The ionospheric communication channel is characterized by its transfer function. Each frequency component of the transfer function is given by the ratio of the wave field received to that transmitted. Many works exist which deal with the computation of the ionospheric transfer function when electron density varies smoothly. As frequently happens, the ionosphere is permeated by random irregularities; this paper is concerned with the computation of transfer functions in such a complex ionosphere. Each frequency component of the transfer function can be computed by using the phase-screen-diffraction-layer method, also called the split-step algorithm, in underwater acoustics. Stepping along the ray path, the random phase fluctuations in each slab are lumped into a phase screen. Diffractions between the phase screens are taken into account by assuming the waves are propagating in the background medium. Since different frequencies follow different paths between the transmitter and the receiver, care must be exercised by taking proper correlations between the different ray paths. The simulation scheme presented briefly in this paper introduces the concept of correlated phase screens to achieve proper correlations between ray paths at different frequencies. Although this concept is not limited by the channel bandwidth, the computations presented here are restricted to a bandwidth of the order of the coherence bandwidth of the channel. The result of the simulation is used to compute the two-frequency mutual coherence function, which is widely used to characterize a random communication channel. One very important parameter of the two-frequency mutual coherence function is the coherence bandwidth. This parameter can also be derived from a much simpler treatment of the phase screen theory. Comparisons are made and show the need for further investigations.