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.

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.

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.

Tightly coupled arrays are a class of antenna arrays that are very wideband and have applications in communication and sensor systems. In both applications, low side-lobe levels are of interest. However, as tightly coupled arrays have high inter-element coupling, care must be taken when finding a suitable set of excitation coefficients. To demonstrate this, we design a tightly coupled array. Second, we extend a previously published convex optimization algorithm to account for strong inter-element coupling. This optimization algorithm solely finds excitations implementable in a simplified hardware model. The results are compared with conventional taperings, and show that our algorithm can achieve an excitation with lower reflected power compared to the conventional taperings, while maintaining similar gain and side-lobe levels.

A convex optimization program is presented for wideband arrays. Constraints are imposed on the frequency variation of excitation coefficients to ensure that the optimal solution can be realized in a wideband active electronically scanned array (AESA). AESA implementation with true time delays (TTDs) and phase shifters are handled separately. We also discuss the general case of combining TTDs and phase shifters. Contrary to single-frequency optimization, the wideband optimization method presented here ensures that the computed excitation is optimal over a specified bandwidth. It is shown that there is a tradeoff between instantaneous bandwidth and sidelobe level. The proposed method works for both narrow and wideband arrays, as illustrated with examples. In addition to regular arrays, the method is also applicable to monopulse arrays. The optimization program is implemented in terms of embedded element patterns (EEPs) to account for and compensate for mutual coupling, radome, and platform effects.

The near-field contribution in the high-frequency method Shooting and Bouncing Rays (SBR) is investigated for installed antenna performance. Three SBR solvers, the in-house solver SIENT and two commercial solvers, are compared to a commercial full-wave solver. SIENT and one commercial solver have an option to disable near-field effects, which allows the strength of these effects to be investigated. The last solver also includes near-field effects. The results indicate an increase in accuracy when including near-field effects. The most notable difference in the far-field phase and the induced surface current are obtained for the in-house solver. Improvements for the surface current density is seen close to the antenna. On the tested platform, the difference in gain is not as notable but it is overestimated for both the in-house solver and the commercial solvers when excluding near-field terms.

This paper investigates the number of required data points to accurately represent the vector far-field information over the radiation sphere and its frequency variation for array antennas. The method needs to be explicit in terms of the excitation of the elements. We compare representations of far-field data on the sphere with two different approaches to spherical wave expansion representations and apply a data-driven model-order reduction to find a small-size representation. As is well known, a spherical wave expansion strongly reduces the number of required data points. Here, we show that accounting for the phase center of the elements further strongly reduces the number of required coefficients in the tested cases. The Loewner framework datadriven model-order reduction shrinks the required far-field data by an additional factor of 8-14 per mode coefficients, depending on the acceptable level of error. This reduction works well for the two investigated cases.