Andrew Nowicki wrote:

If the ET lives near a sun-like star and beams to us 1 watt
of microwave signals, his star makes so much microwave noise
that we cannot read the signal unless one beep lasts at least
10^10 seconds (about 300 years).

I have assumed non-directional transmitter (It radiates
microwaves in all directions.) A directional transmitter
has much better energy density and signal-to-noise ratio,
but it may be aimed in a wrong direction at a wrong time.
The latest Scientific American article about the microwave
SETI ends with a pessimistic statement -- interstellar
distances are too vast for this kind of communication.