A large part of the geometry of array antennas is often partially defined by finite translational symmetries. Applying the method of moments (MoM) with the Rao–Wilton–Glisson (RWG)-like element on an appropriately structured mesh to these arrays results in an impedance matrix where the main part exhibits a multilevel block Toeplitz structure. This article introduces a memory-efficient construction method that effectively represents and reuses impedance calculations. The proposed method, applicable to electrically connected elements, also accounts for all nonsymmetric parts of the array. The core idea involves nine distinct electrically connectable components from which the array can be assembled. The derived multilevel block Toeplitz matrix is further utilized by an in-house inverse solver to achieve faster and more memory-efficient MoM current vector calculations. We demonstrate the method by computing the far-field of a 32×32 array and the scattering parameters of two tightly coupled 9×9 arrays. This approach reduces the memory allocation from O(N2xN2y) to O(NxNy) , for an Nx×Ny array.

Design and simulation of multi-band sharedaperture array antennas are often challenging. It incorporates multiple kinds of elements, and their position is interleaved. Designs often have strong cross-band coupling, and wideband full-wave simulations are required for assessment of their behaviour. Here, we show how a combined mesh decomposition and reusing method can be utilized to effectively investigate how two different edge (margin) elements impact the array behaviour. Utilizing the inherent partial Toeplitz structure of the impedance matrix, we demonstrate that non-conforming margin elements can be effectively included in the calculation framework to a marginal additional computational cost. This work develops an effective combination of our earlier proposed nine-component decomposition and the mesh reusing approach to store a minimal number of submatrices. This enables efficient full-wave analysis of multi-band arrays.

Simulating large, regular rectangular arrays with equidistant interspacing is challenging as the computational complexity grows quickly with array size. More so when considering multiple excitations, for example, to find embedded element patterns (EEPs). However, the array, appropriately meshed, leads to a multilevel Toeplitz structure in the method-of-moment (MoM) impedance matrix that can be used to mitigate the increased complexity. The problem is further complicated when elements are electrically connected, requiring specialized methods to handle currents flowing between elements. These connections also lead to strong coupling, putting high demands on the solvers used. This article presents two different accelerated solvers that both utilize the matrix structure via a novel mesh-partitioning algorithm, reducing storage and computational costs. The first is an iterative method based on multilevel fast Fourier transform (MLFFT), with an option to solve for all excitations at once, reducing solution time at the cost of memory. The MLFFT acceleration is described in detail. The second is based on a fast direct Toeplitz solver, adapted to a block-matrix structure, and shows excellent stability in scaling. Both methods are evaluated on two different array element types, for arrays with up to 900 elements. The results are compared with conventional direct and iterative matrix solvers. Improvements are seen in both time and required storage. The choice of the most efficient method depends on the problem parameters. Two different preconditioners are evaluated for connected elements. The accelerated methods handle connected elements while greatly outperforming regular matrix inversion methods with negligible reduction in accuracy.

The Active Reflection Coefficient (ARC) is a key factor in designing electrically small array antennas, as it accounts for the antenna's performance in a use-case. Accurate modeling of the ARC requires the complete set of scattering parameters, which requires a full-wave simulation. In this paper, we investigate how to accelerate full-wave frequency domain simulations by using the Loewner framework with adaptive frequency sampling, to accurately model the ARC. Here we compare interpolation on the ARC data directly with interpolation on the scattering parameters from which the corresponding ARC is determined, and interpolation on the scattering parameters, but with adaptive frequency sampling according to the estimated ARC error. The three strategies are tested on two cases, one 2 × 2 IoT array, and one 10 × 10 BoR Array. In both antenna cases, the latter strategy for accurately modeling the ARC yields the most accurate model for the least number of interpolation points used.

Large array antennas, constructed from disjoint irregular sub arrays, where each sub array port is digitally con-trolled, are of growing interest for communication and sensor applications. This paper investigates two different 28x30 antenna arrays, both operating as isophoric arrays (equal amplitude excitation), designed to support pencil beams across a large scan window. We focus on how various embedded element pattern approximations influence the optimization outcomes in terms of hexomino-based sub arrays and their effect on the peak sidelobe level (pSLL). Our analysis shows that commonly used embedded pattern approximations can cause peak sidelobe level deviations of up to 1.4 dB. Additionally, we demonstrate properties of a simplified and fast cost function to assess the pSLL in these arrays.

A new, accelerated MoM solver is presented and it is here used to investigate the convergence of active element impedance. The results show that the active impedance of the center element in a sufficiently large finite array is close to that of an element in an infinite array, as is known. The size requirement for this to hold will be investigated and compared to previously published works. The theory and methods behind the effective MoM solver will also be presented.

Frequency domain sweeps of array antennas are well-known to be time-intensive, and different surrogate models have been used to improve the performance. Data-driven model order reduction algorithms, such as the Loewner framework and vector fitting, can be integrated with adaptive frequency sampling algorithms, in an iterative scheme, to reduce the number of full-wave simulations required to accurately capture the requested frequency behavior of multiport array antennas. In this work, we propose two novel adaptive methods exploiting a block matrix function which is a key part of the Loewner framework generating system approach. The first algorithm leverages an inherent matrix parameter freedom in the block matrix function to identify frequency points with large errors, whereas the second utilizes the condition number of the block matrix function. The first method effectively provide a frequency domain error estimator, which is essential for improved performance. Numerical experiments on multiport array antenna S-parameters demonstrate the effectiveness of our proposed algorithms within the Loewner framework, where the proposed algorithms reach the smallest errors for the smallest number of frequency points chosen.

The finite partial translation symmetry apparent in array antennas can be exploited for effective calculation of the Method of Moments (MoM) impedance matrix. With a geometrical array decomposition built on nine subdomain components, the obtained MoM impedance matrix inherits a partial block Toeplitz structure, which enables fast calculation time and reduces memory allocation. In this paper, we further improve the calculation time by reusing already calculated submatrices of the MoM impedance matrix. By identifying corresponding elements between the nine components, already calculated submatrices can be extracted to create submatrices previously deemed as necessary to calculate. The reusing strategy reduces the number of submatrix calculations to perform from O(NxNy) to O(Nx+Ny), of a part of the impedance matrix, for an Nx×Ny array.