A physically based method has been developed to simulate the wideband HF ionospheric propagation channel relevant to the case of wideband spread spectrum HF communications and also other HF applications such as digital broadcasting and over-the-horizon radar. It is based on the consideration and solution of the equations governing pulse signal propagation through a fluctuating time varying random ionosphere. The wideband scattering function has been constructed as the appropriate Fourier transform of the correlation function of a channel impulse response. Numerical codes have been written, which allow numerical simulation of the wideband scattering function of the HF sky wave ionospheric fluctuation channel for any given model of the background ionosphere and time varying ionospheric turbulence with an anisotropic inverse power law spatial spectrum and frozen drift of the ionospheric inhomogeneities. When employed in the simulation of the scattering function for real conditions of propagation, the method provides the possibility of analysing the propagation effects for different relative bandwidths of the background channel, fluctuating channel and transmitted pulse. The effects of the transmitted pulse bandwidth and anisotropy of the irregularities have been studied. The numerical results have been obtained and presented, which demonstrate the contribution of the effects enumerated in the wideband scattering function of the HF ionospheric channel.