Interesting stuff. Thanks for the link.
You're right about GPS but there are other military applications where the receiver hasn't got a precise idea what form a signal may take. The cleverest of these are employed in, and in the detection of, LPI (Low Probability of Intercept) radar systems. In some of the cutting-edge radar warning receivers there is a capability, though admittedly a limited one at present, to discriminate a signal at a S/N ratio of 0 dBm to -27 dBm.
These units don't know what they are looking for, only what sort of form the signal will probably take if there is one.
I would argue that any extra-terrestrial civilisation attempting to be heard across such huge distances would realise that the transmission of an easily recognisable signal, such as groups of prime numbers, would be the only way they could even dream of being heard.
The practicalities of transmitting a large radio signal, even using a focussed antenna array to magnify the power, make it a total nonsense. If you were to even try to transmit a terawatt signal you'd need superconducting elements in the aerial (unless you were willing to have an Australia sized phased array), superconductors in the feeders, a power source 3 - 10 times bigger than the current electrical generating output of the earth (depending on transmitter efficiency, which might be very good if you already have the superconductors)
I wouldn't want to live within a couple of hundred million miles of the thing though, unless our hypothetical ETs have a liking for being microwaved.
I don't mean to be cynical, as I have used my own idling PC as a SETI node in the past, but hoping that our neighbours are shouting loud enough to hear is just hoping. And a bucketful of hope is worth the bucket.
Besides, any ET civilisation with a hundredth the brains to transmit such a signal would presumably have the brains not to. Be fair, if ET made contact tomorrow the first thing we'd figure out how to do is kill him in his/her boots while leaving their planet inhabitable and technology intact. Then we might reply, if sending the message is easier than launching the first strike.
I totally agree with the aims of SETI but also agree with most members of the space-science fraternity. We need to start launching spacecraft instead of endlessly redesigning them. The Americans pride themselves on the pioneer spirit that forged their country. Trouble is, their too scared to BE pioneers anymore. People might get hurt or killed and that's bad for political careers. (Though in my honest opinion, the absolutely LAST person who should be in charge of a country is anyone who wants the job. It should be like jury service. You get conscripted for a term, preferably a short one)
Assuming we ever get over our timidity and strange view that the potential for loss of a human life is worth saying 'not safe, don't try', we might start going to these other solar systems and actually taking a look for ourselves. Somehow I doubt it though. The resources are being wasted as we speak. In 200 years we'll have squandered them and will NEVER get them back. Makes all the things people on this board are doing seem a whole lot more valuable.
Just my two-cents, though.