Performance of XOR Rule for Decentralized Detection of Deterministic Signals in Bivariate Gaussian Noise

In this paper, we consider the performance of exclusive-OR (XOR) rule in detecting the presence or absence of a deterministic signal in bivariate Gaussian noise. Signals, when present at the two sensors, are assumed unequal, whereas the noise components have identical marginal distribution but are correlated. The sensors send their one-bit quantized data to a fusion center, which then employs the XOR rule to arrive at the final decision. Here we prove that, in the limit as the correlation coefficient r approaches 1, the optimum fusion rule for both parallel and tandem topologies is XOR with identical, alternating partitions (XORAP) of the observations at the sensors. We further quantify the asymptotic decrease of the Bayes error of XORAP towards zero as a constant multiplied by \sqrt 1-r , as r approaches 1. When compared to the asymptotic Bayes error of CLRT, which decreases to zero exponentially fast, as a function of 1/(1-r) , the Bayes error of XORAP decreases to zero much slower

Decentralized Narrowband and Wideband Spectrum Sensing with Correlated Observations

This dissertation evaluates the utility of several approaches to the design of good distributed sensing systems for both narrowband and wideband spectrum sensing problems with correlated sensor observations

On Distributed and Acoustic Sensing for Situational Awareness

Recent advances in electronics enable the development of small-sized, low-cost, low-power, multi-functional sensor nodes that possess local processing capability as well as to work collaboratively through communications. They are able to sense, collect, and process data from the surrounding environment locally. Collaboration among the nodes are enabled due to their integrated communication capability. Such a system, generally referred to as sensor networks are widely used in various of areas, such as environmental monitoring, asset tracking, indoor navigation, etc. This thesis consists of two separate applications of such mobile sensors. In this first part, we study decentralized inference problems with dependent observations in wireless sensor networks. Two separate problems are addressed in this part: one pertaining to collaborative spectrum sensing while the other on distributed parameter estimation with correlated additive Gaussian noise. In the second part, we employ a single acoustic sensor with co-located microphone and loudspeaker to reconstruct a 2-D convex polygonal room shape. For spectrum sensing, we study the optimality of energy detection that has been widely used in the literature. This thesis studies the potential optimality (or sub-optimality) of the energy detector in spectrum sensing. With a single sensing node, we show that the energy detector is provably optimal for most cases and for the case when it is not theoretically optimal, its performance is nearly indistinguishable from the true optimal detector. For cooperative spectrum sensing where multiple nodes are employed, we use a recently proposed framework for distributed detection with dependent observations to establish the optimality of energy detector for several cooperative spectrum sensing systems and point out difficulties for the remaining cases. The second problem in decentralized inference studied in this thesis is to investigate the impact of noise correlation on decentralized estimation performance. For a tandem network with correlated additive Gaussian noises, we establish that threshold quantizer on local observations is optimal in the sense of maximizing Fisher information at the fusion center; this is true despite the fact that subsequent estimators may differ at the fusion center, depending on the statistical distribution of the parameter to be estimated. In addition, it is always beneficial to have the better sensor (i.e. the one with higher signal-to-noise ratio) serve as the fusion center in a tandem network for all correlation regimes. Finally, we identify different correlation regimes in terms of their impact on the estimation performance. These include the well known case where negatively correlated noises benefit estimation performance as it facilitates noise cancellation, as well as two distinct regimes with positively correlated noises compared with that of the independent case. In the second part of this thesis, a practical problem of room shape reconstruction using first-order acoustic echoes is explored. Specifically, a single mobile node, with co-located loudspeaker, microphone and internal motion sensors, is deployed and times of arrival of the first-order echoes are measured and used to recover room shape. Two separate cases are studied: the first assumes no knowledge about the sensor trajectory, and the second one assumes partial knowledge on the sensor movement. For either case, the uniqueness of the mapping between the first-order echoes and the room geometry is discussed. Without any trajectory information, we show that first-order echoes are sufficient to recover 2-D room shapes for all convex polygons with the exception of parallelograms. Algorithmic procedure is developed to eliminate the higher-order echoes among the collected echoes in order to retrieve the room geometry. In the second case, the mapping is proved for any convex polygonal shapes when partial trajectory information from internal motion sensors is available.. A practical algorithm for room reconstruction in the presence of noise and higher order echoes is proposed

On Uniformly Most Powerful Decentralized Detection

The theory behind Uniformly Most Powerful (UMP) composite binary hypothesis testing is mature and well defined in centralized detection where all observations are directly accessible at one central node. However, within the area of decentralized detection, UMP tests have not been researched, even though tests of this nature have properties that are highly desirable. The purpose of this research is to extend the UMP concept into decentralized detection, which we define as UMP decentralized detection (UMP-DD). First, the standard parallel decentralized detection model with conditionally independent observations will be explored. This section will introduce theorems and corollaries that define when UMP-DD exists and provide counterintuitive examples where UMP-DD tests do not exist. Second, we explore UMP-DD for directed single-rooted trees of bounded height. We will show that a binary relay tree achieves a Type II error probability exponent that is equivalent to the parallel structure even if all the observations are not identically distributed. We then show that the optimal configuration can also achieve UMP-DD performance, while the tandem configuration does not achieve UMP-DD performance. Finally, we relax the assumption of conditional independence and show under specific constraints that both the parallel and binary relay tree configurations can still be UMP-DD. Throughout, examples will be provided that tie this theoretical work together with current research in fields such as Cognitive Radio

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201

A probabilistic framework for source localization in anisotropic composite using transfer learning based multi-fidelity physics informed neural network (mfPINN)

The practical application of data-driven frameworks like deep neural network in acoustic emission (AE) source localization is impeded due to the collection of significant clean data from the field. The utility of the such framework is governed by data collected from the site and/or laboratory experiment. The noise, experimental cost and time consuming in the collection of data further worsen the scenario. To address the issue, this work proposes to use a novel multi-fidelity physics-informed neural network (mfPINN). The proposed framework is best suited for the problems like AE source detection, where the governing physics is known in an approximate sense (low-fidelity model), and one has access to only sparse data measured from the experiment (highfidelity data). This work further extends the governing equation of AE source detection to the probabilistic framework to account for the uncertainty that lies in the sensor measurement. The mfPINN fuses the data-driven and physics-informed deep learning architectures using transfer learning. The results obtained from the data-driven artificial neural network (ANN) and physicsinformed neural network (PINN) are also presented to illustrate the requirement of a multifidelity framework using transfer learning. In the presence of measurement uncertainties, the proposed method is verified with an experimental procedure that contains the carbon-fiberreinforced polymer (CFRP) composite panel instrumented with a sparse array of piezoelectric transducers. The results conclude that the proposed technique based on a probabilistic framework can provide a reliable estimation of AE source location with confidence intervals by taking measurement uncertainties into account

Common Information and Decentralized Inference with Dependent Observations

Wyner\u27s common information was originally defined for a pair of dependent discrete random variables. This thesis generalizes its definition in two directions: the number of dependent variables can be arbitrary, so are the alphabets of those random variables. New properties are determined for the generalized Wyner\u27s common information of multiple dependent variables. More importantly, a lossy source coding interpretation of Wyner\u27s common information is developed using the Gray-Wyner network. It is established that the common information equals to the smallest common message rate when the total rate is arbitrarily close to the rate distortion function with joint decoding if the distortions are within some distortion region. The application of Wyner\u27s common information to inference problems is also explored in the thesis. A central question is under what conditions does Wyner\u27s common information capture the entire information about the inference object. Under a simple Bayesian model, it is established that for infinitely exchangeable random variables that the common information is asymptotically equal to the information of the inference object. For finite exchangeable random variables, connection between common information and inference performance metrics are also established. The problem of decentralized inference is generally intractable with conditional dependent observations. A promising approach for this problem is to utilize a hierarchical conditional independence model. Utilizing the hierarchical conditional independence model, we identify a more general condition under which the distributed detection problem becomes tractable, thereby broadening the classes of distributed detection problems with dependent observations that can be readily solved. We then develop the sufficiency principle for data reduction for decentralized inference. For parallel networks, the hierarchical conditional independence model is used to obtain conditions such that local sufficiency implies global sufficiency. For tandem networks, the notion of conditional sufficiency is introduced and the related theory and tools are developed. Connections between the sufficiency principle and distributed source coding problems are also explored. Furthermore, we examine the impact of quantization on decentralized data reduction. The conditions under which sufficiency based data reduction with quantization constraints is optimal are identified. They include the case when the data at decentralized nodes are conditionally independent as well as a class of problems with conditionally dependent observations that admit conditional independence structure through the hierarchical conditional independence model

Optimal Inference for Distributed Detection

In distributed detection, there does not exist an automatic way of generating optimal decision strategies for non-affine decision functions. Consequently, in a detection problem based on a non-affine decision function, establishing optimality of a given decision strategy, such as a generalized likelihood ratio test, is often difficult or even impossible. In this thesis we develop a novel detection network optimization technique that can be used to determine necessary and sufficient conditions for optimality in distributed detection for which the underlying objective function is monotonic and convex in probabilistic decision strategies. Our developed approach leverages on basic concepts of optimization and statistical inference which are provided in appendices in sufficient detail. These basic concepts are combined to form the basis of an optimal inference technique for signal detection. We prove a central theorem that characterizes optimality in a variety of distributed detection architectures. We discuss three applications of this result in distributed signal detection. These applications include interactive distributed detection, optimal tandem fusion architecture, and distributed detection by acyclic graph networks. In the conclusion we indicate several future research directions, which include possible generalizations of our optimization method and new research problems arising from each of the three applications considered