I asked AI about it and it told me that large radiotelescope may suffice. However, the main uncertainty is receivers equipment. If they are on Proxima, they suspect that there is life near Sun, so constant observations are possible—but the size of receiver depends on Kardashev level of civilization.
Advance civilizations will have larger receiving dishes, may be the size of Dyson spheres—but such civilizations are farther (or they will be here).
Therefore, relation distanace/reciver-size is approximately constant.
I asked AI about it and it told me that large radiotelescope may suffice. However, the main uncertainty is receivers equipment. If they are on Proxima, they suspect that there is life near Sun, so constant observations are possible—but the size of receiver depends on Kardashev level of civilization.
Advance civilizations will have larger receiving dishes, may be the size of Dyson spheres—but such civilizations are farther (or they will be here).
Therefore, relation distanace/reciver-size is approximately constant.