The signal is always going to be modulated, unless the source is maintaining a position with zero relative velocity to the Earth, or deliberately compensating f

The signal is always going to be modulated, unless the source is maintaining a position with zero relative velocity to the Earth, or deliberately compensating for same - both of which would be far more impressive as a "hello" than a random-ish number which will always be distorted by orbital and proper motion. Otherwise it's going to have a varying frequency - maybe not by much, and maybe not quickly, but certainly not static.