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I've found all sorts of info concerning digital modes, sound samples, spectrum samples, but nobody ever cites what speed a given digital mode can reach.

Could anyone tell me more about that, or point me somewhere where I can find this kind of info, possibly in terms of kbps?

Also, what could be the maximum achievable transfer rate on short waves, specifically?

Edit: I thought that given the premises in first paragraph, it was clear that the heart of the question was about knowing the actually achievable transfer limits using known and used modes, not just understanding theoretical limits... (which is still a precious contribute though). Since it seems this did not come off so clear to some people, so I'm specifying it here and in title too.

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    $\begingroup$ Max legal, or maximum achievable? The two are rather different... $\endgroup$ – PearsonArtPhoto Aug 23 '15 at 11:04
  • $\begingroup$ Max achievable. $\endgroup$ – jj_ Sep 2 '15 at 19:37
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    $\begingroup$ If I understand you based on your response to Phil Frost, you're looking for not what is possible in theory, but rather what the maximum data rates of modes that people actually use are, and what mode has the highest such rate. Is that correct? (If so, perhaps you could edit your question to clarify that.) $\endgroup$ – Kevin Reid AG6YO Sep 2 '15 at 21:51
  • $\begingroup$ @KevinReidAG6YO Given that this question already has two upvoted answers which are based on an interpretation that the OP is asking about theoretically achievable, I'd rather that such a question be posed as a separate question and this one perhaps clarified to ask about theoretically achievable data rates specifically. Both are reasonable questions, but the answers are certainly different. $\endgroup$ – a CVn Sep 24 '15 at 7:26
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    $\begingroup$ Edit your question, then, or ask a new one as Michael Kjörling preferred. $\endgroup$ – Kevin Reid AG6YO Sep 25 '15 at 13:05
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8VSB, as used ATSC digital television, has a gross bit rate of 32 Mbit/s in a 6 MHz channel.

802.11ac's fastest mode (1024-QAM) is capable of a gross bit rate of 1300 Mbit/s in a 160 MHz channel in each spatial stream, with up to 8 spatial streams. (I don't think any 8x8 MIMO APs are on the market yet, but surely someone's tried it in the lab.)

These are just two examples of ubiquitous digital modes which achieve high bit rates. There are undoubtedly modes used in scientific, military, and experimental applications which are orders of magnitude faster.

There is no upper physical limit besides that provided by the Shannon-Hartley theorem. As long as I can do any of:

  • buy more spectrum,
  • transmit with a higher power,
  • use a more directional antenna to reduce received noise, or
  • put the receiver and transmitter closer together,

then I can cram more bits into the æther. The reason it's not done in practice is that at some point there ceases to be a need (do most people have a need for Wi-Fi that's faster than their wired network?) or it becomes more economically feasible to run a wire.

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  • $\begingroup$ +1. Will mark it as correct answer if there aren't more detailed answers. Little side question: at a glance, what would I require, in terms of entry-level/medium-level amateur equipment (and in terms of modes to use) to stream audio/voice/data at an acceptable, non-professional quality over a long/very long/longest available distance? $\endgroup$ – jj_ Sep 29 '15 at 12:52
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    $\begingroup$ @jj_ the most common digital voice modes in amateur use are probably FreeDV (open source HF mode, you'll need a computer or the SM1000 and an SSB HF radio) and D-STAR (VHF/UHF, uses proprietary AMBE CODEC). Easiest way to use D-STAR is to buy an Icom radio or a DV Dongle. $\endgroup$ – Phil Frost - W8II Sep 29 '15 at 13:52
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    $\begingroup$ @jj_ also related to your question, this was just recently asked: ham.stackexchange.com/q/5334/218 $\endgroup$ – Phil Frost - W8II Sep 29 '15 at 13:55
  • $\begingroup$ uses proprietary AMBE CODEC: I digress but, if it's proprietary, doesn't that compare to encrypting content, which for amateurs is prohibited? $\endgroup$ – jj_ Sep 30 '15 at 7:17
  • $\begingroup$ @jj_ it does indeed, and that's why D-STAR is illegal for amateur use in France, for example. But the FCC doesn't care as much, I guess. en.wikipedia.org/wiki/D-STAR#Criticisms $\endgroup$ – Phil Frost - W8II Sep 30 '15 at 13:41
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You are looking for the Shannon-Hartley theorem. Borrowing Wikipedia's summary, because it's better than what I can come up with:

In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise.

The Shannon-Hartley theorem states that the theoretical maximum bandwidth of a communications channel can be stated as:

$$ C = B \log_2{\left( 1 + \frac{S}{N} \right)} $$

where $C$ is the channel capacity in bits per second, $B$ is the bandwidth of the channel in Hz, $S$ is the average received signal power over the bandwidth, $N$ is the average noise power received over the bandwidth, and $S$ and $N$ are in the same unit (here, watts, or a multiple thereof). Notice that no communications channel in practice (not even a crystal-clear FM transmission or studio CD recording) is completely free of noise, so you will always have a $N > 0$. The theorem does not state how to achieve this channel capacity.

It follows from this that if you know the bandwidth, the signal strength received and the noise level, you can compute the maximum theoretical data rate. Transmission frequency does not enter into the picture, although it could place a practical limit on the achievable transmission bandwidth because antennas for lower frequencies tend to be more narrow-band due to employing various forms of matching networks which are not needed when antenna sizes are a considerable fraction of a full-sized antenna for the transmission frequency range employed.

Note that this allows you to compute the maximum theoretical data rate at which transmission is somehow possible practically without errors. This data rate will not always be achievable in practice, and in fact a lot of transmission mode research has gone into getting as close to the theoretical maximum data rate as possible. A transmission actually at the Shannon-Hartley limit would most likely look like white noise across the transmission bandwidth unless you know what to look for; compare ultra-wideband, or the signals used by late-generation dial-up telephone modems.

Since a large factor in the equation is the received signal-to-noise (S/N) ratio, you can increase the achievable transmission rate within a given bandwidth "simply" by increasing transmitter output power, or antenna gain. Conversely, in situations where bandwidth is extremely limited, such as on 136 kHz, the transmission bandwidth is reduced by reducing the data rate. In situations where signal is hard to come by, such as in communication with faraway space probes or again on 136 kHz, the data rate is reduced in order to match the available S/N ratio.

Wikipedia has several examples applying the theorem that you may be interested in.

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  • $\begingroup$ Thanks for your comprehensive answer, however I'd like to see a more pragmatic explaination as to which specific mode I could use to get high transfer rates and as to which transfer rate we would be talking about in terms of kbps. Thanks. $\endgroup$ – jj_ Aug 29 '15 at 15:38
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For what it's worth, I made a graph of a token selection of amateur digital modes with bandwidth vs. frequency (as wavelength) to provide a rough sense of the digital scene.

enter image description here

This came from our feasibility study for a new packet system in the Virginia area.

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  • $\begingroup$ I can understand the correlation between bandwidth and transfer rate, but why you can send more data using a shorter wavelength? From the other answers I've gathered that: longer wavelength accounts for more resiliency to propagation conditions and that shorter wavelength accounts for less noise (highly directional), so is the less noise the prevailing factor here? Or are there others ones? $\endgroup$ – jj_ Aug 2 '16 at 15:24
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    $\begingroup$ The prevailing factor for speed of data transmission is almost always going to be bandwidth and there is simply gobs more of that available at the higher frequencies... hence the correlation. Take 802.11 WiFi for example. Its signal is something like 22 MHz. wide... 3 can nicely fit shoulder to shoulder in the 2400 MHz ISM band without overlap. Try to do this in the HF band and you gobble up over 2/3 of that band. You can begin to see why commercial entities bid enormous sums for the rights to these short wavelength bands. $\endgroup$ – JSH Aug 2 '16 at 20:08
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It really is a function of the bandwidth of the signal which is driven by the speed. Lower-speed, lower-bandwidth signals take up "less space" on the air and are on HF while higher-speed, wider signals are on VHF and higher.

Lower-speed modes also tend to be more resilient in the face of varying band conditions, as found on HF. VHF and higher tend to be more stable but much more local as well.

This is a great resource: http://wb8nut.com/digital/

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  • $\begingroup$ You left out noise (or S/N), which can limit the reliable data rate to well below what a given bandwidth would allow in low noise (RF + receiver-front-end + etc.) $\endgroup$ – hotpaw2 Sep 22 '15 at 22:40
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I thought that given the premises in first paragraph, it was clear that the heart of the question was about knowing the actually achievable transfer limits using known and used modes, not just understanding theoretical limits... (which is still a precious contribute though).

Practically, I have maintained 155Mbps for a while now. - digitally - achieved - maintained long term - very little packet loss (sub 0.1%) - verified

Using "known and used modes" in the form of 802.11n/wifi or if you like: IEEE 802.11n-2009 with 64-QAM modulation on a 40MHz-channel-BW as it is known formally.

I believe the question is a bit "wide" to answer really... you would need to ask the question in reference to which band you use, and which bandwidth you like to use, then you can find protocols to use, or even write your own...

I often thought about increasing bandwidth of PSK by using multiple PSK in parallel... and I actually found someone who implemented this already. Although I forgot the link, I am sure you can search for it.

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  • $\begingroup$ Multiple PSK in parallel is very common. For example FreeDV has a central PSK synchronization signal, with 16 QPSK subcarriers. Many OFDM schemes use PSK (or frequently QPSK since it is more bandwidth efficient) $\endgroup$ – Phil Frost - W8II Aug 2 '16 at 13:15
  • $\begingroup$ @PhilFrost, yes, that is the one meant but couldn't remember. $\endgroup$ – Edwin van Mierlo Aug 7 '16 at 6:24
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Basically the higher the baud rate the greater the frequency bandwidth required. The degree of shift of the FSK signal affects the required bandwidth as well. In practical terms, 300 bd is the norm for HF, 1200 bd is the norm for VHF, 9600 baud on UHF not so common but is used with satellites and there is talk about 19kbd as well but not very common. It's all about the bandwidth allowed by the spectrum administrators. Generally they don't like you using more than 5kHz on voice frequencies on HAM bands. A TV Channel is 7 MHz wide.

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