Just curious: If you wanted to plant a fake signal that looked like it were coming from a distant galaxy (say 3 billion ly), how far away from Earth would you have to place your transmitter?
You can be on Earth and just sabotage the deep space network antennas or radio telescopes or whatever they use to receive the signals to directly inject the signal in the processing pipeline.
Depends on how long the signal lasts. If it's continuous, there's no way to take it with a single transmitter. Astronomers can detect the apparent motion of stars caused by the earth's orbit, and use those measurements to triangulate the distance to stars, even though the stars are many light years away. A single transmitter on a probe near our solar system would be very obvious.