Combining the multilevel fast multipole method with the uniform geometrical theory of diffraction

The presence of arbitrarily shaped and electrically large objects in the same environment leads to hybridization of the Method of Moments (MoM) with the Uniform Geometrical Theory of Diffraction (UTD). The computation and memory complexity of the MoM solution is improved with the Multilevel Fast Multipole Method (MLFMM). By expanding the <i>k</i>-space integrals in spherical harmonics, further considerable amount of memory can be saved without compromising accuracy and numerical speed. However, until now MoM-UTD hybrid methods are restricted to conventional MoM formulations only with Electric Field Integral Equation (EFIE). In this contribution, a MLFMM-UTD hybridization for Combined Field Integral Equation (CFIE) is proposed and applied within a hybrid Finite Element - Boundary Integral (FEBI) technique. The MLFMM-UTD hybridization is performed at the translation procedure on the various levels of the MLFMM, using a far-field approximation of the corresponding translation operator. The formulation of this new hybrid technique is presented, as well as numerical results

Leaky wave antenna with amplitude controlled beam steering based on composite right/left-handed transmission lines

An antenna comprising two different composite right/left-handed transmission line structures is proposed which enables easy beam steering at an operation frequency of 10 GHz. The composite right/left-handed transmission lines are based on planar, periodically arranged via free unit cells, implemented in microstrip technology. Both transmission lines exhibit the infinite wavelength phenomenon which occurs at 9.72 GHz and 9.89 GHz, respectively. Thus, operating the different leaky wave structures at 10 GHz, radiation with azimuth angles of &plusmn;8&deg; and &plusmn;17&deg; can be achieved depending on the selected input port. In order to obtain a tunable main beam direction, the radiation patterns of both structures are superimposed by feeding them simultaneously. The influence of each guiding structure, and hence the direction of the main beam, can be controlled via the feeding amplitude. As a result of this, the beam can be steered between &plusmn;17&deg; with a gain of up to 10 dBi. The guiding structures are arranged in parallel with a clearance of <i>a</i>=12.2 mm which is less than half of the wavelength in free space. This allows in a further step the attachment of additional guiding structures in order to increase the tunable angle range or creating an antenna array with a small beamwidth in the elevation plane without the occurrence of grating lobes. An antenna prototype was fabricated and validated by measurements

Design and analysis of an isotropic two-dimensional planar Composite Right/Left-Handed waveguide structure

A two-dimensional isotropic Composite Right/Left-Handed (CRLH) waveguide structure is proposed which is designed for operation in <i>X</i>-band. The balanced structure possesses left-handed behaviour over a large bandwidth from 7.5 GHz up to its transition frequency at 10 GHz. Above this region, the unit cell behaves in a right-handed manner up to 13.5 GHz. Operating the structure within these bands yields a frequency dependent index of refraction ranging from &minus;2.5 &le; <i>n </i> &le; 0.8. Isotropic characteristics are obtained between 8.5 GHz &le; <i>f </i> &le; 12 GHz resulting in &minus;1.5 &le; <i>n</i> &le; 0.8. The planar CRLH structure is designed based on transmission line theory, implemented in microstrip technology and optimized using full-wave simulation software. An equivalent circuit model is determined describing the electromagnetic behaviour of the structure whose element values are obtained by even and odd mode analysis. The design of the unit cell requires an appropriate de-embedding process in order to enable an analysis in terms of dispersion characteristics and Bloch impedance, which are performed both

On the Hierarchical Preconditioning of the PMCHWT Integral Equation on Simply and Multiply Connected Geometries

We present a hierarchical basis preconditioning strategy for the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation considering both simply and multiply connected geometries.To this end, we first consider the direct application of hierarchical basis preconditioners, developed for the Electric Field Integral Equation (EFIE), to the PMCHWT. It is notably found that, whereas for the EFIE a diagonal preconditioner can be used for obtaining the hierarchical basis scaling factors, this strategy is catastrophic in the case of the PMCHWT since it leads to a severly ill-conditioned PMCHWT system in the case of multiply connected geometries. We then proceed to a theoretical analysis of the effect of hierarchical bases on the PMCHWT operator for which we obtain the correct scaling factors and a provably effective preconditioner for both low frequencies and mesh refinements. Numerical results will corroborate the theory and show the effectiveness of our approach

Ray tracing with multi-radiation transmitters

A restriction in using electromagnetic ray tracing for field prediction is given by the far-field condition: the results are only valid in the far-field region of the radiator. In this paper, it will be shown how ray tracing for accurate field computation can also be applied in the near-field regions of transmitters. The reduction of required large distances between transmitter and receiver is achieved by subdividing the transmitter in smaller subtransmitters. Even for complex transmitters, e.g. antennas with objects in close proximity such as metallic carrier platforms, subtransmitter models can be very efficiently generated by using the Multilevel Fast Multipole Method (MLFMM). This well-known integral equation solving technique makes very large problems in computational electromagnetics manageable. The subtransmitters can be directly generated based on this algorithm. A simulation example will show the improved modeling accuracy and options for simplification and refinement will also be discussed

Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method

Abstract. A hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This assembly procedure applys to both, the FE part as well as the BI part of the algorithm. The geometry is meshed into three-dimensional tetrahedra as finite elements and nearly orthogonal hierarchical basis functions are employed. The boundary conditions are implemented in a strong sense such that the boundary values of the volume basis functions are directly utilized within the BI, either for the tangential electric and magnetic fields or for the asssociated equivalent surface current densities by applying a cross product with the unit surface normals. The self-identified method for the global matrix assembly automatically discerns the global order of the basis functions for generating the matrix elements. Higher order basis functions do need more unknowns for each single FE, however, fewer FEs are needed to achieve the same satisfiable accuracy. This improvement provides a lot more flexibility for meshing and allows the mesh size to raise up to λ/3. The performance of the implemented system is evaluated in terms of computation time, accuracy and memory occupation, where excellent results with respect to precision and computation times of large scale simulations are found

Impact of Additional Antenna Groundplanes on RTK-GNSS Positioning Accuracy of UAVs

Precise position information is important for terrestrial and airborne surveying systems, such as unmanned aerial vehicles (UAVs). Those systems often rely on real-time kinematic (RTK) global navigation satellite systems (GNSSs) for position determination, where the GNSS antenna mounting environment impacts the GNSS position accuracy to a great extent. This paper investigates the impact of different supplementary groundplane shapes, sizes, and materials on multi-band patch and helical GNSS antennas at both, the UAV rover and RTK base station with respect to the achievable position accuracy. The groundplanes consist of solid aluminum sheets or copper plated printed circuit boards (PCBs) and are mounted directly underneath the GNSS antennas. Appropriate supplementary groundplanes are found to significantly improve the GNSS position accuracy in the majority of test cases.</p

Measurement and transformation of continuously modulated fields using a short-time measurement approach

Near-field measurements, which are performed in-situ, may suffer from the fact that the antenna under test (AUT) cannot be accessed to transmit or receive a specifically tailored test signal. In some scenarios, it might also be desired to test the AUT during its real operation state, especially when it comes to the verification of antenna systems. Therefore, the need to handle time- and space-modulated fields in combination with a time-harmonic near-field to far-field transformation (NFFFT) arises. For the case where unmanned aerial vehicles (UAVs) carry the field probe in in-situ measurement scenarios, long observation times, required for the resolution of the frequency spectra of modulated fields, are detrimental due to the UAV movement resulting in blurred measurement positions. The short-time measurement (STM) approach, presented in this article, offers a way to transform the measured field data using a time-harmonic NFFFT with short observation times for the collection of the individual field samples. Measurements are shown which demonstrate the applicability of the STM approach for the measurement and transformation of continuously time-modulated fields in different measurement scenarios.</p

Orthogonal frequency division multiplexing with amplitude shift keying subcarrier modulation as a reliable and efficient transmission scheme for self-mixing receivers

A new receiving scheme for self-mixing receivers is presented that overcomes the disadvantages of the self-heterodyne concept. Generally speaking, the self-mixing receiver offers immunity to phase noise and frequency offsets, especially at very high frequencies, since it does not require radio frequency local oscillators. Our proposed technique eliminates the drawbacks of the self-heterodyne transmission scheme, which are the poor power efficiency and the strong dependence on the continously transmitted carrier. A nonlinear system of equations is constructed that describes a phase retrieval problem for the reconstruction of the original transmit signal before self-mixing. Two different solution strategies, with restrictions in time and frequency domain, are presented. As a consequence, the self-mixing equation system is shown to be solvable with some a-priori information about the transmit signal. With this novel approach, the transmitted information is distributed over the full available bandwidth, and there is no special dependence on a certain subcarrier for the down-conversion. The general performance, regarding bit error ratio over signal to noise ratio, is improved by at least 2 dB as compared to the self-heterodyne transmission scheme. In the case of frequency selective channels, e.g. multi-path propagation, this improvement is shown to be much larger, because the presented approach is able to reconstruct the received subcarriers without the necessity of receiving all subcarriers

A fully probe corrected near-field far-field transformation technique employing plane-wave synthesis

The far-field behavior of an antenna under test (AUT) can be obtained by exciting the AUT with a plane wave. In a measurement, it is sufficient if the plane wave is artificially generated in the vicinity of the AUT. This can be achieved by using a virtual antenna array formed by a probe antenna which is sequentially sampling the radiating near-field of the AUT at different positions. For this purpose, an optimal filter for the virtual antenna array is computed in a preprocessing step. Applying this filter to the near-field measurements, the far-field of the AUT is obtained according to the propagation direction and polarization of the synthesized plane wave. This means that the near-field far-field transformation (NFFFT) is achieved simply by filtering the near-field measurement data. Taking the radiation characteristic of the probe antenna into account during the synthesis process, its influence on the NFFFT is compensated. The principle of the plane-wave synthesis and its application to the NFFFT is presented in detail in this paper. Furthermore, the method is verified by performing transformations of simulated near-field measurement data and of near-field data measured in an anechoic chamber