Analysis of Long-Distance Propagation Characteristics of LF Multi-Hop Sky Waves

This paper focuses on the decomposition of different modes of Loran-C resultant waves, including ground waves and onehop/two-hop sky waves, propagating in the Earth-ionosphere waveguide obtained from direct finite-difference time-domain (FDTD) modeling in the presence of the natural magnetic field. After providing the FDTD iterative formulas for the ionosphere affected by the natural magnetic field, the Loran-C resultant waves propagating in the anisotropic Earth-ionosphere waveguide are estimated using the FDTD algorithm. In both the daytime and nighttime ionosphere models, different orientations of the natural magnetic field are taken into account. The arrival times of the different propagation modes for the resultant waves were then determined using a multipath time-delay estimation method. With the above delays, the amplitudes of the different modes are acquired by solving overdetermined equations. Finally, the decomposition results are compared with those obtained in the absence of the natural magnetic field. The numerical experimental results indicate that, with a radiation power of 1 kW and a natural magnetic field of 0.5 Gs, the influence of the direction of the natural magnetic field on the field strength of one-hop sky waves is significant when the propagation distance of LF radio waves is less than 1000 km. Radio waves have multipath effects such as convergence, divergence, and diffraction due to the curvature of the Earth and the ionosphere. This results in significant interference phenomena when the propagation distance of two-hop sky waves is greater than 500 km.