Having installed 100's of antennas in carbon airframes I generally insist on some type of ground plane. Antenna manufacturers recommend this practice also.
There are guys that say they get satisfactory performance with the carbon as a ground plane. If you plan to try this be sure and scuff the carbon till you see fibers. That is critical to getting the antenna to bond electrically to the carbon.
Good luck

BTW, the copper paint applied inside the airplane is a good ground plane and is easy to apply as a retro fit installation.

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Jon Hadlich
AI Systems
(541) 815-7381