Alejandro Ribeiro

Symbol error probabilities for general Cooperative links

Cooperative diversity (CD) networks have been receiving a lot of attention recently as a distributed means of improving error performance and capacity. For sufficiently large signal-to-noise ratio (SNR), this paper derives the average symbol error probability (SEP) for analog forwarding CD links. The resulting expressions are general as they hold for an arbitrary number of cooperating branches, arbitrary number of cooperating hops per branch, and various channel fading models. Their simplicity provides valuable insights to the performance of CD networks and suggests means of optimizing them. Besides revealing the diversity, they clearly show from where this advantage comes from and prove that presence of diversity does not depend on the specific (e.g., Rayleigh) fading distribution. Finally, they explain how diversity is improved in multihop CD networks.

Consensus in Ad Hoc WSNs With Noisy Links— Part I: Distributed Estimation of Deterministic Signals

We deal with distributed estimation of deterministic vector parameters using ad hoc wireless sensor networks (WSNs). We cast the decentralized estimation problem as the solution of multiple constrained convex optimization subproblems. Using the method of multipliers in conjunction with a block coordinate descent approach we demonstrate how the resultant algorithm can be decomposed into a set of simpler tasks suitable for distributed implementation. Different from existing alternatives, our approach does not require the centralized estimator to be expressible in a separable closed form in terms of averages, thus allowing for decentralized computation even of nonlinear estimators, including maximum likelihood estimators (MLE) in nonlinear and non-Gaussian data models. We prove that these algorithms have guaranteed convergence to the desired estimator when the sensor links are assumed ideal. Furthermore, our decentralized algorithms exhibit resilience in the presence of receiver and/or quantization noise. In particular, we introduce a decentralized scheme for least-squares and best linear unbiased estimation (BLUE) and establish its convergence in the presence of communication noise. Our algorithms also exhibit potential for higher convergence rate with respect to existing schemes. Corroborating simulations demonstrate the merits of the novel distributed estimation algorithms.

Bandwidth-constrained distributed estimation for wireless sensor Networks-part I: Gaussian case

We study deterministic mean-location parameter estimation when only quantized versions of the original observations are available, due to bandwidth constraints. When the dynamic range of the parameter is small or comparable with the noise variance, we introduce a class of maximum-likelihood estimators that require transmitting just one bit per sensor to achieve an estimation variance close to that of the (clairvoyant) sample mean estimator. When the dynamic range is comparable or larger than the noise standard deviation, we show that an optimum quantization step exists to achieve the best possible variance for a given bandwidth constraint. We will also establish that in certain cases the sample mean estimator formed by quantized observations is preferable for complexity reasons. We finally touch upon algorithm implementation issues and guarantee that all the numerical maximizations required by the proposed estimators are concave.

Distributed compression-estimation using wireless sensor networks

This paper provides an overview of distributed estimation-compression problems encountered with wireless sensor networks (WSN). A general formulation of distributed compression-estimation under rate constraints was introduced, pertinent signal processing algorithms were developed, and emerging tradeoffs were delineated from an information theoretic perspective. Specifically, we designed rate-constrained distributed estimators for various signal models with variable knowledge of the underlying data distributions. We proved theoretically, and corroborated with examples, that when the noise distributions are either completely known, partially known or completely unknown, distributed estimation is possible with minimal bandwidth requirements which can achieve the same order of mean square error (MSE) performance as the corresponding centralized clairvoyant estimators.

SOI-KF: Distributed Kalman Filtering With Low-Cost Communications Using the Sign of Innovations

When dealing with decentralized estimation, it is important to reduce the cost of communicating the distributed observations-a problem receiving revived interest in the context of wireless sensor networks. In this paper, we derive and analyze distributed state estimators of dynamical stochastic processes, whereby the low communication cost is effected by requiring the transmission of a single bit per observation. Following a Kalman filtering (KF) approach, we develop recursive algorithms for distributed state estimation based on the sign of innovations (SOI). Even though SOI-KF can afford minimal communication overhead, we prove that in terms of performance and complexity it comes very close to the clairvoyant KF which is based on the analog-amplitude observations. Reinforcing our conclusions, we show that the SOI-KF applied to distributed target tracking based on distance-only observations yields accurate estimates at low communication cost

Symbol error probabilities for general cooperative links

Cooperative diversity (CD) networks have been receiving a lot of attention recently as a distributed means of improving error performance and capacity. For sufficiently large signal-to-noise ratio (SNR), this paper derives the average symbol error probability (SEP) for analog forwarding CD links. The resulting expressions are general as they hold for an arbitrary number of cooperating branches, arbitrary number of cooperating hops per branch, and various channel fading models. Their simplicity provides valuable insights to the performance of CD networks and suggests means of optimizing them. Besides revealing the diversity, they clearly show from where this advantage comes from and prove that presence of diversity does not depend on the specific (e.g., Rayleigh) fading distribution. Finally, they explain how diversity is improved in multihop CD networks.

Bandwidth-constrained distributed estimation for wireless sensor networks-part II: unknown probability density function

Wireless sensor networks (WSNs) deployed to perform surveillance and monitoring tasks have to operate under stringent energy and bandwidth limitations. These motivate well distributed estimation scenarios where sensors quantize and transmit only one, or a few bits per observation, for use in forming parameter estimators of interest. In a companion paper, we developed algorithms and studied interesting tradeoffs that emerge even in the simplest distributed setup of estimating a scalar location parameter in the presence of zero-mean additive white Gaussian noise of known variance. Herein, we derive distributed estimators based on binary observations along with their fundamental error-variance limits for more pragmatic signal models: i) known univariate but generally non-Gaussian noise probability density functions (pdfs); ii) known noise pdfs with a finite number of unknown parameters; iii) completely unknown noise pdfs; and iv) practical generalizations to multivariate and possibly correlated pdfs. Estimators utilizing either independent or colored binary observations are developed and analyzed. Corroborating simulations present comparisons with the clairvoyant sample-mean estimator based on unquantized sensor observations, and include a motivating application entailing distributed parameter estimation where a WSN is used for habitat monitoring

Consensus in Ad Hoc WSNs With Noisy Links—Part II: Distributed Estimation and Smoothing of Random Signals

Distributed algorithms are developed for optimal estimation of stationary random signals and smoothing of (even nonstationary) dynamical processes based on generally correlated observations collected by ad hoc wireless sensor networks (WSNs). Maximum a posteriori (MAP) and linear minimum mean-square error (LMMSE) schemes, well appreciated for centralized estimation, are shown possible to reformulate for distributed operation through the iterative (alternating-direction) method of multipliers. Sensors communicate with single-hop neighbors their individual estimates as well as multipliers measuring how far local estimates are from consensus. When iterations reach consensus, the resultant distributed (D) MAP and LMMSE estimators converge to their centralized counterparts when inter-sensor communication links are ideal. The D-MAP estimators do not require the desired estimator to be expressible in closed form, the D-LMMSE ones are provably robust to communication or quantization noise and both are particularly simple to implement when the data model is linear-Gaussian. For decentralized tracking applications, distributed Kalman filtering and smoothing algorithms are derived for any-time MMSE optimal consensus-based state estimation using WSNs. Analysis and corroborating numerical examples demonstrate the merits of the novel distributed estimators.

Decentralized Quantized Kalman Filtering With Scalable Communication Cost

Estimation and tracking of generally nonstationary Markov processes is of paramount importance for applications such as localization and navigation. In this context, ad hoc wireless sensor networks (WSNs) offer decentralized Kalman filtering (KF) based algorithms with documented merits over centralized alternatives. Adhering to the limited power and bandwidth resources WSNs must operate with, this paper introduces two novel decentralized KF estimators based on quantized measurement innovations. In the first quantization approach, the region of an observation is partitioned into N contiguous, nonoverlapping intervals where each partition is binary encoded using a block of m bits. Analysis and Monte Carlo simulations reveal that with minimal communication overhead, the mean-square error (MSE) of a novel decentralized KF tracker based on 2-3 bits comes stunningly close to that of the clairvoyant KF. In the second quantization approach, if intersensor communications can afford m bits at time n, then the ith bit is iteratively formed using the sign of the difference between the nth observation and its estimate based on past observations (up to time n-1) along with previous bits (up to i-1) of the current observation. Analysis and simulations show that KF-like tracking based on m bits of iteratively quantized innovations communicated among sensors exhibits MSE performance identical to a KF based on analog-amplitude observations applied to an observation model with noise variance increased by a factor of [1-(1-2/pi)m]-1.

Ergodic Stochastic Optimization Algorithms for Wireless Communication and Networking

Ergodic stochastic optimization (ESO) algorithms are proposed to solve resource allocation problems that involve a random state and where optimality criteria are expressed in terms of long term averages. A policy that observes the state and decides on a resource allocation is proposed and shown to almost surely satisfy problem constraints and optimality criteria. Salient features of ESO algorithms are that they do not require access to the states probability distribution, that they can handle nonconvex constraints in the resource allocation variables, and that convergence to optimal operating points holds almost surely. The proposed algorithm is applied to determine operating points of an orthogonal frequency division multiplexing broadcast channel that maximize a given rate utility.