How can I know over what distance or at what speed I can communicate? [closed]

Question

Given some description of some parameters like:

• transmitter power
• frequency
• antenna
• location
• time of day

how can I know over what distance communication is possible? Can I know the limits to these things, like:

• Simplest, smallest antenna for tuning WWV, WWVH?
• What bands and modes will give me voice at 3,000 miles?
• Best QRP HF band for small antenna?
• Smallest HF antenna for DX?

Answer 1

Shannon's law on information communication provides statistical upper limits on data rate given a signal to noise ratio: S/N.

There may be nice physics models on the power coupled between a pair of dipoles in free space, to get a best case on signal power received.

Unfortunately, the transmission channel is usually not in outer space, but contains a huge number of absorptive and reflective bodies (perhaps including the upper atmosphere), often in unknown or nearly randomly changing configurations, ruining any nice clean closed form equation for the the received S in S/N.

Also unfortunately, the noise floor (the N in S/N) is almost always quite indeterminate in the real world, and has to be found by experimentation. Background noise, interfering signals, receiver front-end noise, and etc.

You can test yourself, or perhaps make a reasonable guess at what might be possible based on prior published results. Assuming conditions are fairly similar and don't change much.

Answer 2

You can not know these things except by probabilities. Radio propagation is a stochastic process, the result of many random variables. There are many things that can be done to improve one's chances of success, or worsen them, but always when we are talking about whether something is possible or not, what is the smallest/best/simplest/cheapest piece of equipment, and so on, we are specifying only a small part of the system.

Consider the entire system involved in communicating between point A and point B, and some of the variables involved at each step.

First, we must capture the information to be sent as a baseband signal. Is this a human voice? How intelligible is this voice? Are you repeating everything five times, or just once? Is a good microphone used?

The information must be modulated. Does the modulation limit the fidelity of the baseband signal? How robust in the modulation? Does it employ forward error correction or other redundancy? Does it distort the baseband signal?

The signal must be amplified. What's the transmitter power?

All this must pass through the transmitter's electronics. Are they of good quality? Are they introducing any distortion?

This must pass through a feedline, to an antenna. What are the feedline losses? How efficient is the antenna? Is the antenna directional? Is it pointed in the best direction?

The signal must then propagate to the receiver. What are current propagation conditions? Are there any geomagnetic storms? Even ordinary lightning creates noise. For HF propagation, ionospheric conditions are somewhat predictable, but still highly variable, just like the weather. Line-of-sight propagation is more predictable, but still, is there anything in the propagation path that can absorb/refract/disperse/distort the signal? Dense smog? Cars? Pedestrians? Buildings? Power lines? Airplanes?

The signal must be received. Again, what's the receiving antenna and feedline? Of what quality is the receiver? Does it have good filters?

The signal must be demodulated. What's the noise floor at the receiver? Is there a nearby strong station desensitizing the receiver? What diversity schemes can the receiver employ? What's the operator's skill? What's the modulation's robustness to noise?

These are just a few of the factors that determine the possibility of communicating between A and B. At every step of the way, there are opportunities to improve our chances, or make them worse. To improve your chances of successful communication, you might:

• wait for exceptionally good propagation conditions
• increase transmitter power
• increase antenna gain (on either end)
• use a more robust modulation, like WSPR
• repeat the transmission multiple times, increasing redundancy
• put antennas on a high tower where there are fewer obstructions

The list goes on, and technological advancement is always creating new possibilities. Thus, if we should ask "what's the smallest antenna" or "what's the lowest power" or any similar "what's the worst X could be" type question, the answer is nearly always that there is no limit, because there are always things that can be done to compensate.