Neyman-Pearson detection in sensor networks with dependent observations

In this thesis, within the context of sensor networks, we are interested in the distributed detection problem under the Neyman-Pearson formulation and conditionally dependent sensor observations. In order to exploit all the detection potential of the network, the literature on this issue has faced optimal distributed detection problems, where optimality usually consists in properly designing the parameters of the network with the aim of minimizing some cost function related to the overall detection performance of the network. However, this problem of optimization has usually constraints regarding the possible physical and design parameters that we can choose when maximizing the detection performance of the network. In many applications, some physical and design parameters, for instance the network architecture or the local processing scheme of the sensor observations, are either strongly constrained to a set of possible design alternatives or either cannot be design variables in our problem of optimization. Despite the fact that those parameters can be related to the overall performance of the network, the previous constraints might be imposed by factors such as the environment where the network has to be deployed, the energy budget of the system or the processing capabilities of the available sensors. Consequently, it is necessary to characterize optimal decentralized detection systems with various architectures, different observation processes and different local processing schemes. The mayor part of the works addressing the characterization of distributed detection systems have assumed settings where, under each one of the possible states of our phenomenon of interest, the observations are independent across the sensors. However, there are many practical scenarios where the conditional independence assumption is violated because of the presence of different spatial correlation sources. In spite of this, very few works have faced the aforementioned characterizations under the same variety of settings as under the conditional independence assumption. Actually, when the strategy of the network is not an optimization parameter, under the assumption of conditionally dependent observations the existing literature has only obtained asymptotic characterizations of the detection performance associated with parallel networks whose local processing rules are based on amplify-and-relay schemes. Motivated by this last fact, in this thesis, under the Neyman-Pearson formulation, we undertake the characterization of distributed detection systems with dependent observations, various network architectures and binary quantization rules at the sensors. In particular, considering a parallel network randomly deployed along a straight line, we derive a closed-form error exponent for the Neyman-Pearson fusion of Markov local decisions when the involved fusion center only knows the distribution of the sensor spacings. After studying some analytical properties of the derived error exponent, we carry out evaluations of the closed-form expression in order to assess which kind of trends of detection performance can appear with increasing dependency and under two well-known models of the sensor spacing. These models are equispaced sensors with failures and exponentially spaced sensors with failures. Later, the previous results are extended to a two-dimensional parallel network that, formed by a set of local detectors equally spaced on a rectangular lattice, performs a Neyman-Pearson test discriminating between two di erent two-dimensional Markov causal fields defined on a binary state space. Next, under conditionally dependent observations and under the Neyman-Pearson set up, this thesis dissertation focuses on the characterization of the detection performance of optimal tandem networks with binary communications between the fusion units. We do so by deriving conditions under which, in an optimal tandem network with an arbitrary constraint on the overall probability of false alarm, the probability of misdetection of the system, i.e. at the last fusion node of the network, converges to zero as the number of fusion stages approaches infinity. Finally, after extending this result under the Bayesian set up, we provide two examples where these conditions are applied in order to characterize the detection performance of the network. From these examples we illustrate different dependence scenarios where an optimal tandem network can or cannot achieve asymptotic perfect detection under either the Bayesian set up or the Neyman-Pearson formulation. -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------En esta tesis, dentro del contexto de las redes de sensores, estamos interesados en el problema de detección distribuida bajo la formulación de Neyman-Pearson y observaciones condicionalmente dependientes. Con objeto de explotar el potencial de detección de la red, la literatura sobre este tema se ha enfrentado a problemas de detección distribuida óptima, donde la optimalidad normalmente hace referencia al diseño adecuado de diferentes parámetros de la red con el objeto de minimizar alguna función de coste relacionada con las prestaciones globales de detección. Sin embargo, este problema de optimización tiene normalmente restricciones asociadas con los posibles parámetros físicos y de diseño de la red que pueden ser seleccionados a la hora de maximizar las prestaciones de detección de la misma. En muchas aplicaciones algunos parámetros físicos y de diseño, como por ejemplo la arquitectura de la red o los esquemas de procesado local de las observaciones de los sensores, bien están fuertemente restringidos a un conjunto de posibles alternativas de diseño, o bien no pueden ser variables de diseño en nuestro problema de optimización. A pesar de que estos parámetros pueden estar relacionados con las prestaciones de detección de la red, las anteriores restricciones podrán estar impuestas por factores tales como el entorno en el que la red se despliega, el presupuesto de energía disponible de la red o las capacidades de procesado de los sensores. Consecuentemente, es necesario caracterizar sistemas de detección distribuidos óptimos con varias arquitecturas, diferentes procesos de observación y diferentes esquemas de procesado local. La mayor parte de los trabajos tratando la caracterización de sistemas de detección distribuida han asumido escenarios en los que, bajo cada uno de los posibles estados del fenómeno de interés, las observaciones son independientes de un sensor a otro. Sin embargo, hay muchos escenarios prácticos donde la asunción de independencia condicional es violada como consecuencia de la presencia de diferentes fuentes de correlación. A pesar de esto, muy pocos trabajos han tratado las anteriores caracterizaciones bajo la misma variedad de escenarios que bajo la asunción de independencia condicional. De hecho, cuando la estrategia de la red no es un parámetro a optimizar, bajo la asunción de observaciones condicionalmente dependientes la literatura existente sólo ha obtenido caracterizaciones asintóticas de las prestaciones de detección asociadas con redes paralelas cuyas reglas de procesado local se basan en esquemas de amplificación y retransmisión. Motivado por este útimo hecho, en esta tesis, bajo la formulación de Neyman-Pearson, llevamos a cabo la caracterización de sistemas de detección distribuida con observaciones dependientes, varias arquitecturas de red y reglas de cuantificación binaria en los sensores. En particular, considerando una red paralela desplegada aleatoriamente a lo largo de una línea recta, bajo la formulación de Neyman-Pearson derivamos una expresión cerrada del exponente de error asociado a la fusión de decisiones locales Makovianas cuando, con respecto a los espaciados entre sensores, sólo se conoce su distribución. Después de analizar algunas propiedades analíticas del derivado exponente de error, llevamos a cabo evaluaciones de su expresión cerrada con el objeto de determinar las diferentes tendencias de detección que pueden aparecer con dependencia creciente y bajo dos modelos de espaciado entre sensores muy conocidos. Estos dos modelos son sensores equiespaciados con fallos y sensores exponencialmente espaciados con fallos. Más tarde, los anteriores resultados son extendidos a una red paralela bidimensional que, formada por un conjunto de dispositivos equiespaciados sobre una rejilla rectangular, lleva a cabo un test de Neyman-Pearson para discriminar entre dos diferentes campos aleatorios causales de Markov definidos en un espacio de estados binario. Seguidamente, bajo observaciones condicionalmente dependientes y bajo la formulación de Neyman-Pearson, esta tesis se centra en la caracterización de las prestaciones de detección asociada a redes tándem óptimas con comunicación binaria entre los nodos de fusión. Para hacer eso, derivamos condiciones bajo las cuales, en una red t andem óptima con una arbitraria restricci ón en la probabilidad de falsa alarma global, la probabilidad de pérdida de la red, es decir la asociada último nodo de fusión, converge a cero seg un el número de etapas de fusión tiende a infinito. Finalmente, después de extender este resultado bajo la formulación bayesiana, proporcionamos dos ejemplos donde estas condiciones son aplicadas para caracterizar las prestaciones de detección de la red. A partir de estos ejemplos ilustramos diferentes escenarios de dependencia en los que una red t ándem óptima puede o no lograr detección asintóticamente perfecta tanto bajo la formulación bayesiana como bajo la formulación de Neyman-Pearson

Decentralized detection

Cover title. "To appear in Advances in Statistical Signal Processing, Vol. 2: Signal Detection, H.V. Poor and J.B. Thomas, Editors."--Cover.Includes bibliographical references (p. 40-43).Research supported by the ONR. N00014-84-K-0519 (NR 649-003) Research supported by the ARO. DAAL03-86-K-0171John N. Tsitsiklis

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

Distributed Detection and Estimation in Wireless Sensor Networks

In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint organization of in-network processing and communication. Then, we recall the basic features of consensus algorithm, which is a basic tool to reach globally optimal decisions through a distributed approach. The main part of the paper starts addressing the distributed estimation problem. We show first an entirely decentralized approach, where observations and estimations are performed without the intervention of a fusion center. Then, we consider the case where the estimation is performed at a fusion center, showing how to allocate quantization bits and transmit powers in the links between the nodes and the fusion center, in order to accommodate the requirement on the maximum estimation variance, under a constraint on the global transmit power. We extend the approach to the detection problem. Also in this case, we consider the distributed approach, where every node can achieve a globally optimal decision, and the case where the decision is taken at a central node. In the latter case, we show how to allocate coding bits and transmit power in order to maximize the detection probability, under constraints on the false alarm rate and the global transmit power. Then, we generalize consensus algorithms illustrating a distributed procedure that converges to the projection of the observation vector onto a signal subspace. We then address the issue of energy consumption in sensor networks, thus showing how to optimize the network topology in order to minimize the energy necessary to achieve a global consensus. Finally, we address the problem of matching the topology of the network to the graph describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Distributed Detection over Fading MACs with Multiple Antennas at the Fusion Center

A distributed detection problem over fading Gaussian multiple-access channels is considered. Sensors observe a phenomenon and transmit their observations to a fusion center using the amplify and forward scheme. The fusion center has multiple antennas with different channel models considered between the sensors and the fusion center, and different cases of channel state information are assumed at the sensors. The performance is evaluated in terms of the error exponent for each of these cases, where the effect of multiple antennas at the fusion center is studied. It is shown that for zero-mean channels between the sensors and the fusion center when there is no channel information at the sensors, arbitrarily large gains in the error exponent can be obtained with sufficient increase in the number of antennas at the fusion center. In stark contrast, when there is channel information at the sensors, the gain in error exponent due to having multiple antennas at the fusion center is shown to be no more than a factor of (8/pi) for Rayleigh fading channels between the sensors and the fusion center, independent of the number of antennas at the fusion center, or correlation among noise samples across sensors. Scaling laws for such gains are also provided when both sensors and antennas are increased simultaneously. Simple practical schemes and a numerical method using semidefinite relaxation techniques are presented that utilize the limited possible gains available. Simulations are used to establish the accuracy of the results.Comment: 21 pages, 9 figures, submitted to the IEEE Transactions on Signal Processin

Decentralized detection for censored binary observations with statistical dependence

This paper analyzes the problem of distributed detection in a sensor network of binary sensors. In particular, statistical dependence between local decisions (at binary sensors) is assumed, and two complementary methods to save energy have been considered: censoring, to avoid some transmissions from sensors to fusion center, and a sleep and wake up random schedule at local sensors. The effect of possible failures in transmission has been also included, considering the probability of having a successful transmission from a sensor to the fusion center. In this scenario, the necessary statistical information has been identified, the optimal decision rule at the fusion center has been obtained, and some examples have been used to analyze the effect of statistical dependence in a simple network with two sensors