Stefano Marano

Propagation without wave equation toward an urban area model

Propagation in random media is a topic of great interest, whose application fields include, among others, the so-called last mile problem as well as the modeling of dense urban area radio communication channels. A simple scenario for this issue is considered, with an optical-ray propagation across a medium of disordered lossless scatterers. The propagation medium behaves like a percolating lattice and the goal is to characterize statistically the propagation depth in the medium as a function of the density g of scatterers and of /spl theta/-the ray incidence angle. To the best of our knowledge, this approach is totally new. The problem is mathematically formulated as a random walk and the solutions are based on the theory of the martingale random processes. The obtained (approximate) analytical formulas have been validated by means of numerical simulations, demonstrating the applicability of the proposed model for a wide range of the global parameters q and /spl theta/. We believe that our results may constitute a promising first step toward the solution of more complicated propagation models and a wide class of communication problems.

Practical fusion of quantized measurements via particle filtering

Most treatments of decentralized estimation rely on some form of track fusion, in which local track estimates and their associated covariances are communicated. This implies a great deal of communication; and it was recently proposed that by an intelligent quantization directly of measurements, the communication needs could be considerably cut. However, several issues were not discussed. The first of these is that estimation with quantized measurements requires an update with a non-Gaussian distribution, reflecting the uncertainty within the quantization bin.; In general this would be a difficult task for dynamic estimation, but Markov-chain Monte-Carlo (MCMC, and specifically here particle filtering) techniques appear quite appropriate since the resulting system is, in essence, a nonlinear filter. The second issue is that in a realistic sensor network it is to be expected that measurements should arrive out-of-sequence. Again, a particle filter is appropriate, since the recent literature has reported particle filter modifications that accommodate nonlinear-filter updates based on new past measurements, with the need to refilter obviated. We show results that indicate a compander/particle-filter combination is a natural fit, and specifically that quite good performance is achievable with only 2-3 bits per dimension per observation. The third issue is that intelligent quantization requires that both sensor and fuser share an understanding of the quantization rule. In dynamic estimation this is a problem since both quantizer and fuser are working with only partial information; if measurements arrive out-of-sequence the problem is compounded. We therefore suggest architectures, and comment on their suitabilities for the task. A scheme based on delta-modulation appears to be promising.

Distributed Detection With Censoring Sensors Under Physical Layer Secrecy

We consider distributed binary detection problems in which the remote sensors of a network implement a censoring strategy to fulfill energy constraints, and the network works under the attack of an eavesdropper. The attacker wants to discover the state of the nature scrutinized by the system, but the network implements appropriate countermeasures to make this task hopeless. The goal is to achieve perfect secrecy at the physical layer, making the data available at the eavesdropper useless for its detection task. Adopting as performance metric certain Ali-Silvey distances, we characterize the detection performance of the system under physical layer secrecy. Two communication scenarios are addressed: parallel access channels and a multiple access channel. In both cases the optimal operative points from the network perspective are found. The most economic operative solution is shown to lie in the asymptote of low energy regime. How the perfect secrecy requirement impacts on the achievable performances, with respect to the absence of countermeasures, is also investigated.

Distributed Estimation in Large Wireless Sensor Networks via a Locally Optimum Approach

A wireless sensor network (WSN) engaged in a decentralized estimation problem is considered. The nonrandom unknown parameter lies in some small neighborhood of a nominal value and, exploiting this knowledge, a locally optimum estimator (LOE) is introduced. Under the LOE paradigm, the sensors of the network process their observations by means of a suitable nonlinearity (the score function), before delivering data to the fusion center that outputs the final estimate. Usually continuous-valued data cannot be reliably delivered from sensors to the fusion center, and some form of data compression is necessary. Accordingly, we design the scalar quantizers that must be used at the networks nodes in order to comply with the estimation problem at hand. Such a difficult multiterminal inference problem is shown to be asymptotically equivalent to the already solved problem of designing optimum quantizers for reconstruction (as opposed to inference) purposes.

Cross-Layer Design of Sequential Detectors in Sensor Networks

A network of sensors polled by a mobile agent (the SENMA paradigm) is used for detection purposes, with both the remote nodes and the mobile agent implementing Walds sequential tests. When polled, each remote node transmits its local decision (if any) to the agent, and two network/agent communication schemes are considered. One of these is designed with specific care to the networks energy consumption. In both cases, collisions over the common communication channel are precluded by the sequentiality of the sensors query. The system performances in terms of average decision time, error probability, and network energy consumption are derived in exact analytical form. A tradeoff exists between the amount and the reliability of the information that the rover may collect: At optimality, the decentralized system overcomes a single supernode by orders of magnitude in terms of decision time, while only 30% of the sensors encountered by the mobile agent spend energy to reveal themselves. The remaining sensors contribute to the detection process by their silence

Sequential Sampling in Sensor Networks for Detection With Censoring Nodes

A wireless sensor network designed according to the sensor network with mobile agents (SENMA) architecture is engaged in a detection task, with a mobile agent (MA) that sequentially queries the networks nodes. The focus is on the effect of censoring: sensors respond to the query from the MA only if the local observations are deemed sufficiently informative; otherwise, they stay silent. Delivered data, if any, can be either unquantized or quantized to a single bit. The study is limited to shift-in-mean problems, involving two simple statistical hypotheses, where the noise distribution must be an even function but is otherwise arbitrary. Simple analytical relationships characterizing the tradeoff between the detection delay and the energy consumption of the network are derived, and examples of their applications are provided.

Support-based and ML approaches to DOA estimation in a dumb sensor network

A recent paper by Marano et al. shows that a network of unconnected and completely direction-of-arrival (DOA)-blind sensors (beepers) is able to perform DOA estimation quite effectively within the SENMA architecture (unlabeled polling performed by a mobile agent). The idea is that the mobile agent collects the periodic emissions of the polled sensors, with the time origin of such emissions being the passage of the acoustic wavefront. Depending on the relative orientation between the acoustic wavefront and the field of view of the mobile agent, the impinging times over different sensors are more or less clustered and so are the recorded emissions. On this basis, the DOA may be inferred. Here, two new estimators are proposed. One method (support-based) exploits the maximum spread between recorded times and is simple to implement, and its performance, measured in terms of mean square error, is improved significantly versus that proposed in the recent paper by Marano et al. In fact, the support-based estimator achieves performance close to that of the maximum-likelihood (ML) estimator-also investigated here-indicating that the support-based structure is perhaps suitable for tasks that involve cheap robust designs, such as sea/ground surveillance and sniper location.

Asymptotic Design of Quantizers for Decentralized MMSE Estimation

Conceptual and practical encoding/decoding, aimed at accurately reproducing remotely collected observations, has been heavily investigated since the pioneering works by Shannon about source coding. However, when the goal is not to reproduce the observables, but making inference about an embedded parameter and the scenario consists of many unconnected remote nodes, the landscape is less certain. We consider a multiterminal system designed for efficiently estimating a random parameter according to the minimum mean square error (MMSE) criterion. The analysis is limited to scalar quantizers followed by a joint entropy encoder, and it is performed in the high-resolution regime where the problem can be more easily mathematically tackled. Focus is made on the peculiarities deriving from the estimation task, as opposed to that of reconstruction, as well as on the multiterminal, as opposite to centralized, character of the inference. The general form of the optimal nonuniform quantizer is derived and examples are given.

Distributed Detection in the Presence of Byzantine Attack in Large Wireless Sensor Networks

Wireless sensor networks are vulnerable to Byzantine attacks in which a fraction of sensors are tampered. The intruder can reprogram the compromised sensors, making them behave as if they are authentic nodes. We consider the problem of distributed detection in wireless sensor networks in the presence of Byzantine attacks where the compromised sensors collaboratively send fictitious observations to the fusion center. We define the power of the attacker as the fraction of the sensors that have been compromised for the attack. We present the optimal attacking strategy for any given attacking power. We show that there is a critical power level above which the fusion center is completely blinded in the sense that the optimal detection performs no better than a coin flip independent of collected data. We also present a robust detector to counter the presence of Byzantine attacks

Quantizer Precision for Distributed Estimation in a Large Sensor Network

We investigate the design of simple noncooperative quantizers for distributed estimation of a common random variable. It is assumed that there is a budget of aggregate rate, a criterion of Fisher information, and a large population of sensors. It is further assumed that sensor quantizers are uniform, and that rate is determined by the entropy of the outputs of these. The key question asked is whether it is better to quantize a relatively few sensors finely or as many as possible coarsely