A numerical study of waves propagating in a turbulent, stratified medium, such as the ionosphere, is performed by using the phase-screen-diffraction-layer method.In this method, phase fluctuations due to irregularities and diffraction effects are computed sequentially along the ray path. Stepping in altitude, phase changes are imbedded into phase screens, while diffraction between phase screens is computed using fast Fourier transform techniques. In the reflection region, a careful examination of the propagation is required. The derivation presented in this paper leads to improvements in the computational scheme and gives some physical insights. The resulting scheme is used to compute the angle of arrival and some of its statistics as an example of practical applications.