Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

The Outage Probability of a Finite Ad Hoc Network in Nakagami Fading

An ad hoc network with a finite spatial extent and number of nodes or mobiles is analyzed. The mobile locations may be drawn from any spatial distribution, and interference-avoidance protocols or protection against physical collisions among the mobiles may be modeled by placing an exclusion zone around each radio. The channel model accounts for the path loss, Nakagami fading, and shadowing of each received signal. The Nakagami m-parameter can vary among the mobiles, taking any positive value for each of the interference signals and any positive integer value for the desired signal. The analysis is governed by a new exact expression for the outage probability, defined to be the probability that the signal-to-interference-and-noise ratio (SINR) drops below a threshold, and is conditioned on the network geometry and shadowing factors, which have dynamics over much slower timescales than the fading. By averaging over many network and shadowing realizations, the average outage probability and transmission capacity are computed. Using the analysis, many aspects of the network performance are illuminated. For example, one can determine the influence of the choice of spreading factors, the effect of the receiver location within the finite network region, and the impact of both the fading parameters and the attenuation power laws.Comment: to appear in IEEE Transactions on Communication

Distributed Source Localization and Tracking Algorithms for Ad-hoc Acoustic Sensor Networks

In this dissertation, we construct an algorithmic framework for systematic tracking of moving sources in large-scale sensor networks. The tracking algorithms we developed generate the estimates of the tracking locations from fusion of space-time data by first fusing the data in space and subsequently by fusing the data in time. Fusion in space is performed by fusing current sensed data that is sufficiently high-quality from the sensor nodes to produce the current source location estimate. These location estimates are indexed as they become available and subsequently fused iteratively in time to produce tracking estimates. Both fusion in space and fusion in time are performed distributively over the ad-hoc sensor network by exploiting distributed algorithms of computation of averages. The distributed tracking algorithms are locally constructed at each participating sensor node exploiting only locally available sensor observations and local available network connectivity information. These algorithms we developed are also resource efficient, scalable, fault-tolerant and can readily adapt to local changes in network topologies. We present methods for optimizing and characterizing the performance of the algorithms as a function of the quality of the sensor measurements, the source dynamics, the sensor density and the network connectivity

A time dependent performance model for multihop wireless networks with CBR traffic

In this paper, we develop a performance modeling technique for analyzing the time varying network layer queueing behavior of multihop wireless networks with constant bit rate traffic. Our approach is a hybrid of fluid flow queueing modeling and a time varying connectivity matrix. Network queues are modeled using fluid-flow based differential equation models which are solved using numerical methods, while node mobility is modeled using deterministic or stochastic modeling of adjacency matrix elements. Numerical and simulation experiments show that the new approach can provide reasonably accurate results with significant improvements in the computation time compared to standard simulation tools. © 2010 IEEE

Distributed Recursive Least-Squares: Stability and Performance Analysis

The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary processes. In this paper, a distributed recursive least-squares (D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless sensor networks. Distributed iterations are obtained by minimizing a separable reformulation of the exponentially-weighted least-squares cost, using the alternating-minimization algorithm. Sensors carry out reduced-complexity tasks locally, and exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. A steady-state mean-square error (MSE) performance analysis of D-RLS is conducted, by studying a stochastically-driven `averaged' system that approximates the D-RLS dynamics asymptotically in time. For sensor observations that are linearly related to the time-invariant parameter vector sought, the simplifying independence setting assumptions facilitate deriving accurate closed-form expressions for the MSE steady-state values. The problems of mean- and MSE-sense stability of D-RLS are also investigated, and easily-checkable sufficient conditions are derived under which a steady-state is attained. Without resorting to diminishing step-sizes which compromise the tracking ability of D-RLS, stability ensures that per sensor estimates hover inside a ball of finite radius centered at the true parameter vector, with high-probability, even when inter-sensor communication links are noisy. Interestingly, computer simulations demonstrate that the theoretical findings are accurate also in the pragmatic settings whereby sensors acquire temporally-correlated data.Comment: 30 pages, 4 figures, submitted to IEEE Transactions on Signal Processin

Distributed anonymous function computation in information fusion and multiagent systems

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we exhibit a class of non-computable functions, and prove that every function outside this class can at least be approximated. The problem of computing averages in a distributed manner plays a central role in our development