Fast RCS pattern fill using AWE technique

Abstract

An extrapolation technique is adapted to predict the monostatic radar cross-section (RCS) pattern from a few pattern value calculations. This approach eliminates a need to resolve the system when an iterative solver is employed. A three-dimensional application is considered to demonstrate the accuracy of the technique.Index Terms-Angular extrapolation, electromagnetic scattering, Padè approximation. I. FORMULATIONThe asymptotic waveform evaluation (AWE) method provides a reduced-order model and has already been successfully used in various electromagnetic and circuit applications [1]- [6]. These applications dealt with frequency extrapolation implementations. In this letter, we present a new implementation of AWE for rapid monostatic scattering pattern fill calculations when an iterative solver is employed.On the basis of AWE, a Taylor series expansion is generated about a specific value of the system parameter (frequency, angle, etc.). The Taylor coefficients or moments are then used to extract poles of the system yielding a rational function (Padè approximation) of the system parameter. Padè representations have a larger circle of convergence and can therefore provide a broader extrapolation when compared to Taylor series representations. Below we describe the implementation of AWE in connection with method of moment (MoM) systems for computing monostatic patterns using only a few angular points.A usual form of the MoM system iswhere V m (k; ; ) = T m 1 E inc (k; ; ) ds (1b) and I n refer to the summation coefficients of the current density expansion weighted by the subsectional basis function T n (r). Among the other parameters, Zmn(k) represents the weighted integral used for generating the matrix, fV m (k; ; )g is the excitation vector, and E inc (k; ; ) denotes the external incident field excitation. Also, k is the free-space wave number and (; ) is the incidence angle. For monostatic pattern evaluations using a direct solver, an order of O(N 3 ) computational complexity is required to factorize the dense matrix [Zmn]. Additional O(N 2 ) computations are then needed for each right-hand side term. For iterative solvers, the entire solution must be repeated for each excitation. The proposed pattern fill procedure eliminates repetition of the iterative solutions altogether Manuscript received . Publisher Item Identifier S 0018-926X(98)08910-8. except for a few pattern points used as the expansion points of the extrapolation.To show how AWE can be applied, we assume that fI n (; )g has already been computed at a given direction ( 0 ; 0 ). A Taylor series expansion on (with constant) is then given by fI n ()g = fI n ( 0 )g + 1 q=1 M qwhere V (q) m (0) is the qth derivative of Vm() with respect to evaluated at 0 and we have dropped implied dependencies on and k. For plane wave excitations, the moments M q n can be trivially calculated and one could therefore increase the order of the expansion as needed to extend the validity of the approximation. This is better achieved by casting (2) into a Padè rational functi...

Simulating Wide Band Radar Response From Pec Targets Using Phase Extracted Basis Functions

“…(1) Compared with methods involving the entire impedance matrix, such as AWE/Padé approximation [1,2], MBPE method [6][7][8], and impedance interpolation method [9,10], the proposed method avoids the handling of full impedance matrix. Apparently, in a real world application, which may involve millions of unknowns (for instance, the case shown in Fig.…”

“…Several data reconstruction methods, such as the asymptotic waveform evaluation (AWE)/Padé approximation [1,2], Cauchy method [3][4][5], model-based parameter estimation (MBPE) [6][7][8], impedance matrix interpolation [9,10], and model order reduction [11] etc., have been developed to obtain the scattering results at the points beyond the frequency samples in the bandwidth without the direct calculation.…”

“…In the above methods, AWE/Padé approximation method [1,2] needs to generate a full impedance matrix and calculate its inverse and nth order derivative, which is very time and memory consuming. Cauchy method [3][4][5] uses the ratio of two rational functions to approximate the highly oscillatory function directly, which may compromise the accuracy especially in electrically large problems.…”

Efficient Proper Orthogonal Decomposition for Backscatter Pattern Reconstruction

“…Several methods and algorithms have been proposed for speeding up such a process. Of these, the asymptotic waveform evaluation (AWE) method has been successfully applied to analyze EM problems [1][2][3][4][5][6][7][8][9] and offers some features of model-order-reduction (MOR) techniques.…”

Fast and Accurate Radar Cross Section Computation Using Chebyshev Approximation in Both Broad Frequency Band and Angular Domains Simultaneously

“…For years there is a strong desire to find approximate solution techniques that can efficiently simulate a frequency response or predict monostatic RCS in the angular domains. The asymptotic waveform evaluation (AWE) technique is prevalent method, which provides a reduced-order model and has already been successfully applied to frequency extrapolation or angle extrapolation [7][8][9][10][11].…”