Modeling long‐range propagation of electromagnetic waves is necessary to study the performance of systems, for applications such as radar or navigation. Such models generally rely on split‐step Fourier (SSF) because large mesh sizes can be used. The split‐step wavelet method (SSW) is a recently developed method allowing to perform the same simulations as with SSF but in a shorter computation time. This method requires the pre‐computation of a free‐space propagator. Up to now, one limitation of SSW is that the steps must remain constant during the propagation. In this study, we propose an improvement of SSW in terms of memory size and versatility. This improvement relies on the use of a set of propagators, that is, the propagation of elementary wavelets. The limited support of wavelets renders the computation of the set of propagators fast, approximately as fast as one step of propagation with SSW. First, a numerical test shows the advantage in terms of computation time. Second, a numerical experience shows the advantage in terms of memory. Finally, the SSW method is applied as the direct method for a radio occultation configuration.

In the context of improving the dimensioning of observation and telecommunication, the characterization of the propagation canal is very important. Thus, accurate models of propagation phenomenona in their environment and above a rough surface (maritime or terrestrial) are of major interest for many applications (such as radar, communications, and teledetection). To provide solutions to this problem, in this paper, we propose a fast, memory-efficient, and accurate asymptotic method for 2D tropospheric propagation for a large band of frequency that accounts for relief, as well as ground composition and roughness. This latter is a two-way split-step wavelet scheme with an intrinsic stopping criterion. For overseas propagation, roughness effects are considered through a hybrid method. A complete theoretical comparison with SSF in terms of memory and time efficiency is proposed. Simulations in various environments (ground, sea, and snow), as well as different frequencies (UHF, S, and X-band) are performed to validate the method and highlight its advantages. To highlight the interest of the developed methodology, this latter is applied to different real-life applications, such as the prediction of radar coverage and the optimization of an antenna location.

Computing the Radar Cross-Section (RCS) of a given object is a topic of major importance for many applications, e.g., target detection and stealth technology. In this context, high-frequency asymptotic methods are widely used. In this article, we derive a Gaussian Beam Summation (GBS) method for both metallic and dielectric targets. The basic idea is to use the GBS method to compute the scattering far fields generated by the equivalent currents flowing on the surfaces. The validity of the proposed method is then investigated in the X-band. To accomplish this, the results obtained using this technique were compared to those obtained using other sufficiently accurate methods such as the ray tracing of FEKO and the ray asymptotic solution. As an example of the method’s accuracy, the GBS method was used to obtain the wave field in a homogeneous medium by fitting the results to a point source. In the same way, the method was used to compute the RCS of dielectric cuboids.

Modeling electromagnetic propagation in the maritime environment is a key element in calibrating detection tools, for example in SAR imaging. This article presents a method to compute the propagation above a polluted sea surface. The latter is based on the parabolic wave equation solved with the split-step wavelet method. A hybrid method is also used to account for the sea surface. Indeed, here the sea spectrum is used to both generate random sea surfaces and compute a roughness parameter. The contributions of this article are twofold. First, we improve the calculation of the roughness coefficient in the hybrid method by accounting for the shadowing effect. Second, a stochastic strategy is developed to account for an insoluble oil slick, or pollutant, that covers part of the domain. Numerical tests in the S-band are provided to validate the method and highlight its advantages.