The multiple scattering effect is commonly present in electromagnetic (EM) scattering and can serve as a priori information to guide the solution of inverse scattering problems (ISPs). As depicted by the Green’s function, the multiple scattering effect exhibits both global and local features, i.e., the interaction between subscatterers is in principle global but the coupling strength is usually large in the neighboring region and decays with distance. For solving ISPs, the convolutional layer (CL) has been proven to be highly effective as a fundamental building block in learning-based solvers. Through supervised learning, CL-based networks can predict the refined result from the pre-solution of EM parameters. However, due to the limitation of local perception capability, CL can only model the local feature of the multiple scattering effect. To remedy this, this article proposes a globally perceptive (GP) module that cascades a global self-attention layer (GSAL) and a CL to capture both global interaction and local emphasis. To show the effectiveness of the GP module, a deep-learning scheme with global perception (DLSGP) is constructed using a U-shape structure, where the pre-solution is provided by the backpropagation (BP) or domain current (DC) method. Validation results using cross-set data, noisy data, and measured data demonstrate the high accuracy, strong generalization ability, and robustness of the proposed module. The study on the global perception ability further confirms that the proposed module contains more information on the multiple scattering effect. Since this effect is common in ISPs, this fundamental module can be applied to other learning-based solvers.

This study proposes a collaborative optimization framework for solving directional electromagnetic logging while drilling (LWD) inverse problems that integrates a physics-constrained sample generation strategy, a hybrid feature compression transformation, and an enhanced UNet++ architecture. First, a Markov chain perturbation strategy is employed to generate formation samples with physical continuity, ensuring that the generated samples closely resemble real geological variations. Second, a hybrid compression transformation method is designed to address the heterogeneous distribution of electromagnetic responses, enhancing feature separability. Finally, the proposed network is improved by dynamically fusing multi-scale and directional features through multi-scale convolutional branches and preserving vertical resolution using an asymmetric downsampling strategy. Experiments demonstrate that R-BInvNet reduces the training loss by 57.5% compared to U-Net and further reduces it by 43.1% compared to UNet++. It also exhibits higher inversion accuracy in complex synthetic formation models and MNIST-derived formation models. The framework offers an efficient solution for real-time geosteering and demonstrates potential in high-dimensional electromagnetic inversion.

This paper presents a modified frequency-hopping deep learning fusion framework (MFHFF) to solve multifrequency electromagnetic (EM) inverse scattering problems (ISPs) in real-time with high accuracy. The proposed MFHFF integrates advantages of the high accuracy of frequency-hopping method and the improved stability of simultaneous inversion strategy. First, the MFHFF cascades multiple monofrequency solvers, each combines a scattered field encoder and a pre-reconstructed result encoder. Additionally, the scattered field encoder utilizes adaptive average pooling to dynamically adjust scattered field data dimensions into standardized input specifications for subsequent convolutional layers. Second, the frequency-hopping connection (FHC) is implemented in the MFHFF by concatenating low-frequency inversion result to high-frequency pre-reconstructed result encoder. The low-frequency results serve as initial estimates for the high-frequency solver according to the FHC, thereby reducing the nonlinearity of high-frequency inversion and improving the accuracy of MFHFF. Third, the simultaneous inversion connection (SIC) is integrated into MFHFF to incorporate low-frequency features into high-frequency solver, facilitating simultaneous processing of multifrequency information and ensuring enhanced stability of MFHFF. The proposed MFHFF exploits an effective framework for solving multifrequency ISPs. The superior stability, accuracy, flexibility and generalization ability of the MFHFF have been demonstrated by the synthetic and the experimental results.

Based on the assumption that the pseudo-random characteristic of VBIM, the retrieved contrast parameter distribution in the discrete cells complies with the Gaussian mixture model (GMM). This article presents a constrained optimization framework that combines GMM and a hierarchical domain constraint (HDC) strategy for solving inverse scattering problems (ISPs). This GMM-HDC framework divides the whole inversion process into several stages, each stage operating within a reduced domain and subject to lower and upper bound constraints. The reduced inversion domain is determined by the GMM’s cluster analysis, thereby eliminating the need for manual threshold selection. And the HDC strategy offers a re-classification mechanism to avoid misclassification of scatterer cells. By narrowing the inversion domain, this approach effectively reduces the solution’s dimensionality, and mitigating the ill-posedness of ISPs. The bound constraint is determined by a hypothesis testing method. When there is prior information of contrast bound, the solution during iteration may not be within the exact bound due to the ill-posedness of ISPs. Therefore, the flexibility-bound constraint can provide more stability. When the prior information is not available, the determined upper bound is also guaranteed to converge probabilistically to the exact upper bound in case of degradation. In each iteration, a quadratic programming (QP) formula is introduced to solve the inverse subproblem in the VBIM, which enables the incorporation of the contrast range determined by the GMM-HDC framework. The formula includes both Tikhonov and total variation regularization terms. Several typical models, including synthetic and experimental measurement data, are presented to verify the performance of the proposed method.

The wavefront control of spin or orbital angular momentum (OAM) is widely applied in the optical and radio fields. However, most passive metasurfaces provide limited manipulations, such as the spin-locked wavefront, a static OAM combination, or an uncontrollable OAM energy distribution. We propose a reflection-type multi-feed metasurface to independently generate multi-mode OAM beams with dynamically switchable OAM combinations and spin states, while simultaneously, the energy distribution of carrying OAM modes is controllable. Specifically, four elements are proposed to overcome the spin-locked phase limitation by combining propagation and geometric phases. The robustness of these elements is analyzed. By involving the amplitude term and multi-feed technology in the design process, the proposed metasurface can generate OAM beams with a controllable energy distribution over modes and switchable mode combinations. OAM-based radio communication with four independent channels is experimentally demonstrated at 14 GHz by employing a pair of the proposed metasurfaces. The powers of different channels are adjustable by the provided amplitude term, and the maximum crosstalk is −9 dB, proving the effectiveness and practicability of the proposed method.

A robust hierarchical domain constraint (HDC) strategy is proposed for the multi-scale contrast objects reconstruction in this letter. The Monte Carlo method and point evaluation are adopted and modified for the classification of background and scatterers cells, the parameters of the background cells are set as the same as the actual background and removed from the inversion. The major work of the HDC strategy is to divide the inversion process into several stages, and the classification of cells is evaluated separately at each stage, making the classification reversible. And the HDC can effectively classify the inversion domain of low-contrast objects without negligence in the multi-scale contrast objects case, as well as the continuously varying inhomogeneous objects’ low-contrast parts. Another advantage of HDC is the threshold determining the classification of cells can be flexibly chosen. This robust constraint of the inversion domain compresses the solution space so that the ill-posedness of the inverse problem is mitigated, and better accuracy thus is achieved. In this letter, the HDC strategy is applied to the Variational Born Iterative Method (VBIM), numerical results validate the accuracy, robustness, and antinoise ability of the proposed VBIM-HDC.

This paper presents a novel early fusion framework (EFF) of deep learning (DL) for solving electromagnetic (EM) inverse scattering problems (ISPs) in real-time with high accuracy. The EFF integrates the scattered field encoder (SFE) and the backpropagation encoder (BPE). On the one hand, the nonlinear relationships constrained by the multiple scattering phenomenon, are introduced in the SFE, which guarantees better external scattering manifestations. On the other hand, the pre-reconstructed backpropagation approximation (BP) distributions provide prior information in ISPs via the BPE, which is in accordance with the internal scattering manifestations. The novel EFF concatenates the features extracted from the scattered field and the BP approximation, achieving more scattering manifestations in the solving process. Furthermore, the multiple scattering information and BP distributions regularize each other’s encoding process effectively, which achieves faster convergence and more stable inversion results. It is expected that the EFF exploits a general framework for solving ISPs, which can be adopted to different scenarios by importing different kinds of prior information according to the fusion approach. The superior veracity, stability and generalization ability of the EFF have been demonstrated by the synthetic and the experimental results.

This article proposes convex optimization of mutual inductance between multiantiparallel coils (MACs) for distance-insensitive wireless charging of air–ground robots. In order to reduce optimization costs, the proposed optimization method is developed by hybridizing analytical and numerical models. First, it is shown that the commonly used analytical model for MAC design becomes inaccurate as frequency increases. Second, a trial mutual inductance is introduced as an optimization variable. From the trial mutual inductance, an MAC is designed using the analytical model. Third, the realized mutual inductance of the analytically designed MAC is computed by a numerical model to correct the error of the analytical model. The difference vector$\bar {\rho }$between the realized and optimal mutual inductances is written as a function of the trial mutual inductance, and the$l_{2}$-norm of$\bar {\rho }$is minimized by changing the trial mutual inductance. The resultant optimization problem is shown to be convex, and it is conveniently solved by using a local searching method. Simulation results show that the proposed design method satisfies design specification much better than the conventional analytical-model-based design method. Using the proposed method, an MAC prototype is designed and fabricated, and a wireless charging system for air–ground robots is constructed and tested. Measurement results show that the efficiency of the designed MAC is maintained at around 80% in the transfer distance range of 15–55 mm, and stable efficiency is obtained when charging real air–ground robots of different heights.

ISAR image data of a single target is sparse in the image domain. Based on this sparseness, we could obtain a high-precision image reconstruction by down sampling the imaging data and getting the sparse solution of the indeterminate equations. In this work, we have studied the sparse data processing theory based on the compressed sensing (CS) method. We focus on the sparse reconstruction of the inverse synthetic aperture radar (ISAR) image. The imaging data is sparsely sampled and restored through the norm regularization framework. We compare the reconstruction results onL1andL1/2regularization frameworks, respectively. Then, we concentrate on the relationship between the reconstruction results and parameter settings in the reconstruction framework. Besides, we study the ISAR image in different radar bands. The numerical results show that theL1/2regularization framework is better than theL1framework in recovery accuracy and computational efficiency.

An irregular tiled array technique is proposed for the application of massive MIMO systems, where the uniformly spaced antenna array elements are irregularly divided into subarrays fed by only one radio frequency (RF) chain separately. As compared to conventional beamforming architecture, the number of RF chains is reduced to one-half or one-quarter of the original number by using domino-shaped subarrays or tetromino-shaped subarrays, respectively. Two beamforming architectures for such a framework are proposed and a minimum mean square error (MMSE) method is applied to design the layouts of irregular arrays efficiently. In the framework of single-user massive MIMO systems, numerical simulation results show that the proposed architectures outperform conventional beamforming architectures and antenna selection architecture under the same number of RF chains conditions. With saving half of the transceivers, the loss of gain of the state-of-the-art sparsely sampled array is 1.9dB in the broadside and 2.2 dB for scanning to 30° in comparison with reference array (i.e., one transceiver per element). By contrast, there is no loss of gain of domino-shaped irregular array (i.e., one transceiver per two elements) in the broadside as compared to reference array and the loss of gain will be about 1.5dB for scanning to 30°.

Equivalent models of antennas are useful for the fast simulation of vehicle-to-everything (V2X) communication. The existing antenna-equivalent models are inflexible because they assume rectangular antenna contour. This article presents a hybrid-equivalent surface-edge current model to overcome the limitation of the existing equivalent models. Based on Huygens' principle, a V2X communication antenna is equivalent to a conducting plate excited by equivalent surface magnetic current (ESMC). The sources of fields reflected by the conducting plate and diffracted by its edges are modeled as the image of ESMC and equivalent edge current (EEC), respectively. A hybrid-equivalent surface-edge current model is thus established, and it consists of ESMC, the image of ESMC, and EEC. The unknown sources in the proposed model are solved from near fields of the antennas, and the proposed model is then used to simulate the radiation performance of antennas installed on vehicles. The transmission coefficient between V2X communication antennas can also be calculated by using the proposed model and the electromagnetic reaction theorem. Simulations and experiments are performed to demonstrate the effectiveness of the proposed method. It is shown that the proposed equivalent model not only accurately models antennas with arbitrarily shaped contour but also significantly accelerates the integrated simulation of antennas and vehicles.

Electrical modeling of vehicular antennas is required for design of modern vehicle-to-everything communication networks. However, full-wave modeling and the existing equivalent source methods still ask for long computation time. To address this issue, a fast simulation method is proposed in this paper: a sparse equivalent source model is developed based on Huygens’ principle where a vehicular antenna is made equivalent to magnetic current placed on a finite conducting plate. The image theory and the uniform theory of diffraction are then applied, a modified Green’s function is derived, and the sparse equivalent source model is constructed to replace the original vehicular antenna. Because of its simple geometry and material, in comparisons with the existing methods, the proposed model uses significantly less expenditures for simulation of vehicular antennas while has better accuracy due to the consideration of the finite conducting plate. Simulations are performed to demonstrate the effectiveness and advantages of the proposed method, and a real-world experiment is designed and conducted to demonstrate the superiority of the proposed method with real measurement data. It is shown that the proposed method can save simulation time by four times, with less than 1-dB error compared to measurement.

Radio frequency (RF) source reconstruction is useful for RF radiation analysis and interference diagnosis in Internet of Things. Near field (NF) sampling is a critical step of RF source reconstruction. Accurate RF source reconstruction usually requires a large number of NF samples, which results in tremendous effort of NF sampling. This article presents an adaptive NF sampling method based on the skeletonization scheme. First, sources to be reconstructed are related to NF samples through integral equation (IE). Second, the IE is discretized with the method of moments, and thus the interaction matrix between source and field points is found. Third, strong rank-revealing QR factorization is applied to the interaction matrix, which results in a permutation matrix, a row skeleton matrix, and a transformation matrix. Finally, a small number of skeleton sampling points are selected by analyzing the permutation matrix. The fields at skeleton sampling points can be used to calculate the fields at other sampling points through the transformation matrix. Hence, one only needs to perform NF sampling at a small number of skeleton sampling points, which significantly reduces the expenditure of NF sampling. Simulations using synthetic and measurement data are presented to show the effectiveness and advantages of the proposed sampling method.

Influence of the half-space background on radar signatures of small consumer drones have been investigated in this paper. An integral equation method is presented to calculate the reflections of small drones within a half-space background efficiently and accurately, accelerated by the multilevel fast multiple algorithm. In addition, a two-level discrete complex image method has been applied to speed up the calculations of Sommerfeld integrals existing in the conventional half-space Green's functions. Variations of reflections as a function of variables such as polarization and frequency are explored for free space and half space respectively. Scattering data are also post-processed into two dimensional inverse synthetic aperture radar (ISAR) images to investigate the influence of half-space background further.

Electromagnetic scattering from conducting objects is investigated for the applications of underground detection. The air-soil composite is modeled by a classical half space where the dyadic Green's function can be defined and formulated. The electric field integral equation (EFIE) is employed to guarantee the accuracy and robustness of the analysis for arbitrarily shaped scatterers. The internal resonance of EFIE is first studied under typical working conditions (frequencies, soil water contents, etc.). It is shown that this spurious resonance is much alleviated due to loss of the soil. Next, the unbounded and ill-posed spectrum of the EFIE operator is remedied by a novel localized half-space Calderón preconditioner by further exploring the lossy nature of the background. Such preconditioning is extremely useful for objects containing multiscale features. Finally, the half-space multilevel fast multipole algorithm based on real-image approximation is adopted to accelerate the computation for electrically large scatterers. Several examples in the applications of subsurface sensing are demonstrated to validate the efficiency and accuracy of this method.

In this paper, phase-extracted (MPE) basis functions with both the traveling wave terms and the standing wave terms have been proposed to analyze the scattering from the electrically large targets. This kind of basis functions, called modified phase-extracted (MPE) basis function, can be defined on the relatively large patches and constructed with the higher order hierarchical vector basis functions. The constructing idea of the MPE basis function is first introduced. Then, their characteristics were compared with the relevant basis functions. It has been demonstrated that the MPE basis function is suitable for the scattering analysis of the perfect electric conductors (PECs) with smooth convex surfaces as well as the concave structures, such as the electrically large cavities. The numerical solutions to the electromagnetic scattering from both the convex targets and the cavity-like targets with strong mutual couplings have been given to show the capability of the MPE basis functions in the description of the complex distribution of the induced current on the PEC surfaces. Some numerical examples have been given to demonstrate the validation of this kind of basis functions.

In this paper, the tangential equivalence principle algorithm (T-EPA) combined with characteristic basis functions (CBFs) is presented to analyze the electromagnetic scattering of large-scale antenna arrays. The T-EPA is a kind of domain decomposition scheme for the electromagnetic scattering and radiation problems based on integral equation (IE). CBFs are macrobasis functions which are constructed by conventional local basis functions. By utilizing CBFs together with the T-EPA, the scattering analysis of large-scale arrays will be much more efficient with decreased unknowns compared with the original T-EPA. Further, the multilevel fast multipole algorithm (MLFMA) is applied to accelerate the matrix-vector multiplication in the T-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed technique.