I’ve previously written about ultraslow radio for decentralized global digital communication, but since then I’ve read a bit more about the topic, including a little bit of the ample literature on amateur radio DX, QRP, and contesting.
Due to skywave propagation, hams using MF and HF radio routinely communicate 1000 km or more with transmit powers on the order of one watt (there’s a “thousand-miles-per-watt” award); under exceptional conditions, transmissions of 1000 km on 1 mW of transmitted power have been reported. Typical transmission modes include (very slow “QRSS”) CW and the WSJT modes, many of which are around one bit per second.
So now I see how to build infrastructure that permits global data communication at hundreds of kilobits per second when the ionosphere is favorable, without emitting a noticeable amount of radio interference, and without requiring more power than is easily available by energy harvesting. A global network of low-power kilometer-scale phased arrays can speak ultrawideband MF and HF to each other, but ultrawideband at higher frequencies internally and to nearby mobile radios.
A Wi-Fi card might emit 200 milliwatts, although the little FM radio transmitters you might plug into your MP3 player, legal since 2006 in the EU and longer in the US and Canada, are only about a microwatt, 10 nW in the US, 50 nW in the UK, 25 microwatts in Japan. The US allows 100 mW unlicensed narrowband AM radio transmitters, so I think 10 milliwatts per transmitter site ought to be reasonable.
In a memory-holed YouTube video, Naomi Wu recently reviewed the Ulefone Armor 3WT FRS cellphone, which includes a 2W FRS walkie-talkie. She reports that in Shenzhen she can get several blocks of range, which is to say, several hundred meters. FRS and GMRS radios commonly transmit at such powers; GMRS is permitted up to 50 watts, though WP says 1-5 watts is more common in practice, and FRS in the US was limited to 500 mW until 2017; FRS commonly gets a kilometer or so of range, though (again, WP says) tens of kilometers are possible “under exceptional conditions...such as hilltop to hilltop”. 3G mobile phones also transmit 2 W. So if there’s no regulatory or interference problem, it’s reasonable for even a handheld device to transmit at 1-2 watts. (Most cellphones are, I think, up to 1 watt.)
Handheld ferrite loopstick antennas are capable of transmitting and receiving MF signals like those used for AM radio, but their antenna efficiency is fairly low. A better approach for mobile stations is probably to use higher frequencies to connect handheld devices to large, fixed infrastructure like a long-distance phased array, which then handles the long-range communication. Still, these short-range links might be able to reach many kilometers. (LoRa at 915 MHz can reach 10 km in rural areas, though fewer km in cities; one-watt GSM cellphones can talk to a base station 35 km away, and a “timing advance limit” has been hacked into some GSM equipment to extend that range further.)
A handheld device is inevitably a point source of interference, with the unavoidable inverse-square interference pattern that implies. A kilometer-scale phased array is, by contrast, a diffuse source, so it can emit at a much higher power before it starts to become a nuisance to neighbors.
GPS receivers cost a few dollars and receive signals at -125 dBm or less; some can lock in a signal at -142 dBm, which is quite impressive considering that the thermal noise on a 2-MHz-wide GPS channel is about -111 dBm. They are made cheaper by the fact that they run at over 1 GHz, so they don’t need large antennas. Acquiring these signals is feasible because they are perfectly uncorrelated over long periods of time, like an LFSR. Ultrawideband techniques have the same virtue.
Modern impulse radio (“ultrawideband”) should be able to essentially eliminate interference with the nearly orthogonal narrowband signals conventionally used. A commercial AM radio station, for example, might transmit at 10 to 100 kW over a bandwidth of 20 kHz, on the order of 1 W/Hz. A 10mW impulse radio whose pulses are evenly spread across the whole medium-wave AM broadcast band from 526.5 kHz to 1606.5 kHz would average 9 nW/Hz, eight orders of magnitude quieter, easily below the noise floor, although it might become (faintly) audible if it were 30 dB higher in a particular compass direction because of (see below) phased-array directional transmission.
This 1080 kHz bandwidth gives a temporal precision of about a microsecond, suggesting a few hundred kilobits per second of possible transmission speed.
Transmitting over the shortwave band from 2.3 to 26.1 MHz would permit multi-megabit transmissions, though of course subject to ionospheric conditions; there used to be 500-kW Voice of America broadcasting on this band, though I’m not sure there still is, but Wikipedia tells me there are 1200-kilowatt shortwave broadcasters, and I think their bandwidth may be 10 kHz.
(Commercial FM radio typically also transmits at a few tens of kW, but it’s in the 87-105 MHz range, where there’s no significant ionosphere propagation.)
Chirping the transmitted pulses, like LoRa or chirped radar, would avoid the need for high peak-to-average power ratios that might otherwise pose a difficulty, and would also reduce the time-domain artifacts that would otherwise appear to unintentional wideband receivers. Straightforward chirping wouldn’t help to avoid narrowband receivers, though; if you were to chirp from 526.5 kHz up to 1606.5 kHz in 1.08 milliseconds, you’re only chirping 1 kHz per microsecond, so you only spend 20 microseconds in each 20-kHz-wide AM station. This would only attenuate the part of the impulsive noise added to AM above 50 kHz, which the humans can’t hear anyway.
You could imagine doing several simultaneous chirps, though, which might help more; one that sweeps from 526.5 kHz up to 548.1 kHz over that millisecond, while another sweeps from 548.1 kHz up to 569.7 kHz, and so on. Effectively each chirp would be a single AM station wide, and spread over the whole millisecond, thus strongly attenuating the parts of the impulse above about 1 kHz, making it considerably less audible. Presumably this waveform still retains the time-domain precision deriving from its >1MHz bandwidth.
A more effective way to reduce interference might be simply spreading the signal over a wider bandwidth by using shorter pulses. If the pulses were 30 ns instead of 1000 ns, for example, going up to 33 MHz instead of 1.5 MHz, you’d have 15 dB less power in any given station’s 20 kHz band, 0.3 nW/Hz, about 95 dB quieter than AM broadcasters --- 63 dB because of transmitting at 63 dB lower power, plus 32 dB because it’s spread across 17000 times as much bandwidth.
Directional transmission at MF (300 kHz to 3 MHz) and HF (3 to 30 MHz) would seem to require impractically large antennas: even 30 MHz is 10 meters, and 300 kHz is 1 km. However, phased-array transmission and reception from an antenna array distributed over a significant geographical area should be possible, and with practical numbers of transceivers (10 to 1000 transceivers) significant degrees of directionality should be possible; without understanding the math, I’m guessing it would be 10 to 30 dBi, with the additional advantage (for skywave propagation) that most of the energy would propagate horizontally. (My intuitive reasoning is that in the direction of the wave, all 1000 transmitters are in phase, so the amplitude is 1000 times higher than the wave from a single transmitter, while in other directions, it’s only 32 times higher, so it’s 32 times higher in the direction of transmission, which means 1000 times higher power.)
How would you coordinate a phased array of radio transceivers to transmit data? It’s a bit like the firing-squad problem in cellular automata; they can use lower-power, higher-bandwidth, higher-frequency local radio among themselves to compute precise relative geolocations, synchronize their clocks, and buffer up bits to be sent in a phased-array fashion, or after being received in a phased-array fashion. They could use, for example, the 1800 MHz GSM spectrum, or the 2.4 GHz unlicensed spectrum. Time-domain signaling across a GHz of bandwidth should permit baseline measurements with a precision of a few centimeters.
Of course the same phased-array correlation approach can be used for reception. Probably MIMO techniques to augment bandwidth are not directly applicable over such long distances due to diffraction.
However, such a phased array could easily transmit to several destinations at once, or receive from several senders at once. If there are multiple relay stations available, it may be possible to augment the point-to-point bandwidth between two phased arrays by relaying the information in parallel over geographically diverse routes, like Ethernet channel bonding.
For the diffraction limit to be better than 30 dBi, so the phased array is limited by the number of transmitters rather than the aperture, the diffraction beam divergence needs to be less than 4 pi/1000 steradians, very crudely, which I think means less than about 110 milliradians, 6 degrees. Suppose we’re using 1.220λ/D, the Airy limit for a circular aperture, as an approximation, and we use 1 MHz for λ: 300 m. So we want 1.220 300 m/D = 0.11, so D = 1.220 300 m / 0.11 = 3.3 km, like, a transmitter every 100 m. Or 10 km if we want to get all the way down to 300 kHz. Normally we’d worry about sidelobes from spreading the transmitters too far apart, but I think that problem disappears with ultrawideband signals, since the sidebands for all the different frequencies are in different places.
However, if the transceivers are all on the ground, which is nearly planar, we’re still going to have massive diffraction in the vertical direction, as our energy is spread across 30 degrees or more, even after half of it is reflected from the ground.
If your energy is spread evenly over 6 degrees, then after traveling a quarter of the way around Earth, what is left of it will be spread over some 700 km of width; this is perhaps 200 times the distance it was spread over originally, if the original phased array was 3.3 km, and of course it is also spread out vertically in a nonuniform way between the surface and the ionosphere. 200 times is a surprisingly modest -23 dB, although of course that’s not the attenuation from the transmitter; it’s the attenuation from the open spaces in the tens of meters between the transmitters to the place a quarter of the way around the world.
It might be necessary to confine the beam to a narrower horizontal angle than 6 degrees to compensate for the unavoidable vertical spread.
Running transceivers on harvested RF energy may permit embedding them in concrete or underground, or hanging them from trees. But it probably would not permit average transmitted power of 10 milliwatts or more; 100 microwatts might be more reasonable.
Passive reflection by disconnecting an energy-harvesting antenna might be the most efficient way to produce pulses, and might also be more regulatorily acceptable. In urban areas, energy-harvesting researchers have found 1 to 100 microwatts per square centimeter in each of several different bands, including AM radio, digital TV, and especially the GSM and 3G bands. A simple calculation suggests that an MF AM radio loop antenna enclosing 10 m^2 at 2 km from a 50 kW broadcasting station intercepts about 10 m^2 50 kW / 4 pi (2 km)^2 = 10 mW, although probably in practice the number is somewhat larger. Such an antenna might be illuminated by several such stations. By selectively making the antenna open-circuit at certain moments, those 10 mW will be reflected instead of absorbed at those moments, across all the frequencies that efficiently couple to the antenna.
Such passive reflection avoids the necessity to convert RF energy to stored voltage and then back again, with its attendant losses of probably some 20 dB, and since it does not transmit any energy, it might avoid regulatory entanglements; moreover it will not produce any energy on any frequencies that are not already in use. However, it makes it impossible to harvest energy on one band (such as GSM) and transmit it on another, and it makes chirping impossible. For communication on higher frequencies, antenna directivity might also be relevant; your antenna system might reasonably be organized to reflect the incoming illumination toward the destination.
Worth noting is that 10 milliwatts of full sunlight is 0.1 cm2, or about 0.7 cm2 of a commonplace solar cell. So even a few square centimeters of PV cells would provide much more power on average than all this RF energy-harvesting stuff, even in areas brightly illuminated by cellphone towers. They might be able to produce alternating magnetic fields that transfer power wirelessly to a larger, less visible transceiver, perhaps embedded in a wall.
Lower-duty-cycle communication might reduce the degree of interference with other systems, and would surely reduce the energy transmitted per bit. As I understand it, there’s no floor on energy transmitted per bit with a given noise floor, if you transmit slowly enough. If you’re doing pulse-position modulation with 100-nanosecond timeslots, then you can transmit one bit in 2 timeslots, two bits in 4 timeslots, three bits in 8 timeslots, etc.; at some point your timing synchronization between the transmitter and receiver will start to suffer, but a regular quartz crystal has drift of about 10 ppm, while a temperature-compensated crystal oscillator (TCXO) is typically around 1 ppm. So you could imagine, for example, transmitting one pulse every 65536 timeslots (6.55 ms) to represent a 16-bit symbol. To get the same error probability per symbol, you’d need to send it at a higher amplitude than if you were sending one pulse every other timeslot, but I think only something like 6 times higher, assuming AWGN. (XXX make this rigorous, or at least do some experiments)
If that’s correct, you get about 5x the energy efficiency per bit by using such a low-duty-cycle system, but you transmit 4096 times slower. However, it might increase interference with existing licensed uses of the spectrum, for example introducing more audible impulsive noise into AM radio.
Low-duty-cycle communication has an interesting relationship with chirping, since the effect of chirping is precisely to extend the duty cycle. On one hand, if the underlying signal you’re trying to transmit isn’t low-duty-cycle, chirping it won’t do any good --- your chirps will overlap, and so you won’t get the PAPR improvement you normally get from chirping. On the other hand, that PAPR is precisely what allows you to leave your radio turned off most of the time and save power, so if you “improve” it too far, you will exceed your power budget.
Of course you want to use error-correction coding so that no one pulse is strong enough to be received clearly at the destination; you want the pulses to be tens of dB below the noise floor so that substantial coding gain is needed to detect them, even near the source. The best way to ensure non-interference is non-detectability.
It’s already commonplace for QRP hams to reach 1 bit per second transmitting 1000 km on 1 watt. Conservatively, phased-array transmission should buy you 20 dB, while phased-array reception should buy you another 20 dB. Supposing that those hams are not in the bandwidth-limited regime of the Shannon limit, using ultrawideband may not buy you any extra bandwidth, just keep you from slamming into a narrowband bandwidth ceiling. 1000 transmitters at 10 mW each works out to 10 watts rather than 1 watt, giving you another 10 dB, for a total of 50 dB, or 100 kilobaud, per phased-array-to-phased-array link. If you can talk to ten phased arrays at once, that should give you a megabaud. But if the phased arrays miraculously work out to buy you 30 dB instead of 20, you’d have 100 megabaud.
Earth-moon-earth or “moonbounce” communication is already commonplace among hams and sometimes is high enough bandwidth to hold voice conversations over. Doing the equivalent using passive MEO satellites would require more precise and dynamic tracking, to the point that it’s probably only practical at microwave frequencies, but would suffer the d4 loss of the moonbounce path over a much shorter distance, and still would cover most of a terrestrial hemisphere. LEO satellites have an even shorter path loss and larger cross-section, but only cover a thousand km or so. Meteor-trail communication is an existing well-known technique for high-bandwidth opportunistic communication at a similar range. And the ocean’s SOFAR channel, though it has only a few kHz of bandwidth, has better attenuation characteristics, more consistency, and lower noise than the ionosphere route.