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

Resource Management in Heterogeneous Wireless Sensor Networks

We propose a first approach in the direction of a general framework for resource management in wireless sensor networks (WSN). The basic components of the approach are a model for WSNs and a task model. Based on these models, a first version of an algorithm for assigning tasks to a WSN is presented. The models and the algorithm are designed in such a way that an extension to more complex models is possible. Furthermore, the developed approach to solve the RM problem allows an easy adaptation, to fit more complex models. In this way, a flexible approach is achieved, which may form the base for many RM approaches.\ud The possibilities and limitations of the presented approach are tested on randomly generated instances. The aim of these tests is to show that the chosen models and algorithm form a proper starting point to design RM tools

Impact of network structure on the capacity of wireless multihop ad hoc communication

As a representative of a complex technological system, so-called wireless multihop ad hoc communication networks are discussed. They represent an infrastructure-less generalization of todays wireless cellular phone networks. Lacking a central control authority, the ad hoc nodes have to coordinate themselves such that the overall network performs in an optimal way. A performance indicator is the end-to-end throughput capacity. Various models, generating differing ad hoc network structure via differing transmission power assignments, are constructed and characterized. They serve as input for a generic data traffic simulation as well as some semi-analytic estimations. The latter reveal that due to the most-critical-node effect the end-to-end throughput capacity sensitively depends on the underlying network structure, resulting in differing scaling laws with respect to network size.Comment: 30 pages, to be published in Physica

Two-Hop Connectivity to the Roadside in a VANET Under the Random Connection Model

We compute the expected number of cars that have at least one two-hop path to a fixed roadside unit in a one-dimensional vehicular ad hoc network in which other cars can be used as relays to reach a roadside unit when they do not have a reliable direct link. The pairwise channels between cars experience Rayleigh fading in the random connection model, and so exist, with probability function of the mutual distance between the cars, or between the cars and the roadside unit. We derive exact equivalents for this expected number of cars when the car density $\rho$ tends to zero and to infinity, and determine its behaviour using an infinite oscillating power series in $\rho$, which is accurate for all regimes. We also corroborate those findings to a realistic situation, using snapshots of actual traffic data. Finally, a normal approximation is discussed for the probability mass function of the number of cars with a two-hop connection to the origin. The probability mass function appears to be well fitted by a Gaussian approximation with mean equal to the expected number of cars with two hops to the origin.Comment: 21 pages, 7 figure

Full Connectivity: Corners, edges and faces

We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in three simple but instructive examples and discuss the practical benefits of its application to different models.Comment: 28 pages, 8 figure

TEMPORAL CONNECTIVITY AS A MEASURE OF ROBUSTNESS IN NONORTHOGONAL MULTIPLE ACCESS WIRELESS NETWORKS

Supplementary Material has been provided, but is not yet published.Nonorthogonal multiple access (NOMA) is recognized as an important technology to meet the performance requirements of fifth generation (5G) and beyond 5G (B5G) wireless networks. Through the technique of overloading, NOMA has the potential to support higher connection densities, increased spectral efficiency, and lower latency than orthogonal multiple access. The role of NOMA in 5G/B5G wireless networks necessitates a clear understanding of how overloading variability affects network robustness. This dissertation considers the relationship between variable overloading and network robustness through the lens of temporal network theory, where robustness is measured through the evolution of temporal connectivity between network devices (ND). We develop a NOMA temporal graph model and stochastic temporal component framework to characterize time-varying network connectivity as a function of NOMA overloading. The analysis is extended to derive stochastic expressions and probability mass functions for unidirectional connectivity, bidirectional connectivity, the inter-event time between unidirectional connectivity, and the minimum time required for bidirectional connectivity between all NDs. We test the accuracy of our analytical results through numerical simulations. Our results provide an overloading-based characterization of time-varying network robustness that is generalizable to any underlying NOMA implementation.National Security Agency, Fort George G. Meade, MD 20775Major, United States Marine CorpsApproved for public release. Distribution is unlimited

Symmetric motifs in random geometric graphs

We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are particularly prevalent in random geometric graphs and appear in the Laplacian and adjacency spectrum as sharp, distinct peaks, a feature often found in real-world networks. We look at the probabilities of their appearance and compare these across parameter space and dimension. We then use the Chen-Stein method to derive the minimum separation distance in random geometric graphs which we apply to study symmetric motifs in both the intensive and thermodynamic limits. In the thermodynamic limit the probability that the closest nodes are symmetric approaches one, whilst in the intensive limit this probability depends upon the dimension.Comment: 11 page