Angle Grid Research Articles

Flat Beam Design for Massive MIMO Systems via Riemannian Optimization

In this letter, we propose a novel algorithm to design beamformer with flat beampattern for massive multi-input-multi-output systems where the base station is equipped with large-scale uniform planar array (UPA). This flat beam can be both used for transmissions in broadcast channels and beam alignment for millimeter wave systems. Given the ideal flat beampattern, the beamforming design is formulated as the minimum mean squared error problem under the constraint of total transmit power or equal per-antenna power. A twofold alternative Riemannian optimization algorithm is proposed to solve the problem and the conventional method via multiconvex transformation is used for algorithm initialization. For UPA with massive antennas, the angle grid for beamforming should be dense enough and our proposed scheme can achieve better beampattern with even lower computational complexity compared to conventional schemes. Simulations validate the superiority of our proposed scheme.

Buckling and Postbuckling of Concentrically Stiffened Piezo-Composite Plates on Elastic Foundations

This research presents the modeling and analysis for the buckling and postbuckling behavior of sandwich plates under thermal and mechanical loads. The lay-up configurations of plates are laminated composite with concentric stiffener and surface mounted piezoelectric actuators. The plates are in contact with a three-parameter elastic foundation including softening and/or hardening nonlinearity. Several types of grid shapes of stiffeners are studied such as ortho grid, angle grid, iso grid, and orthotropic grid. The equations of structures are formulated based on the classical lamination theory incorporating nonlinear von-Karman relationships. The stress function and Galerkin procedure are applied to derive explicit formulations of the equilibrium paths. New results are introduced to give the influences of voltage through the thickness of piezoelectric actuators, different stiffeners, and nonlinear elastic foundations.

Semi-Blind Millimeter-Wave Channel Estimation Using Atomic Norm Minimization

Exploiting the inherent sparsity of millimeter-wave channels, the channel estimation problem is formulated as an atomic norm minimization that enhances sparsity in the continuous angles of arrival and departure. A semi-blind channel estimator is developed to track the time-varying channel dynamics, which is formulated as a non-convex problem. To solve the formulated channel estimation problem, we develop a computationally efficient conjugate gradient descent method based on non-convex factorization which restricts the search space to low-rank matrices. Simulation results are presented to illustrate the superior channel estimation performance of the proposed algorithms compared with the existing compressed-sensing-based estimators with finely quantized angle grids.

Bounds and Conditions for Compressive Digital Holography Using Wavelet Sparsifying Bases

Numerous experiments have been conducted with success in the field of compressive digital holography, but the theory to determine optimal measurement conditions is lagging behind. In contrast to a prior study that expects object wavefields to be sparse in the spatial domain, we investigate how the configuration of the interferometer influences the reconstruction of wavefields that are sparse in a multiresolution orthogonal wavelet basis. In particular, we derive expressions for the coherence between the free-space wave propagation operator and the basis functions of a Shannon multiresolution representation as a function of the wavelength, the propagation distance, the image sensor's pixel pitch, and the scale of the basis functions. These expressions reveal that the coherence as a function of the Fresnel number is subject to specific scaling and translating rules as the scale of the basis functions changes. For a multiresolution orthogonal wavelet representation and digital holograms that are recorded in the near field, we deduce subsequently the optimal configuration of the interferometer and we show by means of hypothesis testing that the associated phase transition bound coincides with the weak threshold for block-sparse compressive sensing with a block length of 2, which is an optimal bound for the class of complex-valued compressive sensing problems. By means of experiments with a USAF 1951 resolution target and an angle grid, we validate our findings and demonstrate that the reconstructed object wavefields are resilient to sparsity defects and additive noise.

A simplified GNSS tropospheric delay model based on the nonlinear hypothesis

We have derived a global zenith tropospheric delay simplified model (GZTDS), assuming that the troposphere is a nonlinear system and can be handled as a black box. The GZTDS and its variation in time can be expressed as a series of cosine components, which represent various periods of tropospheric delay changes. Undetermined coefficients are extracted by data fitting from the mean sea level historical data of the global geodetic observing system atmosphere on a 2° × 2.5° grid. A combination of our model and the Vienna Mapping Function 1 can predict slant delays for global navigation satellite system sites using the zenith angle and nearest grid coordinates as the input and generate a global slant tropospheric delay simplified model (GSTDS) and its extension. Comparisons with the zenith delays provided by the International GNSS Service at 358 sites show that the biases are between −3.36 and 2.41 cm, and the mean standard deviation is 3.46 cm for the year 2014. This result is at the same level of accuracy as the global pressure and temperature 2 wet model (GPT2w), with the GZTDS requiring no local meteorological parameters. The accuracy of GSTDS depends on the zenith angle and shows nonlinear characteristics. Several statistics of biases and standard deviations illustrate model adaptation with respect to latitude or altitude.

A Novel STAP Based on Spectrum-Aided Reduced-Dimension Clutter Sparse Recovery

Space-time adaptive processing based on clutter sparse recovery (SR-STAP) methods outperform traditional statistical-STAP algorithms in scenarios with limited training numbers. However, the computational burden of current SR-STAP methods is extremely heavy, particularly when the number of discretized angle and Doppler grid points is large, which hinders these methods from coming into practical use. This letter proposes a spectrum-aided reduced-dimension SR-STAP method to overcome this issue. The proposed method employs the clutter spectrum estimated by training samples to design the reduced-dimension dictionary. By solving a reduced-dimension sparse recovery problem, the computational load of the proposed method can be reduced significantly while only slightly degrading the performance of clutter suppression and target detection compared with current SR-STAP methods. Numerical experiments using both simulated and measured data validate the effectiveness of the proposed method.

Cyclotron resonant scattering feature simulations

Electron cyclotron resonant scattering features (CRSFs) are observed as absorption-like lines in the spectra of X-ray pulsars. A significant fraction of the computing time for Monte Carlo simulations of these quantum mechanical features is spent on the calculation of the mean free path for each individual photon before scattering, since it involves a complex numerical integration over the scattering cross section and the (thermal) velocity distribution of the scattering electrons. We aim to numerically calculate interpolation tables which can be used in CRSF simulations to sample the mean free path of the scattering photon and the momentum of the scattering electron. The tables also contain all the information required for sampling the scattering electron's final spin. The tables were calculated using an adaptive Simpson integration scheme. The energy and angle grids were refined until a prescribed accuracy is reached. The tables are used by our simulation code to produce artificial CRSF spectra. The electron momenta sampled during these simulations were analyzed and justified using theoretically determined boundaries. We present a complete set of tables suited for mean free path calculations of Monte Carlo simulations of the cyclotron scattering process for conditions expected in typical X-ray pulsar accretion columns (0.01<B/B_{crit}<=0.12, where B_{crit}=4.413x10^{13} G and 3keV<=kT<15keV). The sampling of the tables is chosen such that the results have an estimated relative error of at most 1/15 for all points in the grid. The tables are available online at http://www.sternwarte.uni-erlangen.de/research/cyclo.

2, 2′‐Dihydroxybenzophenones and Derivatives. Efficient Synthesis and Structure Endoscopy by DFT and NMR. Credentials as Potent Antiinflammatory Agents.

Abstract2,2’‐dihydroxybenzophenones and derivatives have been synthesized directly or by oxidation of their incipiently obtained benzylic alcohols by diverse efficient methods. Oxime and N‐acyl hydrazone derivatives have also been prepared. Their structure profile has been scrutinized by DFT/B3LYP‐6‐311++G** methodology, NMR spectroscopy and dihedral angle grid scan analysis. Energetically favorable conformations pointed to (i) an almost coplanar bifurcated 6‐membered H bridge in ketones, (ii) a single 6‐membered H bridge, accompanied by a 7‐membered H bonding interaction in oximes and (iii) a single 6‐membered H‐bridge in hydrazones. In the latter case, a stable conformation with an additional 9‐membered pseudo ring was also found. Highly deshielded protons in the NMR spectra are in accordance with the theoretically obtained findings on the H‐bonded conformers. Significant anti‐inflammatory activity of the compounds has been found by in vivo tests with their oxime and hydrazone derivatives showing the highest activity, hydrazone 11, in partucular, competing with marketed drugs. In silico docking studies point to the perspective potency of these structures as COX‐1/COX‐2 inhibitors.

Channel Estimation via Orthogonal Matching Pursuit for Hybrid MIMO Systems in Millimeter Wave Communications

We propose an efficient open-loop channel estimator for a millimeter-wave (mm-wave) hybrid multiple-input multiple-output (MIMO) system consisting of radio-frequency (RF) beamformers with large antenna arrays followed by a baseband MIMO processor. A sparse signal recovery problem exploiting the sparse nature of mm-wave channels is formulated for channel estimation based on the parametric channel model with quantized angles of departures/arrivals (AoDs/AoAs), called the angle grids. The problem is solved by the orthogonal matching pursuit (OMP) algorithm employing a redundant dictionary consisting of array response vectors with finely quantized angle grids. We suggest the use of non-uniformly quantized angle grids and show that such grids reduce the coherence of the redundant dictionary. The lower and upper bounds of the sum-of-squared errors of the proposed OMP-based estimator are derived analytically: the lower bound is derived by considering the oracle estimator that assumes the knowledge of AoDs/AoAs, and the upper bound is derived based on the results of the OMP performance guarantees. The design of training vectors (or sensing matrix) is particularly important in hybrid MIMO systems, because the RF beamformer prevents the use of independent and identically distributed random training vectors, which are popular in compressed sensing. We design training vectors so that the total coherence of the equivalent sensing matrix is minimized for a given RF beamforming matrix, which is assumed to be unitary. It is observed that the estimation accuracy can be improved significantly by randomly permuting the columns of the RF beamforming matrix. The simulation results demonstrate the advantage of the proposed OMP with a redundant dictionary over the existing methods such as the least squares method and the OMP based on the virtual channel model.

Finely sampled 3D angle gathers from sparse OBN data

Large-scale deepwater ocean-bottom node (OBN) surveys typically use a node spacing of about 400 m. We make 3D angle gathers from OBN data by mapping image traces to the reflection azimuth and reflection angle domain. Large node spacing may coarsely sample the seismic data in these angles. This may result in degraded and noisy angle gathers unless we properly account for the sampling during processing. We describe a method for making high-quality 3D angle gathers on finely sampled angle grids. We do this by properly band limiting the mapping operator with sinc functions defined in the angle domain. This method allows us to oversample the 3D angle gathers accurately in the angle domain and obtain high-quality results. We demonstrate our method with deepwater Gulf of Mexico node data and show that we can produce high-quality gathers even with 800 m node spacing. The angle gathers derived from these wider node data preserve residual moveout and therefore are suitable for model building. Our results add confidence that data acquired with nodes spaced farther apart than 400 m can be processed and imaged successfully.

Multidisciplinary Constrained Optimization of Power Quality in Doubly Fed Wind Turbine Induction Generator

Shape optimization of turbine blade to maximize the output power usually changes the power factor due to compensate Repower in a wind turbine. This article presents a multidisciplinary optimization technique to maximize the output power in Doubly Fed Induction Generator (DFIG) wind turbine. The most common parameters when operating the turbine, namely, active power, reactive power and power factor, are considered as the problem constraints and the pitch angle grid side variable frequency converter of the turbine blades are optimized to maximize the output power. Numerical simulation has been illustrated to present the performance of the proposed design approach.

An efficient implementation of iterative adaptive approach for source localization

The iterative adaptive approach (IAA) can achieve accurate source localization with single snapshot, and therefore it has attracted significant interest in various applications. In the original IAA, the optimal filter is performed for every scanning angle grid in each iteration, which may cause the slow convergence and disturb the spatial estimates on the impinging angles of sources. In this article, we propose an efficient implementation of IAA (EIAA) by modifying the use of the optimal filtering, i.e., in each iteration of EIAA, the optimal filter is only utilized to estimate the spatial components likely corresponding to the impinging angles of sources, and other spatial components corresponding to the noise are updated by the simple correlation of the basis matrix with the residue. Simulation results show that, in comparison with IAA, EIAA has significant higher computational efficiency and comparable accuracy of source angle and power estimation.

Bulk Texture Measurement of Interstitial-Free Annealed Steel Using Gaussian Integrated Intensities of Neutron Diffraction Spectra

{110}, {200} and {211} neutron diffraction profiles of an interstitial-free annealed steel sheet were measured on 5 � 5 degrees stereographic angle grids, and several evaluation methods of diffraction intensity were employed to calculate the bulk texture, including the peak intensity at a constant 2theta angle, the simply summed intensity in a constant 2theta angle spread and the Gaussian integrated intensity obtained by single peak fitting of each profile. The comparison among differently evaluated bulk textures shows that a stronger f111ghuvwi fiber component and a weaker f001gh110i rotated cube component appear in the texture of investigated steel and the Gaussian integrated intensity method with proper coefficient constraints possesses a higher sensitivity to both weak texture components and strong ones. The crystallographic orientation maps obtained from electron backscattering diffraction and the bulk textures estimated from X-ray diffraction confirm the feasibility of the neutron bulk texture based on the Gaussian integrated intensity, suggesting that it can be suitably utilized to evaluate the global orientation distribution characteristics of heterogeneous materials. [doi:10.2320/matertrans.MRA2008086]

Direct evidence for channel-coupling effects in molecules: electron impact excitation of the a″ 1Σ+g state of N2

New measurements of differential cross-sections for excitation of the a″ 1Σ+g (v′ = 0, 1) state in molecular nitrogen reveal a cusp-like angular distribution. This feature is distinctly observed for the first time in the present electron energy-loss experiment as a result of finer scattering angle grid and impact energy coverage than previous measurements. This feature is similar to that observed in atomic targets such as He, Hg and Ba. The observed phenomenon suggests an interference effect related to configuration–interaction coupling between lower and excited states that are of the same symmetry. It is hoped that the present work will stimulate theoretical investigations into the physics that governs this cusp-like behaviour.

Local beam angle optimization with linear programming and gradient search

The optimization of beam angles in IMRT planning is still an open problem, with literature focusing on heuristic strategies and exhaustive searches on discrete angle grids. We show how a beam angle set can be locally refined in a continuous manner using gradient-based optimization in the beam angle space. The gradient is derived using linear programming duality theory. Applying this local search to 100 random initial angle sets of a phantom pancreatic case demonstrates the method, and highlights the many-local-minima aspect of the BAO problem. Due to this function structure, we recommend a search strategy of a thorough global search followed by local refinement at promising beam angle sets. Extensions to nonlinear IMRT formulations are discussed.

Improvement in a Surface Motor-Driven Planar Motion Stage

We report a surface motor-driven planar motion stage with an XYθZsurface encoder. The surface motor consists of two pairs of linear motors. Magnetic arrays are installed on the platen and stator windings of linear motors on the stage base. The platen is moved in the X and Y directions by X and Y linear motors. It is rotated around the Z axis by moment generated by the X or Y linear motors. The surface encoder consists of two two-dimensional (2D) angle sensors and an angle grid with 2D sinusoidal surface waves. The angle grid is installed on the platen. Sensors onside make the stage compact. The surface encoder is improved for higher positioning accuracy. Measurement errors of the surface encoder using two detectors – a quadrant PD and 2D PSD – are determined by simulation. The surface motor for increasing stage speed is modified. We conducted experiments comparing the previous prototype stage (Prototype I) and the improved stage (Prototype II).

Precision Fabrication of a Large-Area Sinusoidal Surface Using a Fast-Tool-Servo Technique ─Improvement of Local Fabrication Accuracy─

This paper describes a diamond turning fabrication system for a sinusoidal grid surface. The wavelength and amplitude of the sinusoidal wave in each direction are 100µm and 100nm, respectively. The fabrication system, which is based on a fast-tool-servo (FTS), has the ability to generate the angle grid surface over an area of φ 150mm. This paper focuses on the improvement of the local fabrication accuracy. The areas considered are each approximately 1 × 1mm, and can be imaged by an interference microscope. Specific fabrication errors of the manufacturing process, caused by the round nose geometry of the diamond cutting tool and the data digitization, are successfully identified by Discrete Fourier Transform of the microscope images. Compensation processes are carried out to reduce the errors. As a result, the fabrication errors in local areas of the angle grid surface are reduced by 1/10.

Precision positioning of a five degree-of-freedom planar motion stage

This paper presents the development of a five degree-of-freedom (DOF) planar motion stage with an integrated surface encoder for position detection. The single-level moving element is levitated by three air-bearings without mechanical contact, and is actuated by three linear motors and three piezoelectric transducer (PZT) actuators. The three linear motors are placed on the stage base to generate movement of the stage in the XYθ z directions (in-plane motion), while the three PZT actuators move the stage in the Zθ x θ y directions (out-of-plane motion). A surface encoder composed of three two-dimensional (2D) angle sensors and a 2D angle grid is employed as the position sensor to detect the five DOF position of the stage for feedback control. Experimental results demonstrate that the surface encoder has a resolution of 30 nm and is suitable for sub-micrometer positioning. It is also confirmed experimentally that the stage can be controlled independently in the five DOFs with a positioning resolution of 50 nm and a settling time of 50 ms.

Precision positioning of a Sawyer motor-driven stage by a surface encoder

This paper describes the precision positioning of an XY-planar motion stage driven by a two-axis Sawyer motor. The moving part of the stage is levitated on the stage platen by an air-bearing. The X- and Y-forcers mounted on the moving part generate electromagnetic forces against the platen for the X- and Y-directional motions, respectively. The position of the moving part is feedback-controlled based on the measurement result of a surface encoder, which is composed of a 2-D slope sensor mounted on the stage moving part and an angle grid film stuck on the stage platen. The angle grid film, on which sinusoidal micro-structured surface with 100 nm amplitude and 100 µm wavelength is fabricated by UV replication, is as thin as 100 µm. It is confirmed by experiments that necessary driving performance can be maintained when the forcer moves on the film. Experimental results also indicate that sub-micrometers positioning accuracy can be achieved by closed-loop positioning control based on the surface encoder output.

High-accuracy Fabrication of a Sinusoidal Grid Surface Over a Large Area by Fast Tool Servo (Improvement of Fabrication Accuracy in Local Areas of the Grid Surface)

This paper describes a diamond turning fabrication system for a sinusoidal grid surface, which is a superposition of periodic sinusoidal waves along the X- and Y-directions. The wavelength and amplitude of the sinusoidal wave in each direction are 100 μm and 100 nm, respectively. The fabrication system, based on fast-tool-servo (FTS), has the ability to generate the angle grid surface over an area of φ150 mm, This paper focuses on the improvement of the fabrication accuracy in local areas. Each of these areas is approximately 1 mm × 1 mm, which can be imaged by an interference microscope. Specific fabrication errors, caused by the round nose geometry of the diamond cutting tool and the data digitization, for the manufacturing process are successfully identified by Discrete Fourier Transform of the microscope images. Compensation processes are carried out to achieve a reduction of the errors. As a result, the fabrication errors in local areas of the angle grid surface are reduced to 1/10.