I don't understand the possible benefits of looking for "Space Aliens" that most likely would be hundreds/thousands of light years distant. E.G.: Even with a simple "hello" message both the sender and receiver would be long dead due to tranmission time. Aside from scientific methodologies, perhaps looking for E.T. is not cost justified? Wouldn't an effort to better understand the evolution of H. Sapiens on Earth in the physical, environmental, cultural and psychological matrix that we live in be more efficacious to our species well being?
While an alien Aricebo equivalent might detect our Aricebo's one shot in the dark signal, it would be far more useful to know how far away their SETI could detect our strongest continuously broadcast signals which, I believe are clear channel AM radio stations.
Broadcast signals might make sense for a planet but not for a solar system, much less a galactic empire. They just waste too much power versus directed signals.
The chances of detecting passive signals are slim. The best way to get someone's attention, if your sure you want to do it.......is to transmit a one frequency signal that is offset from the natural spectrum of starlight. And blinking or intermittent. Check all spectrum archives for a small offset light signal. Check all X-ray spectrum archives as well.
Even though communication is probable, knowing that intelligent life is out there will change this world and science very quickly.
I think the chances of a "we are here" narrow cast signal being directed in Earth's vicinity are close to nonexistent because space is big. The LGM signal turned out to be a pulsar (a type of object unknown at the time) and the WOW signal, while still not definitely explained, does not appeal to contain information. Other than those we've found nothing.
OTOH, we, and possibly alien worlds, broadcast a whole spectrum of radio emissions. I presume that if we built an Aricebo equivalent on, say, Ceres, it would be able to detect some of these.
My question is, if there was an Aricebo equivalent in, say, the Proxima Centauri system, would it be able to detect them? If so, how much further out could a stellar system be and still have a chance of detecting them.