We would need a humongous experiment to make that work, with the initial distance between the source and the scatterer necessarily in the 100 to 1000 km minimum.
Secondly, we would need all the space traveled more or less “clean”, to avoid losing our initial signal with the huge distance it has to fly.
Finally, we would need to make sure all of it is aligned, meaning it should be performed in space, where radiation noise is much more significant than here on earth.