This paper is devoted to the investigation of the two-frequency, two-position, time coherence function and the ionospheric scattering function describing the HF ionospheric fluctuating radio channel. The complex phase method is applied to obtain the analytical expressions for the coherence and correlation functions, which are then calculated numerically for the realistic models of the fluctuating ionosphere. The numerical Fourier transformation of the correlation function gives the ionospheric scattering function. The numerical results obtained lead to the conclusion that in the general case the large variability of shapes of the scattering function of the fluctuating ionosphere exists depending on the concrete conditions of propagation. In particular, the well-known delay-Doppler coupling can be more or less pronounced in different propagation conditions. We have shown that the presence of the coupling is exclusively due to the nonzero imaginary part of the correlation function of the scattered field, which means that this effect has a purely diffractional nature and cannot be obtained in the geometrical optics approximation.