FTL radar may be the way we
view the ship's sensors, but they may be something else entirely. Although as CaptainDave1701 noted, it's fiction.
James P. Hogan's novel THE GENESIS MACHINE posited a new type of "telescope" based on a "subspace" realm (called K-space in the book) that may be similar to the Enterprise's
sensors. Without getting into all the technobabble of the book, this "telescope" was a passive sensor for particle annihilations that (according to the fictional physics) occur constantly inside all matter. The researchers in the story start out observing the interior of the Sun and Earth, then later refine the device to pinpoint manmade vehicles on the other side of the Earth. If I'm remembering the story correctly, distance was not a factor—the researchers could view other star systems as easily as a building next door. Remember, this device was passive, so there was no need to "light up" an object untold distance away.
Murray Leinster described a similar device (in much less detail) in THE WAILING ASTEROID. Leinster's telescope worked by gravity. Although not stated explicitly in the story, this telescope appeared to be a passive device, too. (While some real-world physicists may tell you gravity travels no faster than light, many others will tell you gravity—whatever it is—travels much faster than light. The late Tom Van Flandern calculated the speed of gravity at around 20 billion times that of light. Assuming that is true, a gravity telescope would still be beyond our technology, as we don't really know what gravity is, let alone have the ability to manipulate it.)
However you slice it, the Enterprise's
sensors must work at FTL speeds, since the ship itself travels faster than light, also. Trying to navigate by lightspeed information would result in situations like the (ridiculous) "Picard maneuver."