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Considering what kind of intruments it takes just to detect an entire earth sized planet, why do you suppose people think that we could aim some crummy little 100 meter radio scope at such a planet and hope to hear their infant monitors and TV communications, or even a 100 meter radio telescope aimed at us tranmitting 10,000 watts?

Detecting a signal, and resolving a signal are two different issues.

The ability to resolve a signal, such as imaging an extrasolar planet, is proportional to the effective linear dimension (e.g., diameter) of the collecting device. (Do a web search on "Dawes limit" for more details.)

Weak signal detection, on the other hand, depends on the sensitivity of the detector and how much signal you can feed into it. The quantity of signal you can collect is a function of the effective surface area of the "collector," which varies with the SQUARE of the collector's linear dimension, e.g., diameter.

Thus, our ability to detect weak signals improves much faster than our ability to resolve weak signals, as the size of our instruments increase.

That's why it is easier to "detect" a signal from a distant star or planet than it is to "see" distant stars or planets. It is far less demanding.

As always, I defer to the resident FR physics/astronomy factotums if I've mucked up any of the details in my simplified explanantion.

Thus, our ability to detect weak signals improves much faster than our ability to resolve weak signals, as the size of our instruments increase.

I'm an ATM so I know the difference between resolution and light gathering ability thanks.

So do the math and figure out what the requirements for LGM to send a signal that we could detect give that 8 watts is detectable from a 10ish foot dish from 5 billion miles away by a 300 foot dish. Detectable in the sense that we can actually decode data, though at a low data rate. We need more than just a carrier since every single object out there is transmitting a carrier. We need intelligence modulated onto it.