G.T.F. de Abreu

Weighing strategy for network localization under scarce ranging information

We propose a robust non-parametric strategy to weight scarce and imperfect ranging information, which is shown to significantly improve the accuracy of distance-based network localization algorithms. The proposed weights have a dispersion component, which captures the effect of noise under the assumption of bias-free samples, and a penalty component, which quantifies the risk of the latter assumption and penalizes it proportionally. The dispersion weights result from the application of small-scale statistics with confidence bounds optimized under a maximum entropy criterion that mathematizes the empirical concept of reliability commonly found in related literature. In turn, the penalty weights are derived from the relationship between the risk incurred by the bias-free assumption and the geometry of 3-node cliques, established by statistical-geometry. The performance of the distance-based network localization algorithm employing the proposed dispersion-penalty weights is compared against the Cramer-Rao lower bound (CRLB) and to equivalent algorithms employing alternative weights. The comparison reveals that, amongst the alternatives, the network localization algorithm with the proposed weights performs best and closest to an unbiased estimator.

On the generation of Tikhonov variates

A novel, simple and efficient method for the generation of Tikhonov (a.k.a. von Mises) random variates is proposed. In the proposed method, circular variates of a prescribed Tikhonov distribution pT(x;alpha,xi) are generated via the transformation of variates selected randomly, on a one-for-one basis, from a bank of K distinct Cauchy and Gaussian generators. The mutually exclusive probabilities of sampling from each of the Cauchy or Gaussian generators, as well as the variance and half-width parameters that specify the latter, are derived directly from the Cauchy, Gaussian and Tikhonov characteristic functions, all of which are either known or given in closed form. The proposed random mixture technique is extremely efficient in that a single pair of uniform random numbers is consumed in the generation of each Tikhonov (or von Mises) sample, regardless of the prescribed concentration and centrality parameters (alpha, xi), all requiring neither the rejection of samples, nor the repetitive evaluation of computationally demanding functions. Additional attractive features of the method are as follows. By construction, the first (dominant) N circular moments of Tikhonov variates generated with the proposed random mixture technique are the ones that best approximate their corresponding theoretical values, with errors measured exactly. The exact distribution of generated Tikhonov variates is determined analytically, and its (Kullback-Leibler) divergence to the exact Tikhonov PDF is shown also analytically to be negligible. Finally, the technique establishes a connection between Tikhonov and Gaussian variates which can be exploited, e.g., in the generation of piecewise-continuous pseudo-random functions with Tikhonov-distributed outcomes.

Design of jitter-robust orthogonal pulses for UWB systems

The design of a class of Hermite pulses for pulse shape modulated (PSM) ultra-wideband (UWB) communications is presented. The proposed pulses offer robustness against jitter or small imperfections in synchronization between received waveforms and their matched templates. Close form expressions of the auto- and cross-correlation functions of the proposed and conventional Hermite pulses are given, which are used to model the jitter channel as a simple distortive matrix. The set of jitter-robust orthogonal pulses is then obtained by simultaneously diagonalizing a subset of selected samples of such channel matrix realizations for different jitter values. Examples of waveforms derived with the method and simulation results showing the effectiveness of the proposed pulses in combatting jitter in PSM-UWB systems are given.

Localization from Imperfect and Incomplete Ranging

Source localization from imperfect and incomplete range information is considered. The problem is formulated as a combination of the well-known Euclidean distance matrix (EDM) approximation/completion problem and multidimensional scaling (MDS). A powerful technique that solves the EDM approximation/completion problem by exploiting the semi-definiteness property of a corresponding Euclidean kernel has been recently proposed (A.Y. Alfakih et al., 1999). That technique requires, however, that the entries of the input EDM be weighted in accordance to their reliability. In this paper, a formula for such a weight function, based on confidence-bound statistics of the distance estimates and on graph spectral properties is studied. Computer simulations show that significant improvement in localization accuracy can be achieved by utilizing the weight function derived

Network boundary recognition via graph-theory

Wireless sensor networks (WSNs) are considered an adequate solutions for environmental monitoring and surveillance applications, where the physical presence of humans is impossible or costly. In the next future, it is foreseen that nodes will be part of a localization system, that will be able to estimate their locations, aiding the coordination for the most consuming activities such as relaying and routing. However, in some particular conditions, it is useful to know only logical information about the node locations and, specifically it would be sufficient to know if they are in the inner part or at the boundary of the network. In this paper we propose a technique for the identification of nodes at the network boundary, based solely on connectivity information, assumed to be available at a central unit The algorithm is a useful network management tool as it allows one (the central unit) to detect the formation or existence of topological holes, enabling corrective measures such as redeployment in affected areas or warning dead-end nodes of their condition. Since connectivity information is learned overtime by the network sinks (and the coordinator to which they are connected to), the proposed network boundary discovery algorithm incurs no additional cost to the network at steady state of operation. The algorithm is based on a spectral graph clusterization technique, which first tessellates the network in small cells that circumvent (eventual) connectivity holes. Then, the border nodes of each cluster are identified using beetweness centrality scores and clusters are classified by their adjacencies. Since nodes located simultaneously at the boundary of adjacent clusters are obviously not at the border of a hole, the procedure allows the identification of nodes that are exclusively at the boundary of one cluster, ultimately yielding the collection of nodes at the boundaries of the network in general.

Clusterization for Robust Geographic Routing in Wireless Sensor Networks

A cross-layer algorithm for geographic routing in wireless sensor networks (WSNs) is proposed, which is robust to dead-ends and resilient to topological variations due to network dynamics. The solution combines ideas of network tessellation (clusterization) with greedy forwarding, without suffering from the problems afflicting landmark-based alternatives. The clusterization algorithm is based on a discovered graph-spectral property and relies on connectivity information only. Cluster sizes can be varied, allowing for different trade-offs between packet delivery success ratio (PDSR) and average packet delivery latency (APDL) to be reached. Simulation results show that the technique can substantially improve the PDSR in networks where large concave holes (dead-ends) are present, with no or little impact on APDL.

Hypothesis Testing and Iterative WLS Minimization for WSN Localization under LOS/NLOS Conditions

We propose a novel non-parametric solution for accurate distance-based source localization in wireless sensor networks (WSNs). The proposed technique includes a method to detect whether or not ranging is affected by bias due to non- line-of-sight (NLOS) conditions, requiring no a-priori knowledge of distance estimate statistics. Instead, we exploit the triangular inequality property of the Euclidean space and employ hypothesis testing (HT) in order to derive confidence levels on the observations and classify each link in the network as LOS or NLOS. These confidence levels are then incorporated in the formulation of an iterative WLS (IWLS) algorithm for WSN localization. The combination of the two contributions proves a powerful WSN localization algorithm, that is robust to noise, bias and erasure (incompleteness) over ranging data.

Multi-Hop Aggregate Information Efficiency in Wireless Ad Hoc Networks

We introduce multi-hop aggregate information efficiency (MIEA), a comprehensive metric that captures several performance-affecting factors of wireless ad hoc networks in a unified formulation. This metric is then employed to analyze such networks with respect to their spectral efficiencies, network loads, and hopping strategies. The analysis reveals that the hopping strategy that achieves maximum information efficiency is that of multiple short hops with no more than a single packet retransmission allowed at each hop, as opposed to the alternative of fewer long-haul hops with multiple packet retransmissions. The implementation of that preferred strategy withstanding, it is found furthermore that the most efficient networks typically exhibit about 65% of link outage probability, which corroborates similar findings obtained in different network settings and using different metrics. Bearing in mind that link outage is a function not only of deterministic parameters such as node density, but also of design parameters such as modulation, our analysis also shows that the modulation scheme that optimizes the aggregate information efficiency is in fact a function of node density. In that respect, our metric and method is shown to be useful to determining the modulation scheme that optimizes the performance of a network with a certain node density.

Closed-form correlation functions of generalized Hermite wavelets

A closed-form expression is given for the correlation functions of generalized Hermite wavelets, constructed from an also-generalized definition of Hermite polynomials. Due to their Gaussianity, these wavelets can be used as a tool in the analysis or design of systems involving nonsinusoidal wavelets as well as to model impulsive waveforms found in real-world applications and signal processing problems. As such, the formula is potentially applicable to various areas of science.

Band-limited frequency efficient orthogonal pulse shape modulation for UWB communications

This paper addresses the design of an equally frequency limited set of orthogonal pulses adequate for an impulse radio (IR) ultra wideband (UWB) communication system employing M-ary pulse shape modulation (PSM). UWB systems have to face many spectrum restrictions due to potential interference to sensitive existing systems, comply with maximum bandwidth regulations or fit into spectrum masks like the one emitted by the Federal Communications Commission (FCC). Then, UWB systems have to restrict their bandwidth and maximize its usage efficiency. Additionally, future narrowband communication systems can be allocated in portions of the spectrum where UWB systems operate, and they may not tolerate possible interference from UWB emissions, this would lead to the mandatory use of a stop-band filter in the UWB transmitters. The proposed set of orthogonal pulse-shapes provides both pulses equally limited in frequency and robustness against such a narrowband interference canceller filter.