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

Rate Allocation for Decentralized Detection in Wireless Sensor Networks

We consider the problem of decentralized detection where peripheral nodes make noisy observations of a phenomenon and send quantized information about the phenomenon towards a fusion center over a sum-rate constrained multiple access channel. The fusion center then makes a decision about the state of the phenomenon based on the aggregate received data. Using the Chernoff information as a performance metric, Chamberland and Veeravalli previously studied the structure of optimal rate allocation strategies for this scenario under the assumption of an unlimited number of sensors. Our key contribution is to extend these result to the case where there is a constraint on the maximum number of active sensors. In particular, we find sufficient conditions under which the uniform rate allocation is an optimal strategy, and then numerically verify that these conditions are satisfied for some relevant sensor design rules under a Gaussian observation model.Comment: Accepted at SPAWC 201

On optimal quantization rules for some problems in sequential decentralized detection

We consider the design of systems for sequential decentralized detection, a problem that entails several interdependent choices: the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two competing hypotheses), and a set of quantization rules (the local decisions on the basis of which the global decision is made). This paper addresses an open problem of whether in the Bayesian formulation of sequential decentralized detection, optimal local decision functions can be found within the class of stationary rules. We develop an asymptotic approximation to the optimal cost of stationary quantization rules and exploit this approximation to show that stationary quantizers are not optimal in a broad class of settings. We also consider the class of blockwise stationary quantizers, and show that asymptotically optimal quantizers are likelihood-based threshold rules.Comment: Published as IEEE Transactions on Information Theory, Vol. 54(7), 3285-3295, 200

Fusing Censored Dependent Data for Distributed Detection

In this paper, we consider a distributed detection problem for a censoring sensor network where each sensor's communication rate is significantly reduced by transmitting only "informative" observations to the Fusion Center (FC), and censoring those deemed "uninformative". While the independence of data from censoring sensors is often assumed in previous research, we explore spatial dependence among observations. Our focus is on designing the fusion rule under the Neyman-Pearson (NP) framework that takes into account the spatial dependence among observations. Two transmission scenarios are considered, one where uncensored observations are transmitted directly to the FC and second where they are first quantized and then transmitted to further improve transmission efficiency. Copula-based Generalized Likelihood Ratio Test (GLRT) for censored data is proposed with both continuous and discrete messages received at the FC corresponding to different transmission strategies. We address the computational issues of the copula-based GLRTs involving multidimensional integrals by presenting more efficient fusion rules, based on the key idea of injecting controlled noise at the FC before fusion. Although, the signal-to-noise ratio (SNR) is reduced by introducing controlled noise at the receiver, simulation results demonstrate that the resulting noise-aided fusion approach based on adding artificial noise performs very closely to the exact copula-based GLRTs. Copula-based GLRTs and their noise-aided counterparts by exploiting the spatial dependence greatly improve detection performance compared with the fusion rule under independence assumption