There is also an antenna issue with regards to resonance. If the signal spreads to wide, the antenna and associated tuning equipment are going to suffer RF losses, reflections and likely heating.

That is why the 17khz naval CW station has a limitation on cw speed.

The agency running the German equivalent to WWVB, DCF77, has looked into piggybacking an emergency warning signal onto unused bits of the time signal:

https://www.ptb.de/cms/en/presseaktuelles/journals-magazines...

These days though, a more popular idea seem to be to piggy back onto GNSS signals, which are also broadly available (no idea how well they compare in practice to low frequency time beacons), and for which importantly many mobile devices already have a receiver built-in:

https://defence-industry-space.ec.europa.eu/galileo-emergenc...

The US also already has pretty good coverage with the NOAA weather radio system, which supports a digital, zone-based alerting system for both weather and other hazards. That has the big advantage of being regionally steerable.

In fact, I can't imagine many events other than weather (which is usually localized) that warrant such a low-entropy signal on a nationwide basis, and everything I can imagine has very limited actionability. ("Asteroid inbound, prepare to hide in the basement for a few thousand years"?)

> a more popular idea seem to be to piggy back onto GNSS signals

Don’t all GNSS systems provide a highly accurate time signal (maybe needed for computing the distance to satellite)? I know GPS does at least.

Yes, the GPS signal in a way is primarily a very precise time signal :) It’s a TDOA system!

I was referring to piggying back an emergency signal onto that!

Yes, it is needed to compute a location. More accurate time = more accurate location.

As mentioned somewhere else, these time signals also carry information about DST and adapt for leap seconds, both of which GPS doesn't do as far as I know. I remember that earlier versions of Android always set the phone clock to GPS which was then off by a number of seconds.

GPS navigation messages do include information about leap seconds and other stuff necessary to convert between GPS time and UTC. See GPS Interface Specification IS-GPS-200, 30.3.3.6.2 - UTC and GPS Time

> These days though, a more popular idea seem to be to piggy back onto GNSS signals, which are also broadly available (no idea how well they compare in practice to low frequency time beacons), and for which importantly many mobile devices already have a receiver built-in

GPS chips are very very power intensive as the compute power involved to decode a signal out of something that would normally be way below the noise threshold is still very high, despite some two decades worth of optimization. And they're pretty useless outside of direct line of sight towards the sky.

> In fact, I can't imagine many events other than weather (which is usually localized) that warrant such a low-entropy signal on a nationwide basis, and everything I can imagine has very limited actionability. ("Asteroid inbound, prepare to hide in the basement for a few thousand years"?)

It's a trigger signal for a low-power receiver that can then turn on a higher-bandwidth (and thus, higher power) device to detect what is actually going on. Say you're a country at war like Ukraine - have the "emergency bit" on nationwide during Russian air raids so that receivers can listen for area-specific signals and blare horns if affected.

No matter what, we have to prepare for war, and that includes having robust technology that is hard to take out on the sender side (which cellphone stations aren't, they're easy targets in a cyber war!) and, most importantly, can be stored in everyone's garden shed and live on a single battery for years.

>Say you're a country at war like Ukraine - have the "emergency bit" on nationwide during Russian air raids so that receivers can listen for area-specific signals and blare horns if affected.

And what would prevent Russia from continuously broadcasting this emergency bit to cause chaos?

> And what would prevent Russia from continuously broadcasting this emergency bit to cause chaos?

So what, all that would do in my scenario is drain the batteries of the civilian populations' alarms a bit faster as they'd keep their more power-intensive CPU awake.

DCF77 is a natural for this because it already includes a phase-modulated signal (as well as the 1bps amplitude-modulation). At the moment it's a 512-bit pseudo random sequence, but could obviously carry a data stream instead.

If we could have have 58 kHz to 62, that's 4 kHz. Enough for a 300 baud modem to work, which is 300 times faster than 1 bit per second.

We need to know the signal to noise ratio. Not just the bandwidth. 4khz is enough to carry much higher rates on residential phone lines...

Alternatively, it would be fun to see how much noise you can put into the signal and still decode it. Maybe using the knowledge of its structure, kind of how (I believe?) GPS reception works.

GPS is spread spectrum. It's modulated using a pseudo random sequence and then demodulated using the same sequence. All the same theory still applies but it's just a different way of using the spectrum, instead of a fixed band the bandwidth is "spread" across a broader band in a way that allows all these different signals to be multiplexed. Specifically with GPS IIRC the phase of the pseudo random sequence is also conveying timing information because of how it relates to the precise clock on the satellites. Spread spectrum can be a little more resilient to certain kinds of noise, e.g. if you have noise just at one frequency now you've reduced the impact of that noise.

It's fun with software radio to take a long recording of a chunk of spectrum and do the fourier transform and plot it. There will be clear lines indicating carriers, even ones too faint to be heard over the static. Software can do the same trick for decoding a modulation (at the expense of latency in decoding). Modern tech allows a further neat hack here. If you have a very stable local clock (which any modern digital device does) you can correct for frequency errors in the transmission. Once the clocks are synced, you know exactly when the next symbol should be. And you know how much the transmitter frequency as actually received, is varying from what it should be. And since a convolutional coding with a pseudorandom number might be used, you also know what the next symbol will be (only a small number are valid in any state). With all that together, in effect, the decoder knows when and where the signal will be, and at least part of what it will look like, before it receives it. So it can be compared with what is actually received, making it possible to pick it up well below the noise floor. Just add some error correcting codes for robustness.

Amateurs have successfully communicated data between California and New Zealand on longwave using only 1 watt of radiated power at the transmitter. (But the baudrate for that is measured in hours per bit. And the receiving antenna was considerable.)

Could we have something like an AM broadcast, but then the receiver “upsampling” the data? Maybe using some ML?

For example, if you have an AM channel that always transmits some song from a list, then you might not even need to receive the whole song. Or maybe you can have a model that’s good at upsampling those types of songs/data?

This is pretty much what audio compression, like a MP3 file, does: it figures out how to encode perceptually-identical (or close) stuff more densely and remove redundant information.

Every time you listen to "HD Radio" you're doing exactly this.

Yes, but modern ML techniques (particularly with neural networks) are much more impressive at recovering signal with even less information than things like MP3. An example of this in the visual domain is upscaling. So it’s not a bad question at all.

Sure-- as we've discussed endlessly here: compression and ML are really very close cousins. I never said it was a bad question.

You can even win a prize for that https://en.m.wikipedia.org/wiki/Hutter_Prize.

I extremely dislike the Hutter Prize. I think it's generally agreed that intelligence compresses the model better & therefore it's reasonable to assume that the better the compression, the more intelligence you have (at least for now where we are with AI, this seems to be a roughly reasonable assumption). My problem with the Hutter prize is that it makes the leap to say that lossless compression is this when everything about AI is choosing how much error you're willing to tolerate. In other words, intelligence is linked to lossy compression, not lossless - a competition for lossless compression doesn't do anything more than get us better lossless compressors / decompressors.

AM broadcast uses a "band" around the carrier. Whatever tricks you use Shannon's law is going to determine the upper limit of how much data you can carry which depends on the bandwidth and the signal to noise ratio. ML makes no difference from a theoretical perspective. Compression just reduces the bandwidth you'll need assuming your data compresses (with whatever method you choose, ML can be part of that)...

I guess my usual experience is that AM transmissions sound pretty horrible, especially compared to FM

So, my question is more like, can we just upgrade the equipment and keep the channels? And can AM be used more like for signal/indexing rather than full data dump? (eg. instead of transmitting the whole song, transmitting just an id of the song)

AM sounds bad because it’s amplitude modulated. So variation in amplitude (i.e. signal strength) results in noise when decoding. FM however is not sensitive to this issue because its frequency modulated - slight variations in signal strength have no effect on the encoded signal.

And yes, we can always upgrade the equipment. That’s what we did when we transitioned TV to digital signals and FM to digital FM - we reserved some bandwidth for over-the-air while freeing up the rest to be used for other purposes. But it’s an expensive proposition and one that happens rarely (in fact those are the only two times I’m aware of it, they happened at basically the same time, took forever, & there was insane opposition to it).

The limit is Shannon's law which depends on bandwidth and signal to noise. A more advanced modulation technique can get more "information" through up to that limit. A song for this matter can just be considered information as well. So the answer is almost certainly yes, one can get more out of existing channels by upgrading the equipment assuming the current equipment doesn't approach the theoretical limit which is almost certainly the case for this "old" technology we're talking about.

An FM radio channel has a bandwidth of 200Khz. AM radio has a bandwidth of of 10Khz. That's a big part of the reason why AM sounds horrible compared to FM. The way noise impacts AM and FM is also different, especially given human perception. IIRC both these methods were picked for practical reasons not necessarily any optimal criteria. AM is fairly crude, there's only so much you can change the amplitude for any practical purpose. Changing the frequency makes it easier to use more bandwidth so it was a natural evolution. Depending on how you're modulating the amplitude (the naive old school radio IIRC is just using the signal you're transmitting to modulate it) you can make the bandwidth larger or smaller. Random e.g. something like Ethernet on copper can be viewed as a very very fast, high bandwidth, AM. All these things boil down to the same Shannon law just with somewhat different efficiencies depending on how well you can control the frequency domain.

This problem of cramming the most bits into a given channel is something people have been working on for a long time. Some coverage of this here: https://en.wikipedia.org/wiki/Modulation

That's how we got from 300bps modems to 56k modems over the same phone lines way back and how we push more out of radio spectrum today.

> An FM radio channel has a bandwidth of 200Khz.

How gratuitous with modern tech. FM needs tens of decibels of signal to noise ratio to sound reasonable, especially if you want stereo. But a digital signal could fit perfect audio into that range at less than one bit per Hz, which would let it tolerate radio noise that's as strong as the actual signal.

You might be interested in Digital Radio Mondiale: https://en.wikipedia.org/wiki/Digital_Radio_Mondiale

One thing you forgot to mention is that in contrast to an FM receiver, or even more a digital one, AM receivers are incredibly easy to build even with very basic "household items", which I believe is at least part of the motivation to provide emergency services and similar broadcasts over AM.