That a similar setup pointed at the exact location can detect. guess what, that doesn't work well even here on the planet. Point to Point Dish based directed communication is a bitch to get working in insanely small distances like only 10 miles. So we shoot a signal at a single cluster, did we do it for years on end? nope. so nobody will hear anything.
What you have to do is a wide insane power broadcast to cover the entire sky. Broadcast 24/7 for 10 years. That way not only do you have information you sent, but we even encode doppler information about our planet and sun.
Yes for 10 years, 100 years would be better. Because you dont know when someone will be aiming an insane gain antenna in our direction.