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

Bayesian Design of Tandem Networks for Distributed Detection With Multi-bit Sensor Decisions

We consider the problem of decentralized hypothesis testing under communication constraints in a topology where several peripheral nodes are arranged in tandem. Each node receives an observation and transmits a message to its successor, and the last node then decides which hypothesis is true. We assume that the observations at different nodes are, conditioned on the true hypothesis, independent and the channel between any two successive nodes is considered error-free but rate-constrained. We propose a cyclic numerical design algorithm for the design of nodes using a person-by-person methodology with the minimum expected error probability as a design criterion, where the number of communicated messages is not necessarily equal to the number of hypotheses. The number of peripheral nodes in the proposed method is in principle arbitrary and the information rate constraints are satisfied by quantizing the input of each node. The performance of the proposed method for different information rate constraints, in a binary hypothesis test, is compared to the optimum rate-one solution due to Swaszek and a method proposed by Cover, and it is shown numerically that increasing the channel rate can significantly enhance the performance of the tandem network. Simulation results for $M$-ary hypothesis tests also show that by increasing the channel rates the performance of the tandem network significantly improves

Family Watchdog

We consider a distributed detection system under communication constraints, where several peripheral nodes observe a common phenomenon and send their observations to a fusion center via error-free but rate-constrained channels. Using the minimum expected error probability as a design criterion, we propose a cyclic procedure for the design of the peripheral nodes using the person-by-person methodology. It is shown that a fine-grained binning idea together with a method for updating the conditional probabilities of the joint index space at the fusion center, decrease the complexity of the algorithm and make it tractable. Also, unlike previous methods which use dissimilarity measures (e.g., the Bhattacharyya distance), a-prior hypothesis probabilities are allowed to contribute to the design in the proposed method. The performance of the proposed method is comparedto a method due to Longo et al.’s and it is shown that the new method can significantly outperform the previous one at a comparable complexity.QC 20141203</p

Decentralized Hypothesis Testing in Sensor Networks

Wireless sensor networks (WSNs) play an important role in the future ofInternet of Things IoT systems, in which an entire physical infrastructurewill be coupled with communication and information technologies. Smartgrids, smart homes, and intelligent transportation systems are examples ofinfrastructure that will be connected with sensors for intelligent monitoringand management. Thus, sensing, information gathering, and efficientprocessing at the sensors are essential. An important problem in wireless sensor networks is that of decentralizeddetection. In a decentralized detection network, spatially separatedsensors make observations on the same phenomenon and send informationabout the state of the phenomenon towards a central processor. The centralprocessor (or the fusion center, FC) makes a decision about the state of thephenomenon, base on the aggregate received messages from the sensors. Inthe context of decentralized detection, the object is often to make the bestdecision at the FC. Since this decision is made based on the received messagesfrom the sensors, it is of interest to optimally design decision rules atthe remote sensors. This dissertation deals mainly with the problem of designing decisionrules at the remote sensors and at the FC, while the network is subjectto some limitation on the communication between nodes (sensors and theFC). The contributions of this dissertation can be divided into three (overlapping)parts. First, we consider the case where the network is subjectto communication rate constraint on the links connecting different nodes.Concretely, we propose an algorithm for the design of decision rules at thesensors and the FC in an arbitrary network in a person-by-person (PBP)methodology. We first introduce a network of two sensors, labeled as therestricted model. We then prove that the design of sensors’ decision rules,in the PBP methodology, is in an arbitrary network equivalent to designingthe sensors’ decision rules in the corresponding restricted model. We alsopropose an efficient algorithm for the design of the sensors’ decision rules inthe restricted model. Second, we consider the case where remote sensors share a commonmultiple access channel (MAC) to send their messages towards the FC, andwhere the MAC channel is subject to a sum rate constraint. In this situation,ithe sensors compete for communication rate to send their messages. Wefind sufficient conditions under which allocating equal rate to the sensors,so called rate balancing, is an optimal strategy. We study the structure ofthe optimal rate allocation in terms of the Chernoff information and theBhattacharyya distance. Third, we consider a decentralized detection network where not onlyare the links between nodes subject to some communication constraints,but the sensors are also subject to some energy constraints. In particular,we study the network under the assumption that the sensors are energyharvesting devices that acquire all the energy they need to transmit theirmessages from their surrounding environment. We formulate a decentralizeddetection problem with system costs due to the random behavior of theenergy available at the sensors in terms of the Bhattacharyya distance.QC 20161103</p

Optimality of Rate Balancing in Wireless Sensor Networks

We consider the problem of distributed binary hypothesis testing in a parallel network topology where sensors independently observe some phenomenon and send a finite rate summary of their observations to a fusion center for the final decision. We explicitly consider a scenario under which (integer) rate messages are sent over an error free multiple access channel, modeled by a sum rate constraint at the fusion center. This problem was previously studied by Chamberland and Veeravalli, who provided sufficient conditions for the optimality of one bit sensor messages. Their result is however crucially dependent on the feasibility of having as many one bit sensors as the (integer) sum rate constraint of the multiple access channel, an assumption that can often not be satisfied in practice. This prompts us to consider the case of an a-priori limited number of sensors and we provide sufficient condition under which having no two sensors with rate difference more than one bit, so called rate balancing, is an optimal strategy with respect to the Bhattacharyya distance between the hypotheses at the input to the fusion center. We further discuss explicit observation models under which these sufficient conditions are satisfied.QC 20160414</p