The design and operation of transionospheric VHF and UHF radars requires knowledge of amplitude and phase scintillation due to ionospheric scattering. Phase coherence is of particular importance where long coherent integration periods and large bandwidths are required. A thin phase screen, parabolic equation based, Trans-Ionospheric Radio Propagation Simulator (TIRPS) is described. Modeled channel scattering functions (CSFs) are compared to experimental VHF and UHF data derived from the Advanced Research Projects Agency Long-range Tracking and Instrumentation Radar on Kwajalein Island (9.4°N, 166.8°E). TIRPS quantitatively reproduces the experimental results, including the quasi-parabolic profile observed in the measured CSFs under strong turbulence conditions. Variations in the simulated CSF with ionospheric phase screen parameters are also presented. Under conditions of high integrated strength of turbulence (CkL), a low phase spectral index (p = 1), indicating relatively dense small-scale irregularities, produces pronounced range spreading. Conversely, when the spectral index is high (p = 4), indicative of strong focusing/defocusing by large-scale irregularities, there is increased Doppler spreading and, when the outer scale of irregularities is large, a greater likelihood of asymmetry of the CSF about the zero Doppler axis.