Instantaneous Gain Deviation of the Onboard Antennas in Vehicles by Atmospheric Radio Refraction

In radio communication between ground stations and vehicles, the instantaneous gain of the onboard antennas of vehicles may vary according to the direction angle along the propagation path. In the absence of atmospheric radio refraction, the propagation path is represented as a true slant-range vector connecting a ground station to a vehicle along a straight line. This slant-range vector can be expressed in the body frame defined by the position and attitudes of the vehicle to obtain the direction angle of onboard antennas. Based on previously studied refractive error estimation methods, this study proposes the procedures for the direction angle of the onboard antennas when considering atmospheric radio refraction by an apparent slant-range vector according to the refracted propagation path. Using a conversion from the apparent slant-range vector in the local tangent plane system to that in the body frame, the horizontal and vertical components of the apparent direction angle are presented. The proposed scheme generalizes the conventional studies on the direction angle to cases where radio refraction occurs. In a case study considering up to a 700 km altitude of a launch vehicle from the ground, the maximum deviation of the direction angle due to atmospheric radio refraction is found to be less than 0.1 degrees, where the surface refractivity is 369.2 N-units and scale height for altitudinal refractivity is 6.07 km. Furthermore, the maximum deviation of the instantaneous gain of onboard antennas caused by refraction is less than 1.5 dB in the composite radiation pattern of the C-band.