Affiliated with the
Communication & Space
Sciences Laboratory

Computational EM Modeling Techniques

Model-Based Parameter Estimation

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1-) The Simultaneous Interpolation of Antenna Radiation Patterns in Both the Spatial and Frequency Domains Using Model-Based Parameter Estimation
by Douglas H. Werner and Rene J. Allard

ABSTRACT: The Padé rational function fitting model commonly used for model-based parameter estimation (MBPE) in the frequency domain is enhanced to include spatial dependence in the numerator and denominator coefficients. This allows the function to interpolate an antenna radiated electric field pattern in both the frequency and spatial domains simultaneously, such that a single set of coefficients can be used to accurately reconstruct an entire radiation pattern at any frequency in the fitting-model range. A simple procedure is introduced for transforming interpolated electric fields into gain patterns using input impedance versus frequency curves also obtained via MBPE. The utility of this method is demonstrated by applying it to a dipole antenna over a frequency range of 150–950 MHz and using a polynomial representation in θ for the coefficient spatial dependence. It is also used to estimate radiation patterns for a three-element Yagi array between the frequencies of 470 and 500 MHz using a binomial representation for the spatial variation that includes terms dependent on θ as well as Φ. The use of this method for interpolating radiation patterns has at least two significant advantages; one being large compression ratios for the amount of data that must be stored to accurately reproduce patterns and the other being a significant decrease in the amount of time required for modeling problems with large computational domains.

2-) The Model-Based Parameter Estimation of Antenna Radiation Patterns Using Windowed Interpolation and Spherical Harmonics
by Rene J. Allard and Douglas H. Werner

ABSTRACT: Techniques previously reported for interpolating antenna radiation patterns simultaneously in both the spatial and frequency domains are reexamined here in order to develop new algorithms with improved efficiency and speed while maintaining comparable accuracy. To this end, interpolation in the frequency domain is constrained to a windowed scheme whereby a series of reduced-order Padé rational function fitting models of only three or four sampling frequencies are used to interpolate over a relatively large bandwidth. The use of this piece-wise technique is shown to reduce the complexity of determining the unknown coefficients without any significant loss in the resulting interpolation accuracy or increase in the required number of sampling frequencies. In this paper, exact analytical expressions are found for the unknown coefficients that allow the spatial domain interpolation to be performed entirely separate from the frequency domain interpolation. The technique is applied to the case of a 0.5 meter dipole modeled from 150 to 950 MHz, and for θ from 0 to 90 , using fitting windows with three and four sampling frequencies. The results are compared to those obtained using a previously developed generalized simultaneous interpolation procedure. In the spatial domain, spherical harmonics are introduced as model-based fitting functions for antenna radiation patterns. Specifically, interpolation procedures are developed using zonal harmonics and tesseral harmonics to model one- and two-dimensional far-field radiation patterns, respectively. The case of a z-oriented 0.5 meter dipole is considered to demonstrate the efficiency and accuracy obtained by applying these physically-based fitting models in the spatial domain. Zonal harmonics are used to interpolate far-field radiation patterns of this antenna for θ from 0 to 180 for several different frequencies over the range from 150 to 950 MHz. This example demonstrates the attractiveness of using spherical harmonics functions to accurately and efficiently interpolate radiation patterns in the spatial domain.

3-) A Model-Based Parameter Estimation Technique for Wide-Band Interpolation of Periodic Moment Method Impedance Matrices With Application to Genetic Algorithm Optimization of Frequency Selective Surfaces
by Ling Li, Douglas H. Werner, Jeremy A. Bossard, and Theresa S. Mayer
IEEE Transactions on Antennas and Propagation, VOL. 54. NO. 3, pp. 908-924, March 2006.

ABSTRACT: A model-based parameter estimation (MBPE) technique is introduced in this paper for efficiently interpolating periodic moment method (PMM) impedance matrices over a wide frequency band. In the model, only the Floquet harmonics that strongly affect the frequency band of interest are employed to approximate the matrix elements, while the contributions from all other higher-order harmonics are compactly represented by two additional terms. The derivation of the model is physics-based, and the objective is to find the coefficients of the terms in the model by utilizing the values of the impedance matrix elements calculated via PMM at only a few frequency points. The number and position of these fitting points can be pre-determined from the cutoff frequencies of the Floquet harmonics, which allows the MBPE interpolation process in this case to be completely automated. In other words, the number and position of the sampling points are only dictated by the periodicity of the frequency selective surface (FSS) structure and the frequency range of interest. Unlike many of the other scattering parameter-based techniques, the shape and the resonances in the response of the FSS do not have any impact on the construction of the interpolation model. This makes it particularly useful in genetic algorithm (GA) aided FSS design, since for a fixed periodicity and frequency range the MBPE interpolation is independent of the scattering response of candidate FSS designs. Several examples of the new PMM-MBPE approach are presented including one in which it is used to considerably speed up the GA-based design process for a reconfigurable FSS.

4-) A Model-Based Parameter Estimation Technique for Wideband Interpolation of Periodic Moment Method Impedance Matrices
by Ling Li, Douglas H. Werner, and Jeremy Bossard

ABSTRACT: There are several computational electromagnetic modeling techniques that have been developed specifically for the analysis and design of Frequency Selective Surfaces (FSS) [1]. One of the most popular and widely used of these techniques is the Periodic Method of Moments (PMM) [2]. The application of the PMM to the analysis of FSS geometries at a single frequency involves the construction and solution of a linear system of equations of the form Zi = v, where Z is the impedance matrix, i is the vector that contains the unknown coefficients of the basis functions used to expand the surface current, and v is the known excitation vector. For simulations where wideband analysis is required, the entire system has to be reconstructed and solved for each frequency sampling point in the band of interest. Therefore, finding a way to reduce the time involved in calculating the Z matrix is extremely important. In this paper, we introduce a Model-Based Parameter Estimation (MBPE) technique [3] that can be used to accelerate the computation of the PMM impedance matrix Z over wide frequency ranges for efficient analysis and design of FSS.

5-) Improved Model-Based Parameter Estimation Approach for Accelerated Periodic Method of Moments Solutions With Application to the Analysis of Convoluted Frequency Selected Surfaces and Metamaterials
by Xiande Wang, and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 58, Issue 1, pp. 122 - 131, January 2010.

ABSTRACT: An improved “smart” interpolation approach known as model-based parameter estimation (MBPE) is applied to the wide-band interpolation of periodic method of moments (PMM) impedance matrices for normal and oblique incidence cases. Prior to interpolation, easy to calculate but hard to interpolate, phase terms are removed fromthe impedance matrices. An efficient spectral-domain PMM formulation is introduced for the accelerated analysis of frequency selective surface (FSS) problems with a large number of unknowns, employing a one dimensional O(N log N) FFT-based method to speed up the computation of matrix-vector products within the bi-conjugate gradient (BCG) iterative solver, which is made possible by the asymmetric multilevel block-Toeplitz structure of the impedance-matrix. The MBPE interpolation algorithm provides a faster matrix fill time than the brute force method and is comparable or even faster than the 2-D FFT-based method for a large number of unknowns. It also has the advantage that it can be applied to non-uniform gridding cases. The accuracy and efficiency of the proposed techniques for large FSS problems are demonstrated by several design examples for both the normal and oblique incidence cases.We also apply this efficient analysis tool to the design of multiband single-layer FSS filters and artificial magnetic conductors (AMC) comprised of a 2-D periodic arrangement of convoluted metallic strips in the shape of a Hilbert curve. The multiband properties of the Hilbert curve FSS filters are studied for different iteration orders (i.e., different degrees of space-filling).

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