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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.

In this article, a universal methodology for implementing subarray architecture in an actual array antenna is proposed. By rotating the circularly polarized (CP) subarrays, the repetitiveness of the subarrays is ensured, thereby enabling the modularization of the subarrays as their feed layers are identical. Leveraging the characteristic of electromagnetic (EM) waves wherein the polarization orientation of the CP EM wave rotates in accordance with the excitation phase, the disordered polarization orientations induced by the subarray rotations are adjusted and synchronized through phase compensation. To verify the feasibility of the proposed methodology, three synthesized subarrays are implemented, comprising an $8\times 8$ domino-like subarrayed planar array, a $16\,\times \,12$ L-octomino subarrayed planar array, and a 349-element polyhex-shaped circle planar array. To further verify the effectiveness of the proposed methodology, the 349-element circle planar array is fabricated, assembled, and measured. Numerical results indicate that the proposed method is a promising approach for subarray implementation, offering notable radiation performance and facilitating modularization.

In this article, a machine-learning-assisted surrogate modeling (MLSM) method is presented to facilitate the circularly polarized (CP) antenna array synthesis with mutual coupling considered. In the premise that the vectorial active element pattern (Vec. AEP) of an array element is only susceptible to its surrounding region, the MLSM, primarily comprised of two deep neural networks (DNNs), is employed to predict the Vec. AEPs of all the array elements sequentially based on their corresponding subarray features. Subsequently, the co- polarization (CoP) pattern, cross-polarization (XP) pattern, and axial ratio (AR) of the CP array are computed accordingly. In this manner, the MLSM enables the fast performance prediction of arrays with arbitrary geometries and adds an extra degree of freedom (DoF), namely element position, to CP antenna array design. The trained MLSM is also employed to predict the performances of arrays with any given element numbers exploiting the ideology of heterogeneous transfer learning (HTL). To verify the effectiveness of the proposed framework, the MLSM is employed to predict the performance of arrays in several CP array syntheses. Numerical results demonstrate that the proposed MLSM is a feasible and efficient method for the fast prediction of CP arrays with arbitrary geometries and any given element numbers.

In this article, a fast direct solver is proposed for complicated electromagnetic (EM) scattering problems in planarly layered medium (PLM). For an arbitrary metallic object straddling two or more layers of the PLM, surface integral equations (SIEs) based on the matrix-friendly (MF) layered medium Green’s functions (LMGFs) are applied. When dealing with either slowly convergent problems or problems with multiple right-hand side excitations, a system matrix in the format of hierarchically off-diagonal low-rank (HODLR) is chosen, from which a fast matrix inverse can readily be computed. However, directly applying traditional HODLR for PLM cases suffers from fairly low compression rate, especially when large matrix blocks at coarse levels or objects straddling different layers are encountered. Consequently, a modified HODLR (MHODLR) structure involving reconstruction and recompression is further investigated, where key parameters are carefully studied in the context of PLM. Meanwhile, performance differences for PLM and free-space (FS) problems are thoroughly explored. Several numerical examples with increasing complexities are presented to validate the proposed LMGF-MHODLR as a promising fast direct solver for EM scattering problems in a lossless or lossy PLM background.

Based on the assumption that the pseudorandom characteristic of variational Born iterative method (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 bound and upper bound (UB) 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 UB is also guaranteed to converge probabilistically to the exact UB 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 (TK) and total variation (TV) regularization terms. Several typical models, including synthetic and experimental measurement data, are presented to verify the performance of the proposed method.