
So, okay. Two options for you: Maybe we can follow it, because the universe turns out to be more predictable than expected. This is basically a statement that chaos theory is wrong, and entropy isn't increasing as fast as our current understanding of the rules say.
Alternately, maybe the volume of the actual phase space is decreasing over time. This would allow the volume of our estimates to stay constant despite increasing complexity, but breaks linearity and suggests the universe might be going away.
While information theory entropy and physical entropy are not identical concepts, they are coupled. I recommend Isaac Asmiov’s “The Last Question” if you haven’t read it already.
And heck, things like forward error correction and 5/4 encoding are giving up on getting anywhere near the Shannon limit and just trying to boost the average and worst case behavior high enough that people don’t throw their equipment away. If you do both and tcp/ip over the top you’re creeping up on 1/3 of the channel theoretical bandwidth just to make sure something, anything, makes it through.
Does Wi-Fi use the same frequency for a transmitter and receiver? In general, this statement is not true:
"Relatedly, even if there is no explicit beamforming feedback, in theory you can calculate the phase differences by listening to the signals from the remote end on each of your router's antennas. Because the signals should be following exactly the same path in both directions, you can guess what phase difference your signal arrived with by seeing which difference his signal came back with, and compensate accordingly."
But maybe the frequencies are close enough such that the channel matches.
I think it helps to think about the problem from a multiparty standpoint. On wired ethernet the simplest case is one wire going between two machines. In coax everyone shares one channel and so RX and TX have to interlace instead of overlap. You go to twisted pair and it’s unambiguous that full duplex is available and desirable.
But, now you cant just wire three machines together, because everyone’s TX has to connect to your RX and vice versa and how would that work? How about with fifty machines. You’d need some sort of star arrangement, or a little box in the middle to juggle every outbound to every inbound.
With wireless there is no box in the middle (except, very loosely, in two-tier mesh networks where infrastructure nodes talk on two channels and leaf nodes on one), so it’s really like wireless coax with the occasional router. If you want more bandwidth you could run several channels everywhere, or segment fewer machines into separate channels and connect them with more routers.
You actually can overlap RX and TX bandwidth on coax, though you need magic-tees and very good impedance matching in either end, and of course constant impedance cable. That limits it to about 100 Mbps, but you can buy the (magnetic) magic tees to do it. These are specifically for replacing analog video cameras with IP over the existing coax.
Is there any data on real-world performance improvement from beamforming with consumer gear? I know anecdotally 802.11ac is way better than 802.11n (much less .11g) but there's so many related improvements in it that I don't understand how helpful the beamforming part is.
In our hackerspace, using 3 antennas in an ubiquity "UFO" danling in front of a shelf, communicating 2~3m to a thinkpad with afaik 2 antennas, using an 80MHz 5GHz 802.11ac configuration, we get consistently >500Mbit/s (iirc hovering at roughly 600Mbit/s) (unidirectional) to the NAS (1000BASE-T wiring, 1-2 switches in-between) when mounted via NFS. A single stream can't get more than ~420Mbit/s _in the lab_.
One proxy for the benefit of beamforming might be the the available modulation types and coding rates in the various wifi specs.
The wikipedia articles on 802.11g, .11n, and .11ac have tables showing the nominal data rate for different MCS indicies (modulation and coding scheme).
Notably, 11n adds a 5/6 coding rate to 64 QAM modulation (on top of 2/3 and 3/4 found in 11g). In addition to that, 11ac adds another two rates with 256 QAM (3/4 and 5/6).
Since higher modulation indicies are generally only useful at higher S/N ratios, you might argue some combination of the following:
1. These higher rates exist only to boost the advertised speed of 802.11 products, and are useless in real-world scenarios
2. These rates are intended to be used when sitting very close to an 802.11 AP
3. These rates are intended to be used with directional antennas
4. These rates are useful in the real world and made possible by the antenna gain provided by beamforming.
If you believe the last one, then the benefit is around 30% to 50% more throughput (the data rate MCS-9 is 1.48x MCS-6). That's not counting the benefit you get from having multiple spatial streams, so the benefit is available in a scenario where the AP has multiple antennas and the devices has only one.
I can't point you to any study or data, but I've worked around WiFi enough to know that beamforming is one of the first optimizations performed in multi antenna scenarios, mainly because of how easy it is to do. A 3dB bump in SNR for a 2x1 antenna configuration might allow you to transmit at the next modulation depth (QAM16 vs QPSK for instance). That will increase throughput and reduce the retry rate. At low SNRs it can increase router range.
Also don’t be fooled by the last sentence. There is no way to cheat Shannon’s limit. These are all just tricks to try to get closer to Shannon’s limit. TANSTAAFL. You need lots of transistors to implement these complicated tricks and you are always limited by the channel (the signal from transmitter to receiver, including all antenna, multipath, noise, and circuitry effects).
The case of StarLink (in difference to (indoor) 802.11n/ac) won't give you more than polarization duplex (capped at 2x, in practice you'd get up to (iirc) ~30dB isolation) for any individual point-to-point connection. Yes, including the satellite <=> ground-facility "backhaul".
Theoretically it _should_ be possible to get like 10x bandwidth via spatial MIMO when using <3μm (likely <1μm) wavelengths, but that might require optical heterodyne detection to get the MIMO streams separated from another in the speckle pattern the atmosphere caused.
I'd like to read that paper about optical heterodyne detection spatial MIMO for the link to/from a satellite in an 200~1000km orbit.
But you get diminishing returns from around 1bit/s/Hz if you just turn up the power. Your energy efficiency will go down, a lot. The more you can get spatial multiplexing to keep you away from that border, the less energy you'd need to dump into the air. And as computing get's cheaper, that energy tradeoff moves more and more towards MIMO. Back in 2005 we didn't have a need to think of 8x8 MIMO (Laptop <=> AP). Now it becomes realistic, so we got it specified and standardized in 802.11ac to allow everyone to join in the testing/experimental setups.
(This doesn’t have to be possible in our universe; posit a universe where it is possible—maybe one inside a Matrix-like simulation inside our own universe, if you like.)
The statement that we cannot cheat entropy is basically a statement that the volume of an evolving quantum system (in phase space) stays constant over time, but gets more complex.
Entropy increases because our maps of that volume increase in volume, because we can't follow all the little eddies and crinulations.
So, okay. Two options for you: Maybe we can follow it, because the universe turns out to be more predictable than expected. This is basically a statement that chaos theory is wrong, and entropy isn't increasing as fast as our current understanding of the rules say.
Alternately, maybe the volume of the actual phase space is decreasing over time. This would allow the volume of our estimates to stay constant despite increasing complexity, but breaks linearity and suggests the universe might be going away.
https://www.microwaves101.com/encyclopedias/mimo-an-historic...
"Relatedly, even if there is no explicit beamforming feedback, in theory you can calculate the phase differences by listening to the signals from the remote end on each of your router's antennas. Because the signals should be following exactly the same path in both directions, you can guess what phase difference your signal arrived with by seeing which difference his signal came back with, and compensate accordingly."
But maybe the frequencies are close enough such that the channel matches.
But, now you cant just wire three machines together, because everyone’s TX has to connect to your RX and vice versa and how would that work? How about with fifty machines. You’d need some sort of star arrangement, or a little box in the middle to juggle every outbound to every inbound.
With wireless there is no box in the middle (except, very loosely, in two-tier mesh networks where infrastructure nodes talk on two channels and leaf nodes on one), so it’s really like wireless coax with the occasional router. If you want more bandwidth you could run several channels everywhere, or segment fewer machines into separate channels and connect them with more routers.
Yes
One proxy for the benefit of beamforming might be the the available modulation types and coding rates in the various wifi specs.
The wikipedia articles on 802.11g, .11n, and .11ac have tables showing the nominal data rate for different MCS indicies (modulation and coding scheme).
Notably, 11n adds a 5/6 coding rate to 64 QAM modulation (on top of 2/3 and 3/4 found in 11g). In addition to that, 11ac adds another two rates with 256 QAM (3/4 and 5/6).
Since higher modulation indicies are generally only useful at higher S/N ratios, you might argue some combination of the following:
1. These higher rates exist only to boost the advertised speed of 802.11 products, and are useless in real-world scenarios 2. These rates are intended to be used when sitting very close to an 802.11 AP 3. These rates are intended to be used with directional antennas 4. These rates are useful in the real world and made possible by the antenna gain provided by beamforming.
If you believe the last one, then the benefit is around 30% to 50% more throughput (the data rate MCS-9 is 1.48x MCS-6). That's not counting the benefit you get from having multiple spatial streams, so the benefit is available in a scenario where the AP has multiple antennas and the devices has only one.