Hybrid LEGO-EFIE method applied to antenna problems comprising anisotropic media

Linear embedding via Green’s operators (LEGO) is a domain decomposition method in which complex radiation and scattering problems are modelled and solved by means of interacting electromagnetic "bricks". We propose an extension of LEGO able to handle bodies with anisotropic constitutive parameters and metallic objects (e.g., antennas). Since the anisotropic objects are dealt with LEGO, and the metallic parts are treated with the electric field integral equation (EFIE), we refer to the overall approach as hybrid LEGO-EFIE. The characterization of an electromagnetic brick which embeds an anisotropic object requires solving a volume integral equation (VIE). Since this procedure is carried out for each brick independently, the LEGO approach per se is extremely advantageous over the direct solution of a global VIE for all the bodies at once. Nonetheless, we further mix the hybrid LEGO-EFIE approach with the eigencurrents expansion method in order to tackle relatively larger problems. The technique is used to analyze a reconfigurable plasma antenna array (PAA) comprised of magnetized-plasma tubes placed around a two-dipole antenna array

Study of Mutual Coupling in Finite Antenna Arrays for Massive MIMO Applications

This thesis focuses on the study of mutual coupling (MC) in finite antenna arrays for base station antennas (BSAs) for Massive multiple-input multiple-output (MIMO) applications, with an emphasis on the development of a computationally-efficient modeling technique for the analysis of MC which can be readily applied in the design or synthesis schemes for BSAs. Traditionally, the effects of MC have been ignored or underestimated in the analyses performed within the information-theoretic-based communities by assuming idealized antenna elements with no MC between them or by considering the fictitious isotropic radiator models. In contrast, this thesis demonstrates the essentialness of proper modeling and inclusion of the physical antenna effects in the models used to predict the performance of a Massive MIMO system, as evidenced through the performed sum-rate analysis of a downlink line-of-sight (LoS) MIMO system in the presence of MC.The developed model for the analysis of MC is inspired by the concept of multiple scattering by which the overall effect of the antenna array MC can be determined by cascading the scattering responses of all array elements. Such an approach requires the full-wave characterization of only a single element in isolation, while the mutual interactions between different elements are modeled by approximating the incident field as a single plane wave with mutually-orthogonal polarization taken from the spherical wave expansion (SWE) of the field scattered from any other array element. This process is described mathematically through the iterative scheme based on the classical Jacobi and Gauss-Seidel iterative methods.Additionally, a sum-rate model of a downlink LoS multi-user MIMO system including the MC, has been developed. Herein, the effects of MC are accounted through the S-matrix of the BSA and the embedded element patterns (EEPs) of all BSA elements, which are used to approximate the channel matrix in a LoS environment. The S-matrix and the EEPs obtained by using the Jacobi-based MC model have been incorporated into the MIMO system model, showing good agreement in terms of the achievable sum rate compared to the reference result which uses the MoM-based simulation data. The accuracy and run-time benefits of the Jacobi-based model make it a possibly promising candidate for use in BSA design and synthesis applications, particularly when large array configurations need to be (repeatedly) analyzed

Analyzing Electromagnetic Systems on Electrically Large Platform Using a GTM-PO Hybrid Method with Synthetic Basis Functions

A hybrid method of generalized transition matrix (GTM) and physical optics (PO) with synthetic basis functions (SBF) is proposed to analyze electromagnetic systems on electrically large platforms. Based on domain decomposition method (DDM), the proposed approach is to divide the whole problem into a GTM region and a PO region. The GTM algorithm can simulate antennas and scatterers accurately, and the PO algorithm is applied to obtain current distribution on the electrically large platform. With the characteristics extraction technique using SBFs on the GTM models, the number of unknowns can be greatly reduced and the computational efficiency can be further improved. PO region is regarded as an environment background and the unknowns in the PO region need not to be directly solved. Numerical examples will be shown to demonstrate the feasibility of the hybrid method

AN EXTENSION OF THE LINEAR EMBEDDING VIA GREEN'S OPERATORS METHOD FOR THE ANALYSIS OF DISCONNECTED FINITE ANTENNA ARRAYS

We describe an extension of the linear embedding via Green’s operators (LEGO) method to the solution of finite antenna arrays comprised of disconnected elements in a homogeneous medium. The ultimate goal is the calculation of the admittance matrix and the radiation pattern of the array. As the basic idea is the inclusion of an array element inside a LEGO electromagnetic brick, the first step\u3cbr/\u3etowards the solution consists of the definition and numerical calculation of hybrid scattering-admittance operators which extend the notion of scattering operators of equivalent currents introduced in the past. Then again, the combination of many bricks involves the usual transfer operators for the description of the multiple scattering between the bricks. Moreover, to reduce the size of the problem we implement the eigencurrents expansion. With the aid of a numerical example we discuss the validation of the approach and the behaviour of the total CPU time as a function of the elements forming the array

Integral equation analysis of electromagnetic wave propagation in periodic structure and error analysis of various basis functions in projection of plane waves

In the first part of this dissertation, the integral equation approaches are developed to analyze the wave propagation in periodic structures. Firstly, an integral equation approach is developed to analyze the two-dimensional (2-D) scattering from multilayered periodic array. The proposed approach is capable of handling scattering from the array filled with different media in different layers. Combining the equivalence principle algorithm and connection scheme (EPACS), it can be avoided to find and evaluate the multilayered periodic Green\u27s functions. For 2^N identical layers, the elimination of the unknowns between top and bottom surfaces can be accelerated using the logarithm algorithm. More importantly, based on EPACS, an approach is proposed to effectively handle the semi-infinitely layered case in which a unit consisting of several layers is repeated infinitely in one direction. Secondly, the integral-equation (IE) method formulated in the spatial domain is employed to calculate the scattering from the doubly periodic array of three-dimensional (3-D) perfect electric conductor (PEC) objects. The special testing and basis functions are proposed to handle the problem with non-zero normal components of currents at the boundary of one period. Moreover, a relationship between the scattering from the PEC screen and its complementary structure is established. In order to efficiently compute the matrix elements from the IE approach, an acceleration technique with the exponential convergence rate is applied to evaluate the doubly periodic Green\u27s function. The formulations in this technique are appropriately modified so that the new form facilitates numerical calculation for the general cases. In the second part of this dissertation, the error analysis of various basis functions in projection of the plane wave was conducted, including pulse basis, triangular basis, the basis of their higher-order version, and the divergence-conforming basis on rectangular and triangular elements. The projection error is given analytical, asymptotically, and numerically. The application of the p-th order one-dimensional (1D) basis can result in the projection error which is asymptotically proportional to (p+1)-th power of the density of unknowns. Based on the analytical projection errors in 1D case, it is found when the expansion basis is fixed, the application of different testing functions only affect the constant coefficient of the projection error rather than the order. Generally, the error of divergence-conforming basis in projection of curl-free vectors is less than that of divergence-free vectors

Computation of multiscale time-harmonic electromagnetic radiation

The effect of installation for an antenna is key to understanding its performance in the intended operating environments. While existing formulations support such analysis, their mapping of calculations to distributed computing hardware does not support simulating installation environments of arbitrary size. This work builds upon existing techniques to simulate installed antenna behavior using scattering analyses tailored to system components. The scattering operations reveal opportunities to introduce approximate techniques which form generalized hybrid solvers. The source antenna (with both subwavelength-scale and wavelength-scale features) is modeled with the electric field integral equation (EFIE), and it interfaces with the installation site using the equivalence principle algorithm (EPA) as a domain decomposition method (DDM). The use of EPA to enclose the EFIE-modeled antenna generalizes the method to arbitrary antenna models. The electrically large exterior structures are modeled with physical optics (PO) without loss of generality to other approximate or high-frequency asymptotic methods through a Schur complement analysis of the continuous and discretized equations. The proposed Schur complement EPA-PO hybrid introduces clear physics with applicability to other formulations for the individual domains. The proposed hybrid also maps the PO calculations efficiently to distributed parallel computing resources; the parallel computations are demonstrated by executing the simulations on a hybrid parallel distributed- and shared-memory computing cluster. The calculation of antenna interactions with electrically large structures implies transition from wave-physics to ray-physics behaviors, which raises questions of reduced rank in the discretized operators. These questions are addressed by identifying the wave- to ray-physics transition and observing reduced rank in the space of plane wave functions