Second-order Statistical Properties Research Articles

Geometric Algebra based 2D-DOA Estimation for Non-circular Signals with an Electromagnetic Vector Array

This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations.

Simulation of 4th-order non-Gaussian random processes by higher-order spectral representation method

In this study, a new higher-order spectral representation method (HOSRM) is derived to simulate fourth-order (kurtosis-order) non-Gaussian random processes. Applying the HOSRM allows fourth-order non-Gaussian random process (symmetric non-Gaussian) sample functions to be generated accurately. As the number of terms in the cosine function used in the HOSRM increases, the simulated non-Gaussian random process sample functions can more accurately reflect the second-order (variance) and fourth-order (kurtosis) statistical properties of the objective sample functions. In particular, if the number of terms tends to infinity, then the simulated sample function characteristics will be the same as the target value. Meanwhile, a reasonable three-dimensional Hermite interpolation method is proposed to improve the simulation efficiency of stochastic processes. Finally, two examples are provided to demonstrate the accuracy and effectiveness of the proposed HOSRM for generating fourth-order non-Gaussian random processes. The results show that the statistical properties (power spectral density, trispectrum, and kurtosis) of the simulated non-Gaussian random process are consistent with those of the target random process.

Scattering of light waves from a collection of particles of L types.

A new, to the best of our knowledge, pathway is paved within the first-order Born approximation to access light scattering from a collection of particles of L types. Two L×L matrices called a pair-potential matrix (PPM) and a pair-structure matrix (PSM) are introduced to jointly characterize the scattered field. We show that the cross-spectral density function of the scattered field equals the trace of the product of the PSM and the transpose of the PPM, and thus these two matrices allow us to determine all the second-order statistical properties of the scattered field. Based on this, the spectral degree of coherence (SDOC) of the scattered field is further analyzed. In a special case where the spatial distributions of the scattering potentials of particles of different types are similar and the same is true of their density distributions, it is found that the PPM and the PSM will reduce to two new matrices whose elements separately quantify the degree of angular correlation of the scattering potentials of particles and their density distributions, and the number of species of particles in this special case will appear as a scaled factor to ensure the normalization of the SDOC. The importance of our new approach is illustrated by an example.

Super cosh-Gauss nonuniformly correlated radially polarized beam and its propagation characteristics.

In this paper, a new kind of partially coherent vector beam termed as super cosh-Gauss nonuniformly correlated radially polarized (SCNRP) beam is introduced. Such beam source exhibits almost perfect coherence between two points that are within the beam center region or located on a ring concentric with the beam center. However, the coherence drops or even vanishes when the two points leave the central region and are located on the concentric rings with different radii. The second-order statistical properties, such as the spectral density, the state of polarization (SOP), and the degree of polarization (DOP) of such beam upon free-space propagation are studied through numerical examples. Our results reveal that the beam displays a self-focusing property during propagation. The focusing ability can be enhanced with increasing the beam index and decreasing the beam's spatial coherence width, whereas the DOP and SOP remain unchanged on propagation. Meanwhile, we establish an experimental system with the use of a radial polarization converter and a digital micro-mirror device to synthesize the SCNRP beam with controllable beam index and spatial coherence width. The spectral density and polarization properties of the synthesized beam during propagation are measured and analyzed in the experiment. The experimental results agree well with our theoretical predictions.

A 3-D Dynamic Non-WSS Cluster Geometrical-Based Stochastic Model for UAV MIMO Channels

The unmanned aerial vehicle (UAV) channel models are very important and useful for the design and evaluation of UAV communications. In existing works, the terrestrial scatterers are widely stationary or moving all the time, and the UAV is assumed to move at a constant speed. However, these modeling assumptions may not be appropriate in realistic scenarios. In this work, we propose a new 3-dimensional (3-D) dynamic non-wide-sense stationary (non-WSS) cluster-based geometric model for UAV multiple-input multiple-output (MIMO) channels. We assume that a few non-isotropic scatterers are distributed around the terrestrial receiver and have a probabilistic movement behavior. Meanwhile, we consider that the UAV flies at a varying speed, and we design a non-stationary mobility model with acceleration. The proposed channel model performs the birth-death evolutionary process of clusters based on a Markov model, and the time-variant multipath component (MPC) parameters (e.g., angle of arrival/departure (AoA/AoD), power, and delay) are obtained. In addition, we derive the space-time correlation function, mean Doppler spread, and root-mean-square doppler shift spread of the UAV MIMO channels, and provide the quasi-stationary interval. We also investigate the impact of some key model factors on the statistical properties by numerical simulations. Finally, we compare the space-time correlation functions and the second-order statistical properties between the proposed model and the UAV channel measurement results. The close agreements between the numerical simulations and field measurements have validated the proposed model.

Generic identifiability of subnetworks in a linear dynamic network: The full measurement case

Identifiability conditions for single or multiple modules in a dynamic network specify under which conditions the considered modules can be uniquely recovered from the second-order statistical properties of the measured signals. Conditions for generic identifiability of multiple modules, i.e. a subnetwork, are developed for the situation that all node signals are measured and excitation of the network is provided by both measured excitation signals and unmeasured disturbance inputs. Additionally, the network model set is allowed to contain non-parametrized modules that are fixed, and e.g. reflect modules of which the dynamics are known to the user. The conditions take the form of path-based conditions on the graph of the network model set. Based on these conditions, synthesis results are formulated for allocating external excitation signals to achieve generic identifiability of particular subnetworks. If there are a sufficient number of measured external excitation signals, the formulated results give rise to a generalized indirect type of identification algorithm that requires only the measurement of a subset of the node signals in the network.

Second-order statistical properties of conjugate mode "double-H" partially coherent beams in turbulence.

We present an analysis of the propagation properties of a recently introduced class of conjugate mode partially coherent beams (called "double-H" beams) in a turbulent atmosphere using the extended Huygens-Fresnel integral. We investigate how the phase constant φ0 between the modes plays a role in controlling the evolution of the intensity distribution and resisting the degradation effects of the atmosphere. Our results indicate that this new class of structured beams provides a new degree of freedom for controlling the shape of the beams and improves turbulence resistance, with potential application in free-space optical communications.

Channel Estimation for Reconfigurable Intelligent Surface Aided MISO Communications: From LMMSE to Deep Learning Solutions

We consider multi-antenna wireless systems aided by reconfigurable intelligent surfaces (RIS). RIS presents a new physical layer technology for improving coverage and energy efficiency by intelligently controlling the propagation environment. In practice however, achieving the anticipated gains of RIS requires accurate channel estimation. Recent attempts to solve this problem have considered the least-squares (LS) approach, which is simple but also sub-optimal. The optimal channel estimator, based on the minimum mean-squared-error (MMSE) criterion, is challenging to obtain and is non-linear due to the non-Gaussianity of the effective channel seen at the receiver. Here we present approaches to approximate the optimal MMSE channel estimator. As a first approach, we analytically develop the best linear estimator, the LMMSE, together with a corresponding majorization-minimization-based algorithm designed to optimize the RIS phase shift matrix during the training phase. This estimator is shown to yield improved accuracy over the LS approach by exploiting second-order statistical properties of the wireless channel and the noise. To further improve performance and better approximate the globally-optimal MMSE channel estimator, we propose data-driven non-linear solutions based on deep learning. Specifically, by posing the MMSE channel estimation problem as an image denoising problem, we propose two convolutional neural network (CNN)-based methods to perform the denoising and approximate the optimal MMSE channel estimation solution. Our numerical results show that these CNN-based estimators give superior performance compared with linear estimation approaches. They also have low computational complexity requirements, thereby motivating their potential use in future RIS-aided wireless communication systems.

Echo characteristics of laser beams reflected from rough targets with a finite size in atmospheric turbulence

Based on the extended Huygens-Fresnel principle, echo characteristics of the plane and spherical waves reflected from a rough target with a finite size in atmospheric turbulence were studied. The expressions of the intensity variance, covariance functions and scintillation index of the plane and spherical waves reflected from a rough target in double-path propagation through atmospheric turbulence were proposed considering the turbulence perturbations. The expressions were numerically calculated, and the results show that the intensity fluctuation caused by turbulence decreases with increasing target size. It is also found that under weak turbulence, it is mainly the log-amplitude fluctuations that affect the second-order statistical properties of the received beam intensity. Results obtained can potentially provide theoretical and technical guidance for the future applications of laser target detection and target recognition in space.

Modelling Lagrangian velocity and acceleration in turbulent flows as infinitely differentiable stochastic processes

Abstract

Experimental Investigation on Electromagnetic Waves Transmitting Through Exhaust Plume: From Propagation to Channel Characteristics

Exhaust-plume-induced plasma from solid rocket engines absorbs electromagnetic (EM) waves and may cause communication interruptions. Previous articles have proposed both physical phenomena and propagation models for this problem, but few articles have analyzed random fluctuations of EM waves propagating through plumes from a communications perspective. This article attempts to attach these fluctuations, which are caused by the plume-induced turbulent plasma spread medium, to the communications channel characteristics. A multi-parameter stochastic model is established to characterize the exhaust plume channel in which the first-order and the second-order statistical properties are presented. Accordingly, a ground firing test was conducted to validate the EM wave propagation characteristics and the channel characteristics. The experimental results are in good consistence with the theoretical results. The results indicated that the time-varying envelope of the transmitted EM waves obeys a log-normal distribution, whereas the time-varying phase shift obeys a normal distribution. Moreover, the time–frequency analysis method was applied to evaluate the EM–plume interactions in the time–frequency domain. These results are critical for designing the rocket communication systems and evaluating the systems performance.

Statistical properties of twisted Gaussian Schell-model array beams in anisotropic ocean

The effect of anisotropic oceanic turbulence on propagation characteristics of twist Gaussian Schell-model array beams is investigated. The analytical expression for the cross-spectral density function of such beam propagating through turbulent ocean is derived and used to explore the evolution behavior of the spectral intensity and the degree of coherence. An example illustrates the fact that, the most important oceanic effect is destroying the far zone lattice-like beam profile, and the beam shape eventually converges into Gaussian profile. Besides, after passing through the turbulence at sufficiently large distances from the source, the twist phase modulation of the second-order statistical properties is shown to be suppressed by the turbulence fluctuation, the spectral intensity evolves in the same way with different twist strength, and so is the case for the degree of coherence. The impacts, which arise from the source coherence and the turbulence parameters on beam characteristics are analyzed in detail.

Envelope Level Crossing Rate and Average Fade Duration of a Generic 3D Non-Stationary UAV Channel Model

For the unmanned aerial vehicle (UAV) communication scenarios, the time-varying fading characteristics cased by the three-dimensional(3D) scattering environment and 3D trajectory have an important impact on establishing the reliable communication link. In this paper, a generic 3D non-stationary geometry-based stochastic model (GBSM) for UAV channels is developed. Different from the traditional 3D GBSMs, the proposed model takes the 3D arbitrary trajectories of UAV into account. On this basis, two important second-order statistical properties of fading envelope, i.e., the level crossing rate (LCR) and average fading duration (AFD), are investigated and derived in details. The obtained closed-form expressions are explicit functions of flight parameters and compatible with the results in the previous works. Numerical simulations show that the simulated results are in accordance with the theoretical and measurement data under 3D flight scenarios. The proposed model and statistical properties can be applied to the optimal design of channel coding and block interleave schemes for UAV communication systems.

Semi-Blind, Training, and Data-Aided Channel Estimation Schemes for MIMO-FBMC-OQAM Systems

This paper considers and analyzes the performance of semiblind, training, and data-aided channel estimation schemes for multiple-input multiple-output (MIMO) filter bank multicarrier (FBMC) systems with offset quadrature amplitude modulation. A semiblind MIMO-FBMC (SB-MF) channel estimator is developed that exploits both the training symbols and second-order statistical properties of the data symbols, which leads to a significant decrease in the mean squared error (MSE) with respect to its conventional training-based counterpart. Its performance is compared with that of the interference approximation method-based least squares MIMO-FBMC (LS-MF) channel estimator, wherein the channel is estimated using exclusively training symbols. The Cramér-Rao lower bounds are derived to characterize the MSE of the proposed and LS-MF estimators, which interestingly demonstrate that while the MSE per parameter of the proposed scheme decreases with the number of receive antennas, it remains constant for the training-based scheme. The resulting bit error rates are derived for the proposed SB-MF and LS-MF channel estimators. An expectation maximization-based data-aided MIMO-FBMC channel estimator is also investigated that performs iterative maximum a posteriori channel estimation in the E-step followed by data detection in the M-step. A comparative analysis is presented for the computational complexities of the various schemes. Simulation results with practical channel models demonstrate that the proposed semiblind scheme significantly outperforms the training-based and data-aided schemes.

Ultrasound driven mound to self-affine surface structure transition in nanostructured films: one-pot route to cubic CuInS2 quantum dots with controlled structure and tunable band gap energy

In the current study, the first method for synthesis of 3D assemblies composed by close-packed QDs of the cubic modification of CuInS2in thin film form is presented. The developed one-pot synthetic approach enables high tunability of materials’ properties by combining ultrasonic irradiation of the reactor with the one-step colloidal chemical approach or by controlled post-deposition annealing of the deposited samples. The average crystal size of the material can be tuned from ~ 1 up to ~ 36 nm. In-depth studies of the structure, surface morphology and optical properties were carried out. Manifestations of size-quantization effects in the optical properties were analyzed in details. Analysis of the second-order statistical properties of thin films’ surfaces has shown that ultrasonically-supported synthesis enables generation of self-affine surfaces, while the colloidal chemical one leads to mounded surfaces. Such change of the surfaces’ character was attributed to heterogeneous sonochemical effects, leading ultimately to more efficient transport of the clusters formed in the bulk liquid and their improved energizing, enabling them to overcome various diffusion barriers on the growing surface. Sonochemically deposited films are characterized by notably larger values of the Hurst exponent than the chemically deposited ones, and an order of magnitude smaller correlation length. Smaller fractal dimensions in sonochemical films are in line with the smoother surfaces generate by ultrasonically-assisted route.

Widely Linear Complex-Valued Diffusion Subband Adaptive Filter Algorithm

The adaptive algorithms applied to distributed networks are usually real-valued diffusion subband adaptive filter algorithms. However, it cannot be used for processing the complex-valued signals. In this paper, a novel augmented complex-valued diffusion normalized subband adaptive filter (D-ACNSAF) algorithm is proposed for distributed estimation over networks. In order to deal with the noncircular complex-valued signals, the D-ACNSAF algorithm uses the widely linear model for a diffusion network. Due to the second-order statistical properties of signal, the D-ACNSAF algorithm can process the circular and non-circular complex-valued signals simultaneously. Moreover, the stability and mean-square steady-state analysis of the proposed algorithm are derived based on the spatial–temporal energy conservation principle. Computer simulation experiments on complex-valued system identification and prediction show that the proposed algorithm has better performance (lower mean-square deviation and faster convergence rate) than diffusion complex least-mean-square and diffusion augmented complex least-mean-square algorithms. And the simulation results are consistent with the analysis results.

Correlated Source Number Estimation with Gerschgorin Radii of Partitioned Matrices Products

In this paper, a partitioned matrices products approach based on Gerschgorin disk estimation (PM-GDE) method is proposed in order to solve the problem of correlated source number estimation under spatially correlated noise background. This method is based on a uniform linear array. The improved partitioned matrices products of the array receiving data are computed by weighted summation of the rows and adjustment of the element sequence from partitioned matrices products matrix. The auto correlation matrix of the partitioned matrices products and its Gerschgorin radii are computed. A source number estimation criterion based on Gerschgorin radii is deduced by considering the second-order statistical property of the partitioned matrices products auto correlation matrix. Simulations results validate the efficiency and robustness of PM-GDE with correlated signals and spatially correlated noise background. PM-GDE performs better than its counterpart especially for close incident azimuth correlated sources.

Augmented complex-valued normalized subband adaptive filter: Algorithm derivation and analysis

In this paper, a novel augmented complex-valued normalized subband adaptive filter (ACNSAF) algorithm is proposed for processing the noncircular complex-valued signals. Based on the augmented statistics, the proposed algorithm is derived by computing a constraint cost function. Due to contain all second-order statistical properties, the ACNSAF algorithm can process the circular and noncircular complex-valued signals simultaneously. Moreover, the stability and mean square steady-state analysis of the proposed algorithm is derived by using the energy conservation principle. Computer simulation experiments on complex-valued system identification, prediction and noise cancelling show that the proposed algorithm achieves the improved mean square deviation and prediction gain compared to the ACNLMS algorithm. And the simulation results are consistent with the analysis results.

Second-order statistical properties of a J0-correlated Schell-model beam in a turbulent atmosphere

We derive the analytical expressions for the second-order moments of the Wigner distribution function of a J0-correlated Schell-model (JCSM) beam propagating in a turbulent atmosphere. With the help of the second-order moments, we explore the second-order statistical properties (i.e., the M2-factor, the effective radius of curvature and the Rayleigh range) of a JCSM beam propagating in a turbulent atmosphere for different turbulence parameters and beam parameters. It is found that the statistical properties of the JCSM beam are closely related to the initial beam parameters and turbulence parameters, and we can mitigate the negative effect of the turbulence by choosing suitable initial beam parameters. Our results will be useful for long distance free-space optical communications.

Blind Signal Separation Algorithm for Acoustic Echo Cancellation

This paper is to the blind signal separation algorithm applied to acoustic echo cancellation. This algorithm doesn’t degrade the performance of echo cancellation even in the double-talk. In the closed echo environment, the mixing model of acoustic signals has multi-channel, so the convolutive blind signal separation method is applied. And the mixing coefficients are computed by using the feedback model without directly calculating the separation coefficients. The coefficient updating is performed by iterative computations based on the second-order statistical properties, thus estimating the near-end speech. Many simulations have been performed to verify the performance of the proposed blind signal separation. Simulation results show that the proposed acoustic echo canceller operates safely regardless of double-talk, and the PESQ is improved by 0.6 point compared with the general adaptive FIR filter structure.