### Why SETI is a waste of time – take 2A

A quick clarification about the physics of receivers from take 2:

I pointed out that you have a very low received signal power, and a by comparison a high noise power.

In order to recover the information content, you need a reasonable signal to noise ratio. Mathematically, this is:

R = S / N

Where S = signal power, and N = noise power.

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(Aside: we cannot measure S (the signal power) because we only have an imperfect receiver. So the best we can measure is S + N. (The principle of superposition applies to received power – everything is additive).

So, we can measure an approximation to R:

R =approx= (S + N) / N

We can measure N by pointing the antenna somewhere else – not at the signal source, or using other devious tricks like disconnecting the antenna.

Now, when S is about 10 times larger than N, the approximation is a near as damn it to the real ratio.)
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In order to demodulate a signal, we need a signal to noise ratio > about 3 – and that will generally do a lousy job. A ratio > 6 and preferably > 10 is much better.

Now, clever modulation systems (as I pointed out in a reply comment) mean you can do clever things with process gain to improve on all this – but you have to know exactly what was transmitted. So these clever modulation systems, by their nature, mean we have damn near buckleys chance of detecting them, so lets forget them.

Using the example in Take 2 for the transmitter 100 light years away, the signal power is MUCH LESS than the noise power.

This means the signal to noise ratio is MUCH less than 1. Seeing as we can only recover information (in other words, demodulate the signal) when the signal to noise ratio is > about 3, it means the chance of meaningful information recovery is impossibly small. The reason is the signal power is extremely small, and it’s massively swamped by plain old thermal noise power.

Oh – and I did not take into account the extra source of noise power – the cosmic background radiation – which also adds to the noise power in your receiver, and just makes the job even more difficult. (Remember – all sources of power are additive – so the wanted signal is added to the thermal noise, is added to the cosmic background radiation…)

It’s still impossible.

*Note for foreign readers: Buckleys chance is an expression meaning no chance at all.