Doppler frequency shifts of radio waves reflected by parabolic and quasi-parabolic ionospheric layers

Consideration is given to Doppler frequency shifts calculated for parabolic and quasi-parabolic models of the ionosphere. The analytical formulae obtained are used to study the Doppler frequency shift for the case of variations in total electron content. It has been shown that, if the operating frequencies are much below the maximum usable frequency (MUF), the Doppler shifts calculated in terms of the quasi-parabolic model can be satisfactorily described using formulae for an equivalent plane reflector. Special attention is paid to the study of the behavior of frequency shifts on ray paths near the penetration angle and near the MUF.