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It’s not immediately clear that Shannon’s theorem is a good point of comparison here, since it’s only recently that coding schemes have really approached the Shannon limits, and FM and AM do not use these.

Even if one does assume a Shannon-perfect coding scheme, as the noise ratio gets greater the benefits of spreading a signal across a higher bandwidth fades. Furthermore, most coding schemes hit their maximum inefficiency as the signal to noise ratio decreases and messages start to be too garbled to be well decoded.

I’d additionally note that folks get near the Shannon noise limit _through_ ‘magic noise rejection’ (aka turbo and ldpc codes). It’s therefore not obvious that FM isn’t gaining clarity due to a noise rejection mechanic. The ‘capture effect’ is well described as an interference reducing mechanism.

Empirically, radio manufacturers who do produce sophisticated long range radio usually advertise a longer range when spreading available power across a narrower rather than wider bandwidth.

You are applying Shannon theorem incorrectly. Both AM and FM modulations are nowhere even remotely close to using their bandwidth with 100% efficiency, due to technology costs, and the difference in modulation is crucial. The article is correct and the mathematical models of AM and FM are well understood since decades.

Where did I say AM and FM are close to 100% efficiency?

I was only replying to an obviously incorrect statement that by using more bandwidth you decrease SNR. If it were the case, Shannon theorem would not work.

It doesn’t matter how close to the limit your encoding is, whether it is 20% or 99% the relationship between the bandwidth, noise floor and how much data you can send stays the same - by increasing bandwidth you can usually send considerably more information even if your encoding is poor. Which in translates to either a wider useful bandwidth or lower noise floor or any combination of both.

A trivial thought experiment to illustrate this: For any analog encoding, if I double the transmission bandwidth by encoding the same signal over 2 channels instead of one, I can average the output signal coming out the receivers and get better SNR than using one channel and one receiver. That works regardless of AM, FM or whatever fancy encoding you could use.

> A trivial thought experiment..

That's not how this works. That's not how any of this works. Averaging a high SNR channel with a low SNR channel is likely to produce something less good than the high SNR channel. Could you get an improvement over the high SNR channel? Yes, and the limit of the improvement is related to the SNR of each and averaging the signals won't get you anywhere near that.

Averaging two noisy signals increases SNR. That’s not even a thought experiment, that’s a reality. This is a technique used by probably all modern smartphone cameras to do night photos, as well as a common technique used by astrophotographers. Instead of taking one picture, you take a series of pictures and then align them and average. This improves SNR dramatically. A very long time ago we used this technique to get razor sharp, low noise pictures of the Moon at 3k x 3k resolution using… a cheap VGA internet camera: https://astronet.pl/wydarzenia/n2309/ Note that cameras at those times were barely capable of doing videoconferencing in artificial evening light - what you saw was mostly noise. Those sensors were really, really terrible.

What you seem to be missing is the fact we’re talking here about transferring the same fixed bandwidth signal over a wider channel, not transferring a wider bandwidth signal over a wider channel.

// edit: just noticed someone else gave another nice application of this phenomenon: GPS

No, that's one time varying signal.

Let's take it to the limit:

Signal0: infinite SNR. Signal1: anything less.

I just don't see how the output of averaging these would improve over Signal0. I don't think it can.

They're thinking about when you sample from the same noise distribution, averaging gives an unbiased estimator of the mean. But when you know one SNR is higher than the other, maybe this doesn't hold? But maybe if you transform the distributions to look the same, thus taking a weighted average? I'm not sure.

It does hold, it is just weaker. You can improve the SNR of a better signal by adding another signal with worse SNR to it. But you need to normalize the signals the way their noise floors are the same amplitude before addition.

We’re not talking about signals with different SNRs. Where did you get the assumption from?

> This is a technique used by probably all modern smartphone cameras to do night photos, as well as a common technique used by astrophotographers...

I think this is a lot simpler because each of your pixels is assumed to have a single, correct DC value. This doesn't hold for a time varying signal like AM/FM.

If I send the same audio over 2 or more parallel radio channels, that’s essentially the same as taking multiple shots of the same subject. Substitute a pixel with an audio sample. The transmission noise being uncorrelated between channels will average out.

There are notable differences between radio and imagery that might explain why it might be a tricky analogy:

An image is quantized into pixels. A camera pixel is a receiver for a specific wavelength, subjected primarily to internal wideband thermal noise during the read-out process. Each final output pixel is averaged both in time (exposure and stacking) and space (debayer and noise reduction), with the final single being singular amplitudes per location.

An AM audio signal is a single wideband receiver subjected to wideband noise. Or, if viewed differently, a series of quantized frequency receivers each subject to a matching noise frequency. The sampling is in the frequency domain, but the final signal captured is is the amplitude variance over time for each frequency, responsible for a single audio frequency.

But yes, your underlying point stands: A theoretical AM receiver that demodulated repeated signals independently and correctly averaged their outputs might gain better wideband noise rejection. Better, but not good, and at a cost of complexity approaching that of better modulations.

Well, yes and no. It's a bit more complex than just taking the numbers from Shannon-Hartley, but I admit that my original description was at best lacking, so thank you for pointing that out.

Shannon-Hartley describes that the theoretical information capacity of a signal given a bandwidth and an SNR. Doubling bandwidth halves your SNR (received noise increases, received signal does not), in turn reducing the bits gained per unit of bandwidth. At very high SNR, doubling bandwidth almost doubles capacity, but as SNR goes down, the benefit of additional bandwidth levels off until bandwidth no longer has any effect.

However, this provides the number achievable by a perfect modulation scheme using all available bandwidth and signal strength. AM and FM are both incredibly inefficient, and more importantly have very different reactions to noise - something Shannon-Hartley does not concern itself with.

With truly random noise, FM and AM noise both scale based on noise amplitude as you say. In AM, all noise overlapping with the band is played back verbatim, whereas in FM only the noise causing frequency variations in the carrier wave have any effect on the signal, and end up with a non-linear response to noise.

However, we do not deal with purely white noise, and FM has far superior handling of non-random noise. In order to have any effect, it need to either induce frequency shifts to the carrier wave, or have enough power to cause the interference to be captured instead. There's also the far higher power efficiency, as FM puts all its power into the signal, whereas traditional AM puts most of it into a useless carrier and wastes half the remaining power on the redundant sideband (yes, SSB is a thing). These were certainly also factors in FMs demise.

A simpler means to remove bandwidth from the equation would be to compare with a narrow-band FM transmission, or by multiplying the input waveform for an AM transmitter by some factor to fill the bandwidth. I believe FM should still handily beat it at least above its threshold. I don't see anyone giving exact numbers of this though, so I guess it could be a fun SDR project for someone wanting to prove either point. :)

(Neither AM nor FM is of anything but historic value at this point - their only redeeming quality is discrete circuit simplicity if you need to MacGyver one out of shoelace and bubblegum, but that's it.)

> …traditional AM puts most of it into a useless carrier and wastes half the remaining power on the redundant sideband.

I had not thought about this before, and I have no intuition as to what the answer is, but does the redundant sideband have any effect, positive or negative, on noise rejection?

Currently? It provides no benefit and depending on receiver might even be negative, but if an AM receiver was designed to demodulate the sidebands independently and average their output might indeed gain slightly better noise rejection than using just one sideband. That is the idea being suggested by the person talking about a stacked image analogy.

The first step to improving AM (while making the receiver more complex) was removing the carrier wave, which is responsible for most of the transmitted energy (Double-sideband reduced carrier modulation, or DSB-SC). Then, to improve efficiency further without increasing receiver complexity too much, the second sideband is removed (Single-sideband suppressed carrier, SSB-SC - commonly just SSB).

The only benefit of traditional AM is transmitter and receiver simplicity. If you start increasing the complexity, there is no longer any point to using it.

self-nit: I wrote Double-sideband reduced carrier modulation, which is DSB-RC and only reduces the carrier. Double-sideband suppressed carrier modulation is what DSB-RC stands for, which removes the carrier.

"Shannon theorem disagrees with you. The wider the channel, the MORE noise you can tolerate when transmitting signal at a given data rate."

I've spent a lot of time on the development of broadcast-quality FM exciters (as I've posted on HN in the past) but I'm not go to debate the disadvantages/advantages of FM versus AM in depth as most points have already been covered in other posts, I'll just add this:

The quality of AM can be remarkably good if it's engineered with care. The math and engineering tell us that, and excellent results can be and are achieved in practice (as a longtime FM-er I say that about AM as it's just fact)!

The reason why AM has a bad reputation is it's history and background: AM broadcast and other shortwave (3-30MHz) bands are much more prone to impulse and atmospheric noise than VHF and up. Also, the historical nature of RF amp design and detection never put its primary focus on the linearity of RF/IF amps, etc. (good linearity is easily achievable these days).

My primarily reason for responding to this part of your post is to point out that when receiving AM signals one can take excellent advantage of using a wider bandwidth than the actual spectrum occupied by the modulation products.

Unfortunately, most of us don't know or have forgotten about the Lamb Noise Silencer circuit which uses a wider bandwidth signal to gate out impulse noise.

Here, two IF amplifiers [or one especially modified] are employed. The main IF uses the required (narrow) channel bandwidth and the second IF uses a wider bandwidth. Shannon et al tell us the wider signal can arrive at the detector before the narrow BW signal and thus can be used gate out noise in the latter stages and or detector.

In operation a properly designed Lamb Noise Silencer is remarkably effective in reducing AM static etc.

Whilst never used as a broadcast service, I'd posit that if AM with say 20Hz-20kHz audio were put into the existing FM spectrum (88-108MHz) with its lower AM noise background together with receivers that used the Lamb circuit then AM would essentially be indistinguishable in quality from the existing FM service. In fact, it could be even better with audio reaching 20kHz [extra 5kHz] and this could be achieved with a much better utilization of the spectrum (with AM's inherently lower channel bandwidth)—many more stations could be added to the band.

Of course, that would have been impractical back 80 or so years ago when the FM band was conceived for reasons that in the days of tubes the required local oscillator stability would have been very difficult to achieve (but a non issue these days).

Sometimes, we overlook the fact that our predecessors have already been there, thought about and have done these things.