The pulse wave will be affected by the dispersion of the background medium and the scattering of the electron density irregularities while it propagates through the ionosphere turbulent medium. In this article, based on the time moment and the analytical solution of the two-frequency mutual coherence function which obtained by the method of the integral equation iteration. The time characteristic of the pulse signal propagates through the ionospheric media of the polar region was detailedly discussed. By using the ionospheric datum of the south pole, the average arrival time changing with the spectrum index of the irregularities, the inner scale, the outer scale and so on was also analyzed. The numerical simulation show the average arrival time is mainly dominated by the propagation items of the group velocity, and was less affected by the higher-order dispersion of the background medium and the random scattering of the irregularities.