A Wavelet Frames Based Split-Step Method to Model the Tropospheric Long-Range Propagation

Rapid and accurate methods for modeling long-range propagation in the troposphere are of major interest for various applications, including communication, navigation, surveillance, and observation. In this case, the parabolic wave equation model is widely used and commonly solved using split-step methods. In particular, the recent split-step wavelet method has shown promising results in terms of time and memory efficiency. Nonetheless, using a wavelet basis renders the propagation step tricky since the translation invariance property is lost. In this paper, we propose to use wavelet frames in place of the wavelet basis to recover the translation invariance property. This leads to a direct and efficient implementation of the method in the wavelet domain, which can be easily passed on to a GPU. Furthermore, we show that it comes at almost no cost in time or memory efficiency. Numerical experiments are performed to validate the method and highlight its advantages.