Research on the Ionospheric Delay of Long-Range Short-Wave Propagation Based on a Regression Analysis

The ionospheric delay effect is inevitable when a radio signal propagates through the ionosphere. It has been extensively studied in the L-band. Typically, the influence of the ionosphere on the code phase and carrier phase is regarded as the same. In this study, a numerical ratio between the group delay time and phase advance time with reference to the study of the L-band is investigated in the short-wave band. The variation in the numerical ratio with frequency, critical frequency, and elevation angle is discussed in detail. There appears an interesting phenomenon wherein the elevation angle has a greater effect on the ratio than the frequency and critical frequency. The numerical ratio increases with an increasing elevation angle. On the other hand, a regression analysis is used to establish the mapping relation between the ratio and the three factors of frequency, critical frequency, and elevation angle, based on the simulation results obtained by a ray-tracing algorithm. The little relative errors between the fitted values and simulation values under different ionospheric models prove the relationship between the ratio and the three factors of frequency, critical frequency, and elevation angle.