Rick W. Kindt

Array decomposition method for the accurate analysis of finite arrays

Presented in this paper is a fast method to accurately model finite arrays of arbitrary three-dimensional elements. The proposed technique, referred to as the array decomposition method (ADM), exploits the repeating features of finite arrays and the free-space Greens function to assemble a nonsymmetric block-Toeplitz matrix system. The Toeplitz property is used to significantly reduce storage requirements and allows the fast Fourier transform (FFT) to be applied in accelerating the matrix-vector product operations of the iterative solution process. Each element of the array is modeled using the finite element-boundary integral (FE-BI) technique for rigorous analysis. Consequently, we demonstrate that the complete LU decomposition of the matrix system from a single array element can be used as a highly effective block-diagonal preconditioner on the larger array matrix system. This rigorous method is compared to the standard FE-BI technique for several tapered-slot antenna (TSA) arrays and is demonstrated to generate the same accuracy with a fraction of the storage and solution time.

Statistical modeling of site-specific indoor channels in wireless communications

Based on a rigorous and validated full-wave method, we presented the extraction of statistical parameter (i.e. K-factor) for an indoor site-specific environment. These extracted statistics were subsequently used to compute the bit error rate (BER), useful for providing guidelines to network throughput. In this paper, we also provided useful information pertaining to site-planning via BER over our analyzed fading channel at different transmitting locations. It was further conjectured that an optimum transmitting position exists for different propagation channels. Finally, we verified that propagation paths obstructed with chairs resulted in a Rayleigh fading channel whereas line-of-sight channels could be modeled by Ricean distributions.

Propagation studies using rigorous methods for indoor wireless connectivity

We present the validation of a rigorous method for predicting indoor channel parameters at 2.4 GHz. We propose a domain decomposition (DD) technique, the basis of which is to decompose the structure into repeatable sections. In doing so, only the unique repeatable cells need to be stored, and thus a large structure (such as an entire building floor) can be modeled. In addition, we show pertinent statistical parameters of a time varying indoor propagation channel.

A multi-cell array decomposition approach to composite finite array analysis

In this paper, we introduce a multi-cell array decomposition method applicable to complex structures with repeating features. With this method, we demonstrate that some common real-world structures can be decomposed into repeating cells for significant storage reduction, enabling us to analyze the coupling between several configurations of dual-polarized tapered-slot antenna arrays supported by a ground-plane. Measurement comparisons are presented. For brevity, we refer to this analysis technique as the multi-cell array decomposition method (multi-cell ADM).

Input impedance characteristics of tapered slot antennas

Tapered slot antennas (TSA) are attractive because of their simplicity and broadband features. Although TSA have been used for several years in industry, their analysis has been restricted to metallic TSA whereas in most cases a dielectric substrate is employed. Also, so far previous analyses have primarily concentrated on pattern computations rather than input impedance. In this paper, the finite element-boundary integral method is employed for modeling practical TSA and input impedance calculations are given.

Fast frequency domain tools for system analysis of EMI/EMC topologies

With the increased use of wireless devices and applications, coupling and interference in electronic devices due to either intentional or un-intentional electromagnetic sources is of increased concern. Such sources can cause sufficient disruption to the circuit or chip logic to the point where the functionality and logic state of the electronic device can be altered due to such extraneous sources. In this paper, we employ fast EM algorithms such as the multilevel fast multipole moment method (MLFMM) and the hybrid finite-element boundary-integral (FE-BI) method for the analysis of coupling from external sources into realistic geometries. Specifically, the MLFMM is employed to analyze large-scale problems such as vehicular structures whereas the FE-BI method is used to analyze volumetric structures with dielectric media such as printed circuit boards. In this paper, the method of moments (MoM) accelerated by MLFMM is employed to analyze for the fields within an automobile chassis in the presence or absence of a wire harness and for different aperture sizes. The employed FE-BI method focuses on the analysis of plane wave illumination onto passive circuit geometries such as the microstrip interdigital filter and active circuit topologies like an active microstrip low noise amplifier.

Multi-level decomposition approach to translational symmetry problems of several dimensions

Summary form only given. Finite antenna arrays consisting of regularly-spaced, arbitrarily-shaped and identical elements exhibit translational symmetry. This property can easily be exploited in conventional planar (2D) arrays, and the concept can also be applied to structures of higher dimensionality. The rigorous analysis of complex antenna elements in a finite array has been successfully carried out using the finite element-boundary integral (FE-BI) method along with a decomposition approach. In these techniques, complicated and distributed systems are modelled by decomposing the structures into like blocks, where possible, for storage and computational savings. This approach is quite efficient in most regards and when applied to finite array problems, we refer to it as the array decomposition method (ADM). It is quite successful for smaller arrays, but results in a linear increase of matrix storage for increasingly large array problems. To counter the storage problem, the approach was extended to include far-zone decomposition via the fast multipole method (FMM) (Kindt, R. and Volakis, J.L., Radio Science, 2003). This newer approach limits the near-zone interaction storage of array systems to a small number of terms. This combination of simultaneous near-zone and far-zone decompositions, the array decomposition-fast multipole method (AD-FMM), results in fixed near-zone matrix storage, and overall storage requirements of O(N) for any sized array with a system with a total of N degrees of freedom. The effectiveness of this approach for several interesting problem types is discussed.

The array decomposition-fast multipole method [antenna arrays]

An innovative approach is presented for analyzing finite arrays of regularly spaced elements. Our approach is based on coupling an array decomposition technique with a multipole expansion for interacting distant elements. This hybrid technique results in Toeplitz storage for both near-zone matrices and far-zone translation operators, with FFT acceleration for the far-zone element interactions. The matrix storage is of the same order as a single array element, regardless of array size, hence removing the matrix storage bottleneck for large arrays. The total storage requirements of this method are only O(N), where N is the length of the solution vector. Hence, fast and rigorous analysis of very large finite arrays can be accomplished with limited resources.