On the basis of the solution of the space-time characteristic system by the method of geometric optics using symbolic calculations, analytical and numerical simulation of the propagation of the ordinary and extraordinary radio waves in the conducting equatorial ionospheric plasma was made considering the anisotropy of plasma irregularities and non-stationary nature of propagation medium. Broadening of the spectrum and the displacement of its maximum contain velocity of a turbulent plasma flow and parameters characterizing anisotropic plasmonic structures. Statistical moments of both radio waves do not depend on the absorption sign and are valid for both active and absorptive random media. Temporal pulsations and conductivity of a turbulent ionospheric plasma have an influence on the evaluation of the spectrum-varying propagation distances travelling by these waves. The new double-humped effect in the temporal spectrum has been revealed for the ordinary wave varying anisotropy coefficient and dip angle of stretched plasmonic structures. From a theoretical point of view, the algorithms developed in this work allow effective modelling of the propagation of both radio signals in the equatorial conductive ionospheric plasma, considering the external magnetic field, inhomogeneities of electron density in-homogeneities, as well as non-stationary.