Mark wrote:

At least we'll know that aliens with big non-directional
radio transmitters are rare.

We have already learned that.

What we need is a non-directional microwave receiver
on the far side of the Moon. It would be a sort of
phase-array radar in reverse -- lots of small receivers
but no directional antennas. To reduce the noise, it
would be used only during lunar night, when the surface
of the Moon is cold.

The advantage of the non-directional receiver is that
it can detect signals coming from a broad solid angle.
If the ET is using a weak transmitter and he aims a
very narrow beam at randomly chosen stars, we have
good chance of detecting his signal.