Top of my head, so I may be off, but:
The Arecibo message was easily the easiest to detect by far.
Its signal will become indistinguishable from background radiation at a distance of slightly over 625 light years.
The converse: any life out there trying their best to communicate with us, beyond 600 ly... we wouldn't realize it even if we happened to catch (what's left of) the signal.
> Its signal will become indistinguishable from background radiation at a distance of slightly over 625 light years.
Doesn't that depend on how large the receiving antenna is, because the larger the antenna the smaller the source angle you can focus on and the less background radiation will be in that source angle ?
That may not last much longer either. Transponders are more effective/useful for civilian purposes and the military needs to be stealthy. Big radar installations have a sign painted on them that says "take me out first".
The hard part is deciding if it's natural or artificial.