Split-step wavelet with local operators for the 3D long-range propagation

Modeling the long-range propagation in the low troposphere is a topic of major concern for many systems such as radar. In 3D, split-step Fourier methods are limited by both computation time and memory size. Therefore, the N times 2D split-step Fourier method is usually used to model the propagation even if 3D effects are not taken into account. To overcome this, we propose a 3D wavelet-based split-step method that is memory and time efficient. This method is based on the use of the fast wavelet transform, which is of low complexity and allows efficient sparse representations. From numerical experiments, we show that the 3D proposed split-step wavelet method is efficient in terms of precision, time, and memory.