In this paper we develop a method for synthetic-aperture radar (SAR) imaging through a dispersive medium. We consider the case when the sensor and scatterers are embedded in a known homogeneous dispersive material, the scene to be imaged lies on a known surface and the radar antenna flight path is an arbitrary but known smooth curve. The scattering is modeled using a linearized (Born) scalar model. We assume that the measurements are polluted with additive noise. Furthermore, we assume that we have prior knowledge about the power-spectral densities of the scene and the noise. This leads us to formulate the problem in a statistical framework. We develop a filtered-back-projection imaging algorithm in which we choose the filter according to the statistical properties of the scene and noise. We present numerical simulations for a case where the scene consists of point-like scatterers located on the ground, and demonstrate how the ability to resolve the targets depends on a quantity which we call the noise-to-target ratio. In our simulations, the dispersive material is modeled with the Fung-Ulaby equations for leafy vegetation. However, the method is also applicable to other dielectric materials where the dispersion is considered relevant in the frequency range of the transmitted signals.

A Design, simulation and optimal selection of non-linear frequency modulation waveforms (NLFM) based on correlated ambiguity function (AF) quality analysis for the purpose of Synthetic Aperture Radar (SAR) is done in this article. The selected optimum CNLFM waveform in contribution with other waveforms are applied directly into a SAR image formation algorithm (IFA) and their quality metrics in comparison to other waveforms are derived and analyzed in a complex random media (CRM). The total quality performance analysis includes both the qualitative AF diagrams and the objective image quality metrics assessments. The simulation results not only verify the robustness of the proposed NLFM waveforms as a suitable alternative for LFM waveform but also introduce NLFM as a proper method of modulation for SAR in CRM.

In this work, we integrate numerically the Kawahara and generalized Kawahara equation by using an algorithm based on Strang’s splitting method. The linear part is solved using the Fourier transform and the nonlinear part is solved with the aid of the exponential operator method. To assess the accuracy of the solution, we compare known analytical solutions with the numerical solution. Further, we show that astincreases the conserved quantities remain constant.

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We obtain the numerical solution of a Boussinesq system for two-way propagation of nonlinear dispersive waves by using the meshless method, based on collocation with radial basis functions. The system of nonlinear partial differential equation is discretized in space by approximating the solution using radial basis functions. The discretization leads to a system of coupled nonlinear ordinary differential equations. The equations are then solved by using the fourth-order Runge-Kutta method. A stability analysis is provided and then the accuracy of method is tested by comparing it with the exact solitary solutions of the Boussinesq system. In addition, the conserved quantities are calculated numerically and compared to an exact solution. The numerical results show excellent agreement with the analytical solution and the calculated conserved quantities.