[fixedd]

I've written about this elsewhere, but I'll chime in here too.

The largest radio telescope we have (the 305 meter diameter Arecibo) would need to have it's sensitivity increased by around two orders of magnitude JUST to pick up our TV/FM/AM signals from outside the solar system. If we move into the narrowband signals then, depending on the source-strength, it could pick up signals at up to a few thousand light years... if it happened to be pointed in exactly the right direction at exactly the right time.

You'd have to build an absolutely monstrous dish to be able to detect any of our signals at even the center of our own galaxy (much less at the other end)... I haven't run the numbers on it, but I doubt it's physically possible to build a receiver large enough. Add to that that they're highly directional devices and I think you'll find the "N" in your scenario is actually a startlingly small number.