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In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell's equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated. To verify the accuracy and the efficiency of the proposed method, we compare the results of the conventional FDTD method with the proposed method.

A knowledge-aided space-time adaptive processing (STAP) is a quite useful technique to suppress non-stationary and heterogeneous clutter. It estimates a covariance matrix by combining a conventional covariance matrix based on secondary data with a synthesised one by prior information. A new combining method is presented, where weight vectors, rather than constant weights, are used to combine two covariance matrices. In this method, the weight vectors are derived in a way to maximise clutter-to-noise ratio of the combined covariance matrix. A numerical simulation is conducted for a bistatic radar scenario where clutter non-stationarity and heterogeneity can be assumed and the performance of the proposed method is demonstrated in terms of clutter suppression and target detection.

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In this paper, we propose a numerical method to obtain a solution for the time domain electric field integral equation (TD-EFIE) for arbitrary shaped conducting structures. This method does not utilize the customary marching-on in time (MOT) solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the Galerkin temporal testing procedure, the MOT procedure is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the current, the spatial and the temporal variables can be separated and the temporal variables can be integrated out. For convenience, we use the Hertz vector as the unknown variable instead of the electric current density. To verify our method, we compare the results of a TD-EFIE and inverse Fourier transform of a frequency domain EFIE.Index Terms-Electric field integral equation (EFIE), Laguerre, time domain.