Trajectories of short-wave signals, reflected obliquely from the ionosphere

The trajectories of short-wave radio signals undergoing total reflection from the ionosphere when the transmitter and receiver are located at different altitudes within the ionized layer are analyzed. The case of a plane-layer, isotropic ionosphere is considered, and group trajectories of signals reflected from parabolic and exponential layers are examined. The reflection of signals from the external ionosphere during satellite communication is also discussed.