A three-dimensional parabolic equation with fast reordered-alternate direction decomposition in atmosphere duct environment

In the design and optimisation of marine wireless communication and navigation systems, a thorough investigation of radio wave propagation characteristics under atmospheric ducting conditions is essential. The authors aim to enhance the efficiency of radio wave propagation loss prediction in marine atmospheric ducting environments, proposing a prediction model based on Fast Reordered-Alternate Direction Decomposition (FR-ADD). By approximating the diffraction term into three independent components, exploiting the commutative properties of the Fourier transform to reduce the spatial dimensions, and incorporating a rapid algorithm for the parabolic equation, the model optimises the stepping process and significantly improves computational efficiency. Simulation experiments demonstrate that, in the long-distance and complex marine ducting environments, the model not only maintains prediction accuracy but also substantially reduces computational load and prediction time, effectively realising over-the-horizon propagation prediction. In the experiment of radio wave propagation characteristics in the Yellow and Bohai Seas, the simulation data from the FR-ADD model showed significant correlation with actual measurements and simulations from the AREPS software, confirming the method's efficiency and practicality.