A quasi-particle approach is used to analyze the effect of bottomside sinusoidal irregularities on the propagation of beacon satellite signals through the ionosphere. In this work, the radio wave is treated as a distribution of quasi-particles described by a Wigner distribution function, and the irregularities are modeled as a two-dimensional density modulation on a uniform background plasma. The collision of quasi-particles with the irregularities modifies the quasi-particle distribution and gives rise to the wave-scattering phenomenon. The multiple scattering process is generally considered in this deterministic analysis of radio wave scattering off the ionospheric density irregularities. The analysis shows that this two-dimensional density grating effectively modulates the intensity of the beacon satellite signals. This spatial modulation of the wave intensity is converted into time modulation due to the drift of the ionospheric irregularities, which then results in the scintillation of the beacon satellite signals. The modulation is due mainly to the transverse (to the wave propagation) grating. The results of the analysis agree well with the existing experimental data on the scintillation of Atmosphere Explorer satellites signal (Basu et al., 1986). The model is further based on to predict the scintillation of radio signals for their long distance propagation. For a fixed scintillation index (S4) the predicted propagation distance (d) versus the wave frequency (f) follows a power law, namely, d ∝ f&kgr;, where &kgr;≈2. ¿ American Geophysical Union 1994