Giancarlo Pastor

Log-cumulant matching approximation of heavy-tailed-distributed aggregate interference

The Method of Moments (MoM) and Method of Log-cumulants (MoLC) estimate the distribution parameters in terms of First Kind Statistics (FKS) and Second Kind Statistics (SKS), respectively. Although SKS offer a suitable framework to analyze heavy-tailed (and asymmetric) distributions, which are commonly-found in aggregate interference modeling, statistical methods developed within this framework has been understudied. For networks following point processes of varying regularity, this paper evaluates the MoM and MoLC methods to estimate the distribution parameters of interference under Rayleigh fading and log-normal shadowing. The results confirm that the gamma and log-normal models offer accurate approximations only when the interference does not present a heavy-tail. For heavy-tailed interference, the MoLC allows an accurate and fast estimation for the α-stable model.

Log-cumulants-based Edgeworth expansion for skew-distributed aggregate interference

The Edgeworth expansion approximates nearly Gaussian distributions in terms of cumulants. This expansion is developed within the framework of First Kind Statistics, where definitions are derived from the Fourier transform. Alternatively, the framework of Second Kind Statistics offers analogous definitions which are derived from the Mellin transform. Although a formalism with such similarity to the existing definitions cannot lead to intrinsically new results, statistical methods within this new framework has been understudied. This paper introduces an Edgeworth expansion in terms of log-cumulants, which are the analogous to cumulants for the Second Kind statistics. More importantly, this new expansion approximates asymmetric distributions which are commonly-found in aggregate interference modeling.

Wireless Sensor Network for low-complexity entropy determination of human gait

In this work we present a Wireless Sensor Network (WSN) system designed for the on-board determination of human gait entropy. The usage of nonlinear entropy-based metrics has proven to be a useful tool for analyzing the complexity of biological systems. The final goal of entropy calculation in this type of biological system is to identify possible causes of future injuries (in order to improve aging) and the early injury detection (ideal for elite athletes). Existing systems for human gait analysis are limited to traditional data gathering, e.g. continuous measurement and wireless transmission to a Data Fusion Center (DFC), due to the computational burden of entropy calculation. In addition, actual systems are likely to interfere the natural movement due to their cumbersome nature. The WSN presented here uses four sensor nodes, located in both ankles and hip sides, and are equipped with triaxial accelerometers. We propose the use of low-complexity algorithms in order to perform onboard entropy determination prior to wireless transmission. The proposed system can be used to reliably determine long-term human gait entropy.

Asymptotic Expansions for Heavy-Tailed Data

Heavy-tailed distributions are present in the characterization of different modern systems such as high-resolution imaging, cloud computing, and cognitive radio networks. Commonly, the cumulants of these distributions cannot be defined from a certain order, and this restricts the applicability of traditional methods. To fill this gap, the present letter extends the traditional Edgeworth and Cornish-Fisher expansions, which are based on the cumulants, to analogous asymptotic expansions based on the log-cumulants. The proposed expansions inherit the capability of log-cumulants to characterize heavy-tailed distributions and parallel traditional expansions. Thus, they are readily implemented. Interestingly, the proposed expansions are applicable for light-tailed distributions as well.

Incremental similarity metric to evaluate complexity of human gait: A distributed Wireless Sensor Network approach

The analysis of the complexity of biological systems - a proved parameter indicative of the proper functioning of the human body - traditionally involves highly complex algorithms. In this work we use a well-known measure of similarity, the Normalized Compression Distance (NCD), to compute the variation of complexity of the human gait. We define the incremental NCD (iNCD) and analyze the duration of the gait cycle time series. To validate iNCD as a metric for this type of analysis, we perform experiments using a four-nodes Wireless Sensor Network (WSN), with one trained volunteer running on a treadmill during one hour, at a comfortable velocity. We show that the joint use of a WSN with iNCD analysis is a useful tool for detecting human gait anomalies at controlled computational load.

Compressive Data Aggregation from Poisson point process observations

This paper introduces Stochastic Compressive Data Aggregation (S-CDA) for wireless sensor networks (WSN) under random deployments. The Poisson point process (PPP) models the random deployment, and at the same time, allows the efficient implementation of an adequate sparsifying matrix, the random discrete Fourier transform (RDFT). The signal recovery is based on the RDFT which reveals the frequency content of smooth signals, such as temperature or humidity maps, which consist of few frequency components. The recovery methods are based on the accelerated iterative hard thresholding (AIHT) which sets all but the largest (in magnitude) frequency components to zero. The adoption of the PPP allows to analyze the communication and compression aspects of S-CDA using previous results from stochastic geometry and compressed sensing, respectively.

Message-passing algorithms for link monitoring

Given the high uncertainty in the dynamics of Wireless Sensor Networks (WSN), it is essential to monitor the Quality-of-Service metrics in order to find the links with poor characteristics. This would allow to implement fault-tolerant protocols to reroute the control packets and avoid zones with untrusted links. However, network monitoring is not used as a permanent analysis tool. This is due both to the conventional use of highly-complex inference algorithms and active approaches such as injection of probing packets. In this paper, we introduce a tree-graph representation for WSN with a general topology, and also suitable for link parameters inference problems. Factor Graphs and the Sum-Product algorithm are considered to develop low complexity schemes for permanent and passive monitoring of multiple link parameters such as Link Loss Rate, Link Error Rate and Link Delay.