Angular Spread Research Articles

Estimation for Two-Dimensional Nonsymmetric Coherently Distributed Source in L-Shaped Arrays

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

2.4 to 61 GHz Multiband Double-Directional Propagation Measurements in Indoor Office Environments

This paper presents the details and results of double-directional propagation measurements carried out in two indoor office environments: a semi-open, cubicle-type office space and a more traditional work environment with closed offices. The measurements cover seven frequency bands from 2.4 to 61 GHz, permitting the propagation characteristics to be compared over a wide range of candidate radio frequencies for next-generation mobile wireless systems, including ultra high frequency and millimeter-wave bands. A novel processing algorithm is introduced for the expansion of multiband measurement data into sets of discrete multipath components. Based on the resulting multipath parameter estimates, models are presented for frequency-dependent path loss, shadow fading, copolarization ratio, delay spread, and angular spreads, along with their interfrequency correlations. Our results indicate a remarkably strong consistency in multipath structure over the entire frequency range considered.

Cross-Polarized Three-Dimensional Channel Measurement and Modeling for Small-Cell Street Canyon Scenario

In emerging heterogeneous networks, small-cell base stations deployed along urban streets can increase the network capacity for vehicular access significantly. To fully exploit the potential of full-dimensional multiple-input-multiple-output technologies, it is critical to understand the propagation characteristics of the small-cell vehicle-to-infrastructure (V2I) access channels. In this paper, a measurement campaign for the three-dimensional propagation with $\pm 45^\circ$ polarizations was conducted at 2.6 GHz in a typical urban street canyon environment. We utilized a sounder with two cross-polarized uniformed planar arrays. The transmitter was placed on the rooftop of a five-storey building and the receiver was placed at the 15th position along a street with the line of sight (LOS). The elevation/azimuth of arrival (EoA/AoA), power spectrum, and root-mean-square angular spread of arrival (ESA/ASA) of the multipath components were measured. We propose a dual-Laplace probability density function (PDF) model for the EoA distributions that have LOS clusters and ground reflections. We propose two models, the flat-bottom Laplace PDF and the superposed Laplace PDF, to describe the clustering behavior of the AoA distributions. We also propose the Lognormal models for the ESA and ASA distributions. Furthermore, it is found that polarization does not affect the EoA and AoA distributions, but has a significant impact on the ASA and ESA. The measurement results and channel models can help with the design and evaluation of the spatial transmission/multiplexing technologies in the small-cell V2I access.

Determining the Kappa Distributions of Space Plasmas from Observations in a Limited Energy Range

Abstract Spacecraft observations allow us to reconstruct the velocity distributions of space plasmas, which fully describe the kinetic state of the plasma. Space plasmas often exist in stationary states out of equilibrium, which are typically described by kappa distributions. Thus, the kappa index and temperature that govern these distributions are parameters that need to be determined for a full and accurate description of these plasmas. In this study, we demonstrate a novel and reliable way to determine the kappa index and temperature of plasma distribution functions constructed from counts observed in a narrow energy range by typical electrostatic sensors. Our method applies to cases in which the high-energy tail of the plasma is observed with significant uncertainty, or not observed at all. For the validation of our method, we produce pseudo-observations for typical input plasma parameters, specifically considering the design of the ion plasma instrument SWA-PAS on board the Solar Orbiter mission. Our method reliably estimates the relevant plasma parameters by fitting the angular spread of the distribution in a narrow energy range around the core bulk energy. We compare the output of our technique with the input parameters used to generate artificial data for a selected range of the kappa index and the temperature, and for a bulk energy typical for the solar wind. In addition, we study the effects of Poisson errors on the instrument’s counting statistics, test our method against Helios 2 measurements, and discuss its potential applications and limitations.

Second‐order fading statistics of massive‐MIMO vehicular radio communication channels

AbstractThis paper presents an intensive study on the fading statistics of massive multiple‐input–multiple‐output vehicular communication channels. A geometry‐based channel model is proposed, where both ends of the link are considered to be equipped with large‐scale three‐dimensional antenna arrays, whereas the scattering volumes in their vicinity are modeled as flexible (ie, shiftable, scalable, and rotatable) along all the dimensions to adapt various dynamic vehicle‐to‐everything radio propagation scenarios. Both ends of the link are modeled as flexible to be static or mobile in different directions and with independent velocities, to adapt both the vehicle‐to‐vehicle and vehicle‐to‐infrastructure scenarios. Joint and marginal three‐dimensional angle‐of‐arrival and angle‐of‐departure statistics of the channel are studied. The analysis is further extended from plain angle‐of‐arrival/angle‐of‐departure statistics to the characterization of dispersion of energy in the angular domain by using various notable angular spread quantifiers. A correlation between the received signals on two different antenna elements of the array, at two different time instants, on two distinct frequencies, and at two different spatial positions along the node mobility route is thoroughly investigated. This analysis is further extended to analytically study the Doppler spectrum characteristics and second‐order fading statistics of the channel. The considered second‐order fading statistics quantifiers are fading rate variance, level crossing rate, average fade duration, and coherence distance. The impact of various physical (eg, link distance, direction, and speed of node mobility), geometric (eg, shape and orientation of scattering volume), and antenna (eg, beam pattern, beam width, and beam switching) parameters on the angular spread, received signal correlations, Doppler spectrum characteristics, and second‐order fading statistics of the channel is thoroughly investigated. The conducted analysis is highly significant for devising efficient interference mitigation methods, error correction codes, modulation schemes, antenna beams, and receiver designs for emerging massive multiple‐input–multiple‐output vehicle‐to‐vehicle communication links, which, in turn, serves the purpose of efficient spectrum utilization.

Chromatic properties of astigmatic eyes

Background: Chromatic differences in power, refractive compensation, position and magnification have been described in the literature for Gaussian eyes. Aim: This article explores these definitions and defines chromatic properties for eyes that have astigmatic and decentred or tilted elements. Setting: Linear optics. Methods: The optical model is linear optics and makes use of the ray transference T . Results: Results are presented as either 2 × 2 matrices or 2 × 1 vectors. The dependence of the chromatic properties on the position of an object and the limiting aperture is explored and results are presented as independent of, or dependent on, object and aperture position. Apertures undergo both longitudinal and transverse shifts in position. The results are general and apertures may include pupils or pinholes, either surgically inserted inside the eye or held in front of the eye. Numerical examples are provided for Le Grand’s four-surface eye and an arbitrary astigmatic heterocentric four-surface eye. Conclusion: Aperture-independent chromatic properties include chromatic difference in power and refractive compensation, both given as 2 × 2 matrices. Aperture-dependent chromatic properties are all dependent on longitudinal shifts in the plane of the limiting aperture. In addition, chromatic difference in position and inclination depend on both object and transverse aperture position. Chromatic difference in image size or angular spread depends on object position and is independent of transverse aperture position. These four aperture-dependent chromatic properties are given as 2 × 1 vectors. Chromatic magnifications are independent of object and transverse aperture position and are given as 2 × 2 matrices.

Autofocusing and spreading of partially coherent Butterfly beams modulated by flat-topped factor in atmospheric turbulence

By transferring higher hierarchy Butterfly catastrophe to optical field, the autofocusing behavior and beam spreading of partially coherent Butterfly beams modulated by flat-topped factor in atmospheric turbulence are investigated, where the input power is fixed. In the process of autofocusing behavior the main lobe remains its location near origin, which is different from the movement of main lobe in a lower hierarchy Pearcey beam. The turbulence does not change the autofocusing behavior, but accelerates the decaying in side lobes of butterfly structure. A higher coherence length can lead to a more concentrated intensity at autofocusing plane. The analysis of beam spreading also indicates that there exist critical values of propagation distance of zc. A smaller flat-topped factor tends to maintain a smaller spreading for z<zc, while for z>zc the opposite case can be found. Angular spread decreases with an increasing of coherence length, and a smaller beam order shows a larger far field divergence angle. The study of partially coherent Butterfly beams in turbulence provides the possibility of the atmospheric laser communication by using higher-order catastrophe optical field.

Wavelet spectral analysis of the free surface of turbulent flows

ABSTRACTThis work demonstrates the applicability of the wavelet directional method as a means of characterizing the free surface dynamics in shallow turbulent flows using a small number of sensors. The measurements are obtained with three conductance wave probes in a laboratory flume, in a range of subcritical flow conditions where the Froude number was smaller than one, and the bed was homogeneously rough. The characteristic spatial scale of the surface elevation is found to correspond to the wavelength of stationary waves oriented against the flow. The spectrum of the dominant distribution of waves is characterized in terms of an angular spreading function. A new procedure to estimate the mean surface velocity based on measurements of the surface elevation at only two locations is proposed. The results can inform the development of more accurate models of the surface behaviour, with applications for the remote sensing of rivers and open channel flows.

Sea Surface Monostatic and Bistatic EM Scattering Using SSA-1 and UAVSAR Data: Numerical Evaluation and Comparison Using Different Sea Spectra

The microwave scatterometer is one of the most effective instruments in ocean remote sensing, which urges the need for some theoretical models to accurately estimate the scattering coefficient of the sea surface. For the simulation of the scattering from an ocean surface, the sea spectrum, or its inverse Fourier transform, autocorrelation function is essential. Currently, many sea spectral models have been proposed for describing sea waves. However, which spectrum should be adopted during electromagnetic (EM) computations? A systematic comparison of these models is needed to evaluate their accuracies. In this paper, we focus on numerical simulations of scattering from a rough sea surface in monostatic and bistatic configurations by using six different sea spectral models and the first-order small slope approximation (SSA-1). First, sea spectral models proposed by Elfouhaily et al., Hwang et al., Romeiser et al., Apel et al., Fung et al., and Pierson et al., are compared with each other from different points of view, e.g., the omnidirectional parts, the angular spreading functions, the autocorrelation functions, and the slope variances. We find that the spectra given by Elfouhaily and Hwang could reflect realistic wind sea waves more accurately. Then, the scattering coefficients are simulated in fully monostatic and bistatic configurations. Regarding the monostatic scattering, the results simulated using EM scattering models are compared with those obtained from the measured UAVSAR data in the L band and the empirical model CMOD5 in the C band. Comparisons are made for various incident angles, wind speeds, and wind directions. Meanwhile, special attention is paid to low to moderate incident angles. The comparisons show that, it is difficult to find one certain spectral model to simulate scattering coefficient accurately under all wind speeds or wind directions. Accurate estimations will be obtained using different methods according to different situations.

Developing a generalized BRDF model from experimental data.

In this paper, we present a model for BRDF that can be developed from a limited set of experimentally observed data, and which then can be used for predictive purposes in scene-generation or sensor-performance applications. The model is physics based and can be as detailed as desired, depending on the scope of experimental data available. Basic input parameters required are the complex refractive index of the material, or the directional hemispherical reflectivity (DHR) for s- and p-polarized radiation. At least one BRDF measurement is needed to determine the angular spread function. Incorporating BRDF measurements at several angles of incidence into the model yields better accuracy for describing behavior such as forward scatter, depolarization, the participation of volumetric and surface-scattering mechanisms in layered surfaces, diffuse-scatter coherence properties, and narrowing of the angular spread function which provides an indication of optical depth. Illustrations and demonstrations of the methodology are drawn from data sets measured on bead-blasted aluminum, automotive paint incorporating a clear-coat layer, and green low-gloss vehicle paint.

Influence of Short Time-Scale Water-Column Temperature Fluctuations on Broadband Signal Angular Beam Spreading

Temporal fluctuations in vertical thermocline structure and depth span (on a time scale of 30 to 40 min) are shown to affect the arrival angle, and focusing of measured broadband (22–28 kHz) non-surface-interacting acoustic signals at a depth of ~100 m. Measurements were taken in the Pacific Missile Range Facility near Kauai island, Hawaii, for a source-receiver range of 1.0 km. The arrival time and angular spread of acoustic beams are obtained for measured signals using a plane wave beamformer with a-prior gaussian weighting. The weighting process reduces ambiguity in angular measurements due to spatial aliasing from a vertical array with element spacing d much greater than half the acoustic wavelength $$ \left(\frac{\lambda_{\mathrm{a}}}{2}\right) $$ of the highest frequency in the broadband signal. Over two full periods of thermocline oscillation, 2 times of high and 2 times of low isotherm depth are selected to show fluctuations in angular beam spreading, focusing, and the robustness of the weighted beamformer routine. To benchmark the performance of the weighted beamformer, a two-dimensional (2D) Parabolic Equation (PE) model calculates the angular signal spread and focusing using parameters to satisfy spatial sampling requirements for broadband beamforming. In the absence of spatial aliasing, beamforming the output of the 2D PE can be conducted without weighting. Comparison of measured and modeled results shows less than a degree of difference in the angular beam spread of direct, bottom reflected, and refracted paths. It is shown that a vertical array with $$ d\gg \left(\frac{\lambda_{\mathrm{a}}}{2}\right) $$ and gaussian weighting can resolve changes in angular spread and beam focusing as a function of vertical isotherm displacement.

Estimation of Broadband Multiuser Millimeter Wave Massive MIMO-OFDM Channels by Exploiting Their Sparse Structure

In millimeter wave (mm-wave) massive multiple-input multiple-output (MIMO) systems, acquiring accurate channel state information is essential for efficient beamforming (BF) and multiuser interference cancellation, which is a challenging task since a low signal-to-noise ratio is encountered before BF in large antenna arrays. The mm-wave channel exhibits a 3-D clustered structure in the virtual angle of arrival (AOA), angle of departure (AOD), and delay domain that is imposed by the effect of power leakage, angular spread, and cluster duration. We extend the approximate message passing (AMP) with a nearest neighbor pattern learning algorithm for improving the attainable channel estimation performance, which adaptively learns and exploits the clustered structure in the 3-D virtual AOA-AOD-delay domain. The proposed method is capable of approaching the performance bound described by the state evolution based on vector AMP framework, and our simulation results verify its superiority in mm-wave systems associated with a broad bandwidth.

Application of Manifold Separation to Parametric Localization for Incoherently Distributed Sources

By using the manifold separation technique (MST), we develop a computationally efficient yet accurate estimator for localization of multiple incoherently distributed (ID) sources. In this paper, we have made the following main contributions: first, we use the MST to derive a closed-form expression for the ID signal covariance matrix that is applicable to the case with arbitrary array geometries or large angular spreads; second, we find that the two-dimensional spatial spectrum can be computed efficiently by using the discrete Fourier transform algorithms coupled with the unweighted (or Gaussian-weighted) moving average for the uniformly (or Gaussian) distributed ID sources; finally, we employ the first-order Taylor expansion to formulate a weighted least-squares approach that can improve the estimation performance significantly. Numerical results demonstrate that with less complexity, the proposed estimator offers better estimation performance compared with several classical estimators.

Target normal sheath acceleration of protons using triple-layer target with long preplasma

Target-normal sheath acceleration (TNSA) of monoenergetic proton bunches using a triple-layer target consisting of a long slightly-above-critical-density carbon preplasma, a thin solid-density carbon main target layer, and a thin hydrogen layer attached to its back, is considered. The target-back space-charge field the consists of mainly the preplasma electrons that have been accelerated and heated by the relativistic laser pulse. The backside electron cloud is thus denser and more favorably profiled for TNSA of the protons from the hydrogen layer. It is found that a proton beam with a $\ensuremath{\sim}460\text{ }\text{ }\mathrm{MeV}$ monoenergetic peak energy can be generated. The corresponding energy and angular spread are $\ensuremath{\sim}33\text{ }\text{ }\mathrm{MeV}$ and $\ensuremath{\sim}3\ifmmode^\circ\else\textdegree\fi{}$, respectively.

Joint Estimation of MIMO Channel Parameters Using Space–Time Correlation Matrix for Different Angular Distributions

In this paper, we propose a new low-complexity method to jointly estimate the multiple-input multiple-output (MIMO) channel parameters namely the mean angle of arrival (AoA), the angular spread (AS) and the maximum Doppler spread (DS). We consider Gaussian and Laplacian angular distributions for the incoming AoAs in the case of a Rayleigh channel model. Our estimator is based on the magnitudes and phases of the space–time correlation functions of the received signals. To this end, closed-form expressions of the required functions were derived. Two different approaches are studied using these cross-correlation functions; first at a non zero time lag and second at two different time lags. To evaluate the robustness of the proposed estimator, the two Stage approach and the improved maximum likelihood method based on the Gauss Newton algorithm are taken as benchmarks for the mean AoA and the AS estimation. For the maximum DS, the two Rays and the auto-correlation based algorithms are chosen. Simulation results show that the proposed estimator offers more accurate estimates in almost all considered scenarios. We also compare our work to a recent joint estimator which exploits the Derivatives of the cross-correlation function (DCCF). Our method outperforms the DCCF algorithm at a lower computational cost.

Exploring proximity effects and large depth of field in helium ion beam lithography: large-area dense patterns and tilted surface exposure

Helium ion beam lithography (HIL) is an emerging nanofabrication technique. It benefits from a reduced interaction volume compared to that of an electron beam of similar energy, and hence reduced long-range scattering (proximity effect), higher resist sensitivity and potentially higher resolution. Furthermore, the small angular spread of the helium ion beam gives rise to a large depth of field. This should enable patterning on tilted and curved surfaces without the need of any additional adjustments, such as laser-auto focus. So far, most work on HIL has been focused on exploiting the reduced proximity effect to reach single-digit nanometer resolution, and has thus been concentrated on single-pixel exposures over small areas. Here we explore two new areas of application. Firstly, we investigate the proximity effect in large-area exposures and demonstrate HIL’s capabilities in fabricating precise high-density gratings on large planar surfaces (100 μm × 100 μm, with pitch down to 35 nm) using an area dose for exposure. Secondly, we exploit the large depth of field by making the first HIL patterns on tilted surfaces (sample stage tilted 45°). We demonstrate a depth of field greater than 100 μm for a resolution of about 20 nm.

On the Ergodic Rate Lower Bounds With Applications to Massive MIMO

A well-known lower bound widely used in the massive MIMO literature hinges on channel hardening , i.e., the phenomenon for which, thanks to the large number of antennas, the effective channel coefficients resulting from beamforming tend to deterministic quantities. If the channel hardening effect does not hold sufficiently well, this bound may be quite far from the actual achievable rate. In recent developments of massive MIMO, several scenarios where channel hardening is not sufficiently pronounced have emerged. These settings include, for example, the case of small scattering angular spread, yielding highly correlated channel vectors, and the case of cell-free massive MIMO . In this short contribution, we present two new bounds on the achievable ergodic rate that offer a complementary behavior with respect to the classical bound: while the former performs well in the case of channel hardening and/or when the system is interference-limited (notably, in the case of finite number of antennas and conjugate beamforming transmission), the new bounds perform well when the useful signal coefficient does not harden but the channel coherence block length is large with respect to the number of users, and in the case where interference is nearly entirely eliminated by zero-forcing beamforming. Overall, using the most appropriate bound depending on the system operating conditions yields a better understanding of the actual performance of systems where channel hardening may not occur, even in the presence of a very large number of antennas.

Quasi-Deterministic Channel Model Parameters for a Data Center at 60 GHz

We describe a measurement campaign conducted in a data center, a unique environment in which transceivers are positioned above the server racks. A total of 80 channel acquisitions, including small-scale measurements, were recorded using our three-dimensional double-directional 60 GHz channel sounder with 0.5 ns delay resolution and 2° average angle error. For each acquisition, the channel multipath components were extracted in the delay-angle space and subsequently reduced to the parameters of the Quasi-Deterministic channel model: a stochastic map-based model that represents the scattering of incident waves off ambient reflectors as specular components, each surrounded by a cluster of diffuse components. The weaker diffuse components interfere with the stronger specular component, giving rise to small-scale fading. Only with super-resolution capabilities, such as that of our system, were we able to show how densely the diffuse components were packed, with 1/ns to 2/ns arrival rates and cluster angular spreads between 3° and 4°. Most importantly, we measured the diffuse power to be as high as 26% of the total cluster power, demonstrating that small-scale fading at millimeter-wave frequencies can be significant.

Indoor wideband directional millimeter wave channel measurements and analysis at 26 GHz, 32 GHz, and 39 GHz

AbstractThis paper presents details of the wideband directional propagation measurements of millimeter‐wave (mmWave) channels in the 26 GHz, 32 GHz, and 39 GHz frequency bands in an indoor typical office environment. More than 14 400 power delay profiles (PDPs) were measured across the 26 GHz band and over 9000 power delay profiles have been recorded for the 32 GHz and 39 GHz bands at each measurement point. A mmWave wideband channel sounder has been used, where signal analyzer and vector signal generator were employed. Measurements have been conducted for both co and cross‐antenna polarization. The setup provided 2 GHz bandwidth and the mechanically steerable directional horn antenna with 8 degrees beamwidth provides 8 degrees of directional resolution over the azimuth for 32 GHz and 39 GHz, whereas 26 GHz measurement setup provides the angular resolution of 5 degrees. Measurements provide path loss, delay, and spatial spread of the channel. Large‐scale fading characteristics, RMS delay spread, RMS angular spread, and angular and delay dispersion are presented for 3 mmWave bands for the line‐of‐sight scenario.

Probe measurements of the electron velocity distribution function in beams: Low-voltage beam discharge in helium

Previously developed methods based on the single-sided probe technique are altered and applied to measure the anisotropic angular spread and narrow energy distribution functions of charged particle (electron and ion) beams. The conventional method is not suitable for some configurations, such as low-voltage beam discharges, electron beams accelerated in near-wall and near-electrode layers, and vacuum electron beam sources. To determine the range of applicability of the proposed method, simple algebraic relationships between the charged particle energies and their angular distribution are obtained. The method is verified for the case of the collisionless mode of a low-voltage He beam discharge, where the traditional method for finding the electron distribution function with the help of a Legendre polynomial expansion is not applicable. This leads to the development of a physical model of the formation of the electron distribution function in a collisionless low-voltage He beam discharge. The results of a numerical calculation based on Monte Carlo simulations are in good agreement with the experimental data obtained using the new method.