Earth just received a radio signal sent from a galaxy 9B light years away

I know the article says it's not aliens, but... What happens to a very high power communication over intergalactic distances? Supposing you had a very high power radio transmitter, and you modulated it somehow. Over how long a distance can it be demodulated? What would a signal look like after you can't discern the modulation?

Astronomers and science journalists should consider adjusting their terminology, eg 'detected a radio wave'. Saying you received a signal implies communication, and then requires 1-2 paragraphs in the story refuting the misleading aspect of the headline, wasting everyone's time.