5 research outputs found
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FFT and multigrid accelerated integral equation solvers for multi-scale electromagnetic analysis in complex backgrounds
textNovel integral-equation methods for efficiently solving electromagnetic problems that involve more than a single length scale of interest in complex backgrounds are presented. Such multi-scale electromagnetic problems arise because of the interplay of two distinct factors: the structure under study and the background medium. Both can contain material properties (wavelengths/skin depths) and geometrical features at different length scales, which gives rise to four types of multi-scale problems: (1) twoscale, (2) multi-scale structure, (3) multi-scale background, and (4) multi-scale-squared problems, where a single-scale structure resides in a different single-scale background, a multi-scale structure resides in a single-scale background, a single-scale structure resides in a multi-scale background, and a multi-scale structure resides in a multi-scale background, respectively. Electromagnetic problems can be further categorized in terms of the relative values of the length scales that characterize the structure and the background medium as (a) high-frequency, (b) low-frequency, and (c) mixed-frequency problems, where the wavelengths/skin depths in the background medium, the structure’s geometrical features or internal wavelengths/skin depths, and a combination of these three factors dictate the field variations on/in the structure, respectively. This dissertation presents several problems arising from geophysical exploration and microwave chemistry that demonstrate the different types of multi-scale problems encountered in electromagnetic analysis and the computational challenges they pose. It also presents novel frequency-domain integral-equation methods with proper Green function kernels for solving these multi-scale problems. These methods avoid meshing the background medium and finding fields in an extended computational domain outside the structure, thereby resolving important complications encountered in type 3 and 4 multi-scale problems that limit alternative methods. Nevertheless, they have been of limited practical use because of their high computational costs and because most of the existing ‘fast integral-equation algorithms’ are not applicable to complex Green function kernels. This dissertation introduces novel FFT, multigrid, and FFT-truncated multigrid algorithms that reduce the computational costs of frequency-domain integral-equation methods for complex backgrounds and enable the solution of unprecedented type 3 and 4 multi-scale problems. The proposed algorithms are formulated in detail, their computational costs are analyzed theoretically, and their features are demonstrated by solving benchmark and challenging multi-scale problems.Electrical and Computer Engineerin
New methods of partial transmit sequence for reducing the high peak-to-average-power ratio with low complexity in the ofdm and f-ofdm systems
The orthogonal frequency division multiplexing system (OFDM) is one of the most important components for the multicarrier waveform design in the wireless communication standards. Consequently, the OFDM system has been adopted by many high-speed wireless standards. However, the high peak-to-average- power ratio (PAPR) is the main obstacle of the OFDM system in the real applications because of the non-linearity nature in the transmitter. Partial transmit sequence (PTS) is one of the effective PAPR reduction techniques that has been employed for reducing the PAPR value 3 dB; however, the high computational complexity is the main drawback of this technique. This thesis proposes novel methods and algorithms for reducing the high PAPR value with low computational complexity depending on the PTS technique. First, three novel subblocks partitioning schemes, Sine Shape partitioning scheme (SS-PTS), Subsets partitioning scheme (Sb-PTS), and Hybrid partitioning scheme (H-PTS) have been introduced for improving the PAPR reduction performance with low computational complexity in the frequency-domain of the PTS structure. Secondly, two novel algorithms, Grouping Complex iterations algorithm (G-C-PTS), and Gray Code Phase Factor algorithm (Gray-PF-PTS) have been developed to reduce the computational complexity for finding the optimum phase rotation factors in the time domain part of the PTS structure. Third, a new hybrid method that combines the Selective mapping and Cyclically Shifts Sequences (SLM-CSS-PTS) techniques in parallel has been proposed for improving the PAPR reduction performance and the computational complexity level. Based on the proposed methods, an improved PTS method that merges the best subblock partitioning scheme in the frequency domain and the best low-complexity algorithm in the time domain has been introduced to enhance the PAPR reduction performance better than the conventional PTS method with extremely low computational complexity level. The efficiency of the proposed methods is verified by comparing the predicted results with the existing modified PTS methods in the literature using Matlab software simulation and numerical calculation. The results that obtained using the proposed methods achieve a superior gain in the PAPR reduction performance compared with the conventional PTS technique. In addition, the number of complex addition and multiplication operations has been reduced compared with the conventional PTS method by about 54%, and 32% for the frequency domain schemes, 51% and 65% for the time domain algorithms, 18% and 42% for the combining method. Moreover, the improved PTS method which combines the best scheme in the frequency domain and the best algorithm in the time domain outperforms the conventional PTS method in terms of the PAPR reduction performance and the computational complexity level, where the number of complex addition and multiplication operation has been reduced by about 51% and 63%, respectively. Finally, the proposed methods and algorithms have been applied to the OFDM and Filtered-OFDM (F-OFDM) systems through Matlab software simulation, where F-OFDM refers to the waveform design candidate in the next generation technology (5G)
Novel Inverse-Scattering Methods in Banach Spaces
The scientific community is presently strongly interested in the research of new microwave imaging methods, in order to develop reliable, safe, portable, and cost-effective tools for the non-invasive/non-destructive diagnostic in many fields (such as medicine, civil and industrial engineering, \u2026). In this framework, microwave imaging techniques addressing the full three-dimensional nature of the inspected bodies are still very challenging, since they need to cope with significant computational complexity. Moreover, non-linearity and ill-posedness issues, which usually affects the related inverse scattering problems, need to be faced, too. Another promising topic is the development of phaseless methods, in which only the amplitude of the electric field is assumed to be measurable. This leads to a significant complexity reduction and lower cost for the experimental apparatuses, but the missing information on the phase of the electric field samples exacerbates the ill-posedness problems.
In the present Thesis, a novel inexact-Newton inversion algorithm is proposed, in which the iteratively linearized problems are solved in a regularized sense by using a truncated Landweber or a conjugate gradient method developed in the framework of the l^p Banach spaces. This is an improvement that allows to generalize the classic framework of the l^2 Hilbert spaces in which the inexact-Newton approaches are usually defined. The applicability of the proposed imaging method in both the 3D full-vector and 2D phaseless scenarios at microwave frequencies is assessed in this Thesis, and an extensive validation of the proposed imaging method against both synthetic and experimental data is presented, highlighting the advantages over the inexact-Newton scheme developed in the classic framework of the l^2 Hilbert spaces