Oh ya, radio engineering at relativistic speeds?
That’s what you do for a living?
You do understand the actual CARRIER is NOT RELATIVE TO THE SHIP. NO DOPPLER SHIFT.
"Wavelength" itself is based on the speed of light. It is the distance at which maxima nodes will appear with a wave alternating it's field while propagating at light velocity.
Radar guns rely on the principle that frequency will Doppler shift based on the velocity of the moving object. On this issue, you are simply misinformed.