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I would like to transmit trinary data (-1,0,+1) on 20-30m wave to be received 10,000km away. From Europe to US.

My first thought was this: https://www.researchgate.net/figure/Burst-modulation-mode-f-BM-280-Hz-duty-cycle-50-as-an-example_fig2_231130256 I am open to different suggestions

Desired performance here is:

  • max latency of signal processing (to increase SNR) is 4ms
  • data rate 2 tribit per second
  • as its not commercial i'd rather calibrate optimal missing reception etc per session (dependent on weather etc), so 20-80%..

What kind of power would I need on TX side for the above SNR?

Also note: I looked into known ham radio digital modes and signal processing algorithms - they seems to be too slow as they are designed to use minimal power for reasonable detection rates with pretty much infinite latency. My task is the other way around - to use maximal reasonable power to achieve low latency.

Boppity Bop
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    hey, what's a tribit? – Marcus Müller Jun 18 '20 at 22:22
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    Like a bit, but with 3 states instead of 2. In other words, about 1.58 bits. – Phil Frost - W8II Jun 18 '20 at 22:28
  • Ah, thank you! That makes sense, so that's a data rate of $\log_2\left(3^2\right)/\text{s}\approx 3.16,\text{b}/\text{s}$. Gotcha! – Marcus Müller Jun 18 '20 at 22:31
  • I'm a bit confused now, though: because at that data rate, you can't even transmit a single bit (or tribit) within 4 ms. Not quite sure what the latency then captures? – Marcus Müller Jun 18 '20 at 22:32
  • no you asked me what are desired params :) so there you are.. but anyway - how much time one need to transmit 4 bit/sec ? – Boppity Bop Jun 20 '20 at 10:44
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    I'm not really following there: 4bit/s is a rate of how much information you can put across in a fixed amount of time. So, if you define a data rate of 4 bit/s, then in 4ms you can transmit 4 ms · 4 bit/s = 16 millibit. A millibit is not really a useful thing? It's not even 1/30 of the information of "yes|no". So: where does the 4bit/s data rate requirement come from, what's the motivation to demand that data rate? – Marcus Müller Jun 22 '20 at 18:17
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    Boppity Bob, all your (many other) questions are related to the impulse response of a transatlantic data link. (Is your plan to get rich with high-frequency trading?). What you are asking in this forum is all that knowledge: latency, impulse response, spread in time, signal coherency versus bandwidth, reliability of the link, best frequency and so on. Hesitate to post this, but I do. Brightnoise, PA0FSB –  Jun 24 '20 at 21:52
  • @BoppityBop your edit is much appreciated! Couple of comments: – Marcus Müller Jun 25 '20 at 18:55
  • "data rate 2 tribit per second" data rate is really usually measured in bits/s. You don't send tribits instead of binary bits, you send symbols (basically, any complex number is a potential symbol. You restrict yourself to a set of symbols, so that your receiver knows what they mean). And your idea of sending +1, -1 or 0 is interesting, but ultimately a bad idea. Sending +1 and -1 is hard enough to distinguish at the receiver, sending 0 only makes the decision problem harder, so that you'd need to spend more amplitude on the +1 and -1 to make it clear whether you've send a 0 or not. – Marcus Müller Jun 25 '20 at 18:57
  • "They seems to be too slow as they are designed to use minimal power for reasonable detection rates with pretty much infinite latency. My task is the other way around - to use maximal reasonable power to achieve low latency." That's not really true: They maximize the reliability given the transmit power they have. And: that's exactly the same problem you have, and any other communications engineer always has to solve :) – Marcus Müller Jun 25 '20 at 18:58
  • You're arguing about mathematical truths here, by the way. The first thing you always do is come up with a mathematical model of both your noise and your signal given you've sent one of your symbols, and then define how you plan to distinguish the "I sent this and that symbol" at the receiver. That gives you a probability that you make a decision mistake. This symbol error rate then is used to decide whether your system is feasible, or whether you need to spend more energy per symbol – for example, by transmitting with higher power,or slower, or by adding redundant information(channel coding). – Marcus Müller Jun 25 '20 at 19:03
  • And the truth is that sending your 0-symbol is very power efficient (you don't need any power on the transmitter), but that you get better reception reliabilty if you actually used that time to send a +1 or -1, and in exchange had a clearer decision to make at the receiver (+1 is farther away from -1 than from 0). – Marcus Müller Jun 25 '20 at 19:05
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    So, really, I know you don't like to hear this, we really need to know what you're trying to transmit for which purpose to help you any further, but really the data you're giving is still not explicit enough. How many bits (in information, not in symbols you need to send to get the information across) is a session in your question? What is "reasonable power"? What exactly is an acceptably low latency – your 4ms seem to be pretty strange, considering the time it takes your signal to propagate around earth is significantly longer than that. – Marcus Müller Jun 25 '20 at 19:09

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What you're asking for is a link budget.

For HF, you can use software like VOACAP to estimate path loss. There are several ways you might use the software, but to start I'd suggest:

  1. Click the antennas button, and enter the kinds of antennas you have available for each band.
  2. Drag the location markers to the relevant places. Not all 10,000 km paths are the same. Things like water vs land make a difference, as well as alignment with the greyline, among other factors.
  3. Change the date in the lower-left to at least the month of interest. The sun influences HF propagation significantly, so the season is important. Over longer timescales, the sunspot cycle is also relevant.
  4. After editing these and other relevant parameters, click the "Prop Charts" button, and select the "SDBW Short-Path" chart. This shows the received power in dBW for each band and each hour of the day.
  5. Note the transmit power selected in the upper-right. It's in watts, but if you convert it to dBW then the difference between that and the "SDBW" chart is the path loss. It includes propagation loss and antenna gain.

Of note, HF propagation is highly variable. The number VOACAP gives for SDBW is a median value. Half the days will be better, half will be worse. Add or subtract some margin depending on how many days out of the month you are OK with communication not working. VOACAP can also generate 10th and 90th percentile values for this metric, but as far as I've found not in the online version.

Great, now you know how much power from the transmitter arrives at the receiver. Now how much power must arrive at the receiver to achieve your communication objectives?

The first part of this question is determining the noise at the receiver site. Perhaps you can measure it directly. If not, ITU-R P.372-13 is a good source of data on what noise can be expected generally.

Now you need to set a signal to noise ratio (SNR) objective. You could do this a couple ways:

  1. Use the Shannon-Haltley theorem to put a best-case lower-bound on the required SNR, or
  2. Find the bit error rate curve for a specific modulation you are considering. I have no idea what the thing you linked in the question is. BPSK might be a good starting point.

If this sounds complicated, it's because it is. There are a lot of variables required besides "how much power". But hopefully this gives you enough of an outline of the procedure that you can ask follow-up questions for additional detail as you need it.

Phil Frost - W8II
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  • 4ms meant - margin to error-proof the signal. not the whole latency.. Using your figure the total tolerable latency is ~35+4 – Boppity Bop Jun 18 '20 at 19:14
  • @BoppityBop then, do these 4 ms put an upper limit on the duration of the transmission? – Marcus Müller Jun 18 '20 at 22:21
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    @BoppityBop Please edit the question to clarify. – Phil Frost - W8II Jun 18 '20 at 22:27
  • Note that propagation effects will cause latency to vary by a lot, and no amount of power will help this. Also, when they say "highly variable" they mean it; on a very good day, 1w is plenty for a 10000Km path and higher power will probably cause unmanagable multipath propagation. On a bad day, 50Kw won't be enough, and if there's a solar flare, the S/N ratio will also be terrible. I suspect you can use the predictions from this answer only as upper and lower bounds on your power, and will need to do active feedback probing to set the power usefully. – user10489 Jun 19 '20 at 11:40
  • @user10489 yes I fiddled with VOACAP before asking the question. yes i know it varies but then i can skip the bad days (its an amateur project). would you say 500w is enough for most days? – Boppity Bop Jun 19 '20 at 12:42
  • @PhilFrost-W8II thank you very much.. are you saying that my objective (re: 4ms) is viable if power and antenna are in line. whats your gut feeling? is it possible to build and operate for an individual? I will have to look into BER thanks again. – Boppity Bop Jun 19 '20 at 12:47
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    For ssb, 100w is enough for most days. For digital modes using full modulation, 30w is similar. For narrow band slow digital modes (3bps is reasonable) 10w might be plenty. – user10489 Jun 19 '20 at 12:59
  • The latency issue depends on how variable your path is. If I'm not confused, 4ms is ~800 miles. A path variance to exceed that isn't impossible. Ionospheric variation combined with 4-5 bounces might give you 4ms variance even without the path wandering around and going the long way. – user10489 Jun 19 '20 at 13:04
  • consider 4ms is a maximum length of a single data package. its nothing to do with propagation (I assume a propagation distance wont change much within 500ms - distance between packages - am i wrong?) – Boppity Bop Jun 19 '20 at 18:49
  • @BoppityBop we call the time that we can assume propagation to stay the same the coherence time. 500 ms would indeed be an extremely long coherence time for a far-reach channel, unless you restrict your bandwidth very much, but that may be feasible here. – Marcus Müller Jun 22 '20 at 18:19
  • @MarcusMüller I'm not sure 500ms is a reasonable coherence time for even the best case ionospheric paths: https://www.itu.int/rec/R-REC-F.1487-0-200005-I/en – Phil Frost - W8II Jun 22 '20 at 21:31
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    @BoppityBop Receiver ambient noise, solar weather, your definition of "most days", antenna gain, and your maximal permissible bit error rate can cause the required power to vary by several orders of magnitude. My gut feeling is you will require somewhere between 10W and 10,000W, depending on your particular parameters. – Phil Frost - W8II Jun 22 '20 at 21:46
  • @PhilFrost-W8II yeah, I should have worded very carefully there. A pure power-detection channel with a symbol duration of a couple dozen seconds might see the channel as sufficiently consistent again... due to averaging of effects. – Marcus Müller Jun 22 '20 at 22:11
  • @Marcus - I apologise for "bit rate" mishap. It is not 4bps.. But anyway I tried again to simplify the question : https://ham.stackexchange.com/questions/16885/transmit-morse-like-code-over-hf-long-distance – Boppity Bop Jun 23 '20 at 16:37
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    @BoppityBop please stop "simplifying" your question. You're honestly lacking the insight to understand what's important and what not. Instead, extend your question to explain what you want to do in the bigger picture, please. You're binding so much time through this. – Marcus Müller Jun 23 '20 at 22:39
  • @BoppityBop IMHO, Marcus has a point. Since we are all unpaid volunteers here and our time is limited, it is expected that users will do a reasonable amount of research before asking a question here. Please see How do I ask a good question? – Mike Waters Jun 23 '20 at 23:41