An algorithm for calculations of phase and amplitude scintillation of satellite signals in the equatorial region will be described in detail. The algorithm will be developed by initially transforming the discrete version of the Huygens-Fresnel integral into a convolution involving a series of coefficients with decreasing amplitudes. Next, the Fourier transform of the corresponding series of coefficients is stored for all the frequencies of interest, and the fast Fourier transform algorithm is used to evaluate discrete convolutions. Two phase screen models will be described. The first assumes that the phase fluctuations of the wave front emerging from the bottom of the irregularity layer are proportional to electron density fluctuations directly obtained from satellite in situ measurements. The second assumes that the same phase fluctuations can be obtained from their power spectral densities and phase spectra, represented by analytical functions with parameters provided by physics-based or morphological models of ionospheric irregularities. The propagation algorithm will be applied to both phase screen models, assuming five frequencies in the high-VHF to low-SHF band (suffering strong to weak scattering), to display its potential in the prediction of phase and amplitude scintillation of satellite signals.