It's not a "radio dish." It's a sensor dish. A radio-based sensor dish would be useless for a ship that travels faster than light, because it would outpace its own sensors. Its intended function is analogous to a radar dish, but it would have to use some kind of FTL sensing method.
Exactly right.
In my personal conceit on the topic, what this is, is a gravity-based beam. Because it's "gravity-based," and if you accept the model that gravity is basically a "depression" in the fabric of space/time (and that warp drive is also a form of depression in space/time), it's not unreasonable to assume that you could direct a pseudo-gravity beam "below the surface" of space/time, and use it FTL. Heck, we don't know that there's any limitation to the speed at which gravity works... it's entirely possible that gravity is effectively instantaneous, and many many times faster than light (which we HAVE managed to measure).
Now, if that is a "gravity emitter and receiver"... it's easy to see how it would work. You could use that to push objects, and you could also use it to collect certain types of information about certain types of objects.
I've given the dish a capacitor bank which drives it... the main power system charges the capacitors, and every so often, once the capacitors are charged, the thing puts out a big pulse of gravitational energy. Some of it "reflects" back to the ship, and interacts with the "rings" behind the dish (which I refer to as the gravitational resonator), much as a radar collects information by putting out a pulse of a certain frequency of electromagnetic radiation and analyzing the reflected energy.
Think of this as a "gravity-radar." This lets the whole concept work, I think.
But it has ZERO to do with radio. And stating that it's "radio" in any fashion is not only wrong, but it misleads people into incorrectly concluding that it's a communication system.
RADIO IS, BY DEFINITION, A COMMUNICATION SYSTEM.
Radio waves are a subset of "electromagnetic radiation," as is visible light, and as are "radar pulses." And so on and so on. This isn't electromagnetic. It's gravitational. Or it's "subspace"... or some other magic. But it can't be E/M energy.