First-and Second-order Statistics Research Articles

On the Skewness of the LMS Adaptive Weights

The adjustable weights of adaptive filtering algorithms are usually assumed to obey a Gaussian distribution. This is somewhat natural under maximal-entropy considerations, since most analyses in the open literature only take into account first-and second-order statistics. This work investigates the third-order statistical feature known as skewness of the least mean square parameters distribution. Two theoretical analyses for skewness estimation are proposed: i) one that employs the independence assumption, which states that the excitation data is statistically independent from the adaptive weights; ii) one derived from the exact expectation analysis, a method that is able to predict the learning capabilities of the least mean square algorithm even when the step size is not infinitesimally small. This brief shows that the skewness of the adaptive weights distribution may present a large deviation from the common Gaussian assumption, especially in the first phase of the learning. Furthermore, it is also demonstrated that the skewness may grow without limit even when adaptive weights present convergence in both average and mean square behaviors.

The Energized Point Process as a Model for Wirelessly Powered Communication Networks

The spatial correlation of the RF-powered nodes that harvest enough energy plays a critical role in the performance evaluation of large-scale wirelessly powered communication networks (WPCNs). However, such correlation is mostly ignored in the literature for analytical tractability. In this paper, we explore the correlation and propose a new point process, named energized point process (EPP), as a model for the RF-powered nodes that succeed in harvesting energy. Specifically, we focus on the spatial correlation of the energy harvested from a Poisson field of RF power sources. Two energy harvesting models with different degrees of practicality are introduced to concretize the EPP with the aim of visualizing the point process of the energized nodes and characterizing its density and pair correlation function theoretically. It turns out that for both models the resulting process exhibits positive correlation. With the first-and second-order statistics of the EPP, we use a fitted Poisson cluster process to provide good approximations of the success probability and area spectral efficiency in the information transmission phase. Numerical results investigate the impacts of the key parameters related to the energy transfer on the spatial correlation of the EPP and the communication performance. An important conclusion is that although the Poisson point process has been so far the most widely used model for wirelessly powered networks, it is inadequate due to the positive energy correlation.

Channel Characterization and Modeling for Optical Wireless Body-Area Networks

We address channel characterization and modeling for medical wireless body-area networks (WBANs) based on the optical wireless technology. We focus on the intra-WBAN communication links, i.e., between a set of medical sensors and a coordination node, placed on the patient’s body. We consider a realistic mobility model, e.g., inside a hospital room, which takes into account the effect of shadowing due to body parts movements and the variations of the underlying channels. To take into account the global and local user mobility, we consider a dynamic model based on a three-dimensional animation of a walk cycle, as well as walk trajectories based on an improved random way-point mobility model. Then, Monte Carlo ray-tracing simulations are performed to obtain the channel impulse responses for different link configurations at different instants of the walk scenarios. We then derive first-and second-order statistics of the channel parameters such as the channel DC gain, delay spread, and coherence time, and furthermore, propose best fit statistical models to describe the distribution of these parameters for a general scenario.

A novel contrast enhancement forensics based on convolutional neural networks

Contrast enhancement (CE), one of the most popular digital image retouching technologies, is frequently utilized for malicious purposes. As a consequence, verifying the authenticity of digital images in CE forensics has recently drawn significant attention. Current CE forensic methods can be performed using relatively simple handcrafted features based on first-and second-order statistics, but these methods have encountered difficulties in detecting modern counter-forensic attacks. In this paper, we present a novel CE forensic method based on convolutional neural network (CNN). To the best of our knowledge, this is the first work that applies CNN to CE forensics. Unlike the conventional CNN in other research fields that generally accepts the original image as its input, in the proposed method, we feed the CNN with the gray-level co-occurrence matrix (GLCM) which contains traceable features for CE forensics, and is always of the same size, even for input images of different resolutions. By learning the hierarchical feature representations and optimizing the classification results, the proposed CNN can extract a variety of appropriate features to detect the manipulation. The performance of the proposed method is compared to that of three conventional forensic methods. The comparative evaluation is conducted within a dataset consisting of unaltered images, contrast-enhanced images, and counter-forensically attacked images. The experimental results indicate that the proposed method outperforms conventional forensic methods in terms of forgery-detection accuracy, especially in dealing with counter-forensic attacks.

Air turbulence effects on performance of optical wireless communication with crosstalk in server backplane

Free space optical interconnections (FSOIs) are anticipated to become a prevalent technology for short-range high-speed communication. FSOIs use lasers in board-to-board and rack-to-rack communication to achieve improved performance in next generation servers and are expected to help meet the growing demand for massive amounts of inter-card data communication. An array of transmitters and receivers arranged to create an optical bus for inter-card and card-to-backplane communication could be the solution. However, both chip heating and cooling fans produce temperature gradients and hot air flow that results in air turbulence inside the server, which induces signal fading and, hence, influences the communication performance. In addition, the proximity between neighboring transmitters and receivers in the array leads to crosstalk in the received signal, which further contributes to signal degradation. In this Letter, the primary objective is to experimentally examine the off-axis crosstalk between links in the presence of turbulence inside a server chassis. The effects of geometrical and inter-chassis turbulence characteristics are investigated and first-and second-order statistics are derived.

Optimal Diagonal Power Loading Minimizing Asymptotic Symbol Error Probability for Distributed MIMO Systems With ZF Receivers

In this paper, we consider a distributed multiple-input–multiple-output (D-MIMO) system, where the channel is flat fading and may be correlated, and experiences both small- and large-scale fading. We assume that full knowledge of channel state information (CSI) is available at the receiver and that only the first-and second-order statistics of the channel are available at the transmitter. For such a system with square quadrature amplitude modulation (QAM), an asymptotic symbol error probability (SEP) is derived for the linear zero-forcing (ZF) receiver. Then, we propose an optimal diagonal power loading (PL) strategy that minimizes the dominant term of the asymptotic SEP subject to either a total transmission power constraint when the total power normalization coefficient can be fed back to the transmitter from the receiver or an individual transmission power constraint. A simple closed-form solution is obtained. Computer simulations show that our presented optimal system attains significant performance gains over the currently available equal PL system.

Optimal Precoder Design Maximizing the Worst-Case Average Received SNR for Massive Distributed MIMO Systems

In this letter, we consider a distributed multiple-input multiple-output (D-MIMO) system, where the channel is flat fading and may be correlated, and experiences both small and large-scale fading. We assume that the full knowledge of channel state information (CSI) is available at the receiver and only the first-and second-order statistics of the channel are available at the transmitter. For such a system employing the linear zero-forcing (ZF) receiver, an efficient linear precoding technique is proposed to optimize the worst-case performance of average signal-to-noise ratio (SNR) at the receiver and a simple closed-form optimal precoder is derived. In addition, under some realistic assumptions, some significant asymptotic properties are established for the massive D-MIMO system designed in this letter. Computer simulations verify our theoretic analysis and show that our presented optimal system attains significant performance gains over the currently available equal power-loading system.

UDNS or LES, That Is the Question

In the framework of the spectral element method, a comparison is carried out on turbulent first-and second-order statistics generated by large eddy simulation (LES), under-resolved (UDNS) and fully resolved direct numerical simulation (DNS). The LES is based on classical models like the dynamic Smagorinsky approach or the approximate deconvolution method. Two test problems are solved: the lid-driven cubical cavity and the differentially heated cavity. With the DNS data as benchmark solutions, it is shown that the numerical results produced by the UDNS calculation are of the same accuracy, even in some cases of better quality, as the LES computations. The conclusion advocates the use of UDNS and calls for improvement of the available algorithms.

Classification of Alzheimer’s from T2 Trans-Axial Brain MR Images

Alzheimer’s disease is the most common form of dementia occurring in the elderly persons. Its early diagnosis may help in providing proper treatment. To date, there is no appropriate technique available to automatically classify it using MR brain images. In this work, first-and-second-order-statistics (FSOS) was employed for classification of Alzheimer’s from T2 trans-axial brain MR images. Although FSOS is a simple and well known feature extraction technique, it is not yet explored for Alzheimer’s classification. Performance of FSOS was compared with the state-of-the-art feature extraction techniques. Five commonly used classifiers were employed to build decision models. The performance of the models was evaluated in terms of sensitivity, specificity, accuracy, F-measure, training, and testing time. These models were built with varying number of training samples. Results showed that FSOS outperforms all the other existing feature extraction techniques in terms of all the considered performance measures. This was also validated by a statistical test. Interestingly, it was found that FSOS gives high performance irrespective of the choice of classifier and it works well even on small available number of samples, which is usually desired for all real time problems.Keyword: Discrete Wavelet Transform, Feature Extraction, First and Second Order Statistics, Gabor Transform, Magnetic Resonance Imaging, Slantlet Transform

Phase modeling of indoor radio propagation channels

Two models for generating phase of individual multipath components in an indoor environment, partly developed in Hashemi (1993), have been studied in detail. In the deterministic phase increment model (model I), the phase of each multipath component is updated deterministically using several independent random scatterers. In the random phase increment model (model II), the phase of each multipath component is updated by adding independent random phase increments. Performance of these models has been evaluated by means of extensive computer simulations. Statistical properties of narrow-band CW fading signals obtained using each phase model have been compared with the corresponding results for a large empirical wide-band database of 12000 impulse response estimates of indoor radio propagation channels. A major conclusion is that model I (with five scatterers for each multipath component) and model II (with proper choice for phase increments) provide fading results consistent with those obtained from measurements. In this paper, properties of each phase model are described, and an algorithm for generating each is presented. Firstand second-order statistics [amplitude distributions, level crossing rates (LCRs), and average duration of fades (ADFs)] and Doppler spectra of narrow-band CW fading waveforms obtained using simulated phases are reported, and detailed comparison between the simulated and empirical results is carried out. Furthermore, the two models are also compared with each other, and advantages and disadvantages of each are explored. The effect of increasing the number of scatterers and statistical properties of phase increments in model I are studied, simulated, and compared with model II. A major conclusion is that for an appropriate choice of parameters, both models provide satisfactory performance.

Correlation functions on the upper half space

The boundary condition and solution of a Dirichlet problem on the upper half space are treated as random processes. It is shown that the first-and second-order statistics of the solution to this problem are completely determined by the corresponding statistics of the boundary condition. The mean of the solution is the mean of the process on the boundary. The correlation function of the solution above the boundary is related to its value on the boundary by a Poisson integral formula.

Re-entry filtering, prediction, and smoothing.

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.