Spatial Correlation Properties Research Articles

Novel methods of DOA estimation based on compressed sensing

Making use of the sparsity of targets, three novel direction of arrival (DOA) models based on compressed sensing (CS) theory are proposed. Covariance matrix CS, interpolated array CS and beam space CS carry out compressive sampling on covariance matrix, interpolated array and beam space, respectively. High-resolution DOA estimations are obtained through reconstruction of sparse signal by convex optimization problem resolution. The proposed methods are conceptually different from subspace-based methods and provide high resolution using a uniform linear array without restricting requirements on the spatial and temporal stationary and correlation properties of the sources and the noise. Results of both simulated data and measured data show that these methods are superior to conventional DOA methods in angular estimation performance.

Spoofing detection in IEEE 802.15.4 networks based on received signal strength

The shared medium used in wireless networks makes them vulnerable to spoofing attacks, in which an adversary masquerades as one or more legitimate nodes to disturb normal operation of the network. In this paper we present a novel spoofing detection method for static IEEE 802.15.4 networks based on spatial correlation property of received signal strength (RSS). While most existing RSS based techniques directly process RSS values of the received frames and rely on multiple traffic air monitors (AMs) to provide an acceptable detection performance, we extract features of RSS streams to reduce data redundancy and provide a more distinguishable representation of the data. Our algorithm employs two features of RSS streams, summation of detailed coefficients (SDCs) in discrete Haar wavelet transform (DHWT) of the RSS streams and the ratio of out-of-bound frames. We show that in a typical scenario, a single AM with SDC as detection parameter, can theoretically outperform a system with 12 AMs which directly applies RSS values as detection parameter. Using ratio of out-of-bound frames facilitates detection of high rate attacks. In addition, we suggest adaptive learning of legitimate RSS values which enhances the robustness of the attack detector against environmental changes. Using both magnitude and frequency related features, we achieved high detection performance with a single AM; this enables development of preventive measures for spoofing attacks. The performance of our approach was evaluated through an IEEE 802.15.4 testbed in an office environment. Experimental results along with theoretical analysis show that the proposed method outperforms the existing RSS-based spoofing detection solutions. Using a single AM, we were able to attain 94.75% detection rate (DR) with 0.56% false positive rate (FPR). For 4 AMs, the results improved to 99% DR and 0% FPR.

Spatial Correlation Properties of Tightly Focused J0-Correlated Azimuthally Polarized Vortex Beams

Based on vectorial Debye diffraction theory, the spatial correlation properties in the focal region of a J0-correlated azimuthally polarized vortex beam through a high numerical aperture (NA) are analyzed. The expressions for a pair of points on the axis of symmetry and for a pair of points in the focal plane are derived. It is found that the longitudinal and transverse coherence lengths in the focal region change with the variation in the topological charge and coherence parameter of the vortex field, together with the NA values. In addition, the degree of coherence is shown to possess phase singularities.

Application of three-dimensional spatial correlation properties of coherent noise in phase noise suppression for digital holographic microscopy

The inherited coherent noise degrades the phase imaging quality in digital holographic microscopy (DHM). To overcome the problem, an experimental investigation on the three-dimensional (3D) spatial correlation properties of coherent noise is carried out. Multiple blank holograms are recorded without any specimen in DHM setup by consecutively shifting camera along the optical axis, and a series of phase distribution of coherent noise can be obtained by numerical reconstruction. Then, based on the phase distributions, the lateral and longitudinal correlation properties of coherent noise are analyzed by a discrete correlation algorithm. Furthermore, a method for reducing phase noise is proposed by use of multiple holograms. Firstly, a series of holograms are recorded by shifting the camera longitudinally with the step more than longitudinal correlation length of coherent noise field. Secondly, the reconstruction of the holograms leads to a series of phase images of object, in which the coherent noise has different patterns. Consequently, by averaging the phase images, the reductions of phase noise are achieved. The applicability of the method is demonstrated by imaging of the resolution targets and the grating.

Interaction of Additive Noise and Nonlinear Dynamics in the Double-Gyre Wind-Driven Ocean Circulation

Abstract In this paper the authors study the interactions of additive noise and nonlinear dynamics in a quasigeostrophic model of the double-gyre wind-driven ocean circulation. The recently developed framework of dynamically orthogonal field theory is used to determine the statistics of the flows that arise through successive bifurcations of the system as the ratio of forcing to friction is increased. This study focuses on the understanding of the role of the spatial and temporal coherence of the noise in the wind stress forcing. When the wind stress noise is temporally white, the statistics of the stochastic double-gyre flow does not depend on the spatial structure and amplitude of the noise. This implies that a spatially inhomogeneous noise forcing in the wind stress field only has an effect on the dynamics of the flow when the noise is temporally colored. The latter kind of stochastic forcing may cause more complex or more coherent dynamics depending on its spatial correlation properties.

Area-Correlated Spectral Unmixing Based on Bayesian Nonnegative Matrix Factorization

To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. In the proposed me-thod, the spatial correlation property between two adjacent areas is expressed by a priori probability density function, and the endmembers extracted from one of the adjacent areas are used to estimate the priori probability density func-tions of the endmembers in the current area, which works as a type of constraint in the iterative spectral unmixing process. Experimental results demonstrate the effectivity and efficiency of the proposed method both for synthetic and real hyperspectral images, and it can provide a useful tool for spatial correlation and comparation analysis between ad-jacent or similar areas.

Spatial correlation properties of twisted partially coherent light focused by diffractive axicons

We investigate the spatial coherence properties of a twisted, partially coherent field in the focal region of diffractive axicons. We demonstrate that the focused field is a combination of an infinite number of weighted, mutually uncorrelated, helical components, whose weights depend on both the coherence width and the twist strength, and the total helicity of the field inverts its handedness depending on the twist handedness and vanishes at the nontwist limit. Depending on the variances of whichever the effective coherence width, the twist strength, the twist handedness of the illumination, or the shape of the axicon phase function, substantive changes will intervene on the distribution of the spatial coherence degree of the focused field. In particular, the twist strength of the illumination influences both the phase and amplitude of the spatial degree of coherence, while the twist handedness just inverts its phase. In addition, the spectral degree of coherence of the focused field possesses phase singularities, and their locations and shapes are affected by the coherence and twist properties of the illumination and the shape of the axicon phase function.

A wave field synthesis approach to reproduction of spatially correlated sound fields

This article discusses an open-loop wave field synthesis (WFS) approach for the reproduction of spatially correlated sound fields. The main application concerns laboratory reproduction of turbulent boundary layer wall pressure on aircraft fuselages and measurement of their sound transmission loss. The problem configuration involves reconstruction of random sound pressure distributions on a planar reproduction surface using a planar array of reproduction monopoles parallel to the reproduction plane. In this paper, the WFS formulation is extended to sound fields with imposed time and spatial correlation properties (or equivalently imposed cross-spectral density in the frequency and wave number domains). Numerical examples are presented for the reproduction of a propagating plane wave, diffuse acoustic field and wall pressure in subsonic or supersonic turbulent boundary layers. The reproduction accuracy is examined in terms of the size of the source plane and reproduction plane, their separation, and the number of reproduction sources required per acoustic wavelength. While the reproduction approach cannot reconstruct sub-wavelength correlation scales of subsonic turbulent boundary layers, it effectively reconstructs correlation scales larger than the acoustic wavelength, making it appropriate for diffuse acoustic field and supersonic turbulent layers.

Cooperative MIMO Channel Modeling and Multi-Link Spatial Correlation Properties

In this paper, a novel unified channel model framework is proposed for cooperative multiple-input multiple-output (MIMO) wireless channels. The proposed model framework is generic and adaptable to multiple cooperative MIMO scenarios by simply adjusting key model parameters. Based on the proposed model framework and using a typical cooperative MIMO communication environment as an example, we derive a novel geometry-based stochastic model (GBSM) applicable to multiple wireless propagation scenarios. The proposed GBSM is the first cooperative MIMO channel model that has the ability to investigate the impact of the local scattering density (LSD) on channel characteristics. From the derived GBSM, the corresponding multi-link spatial correlation functions are derived and numerically analyzed in detail.

Spatial correlation properties of focused spatially and spectrally partially coherent Hemite-Gaussian pulsed beams

Based on the propagation law of partially coherent beams and Fourier transform, the analytical expressions for the spectral intensity and spectral degree of coherence of focused spatially and spectrally partially coherent Hermite-Gaussian (H-G) pulsed beams are derived and used to study the spatial correlation properties in the focal region. It is shown that the spectral degree of coherence depends on the spatial correlation length, temporal coherence length and beam order. As the temporal coherence length decreases, the spectral degree of coherence decreases, whereas the temporal coherence length does not contribute to the spatial distribution of the spectral degree of coherence. An increase of the beam order results in an oscillatory behavior of the spectral degree of coherence, which becomes more prominent with the increase of beam order or the decrease of spatial correlation length.

A Fast and Adaptive Search Algorithm Based on Rood Pattern and Gradient Descent

Abstract In order to achieve the real-time property for video coding, a fast and adaptive algorithm based on starting search point prediction and early-termination strategy is proposed. It analyzes center-bias property and spatial correlation property of motion vector field, and utilizes the respective characteristics of block based gradient descent search (BBGDS) and adaptive rood pattern search (ARPS) algorithm. The proposed algorithm adaptively chooses different searching strategies according to the type of the image, makes full use of the cross image motion vector distribution characteristics and optimizes the traditional ARPS algorithm. The experimental results show that the proposed algorithm is about 2.3∼9.2 times faster than Diamond Search (DS), 1.2∼4.0 times than ARPS. The algorithm can meet the real-time demand without reducing the image quality.

Orthogonal expansion of Gaussian wind velocity field and PDEM-based vibration analysis of wind-excited structures

An effective procedure for simulation of random wind velocity field by the orthogonal expansion method is proposed in this paper. The procedure starts with decomposing the fluctuating wind velocity field into a product of a stochastic process and a random field, which represent the time property and the spatial correlation property of wind velocity fluctuations, respectively. By an innovative orthogonal expansion technology, the stochastic process for wind velocity fluctuations may be represented as a finite sum of deterministic time functions with corresponding uncorrelated random coefficients. Similarly, the random field can be expressed as a combination form with only a few random variables by the Karhunen–Loeve decomposition. This approach actually simulates the wind velocity field with stochastic functions other than methods such as spectral representation and proper orthogonal decomposition. In the second part of the paper, the probability density evolution method (PDEM) is employed to predict the stochastic dynamic response of structures subjected to wind excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic responses of structures. The solution of this equation will give rise to instantaneous probability density function of the responses. Finally, the accuracy and effectiveness of the approach in representing the random wind velocity field and PDEM-based dynamic response of wind-excited building are investigated.

Spatial Compressive Sensing for Direction-of-Arrival Estimation of Multiple Sources using Dynamic Sensor Arrays

This work addresses the problem of direction-of-arrival (DOA) estimation of multiple sources using short and dynamic sensor arrays. We propose to utilize compressive sensing (CS) theory to reconstruct the high-resolution spatial spectrum from a small number of spatial measurements. Motivated by the physical structure of the spatial spectrum, we model it as a sparse signal in the wavenumber-frequency domain, where the array manifold is proposed to serve as a deterministic sensing matrix. The proposed spatial CS (SCS) approach allows exploitation of the array orientation diversity (achievable via array dynamics) in the CS framework to address challenging array signal processing problems such as left-right ambiguity and poor estimation performance at endfire. The SCS is conceptually different from well-known classical and subspace-based methods because it provides high azimuth resolution using a short dynamic linear array without restricting requirements on the spatial and temporal stationarity and correlation properties of the sources and the noise. The SCS approach was shown to outperform current superresolution and orientation diversity based methods in single-snapshot simulations with multiple sources.

A Geometrical Three-Ring-Based Model for MIMO Mobile-to-Mobile Fading Channels in Cooperative Networks

This paper deals with the modeling and analysis of narrowband multiple-input multiple-output (MIMO) mobile-to-mobile (M2M) fading channels in relay-based cooperative networks. In the transmission links from the source mobile station to the destination mobile station via the mobile relay, non-line-of-sight (NLOS) propagation conditions are taken into account. A stochastic narrowband MIMO M2M reference channel model is derived from the geometrical three-ring scattering model, where it is assumed that an infinite number of local scatterers surround the source mobile station, the mobile relay, and the destination mobile station. The complex channel gains associated with the new reference channel model are derived, and their temporal as well as spatial correlation properties are explored. General analytical solutions are obtained for the four-dimensional (4D) space-time cross-correlation function (CCF), the three-dimensional (3D) spatial CCF, the two-dimensional (2D) source (relay, destination) correlation function (CF), and the temporal autocorrelation function (ACF). Exact closed-form expressions for different CFs under isotropic as well as nonisotropic scattering conditions are provided in this article. A stochastic simulation model is then drawn from the reference model. It is shown that the CCFs of the simulation model closely approximate the corresponding CCFs of the reference model. The developed channel simulator is not only important for the development of future MIMO M2M cooperative communication systems, but also for analyzing the dynamic behavior of the MIMO M2M channel capacity.

Spatial Correlation Analysis of On-Body Radio Channels Considering Statistical Significance

On-body radio channel modeling and measurement has been studied extensively. However, the spatial correlation properties of channel parameters and the reliability of on-body channel measurements remain poorly understood. In this letter, a K-weight-based spatial autocorrelation model and corresponding Z-score is used to investigate the spatial correlation of on-body radio propagation and the degree of confidence in measurement results. It is demonstrated that, due to rich multipath scattering in an indoor environment, both the spatial autocorrelation and corresponding confidence level are higher compared to those in the chamber environment. These findings have the profound implication that, for less scattered environments, the locations of transmitter (Tx) and receiver (Rx) need to be very accurate in order to achieve high repeatability in on-body channel measurements.

Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams

By expanding the Debye theory into the tight focusing of partially coherent field, the intensity and spatial correlation properties of partially coherent radially polarized vortex beams are studied. Expressions are derived for the intensity distribution and the spectral degree of coherence in the focal region. It is found that the intensity and the transverse and longitudinal coherence degrees in the focal region change with the variation of the topological charge and coherence length of the vortex beam. In addition, the degree of coherence is shown to exhibit phase singularities.

Study correlation vortices in the near-field of partially coherent vortex beams diffracted by an aperture

We have derived the analytical expression of the electric cross-spectral density in the near- field of partially coherent vortex beams diffracted by an aperture. Taking the Gaussian Schell-model vortex beam as a typical example of partially coherent vortex beams, the spatial correlation properties and correlation vortices in the near-field of partially coherent vortex beams diffracted by a rectangle aperture are studied. It is shown that the off-axis displacement, spatial degree of coherence parameter, propagation distance, and the opening factor of the aperture affect the spectral degree of coherence and positions of correlation vortices. With the optimization algorithm, we obtain the symmetric distributing coherent vortex.

Two-photon subwavelength lithography with thermal light

We propose an incoherent interferometer which can partly modify the spatial correlation property of thermal light. Applying the interferometer to the two-photon double-slit interference with thermal light, we find that the subwavelength interference patterns appear in the intensity correlation not only between two same polarized photons at different positions but also between two orthogonally polarized photons at the same position. The latter can correspond to the two-photon double-slit interference using a two-photon entangled source. Our experimental result suggests that a thermal light source is capable of accomplishing subwavelength lithography technique to surpass the Rayleigh resolution limit.

Fluctuations of the wave amplitude level in a plane-layered medium with random irregularities

The spatial correlation properties of the amplitude (amplitude level) of a wave existing in a random medium and at the exit from it are determined. It is shown that, within the framework of geometric optics, the oblique incidence of a wave on a refractive medium accounts for the anisotropy of the spatial correlation characteristics of the medium in the case of the statistical isomerism of the medium’s permittivity. Special attention is focused on the investigation of the reflection region where the geometric optics method is invalid.

Gravitational force in an infinite one-dimensional Poisson distribution

We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles using an exponential cutoff of the pair interaction to control and study the divergences which arise. Deriving an exact analytic expression for the probability density function (PDF) P(F) , we show that it is badly defined in the limit in which the well-known Holtzmark distribution is obtained in the analogous three-dimensional case. A well-defined P(F) may, however, be obtained in the infinite range limit by an appropriate renormalization of the coupling strength giving a Gaussian form. Calculating the spatial correlation properties we show that this latter procedure has a trivial physical meaning. Finally we calculate the PDF and correlation properties of differences of forces (at separate spatial points), which are well defined without any renormalization. We explain that the convergence of these quantities is in fact sufficient to allow a physically meaningful infinite system limit to be defined for the clustering dynamics from Poissonian initial conditions.