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:
- Click the antennas button, and enter the kinds of antennas you have available for each band.
- 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.
- 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.
- 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.
- 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:
- Use the Shannon-Haltley theorem to put a best-case lower-bound on the required SNR, or
- 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.