As wideband digital HF radio is being developed, it is necessity to characterise the HF wideband channel that arises as such information will be important for designing optimum wideband HF modems and systems for particular applications. It is common practice to characterise a wideband channel in terms of a scattering function, which provides the Doppler spread and the group delay time spread of a signal that is propagating through the fluctuating ionosphere. In this paper the determination of the scattering function for the HF ionospheric sky wave random channel is based on the theory of HF wave propagation in the real fluctuating ionosphere. Thus no empirical models of the shapes of the scattering function are utilised, but, instead, they are determined by the conditions of propagation, i.e. by the models of the background ionosphere and ionospheric electron density fluctuations and the particular propagation path. To characterise the HF channel of propagation an analytic-numerical technique is used, which employs the complex phase method, or generalised Rytov's approximation. It deals with a point source field rather than with the plane wave propagation, and takes into account the ray bending due to the inhomogeneous background ionosphere and the diffraction effects on local random ionospheric inhomogeneities. The method provides the ability to simulate the scattering function of a wideband channel for any background electron density profile, for different geophysical conditions of propagation and parameters of ionospheric fluctuations.