arXiv subjects

Thomas F. Eibert

Publications and source records attributed to Thomas F. Eibert.

At least 19 recordsLinked to original sources

arXiv2026

An Explicit Higher-Order Dual Basis for a Multiplicatively Calderón Preconditioned Electric Field Integral Equation

One of the most effective means to precondition the electric field integral equation (EFIE) discretized with Rao-Wilton-Glisson (RWG) functions is the multiplicative Calderón preconditioner employing Buffa-Christiansen (BC) functions as a basis dual to the RWG basis. It results in a formulation that is free from the dense-discretization and the low-frequency breakdown. To generalize the multiplicative Calderón preconditioner from the low-order BC and RWG basis to higher orders, we utilize B-spline-based basis functions and establish the first explicit high-order dual basis. It can be regarded as a generalization of the BC functions to arbitrary polynomial degrees and constitutes a fundamental building block for other approaches that rely on a dual basis. Numerical results for the obtained preconditioner demonstrate a low and constant number of generalized minimum residual (GMRES) iterations independent of the number of unknonws and the polynomial degree for canonical and realistic perfectly electrically conducting (PEC) scatterers; a key to enable the full potential of higher-order bases.

math.NA↗

arXiv2026

High Speed High Signal-to-Noise Ratio Antenna Measurements -- Demonstration for UAV-Based Near-Field Measurements of Modulated Terrestrial Navigation Signals

Antenna measurements with high signal-to-noise ratio (SNR) require long measurement or integration times of the receiver and can, thus, lead to a very long duration of the measurements, especially if many frequency and spatial samples need to be collected. In order to speed up such measurements, an approach is presented, which collects all measurement samples with short measurement times, performs a Fourier transform of the measurement samples, bandpass filters the desired measurement signals with a small bandwidth, and obtains high-SNR measurement samples according to the short measurement times by inverse Fourier transform. This approach can be utilized with single-frequency continuous wave (CW) transmit signals, but also with transmit signals containing several discrete frequency components, as, e.g., found for periodically modulated CW carriers. The approach is first worked out and demonstrated for simulated test data. Next, it is utilized for the processing of modulated near-field (NF) measurement data collected via an uninhabited aerial vehicle (UAV) at a Doppler high-frequency omnidirectional radio range (DVOR) and at the localizer of an instrument landing system (ILS). The extracted CW NF data is transformed into the far field (FF) and diagnostic information is obtained from the underlying inverse source solutions.

eess.SP↗

arXiv2026

A Stabilized Multilevel B-Spline-Based Fast Integral Method for the Solution of the Electric Field Integral Equation

We present a multilevel B-spline-based fast integral method for the solution of the electric field integral equation (EFIE), combining fast Fourier transformation (FFT)-compatible kernel interpolation with robust high-order interpolation. Existing FFT-accelerated global Lagrange-based approaches rely on equidistant interpolation points and can, therefore, suffer from Runge-type instabilities at high interpolation orders, limiting robust high-accuracy compression. In contrast, B-splines on equidistant knot vectors overcome these instabilities and enable robust high-order interpolation for accurate matrix compression. Replacing Lagrange interpolation by B-spline interpolation is, however, non-trivial: B-spline coefficients do not coincide with function values at the interpolation points, and the associated sampling matrices can become ill-conditioned. To address these challenges, we introduce a knot-removal stabilization strategy, combined with exact interlevel transfers based on knot insertion, yielding accurate, well-conditioned multilevel interpolation. Moreover, we propose a factorization strategy that preserves the null space of the scalar potential operator up to machine precision and is compatible with low-frequency preconditioning techniques. Numerical results for both canonical and realistic geometries demonstrate robust high-order interpolation without the breakdown observed for Lagrange-based approaches and confirm $\mathcal{O}(N)$ complexity.

math.NA↗

arXiv2026

An Indoor Localization Technique Utilizing Passive Tags and 3-D Microwave Passive Radar Imaging

A privacy-compliant indoor localization approach utilizing a 3-D near-field (NF) passive radar imaging technique is presented. This technique leverages ubiquitously radiated electromagnetic fields for imaging, with passive tags introduced to enhance the strength of scattering fields, thereby enabling precise localization at the imaging level. The method also supports localization in non-ideal imaging scenarios, such as for limited bandwidth or in highly-reflective environments. Based on their geometrical properties the simple and low-cost passive tags enable intuitive differentiation between individuals or objects. Associated privacy protection mechanisms are discussed, where the frequency-varying properties of the passive tags provide additional flexibility and potential applications under privacy and ethical considerations. Several forms of passive tags are presented, where both simulation and experimental results validate the effectiveness of the proposed passive tag designs.

eess.IV↗

arXiv2026

Polarization-Aware Ray-Tracing Enhanced Back-Projection Algorithm for Microwave Imaging in Complex Multipath Environments

A ray-tracing (RT) enhanced back-projection algorithm (RT-BPA) for microwave imaging in multipath environments is presented. By tightly incorporating the concept of ray-tracing into a generalized version of traditional BPA, this method ensures improved image quality by addressing two important issues. First, when the line-of-sight (LOS) path is obstructed, reflected paths, if available, enable imaging of hidden targets, which extends the applicability of the standard BPA beyond its normal use case. Second, the consideration of reflected ray-paths is equivalent to virtually increasing the aperture size, thus, improving image resolution without requiring new measurements. A key factor in achieving these advancements is the consideration of the vector nature of electromagnetic waves with polarization-dependent phase compensation, which is often ignored when employing a scalar-wave based formulation of the electromagnetic vector field. In addition, the presented method employs a shooting and bouncing rays (SBR) framework, offering better flexibility compared to manual path evaluation in existing RT-BPAs.

eess.IV↗

arXiv2026

Multipath Exploitation in Highly Reflective Environments for Enhanced Microwave Imaging via Inverse Source Reconstruction

Multipath effects significantly influence the quality of microwave imaging in highly reflective environments, while the physical measurement aperture size constrains resolution. It is shown that by exploiting multipath reflections, improved resolution can be achieved while maintaining acceptable artifact levels. Based on image theory, strong scattered fields from an ideal reflection plane can be represented by virtual image sources. Using a single-frequency inverse source solver, the spatially distributed original and image sources are reconstructed and separated, which allows separate application of the imaging algorithm for both of them. The coherent combination of both sets of sources together with appropriate phase correction results in an effective aperture expansion that yields superior resolution. Furthermore, this separation strategy significantly mitigates interference artifacts. Simulation results, supported by theoretical analysis and comparison with a ray-tracing enhanced backprojection algorithm are presented to verify the effectiveness of the proposed approach.

eess.IV↗

arXiv2026

Phase-Corrected Near-Field Microwave Imaging via Inverse Source Reconstruction with Modulated Signals

An inverse source reconstruction (ISR) based 3-D near-field (NF) passive radar microwave imaging method utilizing modulated signals is presented. The modulated signals from a non-cooperative transmitter are scattered by the targets of interest and captured by a fixed reference antenna together with an NF scanning probe at different positions. By normalizing with the reference signals, spatial coherence of the NF observations is obtained, and a single-frequency inverse source solver is subsequently utilized for ISR and image generation. A corresponding phase correction method is proposed for the coherent superposition of multi-frequency images and verified through simulations. In addition, it is shown that for realistic narrowband signals, an incoherent imaging approach is sufficient. The presented technical scheme is validated using a planar scanning system in a typical office room, where software-defined radios are employed for the transmitting and receiving of narrowband orthogonal frequency-division multiplexing signals at Wi-Fi operating frequencies. With the aid of background subtraction and reference signals, images of a mannequin placed in the office room are successfully obtained.

eess.IV↗

arXiv2026

3-D Near-Field Passive Radar Imaging Using Multiple Illumination Sources

Near-field (NF) passive radar imaging depends on the illumination of the imaging scene by a non-cooperative transmitter (Tx). It is demonstrated that combining imaging results obtained with Tx antennas at different positions can enhance the performance of passive radar imaging. On the one hand, multiple Tx antennas provide diverse illumination perspectives, reducing the likelihood of unilluminated regions on the targets of interest (TOIs). On the other hand, the coherent summation of imaging results obtained for different illuminations helps to suppress potential artifacts. This approach is in particular advantageous for imaging complex objects with concave structures such as dihedral arrangements, where the ghosts due to multiple reflections are highly configuration-dependent. For each illuminating configuration, a single-frequency inverse source solver is utilized to reconstruct the equivalent sources of the TOIs and the resulting single-frequency images are then superimposed coherently with corresponding phase and magnitude correction methods. The obtained multi-frequency images are finally coherently combined to enhance the imaging quality. Both simulation and measurement results are presented to validate the effectiveness of the approach.

eess.IV↗

arXiv2024

On the Solution of Linearized Inverse Scattering Problems in Near-Field Microwave Imaging by Operator Inversion and Matched Filtering

Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous approach is the explicit inversion of the forward scattering operator, which is performed in this work for quasi-monostatic imaging scenarios based on a planar plane-wave representation according to the Weyl-identity and hierarchical acceleration algorithms. The inversion is achieved by a regularized iterative linear system of equations solver, where irregular observations as well as full probe correction are supported. In the spatial image generation low-pass filtering can be considered in order to reduce imaging artifacts. A corresponding spectral backprojection algorithm and a spatial back-projection algorithm together with improved focusing operators are also introduced and the resulting image generation algorithms are analyzed and compared for a variety of examples, comprising both simulated and measured observation data. It is found that the inverse source solution generally performs better in term of robustness, focusing capabilities, and image accuracy compared to the adjoint imaging algorithms either operating in the spatial or spectral domain. This is especially demonstrated in the context of irregular sampling grids with non-ideal or truncated observation data and by evaluating all reconstruction results based on a rigorous quantitative analysis.

eess.IV↗

arXiv2022

Phase Retrieval for Partially Coherent Observations

Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets are coherently linked to each other - which is a reasonable assumption for our objective of antenna measurements. Two classes of measurement setups are discussed which can provide this kind of extra information: multi-probe systems and holographic measurements with multiple reference signals. We propose several formulations of the corresponding phase retrieval problem. The simplest of these formulations poses a linear system of equations similar to an eigenvalue problem where a unique non-trivial null-space vector needs to be found. Accurate phase reconstruction for partially coherent observations is, thus, possible by a reliable solution process and with judgment of the solution quality. Under ideal, noise-free conditions, the required sampling density is less than two times the number of unknowns. Noise and other observation errors increase this value slightly. Simulations for Gaussian random matrices and for antenna measurement scenarios demonstrate that reliable phase reconstruction is possible with the presented approach.

eess.SP↗

arXiv2022

A Weak-Form Combined Source Integral Equation with Explicit Inversion of the Combined-Source Condition

The combined source integral equation (CSIE) for the electric field on the surface of a perfect electrically conducting scatterer can be discretized very accurately with lowest-order Rao-Wilton-Glisson basis and testing functions if the combined-source (CS) condition is enforced in weak form. We introduce a technique to accelerate the iterative solution for this kind of CSIE. It is demonstrated that the iterative solution of the equation system can be performed very efficiently by explicitly inverting the weak-form CS condition in any evaluation of the forward operator. This reduces the number of unknowns and results in improved convergence behavior at negligible, linear cost. Numerical results demonstrate that the new CSIE outperforms the classical CFIE for high-accuracy simulations.

math.NA↗

arXiv2022

A mm-Wave Patch Antenna with Broad Bandwidth and a Wide Angular Range

A novel mm-wave microstrip-fed patch antenna with broad bandwidth and wide angular coverage suitable for integration in planar arrays is designed, analyzed and verified by measurements. The antenna provides a bandwidth of 13.1% between 34.1 GHz and 38.9 GHz, which is achieved by a slotted multiple resonances microstrip patch and a matching circuit in microstrip technology. The antenna is built on RO3003 substrate with top and ground layers, which is low cost compared to other techniques. For simple integration with microstrip and frontend circuits, the feeding happens in the top layer with a microstrip coupling gap feed. The wide half power beamwidth is achieved by suitably designed parasitic patches for the first resonant mode. The second resonant mode has a wide half power beamwidth by default. The half power beamwidth is between 100° and 125° within the matched bandwidth, which is a very good value for a microstrip patch antenna radiating over a ground plane. The measured input impedance and radiation characteristic show very good agreement with simulation results.

eess.SP↗

arXiv2022

A Millimeter-Wave Self-Mixing Array with Large Gain and Wide Angular Receiving Range

The concept of self-mixing antenna arrays is presented and analyzed with respect to its beneficial behavior of large gain over a wide angular range. The large gain is attained by an antenna array with large element spacing, where all array element signals are combined approximately coherently over the entire angular receiving range. This functionality is achieved by the self-mixing principle, where an exact description via an intermediate frequency (IF) array factor is derived. For verification purposes, a 4 x 2 self-mixing array is fabricated and measured in the frequency range from 34 GHz to 39 GHz. A multiple-resonances millimeter-wave microstrip patch antenna has been especially developed to achieve large bandwidth and a wide angular receiving range. The broad beamwidth is achieved by two parasitic patches and suitable radiation characteristics of the resonant modes. The self-mixing of the receive signal is realized at each antenna element by a Schottky diode with an optimized operating point. The down-converted array element signals are then combined and measured at the IF. The receive power is increased significantly over a large angular range as compared to conventional array feeding techniques. The simulation results are verified by measurements, which show very good agreement.

eess.SP↗

arXiv2022

A Combined Source Integral Equation with Weak Form Combined Source Condition

A combined source integral equation (CSIE) is constructed on the basis of the electric field integral equation (EFIE) to solve electromagnetic radiation and scattering problems containing perfect electrically conducting bodies. It is discretized with Rao-Wilton-Glisson basis functions only, for both electric and magnetic surface current densities. The combined source condition, which ensures the uniqueness of the solution and circumvents the interior resonance problem, is implemented as a weak form side condition. Compared to the common combined field integral equation, the proposed CSIE shows superior accuracy for sharp edges as well as structures with the interior resonance problem. Furthermore, the iterative solver convergence of the CSIE is faster than for the EFIE, which shows about the same accuracy as the CSIE. Results of numerical scattering simulations are presented to demonstrate the accuracy of the presented CSIE.

math.NA↗

arXiv2022

An Accurate Low-Order Discretization Scheme for the Identity Operator in the Magnetic Field and Combined Field Integral Equations

A new low-order discretization scheme for the identity operator in the magnetic field integral equation (MFIE) is discussed. Its concept is derived from the weak-form representation of combined sources which are discretized with Rao-Wilton-Glisson (RWG) functions. The resulting MFIE overcomes the accuracy problem of the classical MFIE while it maintains fast iterative solver convergence. The improvement in accuracy is verified with a mesh refinement analysis and with near- and far-field scattering results. Furthermore, simulation results for a combined field integral equation (CFIE) involving the new MFIE show that this CFIE is interior-resonance free and well-conditioned like the classical CFIE, but also accurate as the EFIE.

math.NA↗

arXiv2022

Multi-Frequency Phase Retrieval for Antenna Measurements

Phase retrieval problems in antenna measurements arise when a reference phase cannot be provided to all measurement locations. Phase retrieval algorithms require sufficiently many independent measurement samples of the radiated fields to be successful. Larger amounts of independent data may improve the reconstruction of the phase information from magnitude-only measurements. We show how the knowledge of relative phases among the spectral components of a modulated signal at the individual measurement locations may be employed to reconstruct the relative phases between different measurement locations at all frequencies. Projection matrices map the estimated phases onto the space of fields possibly generated by equivalent antenna under test (AUT) sources at all frequencies. In this way, the phase of the reconstructed solution is not only restricted by the measurement samples at one frequency, but by the samples at allfrequencies simultaneously. The proposed method can increase the amount of independent phase information even if all probes are located in the far field of the AUT.

eess.SP↗

arXiv2022

Compact Uniform Circular Quarter-Wavelength Monopole Antenna Arrays with Wideband Decoupling and Matching Networks

Two novel decoupling and matching networks (DMNs) in microstrip technology for three-element uniform circular arrays (UCAs) are investigated and compared to a more conventional DMN approach with simple neutralization lines. The array elements are coaxially-fed quarter-wavelength monopole antennas over a finite groundplane. Three-element arrays are considered since UCAs with an odd number of elements are able to provide an almost constant maximum array factor over the whole azimuthal angular range. The new designs are explained from a theoretical point of view and their implementations are compared to four- and three-elements UCAs without DMN in terms of decoupling and matching bandwidth as well as beamforming capabilities. In addition to excellent decoupling and matching below -16 dB, a broader bandwidth is obtained by the two DMNs. The reasons for the enhanced bandwidth are similar in both cases: By introducing several circuit elements offering additional degrees of freedom, matching of the monopole input impedances at different frequencies becomes feasible. One of the presented designs offers a larger bandwidth, while the other design is able to provide a better total efficiency. Scattering parameters, radiation patterns, beamforming capabilities, and enhanced gain are all verified by measurements over the operating bandwidth.

eess.SP↗

arXiv2022

Accuracy and Conditioning of Surface-Source Based Near-Field to Far-Field Transformations

The conditioning and accuracy of various inverse surface-source formulations are investigated. First, the normal systems of equations are discussed. Second, different implementations of the zero-field condition are analyzed regarding their effect on solution accuracy, conditioning, and source ambiguity. The weighting of the Love-current side constraint is investigated in order to provide an accurate problem-independent methodology. The transformation results for simulated and measured near-field data show a comparable behavior regarding accuracy and conditioning for most of the formulations. Advantages of the Love-current solutions are found only in diagnostic capabilities. Regardless of this, the Love side constraint is a computationally costly way to influence the iterative solver threshold, which is more conveniently controlled with the appropriate type of normal equation. The solution behavior of the inverse surface-source formulations is mostly influenced by the choice of the reconstruction surface. A spherical Huygens surface leads to the best conditioning, whereas the most accurate solutions are found with a tight, possibly convex hull around the antenna under test.

physics.comp-ph↗